This is the fifth time the event is an official stop on the Indoor World Series circuit On the entry list – three of four winners from the first event of the season held in Lausanne just two weeks ago, and the two world number ones from the compound division, Mike Schloesser and Ella Gibson For the opening of the indoor season at the Swiss Open, competitors were looking sharp already, with three of them – Braden Gellenthien, Nicolas Girard and Mathias Fullerton – within one point of a clean scoresheet in the compound men’s qualifying round Fullerton lost to Schloesser for gold and Girard to Gellenthien for bronze in Lausanne only the US archer does not make the second indoor stopover The promise of further top performances in Strassen The event is also hosting competitions for the under-21s age group that count towards the open ranking What’s happening? The GT Open at the Guillaume Tell Archery Club on 15-17 November 2024 in Strassen elite and open ranking points for the international circuit What’s the story? The season opening event at the World Archery Excellence Centre in Lausanne two weeks ago was a sell-out event with high scores in qualifying and matchplay. Winners Denisa Barankova, Mike Schloesser and Lisell Jaatma are back for another first-class performance at the second leg in Strassen ScheduleFriday 15 November: Qualifying (two sessions)Saturday 16 November: Qualifying (two sessions) and eliminationsSunday 17 November: FinalsWho’s competing?Full entries are available online. These are the top-ranked archers shooting in Strassen: Competition at the GT Open starts on Friday. Maison du Sport International, Avenue de Rhodanie 54, 1007 Lausanne, Switzerland 16 Feb 2025 14:00:00 GMT?.css-1txiau5-AnswerContainer{color:var(--GlobalColorScheme-Text-secondaryText2);}Una Strassen won 3–0 over FC Wiltz 71 on Sun Predicted lineups are available for the match a few days in advance while the actual lineup will be available about an hour ahead of the match The current head to head record for the teams are Una Strassen 5 win(s) Have scored 7 goals in their last 5 matches Who won between Una Strassen and FC Wiltz 71 on Sun 16 Feb 2025 14:00:00 GMT?Una Strassen won 3–0 over FC Wiltz 71 on Sun 16 Feb 2025 14:00:00 GMT.InsightsHave scored 16 goals in their last 5 matches Una Strassen is playing home against FC Wiltz 71 on Sun The new National Health School has a brick façade. (Photo: M3 Architectes) The new Luxembourg National Health School in Strassen has been inaugurated. In addition to the school, the campus includes student accommodation and a sports hall linked to the Centre de Logopédie. Not far from Luxembourg, at the entrance to Strassen, new buildings have been constructed for the needs of the Luxembourg National Health School, ENSA and Jugend Wunnen – Villa Flo student accommodation, as well as a sports hall for the Logopédie Centre. The main entrance is from the route d’Arlon, via the rue Thomas Edison. These new buildings are part of the existing Val St André school campus in Strassen, which already includes the Centre for Motor Development and the Logopaedic Centre. In total, 28,950 m2 gross have been built. Each function is housed in a separate building, providing an optimal response to users’ needs. The architectural design was initially entrusted to Arlette Schneiders Architectes, then taken over by M3 Architectes after Arlette Schneiders retired. The Public Buildings Administration, assisted by INCA, was the project manager. The consulting engineers were ICLUX (civil engineering) and RMC Consulting (technical engineering). Landscape studies were carried out by AREAL Landscape Architecture. The school is located at the heart of the urban layout and welcomes the 1,200 high school students at the entrance to the campus. It comprises three wings containing classrooms and an administration building. This building is part of the second phase of the project and was brought into service in July 2024. The accommodation is located to the north of the site, in a more secluded area. On the ground floor are the communal areas (kitchen, dining room, living rooms). The 35 student rooms are on the first and second floors, while the 14 rooms for young people with their kitchen and living room are on the third floor. These homes were part of phase 1 of the project and have already been delivered at the end of 2021. These two buildings share architectural elements, proportions and materials. The sports hall and swimming pool are located right next to the Logopédie Centre, providing an easy link with the latter. This building was also handed over at the end of 2021. The landscaped areas have been completely redeveloped. (Photo: M3 Architectes) A central circulation axis links the three establishments, with separate lanes for school transport, cars, cyclists and pedestrians, to ensure smooth and safe traffic flow. The other outdoor areas have been redesigned to accommodate the increased use of the site, with planting and trees encouraged. The new buildings are low-energy, with technical installations kept to a minimum in order to keep maintenance costs as low as possible. Heating is provided by the biomass district heating plant. The roofs are fitted with photovoltaic panels. The project cost 135 million euros. who was one of 72 French entries across all senior compound and recurve events in Strassen fourth (2022) and 17th (2023) in his previous efforts but put in a career best string of results at this year’s second stage of the Indoor World Series to end his hunt for a podium finish It culminated in him beating second qualifying seed Remar in the gold medal match on Sunday afternoon 6-4 in the recurve set point scoring system “I’m obviously really happy,” said 24-year-old Barbier It’s a lot of work that’s paying right now.” I struggled a little bit with my mental game I was not really satisfied with my first two matches but then this morning things went better and I’m quite happy with how I shot.” The tone of the match was set after the first two ends as Barbier dropped an opening 30 to take the first set Remar responding with his own in the second to tie the scores at 2-2 Both shot 29 in the next two sets meaning the match was left on a knife edge with it being 4-4 heading into the fifth and final end But it was 25-year-old Remar who blinked first dropping two nines for the first time in the match to hit 28 Barbier hitting his last two arrows into the 10-ring to capitalise and take the gold “A lot of mental work,” Barbier responded when asked about this massive improvement in results to be more relaxed and to fight a little bit of the stress.” Although he lost, Croatian Remar should be leaving Luxembourg with his head held high having defeated Paris 2024 mixed team silver medallist Florian Unruh and Tokyo 2020 individual silver medallist Mauro Nespoli in two shoot-offs en route to Sunday’s final as well as shooting an impressive tally of 587 from 60 arrows in the qualifying round The silver medal is also his best return as an individual athlete, bettering the bronze he got in the Sud de France – Nimes Archery Tournament two years ago and Croatia’s men’s team bronze at the European Indoor Championships earlier this year. Having seen their Olympic clean sweep at Paris 2024 Korea’s indoor prowess was also shown at the Guillaume Tell Archery Club with three of their four recurve women’s entries making it into the quarterfinals That was before an all Korean gold medal match Lim Duna’s candle has burnt brightly since her 2023 international debut, and it remained very much lit as she beat teammate and twin sister Lim Hana 6-2 to get the top podium finish The 23-year-old has now won every international competition she has entered with her GT Open triumph, adding to two Vegas Shoot titles (2023 and 2024) and the 2023 Indoor World Series Finals gold In the compound events, Mike Schloesser lived up to his ‘Mister Perfect’ tag as he shot 150 in the men’s final but so did Abhishek Verma who was the only archer to drop a perfect 600 in the qualifications Schloesser however shot a 10 closer to the X-ring than his Indian counterpart to wrap up the gold, two weeks after winning the opening Indoor World Series stage in Lausanne “The level in general was really high here,” said the 2024 World Field Champion “I don’t think I’ve ever seen a 590 not make the top 32 here.” The reigning Asian Games Champion Jyothi Surekha Vennam defeated Belgium’s Sarah Prieels in the compound women’s gold medal match 147-145 the world number four’s first ever GT Open medal let alone gold The third stage of archery’s premier indoor circuit continues next month at the Taipei Archery Open in Taoyuan City, from 6-8 December. 09 Feb 2025 14:00:00 GMT?.css-1txiau5-AnswerContainer{color:var(--GlobalColorScheme-Text-secondaryText2);}FC Rodange 91 vs Una Strassen on Sun The current head to head record for the teams are FC Rodange 91 1 win(s) Haven't kept a clean sheet in 8 matches Have scored 14 goals in their last 5 matches Who won between FC Rodange 91 and Una Strassen on Sun 09 Feb 2025 14:00:00 GMT?FC Rodange 91 vs Una Strassen on Sun 09 Feb 2025 14:00:00 GMT ended in a 2–2 tie.InsightsHave scored 6 goals in their last 5 matches FC Rodange 91 is playing home against Una Strassen on Sun Strassen or Stroossen is one of the smallest communes in Luxembourg there are more than 10,588 residents representing 112 nationalities giving it a distinctly international flavour Its ideal location (close to two motorway junctions) As it is on one of the main arteries into Luxembourg but it's well served by public transport and it has a village feel despite its close proximity to the city Strassen was formed in 1851 when it was detached from the commune of Bertrange but the origins of the town date back to Roman times The name Strassen comes from the Latin word 'strata' which means military road the remains of which were found near Kiem Street In the 18th century the population of Strassen was just 417 and in the 1850s the area saw emigration to the United States For the one hundred years up to 1946 the population remained static at about 1,400 citizens but in recent times it has grown exponentially You can find out more about Strassen's history and coat of arms here Engineer Paul Barble hails from Strassen and built many constructions from bridges to radio transmitters and factories in Luxembourg Due to its attractive location, property prices in this suburb can be as high as in Luxembourg City. According to Wort Immo the current price per square metre of real estate in the area is: There's also a pharmacy at 76 rue des Romains The Confederation for the Portuguese Community in Luxembourg also organises cultural events and language courses is located at 30 rue de l'Industrie There's a state run pre-school and primary in Strassen, in addition to the Maria Montessori School which teaches children from three-to-12 years Strassen is also well-located for the European School Luxembourg 2 in Mamer (English the Geesseknappchen area which is home to ISL and Lycées Michel Rodange and Aline Mayrisch The Over the Rainbow private school in Belair has French & English IB sections In addition to national state aid for the purchase of electric or hybrid cars and electric bicycles, the commune of Strassen applies an additional subsidy of 25% for its residents registered for more than 6 months. You can find out more here Cycle track PC1 covers Strassen, whilst bike path Nicolas Franz (PC13) runs from Strassen to Kleinbettingen It is possible to walk the 20km from Strassen to Mersch without leaving the forest FC Una is the local club but you can find a list of associations including choral, biking, rambling and much more here Luxembourg National Day is also celebrated in Park Riedgen with animations for kids The next one is planned for September 2025 The cultural centre also houses an art gallery "A Spiren" with two exhibition halls that host national and international artists Every second and fourth Friday there is a bio and alternative produce market held from 16.00 to 19.00 outside the cultural centre In addition to fruit and vegetables you can buy honey There's no shortage of restaurants in Strassen from some fine dining to a spot of sushi or lunch from a food truck Baker and patisserie Jos & Jean-Marie sells bread and baguettes, tarts and cakes at Rue des Romains, whilst there is a Fischer in the Pall Centre French kitchen grill, Meat Me, is the place to head for steak and charcuterie boards, whilst if you want to catch a football match, eat pizza and try a shisha, you can do so at Infinity Lounge The Pizza Lux food truck dishes up authentic wood-fire cooked pizza opposite the town hall on Wednesday and Friday nights, and Verace food truck has pizza on Tuesday evenings Brasserie Benelux holds karaoke nights and looks like a lively place if you fancy a drink You can find out more about commune events here and local residents can join the My Strassen Facebook group. City living In the neighbourhood: Merl Merl is home to polo clubs, a comic and manga store and the Luxembourg Conservatory Architectural iconsTour: a blast from the past at Belval’s restored furnacesDiscover the giant blast furnaces on Belval’s skyline that pay tribute to Luxembourg’s industrial heritage City quarters In the neighbourhood: BeggenBeggen may appear to be just a traffic-filled thoroughfare with petrol stations, but it's the place to pick up Asian spices or catch some live music Rejuvenation In the neighbourhood: GasperichThis tiny city neighbourhood is just 4km squared but is home to some 10,200 residents and the capital’s largest park ResidentialIn the neighbourhood: WalferdangeRoman ruins, a great selection of shops and restaurants, forest walks and connection by rail and bus make Walferdange a popular residential neighbourhood Well-connectedIn the neighbourhood: Niederanven & SenningerbergIn this edition of our neighbourhood series, we head to Niederanven, with its Italian restaurant terraces and orchid-growing nature reserve West LuxembourgIn the neighbourhood: Kehlen The idyllic rural villages of Kehlen commune combine a commuter base with a pottery and distilling past, and some great walks and restaurants Grevenmacher districtIn the neighbourhood: JunglinsterHome to an international school and well-connected to the city, Junglinster is the largest municipality in the east of the country Advertiser contentTreat yourself to a stress-free holidayDreaming of a worry-free trip What if the secret to a smooth getaway was simply good preparation and the right protection Advertiser contentReal estate: Why should you take advantage of the start of 2025 to begin your real estate project?The main things we remember about the housing sector over the past 12 months are the rise in interest rates and the fall in property prices Advertiser contentProperty: I've decided to invest!The various forms of government support for investment Advertiser contentThe Luxembourg Times BusinessRun is happening again on 18th September!On Thursday 18th September with the starting gun of the 11th Luxembourg Times BusinessRun fired at the Coque at 7 pm Share this with instagramSections Bernhard zur Strassen is set to become the new MD and CEO of time:matters from tomorrow Mr zur Strassen has extensive experience in international management for logistics service providers and shippers and was chief revenue officer at software company Shipsta Airlines have suspended services into Israel’s key gateway of Ben Gurion Gal Dayan has quit his role as head of inbound logistics for Apple Avianca Cargo has appointed Diogo Elias its new CEO to lead the fleet expansion plan .. Looming tariffs on imported pharmaceuticals could push up the cost of US drugs by $51bn .. Following its clearance by competition regulators to complete its acquisition of DB Schenker the less-than-container load (LCL) consolidator owned by India’s Allcargo Logistics Lithuanian road freight and logistics firm Girteka Group appointed Edvardas Liachovi?ius (above) as its new .. Freight forwarding veteran Marco Nazarri (above) has been appointed chief commercial officer (CCO) of German .. email: [email protected] email: [email protected] email: [email protected] email: [email protected] email: [email protected] Metrics details We further showcase the flexibility of AlphaTensor through different use-cases: algorithms with state-of-the-art complexity for structured matrix multiplication and improved practical efficiency by optimizing matrix multiplication for runtime on specific hardware Our results highlight AlphaTensor’s ability to accelerate the process of algorithmic discovery on a range of problems where a neural network is trained to guide a planning procedure searching for efficient matrix multiplication algorithms Our framework uses a single agent to decompose matrix multiplication tensors of various sizes yielding transfer of learned decomposition techniques across various tensors To address the challenging nature of the game AlphaTensor uses a specialized neural network architecture exploits symmetries of the problem and makes use of synthetic training games AlphaTensor scales to a substantially larger algorithm space than what is within reach for either human or combinatorial search AlphaTensor discovers from scratch many provably correct matrix multiplication algorithms that improve over existing algorithms in terms of number of scalar multiplications We also adapt the algorithm discovery procedure to finite fields and improve over Strassen’s two-level algorithm for multiplying 4 × 4 matrices for the first time AlphaTensor also discovers a diverse set of algorithms—up to thousands for each size—showing that the space of matrix multiplication algorithms is richer than previously thought We also exploit the diversity of discovered factorizations to improve state-of-the-art results for large matrix multiplication sizes we highlight AlphaTensor’s flexibility and wide applicability: AlphaTensor discovers efficient algorithms for structured matrix multiplication improving over known results and finds efficient matrix multiplication algorithms tailored to specific hardware These algorithms multiply large matrices faster than human-designed algorithms on the same hardware where ⊗ denotes the outer (tensor) product, and u(r), v(r) and w(r) are all vectors. If a tensor ${\mathscr{T}}$ can be decomposed into R rank-one terms, we say the rank of ${\mathscr{T}}$ is at most R, or $\,\text{Rank}\,({\mathscr{T}}\,)\le R$. This is a natural extension from the matrix rank, where a matrix is decomposed into ${\sum }_{r=1}^{R}{{\bf{u}}}^{(r)}\otimes {{\bf{v}}}^{(r)}$. A meta-algorithm parameterized by ${\{{{\bf{u}}}^{(r)},{{\bf{v}}}^{(r)},{{\bf{w}}}^{(r)}\}}_{r=1}^{R}$ for computing the matrix product C = AB It is noted that R controls the number of multiplications between input matrix entries Parameters: ${\{{{\bf{u}}}^{(r)},{{\bf{v}}}^{(r)},{{\bf{w}}}^{(r)}\}}_{r=1}^{R}$: length-n2 vectors such that ${{\mathscr{T}}}_{n}={\sum }_{r=1}^{R}{{\bf{u}}}^{(r)}\otimes {{\bf{v}}}^{(r)}\otimes {{\bf{w}}}^{(r)}$ (2) ${m}_{r}\leftarrow \left({u}_{1}^{(r)}{a}_{1}+\cdots +{u}_{{n}^{2}}^{(r)}{a}_{{n}^{2}}\right)\left({v}_{1}^{(r)}{b}_{1}+\cdots +{v}_{{n}^{2}}^{(r)}{b}_{{n}^{2}}\right)$ (4) ${c}_{i}\leftarrow {w}_{i}^{(1)}{m}_{1}+\cdots +{w}_{i}^{(R)}{m}_{R}$ We cast the problem of finding efficient matrix multiplication algorithms as a reinforcement learning problem modelling the environment as a single-player game The game state after step t is described by a tensor ${{\mathscr{S}}}_{t}$ which is initially set to the target tensor we wish to decompose: ${{\mathscr{S}}}_{0}={{\mathscr{T}}}_{n}$ and the tensor ${{\mathscr{S}}}_{t}$ is updated by subtracting the resulting rank-one tensor: ${{\mathscr{S}}}_{t}\leftarrow {{\mathscr{S}}}_{t-1}-{{\bf{u}}}^{(t)}\otimes {{\bf{v}}}^{(t)}\otimes {{\bf{w}}}^{(t)}$ The goal of the player is to reach the zero tensor ${{\mathscr{S}}}_{t}={\bf{0}}$ by applying the smallest number of moves the sequence of selected factors satisfies ${{\mathscr{T}}}_{n}={\sum }_{t=1}^{R}{{\bf{u}}}^{(t)}\otimes {{\bf{v}}}^{(t)}\otimes {{\bf{w}}}^{(t)}$ (where R denotes the number of moves) which guarantees the correctness of the resulting matrix multiplication algorithm we limit the number of steps to a maximum value The neural network (bottom box) takes as input a tensor ${{\mathscr{S}}}_{t}$ w) from a distribution over potential next actions to play and an estimate of the future returns (for example of $-{\rm{Rank}}\,({{\mathscr{S}}}_{t})$) The network is trained on two data sources: previously played games and synthetic demonstrations The updated network is sent to the actors (top box) where it is used by the MCTS planner to generate new games This mixed training strategy—training on the target tensor and random tensors— substantially outperforms each training strategy separately This is despite randomly generated tensors having different properties from the target tensors This crucial step injects diversity into the games played by the agent we can extract additional tensor-factorization pairs for training the network as factorizations are order invariant (owing to summation) we build an additional tensor-factorization training pair by swapping a random action with the last action from each finished game We train a single AlphaTensor agent to find matrix multiplication algorithms for matrix sizes n × m with m × p p) and train AlphaTensor to decompose the tensor ${{\mathscr{T}}}_{n,m,p}$ Although we consider tensors of fixed size (${{\mathscr{T}}}_{n,m,p}$ has size nm × mp × pn) the discovered algorithms can be applied recursively to multiply matrices of arbitrary size We use AlphaTensor to find matrix multiplication algorithms over different arithmetics—namely multiplying matrices in the quotient ring ${{\mathbb{Z}}}_{2}$) A crucial aspect of AlphaTensor is its ability to learn to transfer knowledge between targets (despite providing no prior knowledge on their relationship) By training one agent to decompose various tensors AlphaTensor shares learned strategies among these thereby improving the overall performance (see Supplementary Information for analysis) it is noted that AlphaTensor scales beyond current computational approaches for decomposing tensors no previous approach was able to handle ${{\mathscr{T}}}_{4}$ which has an action space 1010 times larger than ${{\mathscr{T}}}_{3}$ discovering decompositions matching or surpassing state-of-the-art for large tensors such as ${{\mathscr{T}}}_{5}$ Decompositions found by AlphaTensor for the tensors of size $\frac{n(n-1)}{2}\times n\times n$ (with n = 3 6) representing the skew-symmetric matrix-vector multiplication the blue pixels denote −1 and the white pixels denote 0 Extrapolation to n = 10 is shown in the rightmost figure Skew-symmetric matrix-by-vector multiplication algorithm obtained from the examples solved by AlphaTensor The wij and qi terms in steps 3 and 5 correspond to the mr terms in Algorithm 1 It is noted that steps 6–9 do not involve any multiplications We show a use-case where AlphaTensor finds practically efficient matrix multiplication algorithms we modify the reward of AlphaTensor: we provide an additional reward at the terminal state (after the agent found a correct algorithm) equal to the negative of the runtime of the algorithm when benchmarked on the target hardware we set ${r}_{t}^{{\prime} }={r}_{t}+\lambda {b}_{t}$ where rt is the reward scheme described in ‘DRL for algorithm discovery’ bt is the benchmarking reward (non-zero only at the terminal state) and λ is a user-specified coefficient the exact same formulation of TensorGame is used Speed-ups (%) of the AlphaTensor-discovered algorithms tailored for a GPU (a) and a TPU (b) optimized for a matrix multiplication of size 8,192 × 8,192 Speed-ups are measured relative to standard (for example cuBLAS for the GPU) matrix multiplication on the same hardware Speed-ups are reported for various matrix sizes (despite optimizing the algorithm only on one matrix size) We also report the speed-up of the Strassen-square algorithm The median speed-up is reported over 200 runs The standard deviation over runs is <0.4 percentage points (see Supplementary Information for more details) Speed-up of both algorithms (tailored to a GPU and a TPU) benchmarked on both devices AlphaTensor discovers matrix multiplication algorithms that are more efficient than existing human and computer-designed algorithms we note that a limitation of AlphaTensor is the need to pre-define a set of potential factor entries F which discretizes the search space but can possibly lead to missing out on efficient algorithms An interesting direction for future research is to adapt AlphaTensor to search for F One important strength of AlphaTensor is its flexibility to support complex stochastic and non-differentiable rewards (from the tensor rank to practical efficiency on specific hardware) in addition to finding algorithms for custom operations in a wide variety of spaces (such as finite fields) We believe this will spur applications of AlphaTensor towards designing algorithms that optimize metrics that we did not consider here such as numerical stability or energy usage We also note that our methodology can be extended to tackle related primitive mathematical problems such as computing other notions of rank (for example border rank—see Supplementary Information) and NP-hard matrix factorization problems (for example By tackling a core NP-hard computational problem in mathematics using DRL—the computation of tensor ranks—AlphaTensor demonstrates the viability of DRL in addressing difficult mathematical problems and potentially assisting mathematicians in discoveries The start position ${{\mathscr{S}}}_{0}$ of the game corresponds to the tensor ${\mathscr{T}}$ representing the bilinear operation of interest the player writes down three vectors (u(t) which specify the rank-1 tensor u(t) ⊗ v(t) ⊗ w(t) and the state of the game is updated by subtracting the newly written down factor: we also impose a limit Rlimit on the maximum number of moves in the game so that a weak player is not stuck in unnecessarily (or even infinitely) long games When a game ends because it has run out of moves a penalty score is given so that it is never advantageous to deliberately exhaust the move limit when optimizing for asymptotic time complexity this penalty is derived from an upper bound on the tensor rank of the final residual tensor ${{\mathscr{S}}}_{{R}_{\text{limit}}}$ This upper bound on the tensor rank is obtained by summing the matrix ranks of the slices of the tensor We note that integer-valued decompositions u(t) v(t) and w(t) lead to decompositions in arbitrary rings ${\mathcal{E}}$ algorithms we find in standard arithmetic apply more generally to any ring combining a deep neural network with a sample-based MCTS search algorithm where c(s) is an exploration factor controlling the influence of the empirical policy $\hat{\pi }(s,a)$ relative to the values Q(s a transposition table is used to recombine different action sequences if they reach the exact same tensor This can happen particularly often in TensorGame as actions are commutative which returns K actions {ai} sampled from π(a∣sL) alongside the empirical distribution $\hat{\pi }(a| {s}_{{\rm{L}}})=\frac{1}{K}{\sum }_{i}{\delta }_{a,{a}_{i}}$ and a value v(sL) constructed from z(⋅∣sL) Differently from AlphaZero and Sampled AlphaZero we chose v not to be the mean of the distribution of returns z(⋅∣sL) as is usual in most reinforcement learning agents leveraging the facts that TensorGame is a deterministic environment and that we are primarily interested in finding the best trajectory possible The visit counts and values on the simulated trajectory are then updated in a backward pass as in Sampled AlphaZero After simulating N(s) trajectories from state s using MCTS the normalized visit counts of the actions at the root of the search tree N(s a)/N(s) form a sample-based improved policy we use an adaptive temperature scheme to smooth the normalized visit counts distribution as some states can accumulate an order of magnitude more visits than others because of sub-tree reuse and transposition table we define the improved policy as ${\mathcal{I}}\hat{\pi }(s,a)={N}^{1/\tau (s)}(s,a)/{\sum }_{b}{N}^{1/\tau (s)}(s,b)$ where $\tau (s)=\log N(s)/\log \bar{N}\,{\rm{if}}\,N > \bar{N}$ and 1 otherwise we use ${\mathcal{I}}\hat{\pi }$ directly as a target for the network policy π we additionally discard all actions that have a value lower than the value of the most visited action and sample proportionally to ${\mathcal{I}}\hat{\pi }$ among those remaining high-value actions We also train a single agent to decompose tensors in both arithmetics Owing to learned transfer between the two arithmetics this agent discovers a different distribution of algorithms (of the same ranks) in standard arithmetic than the agent trained on standard arithmetic only thereby increasing the overall diversity of discovered algorithms The synthetic demonstrations buffer contains tensor-factorization pairs where the factorizations ${\{({{\bf{u}}}^{(r)},{{\bf{v}}}^{(r)},{{\bf{w}}}^{(r)})\}}_{r=1}^{R}$ are first generated at random after which the tensor ${\mathscr{D}}={\sum }_{r=1}^{R}{{\bf{u}}}^{(r)}\otimes {{\bf{v}}}^{(r)}\otimes {{\bf{w}}}^{(r)}$ is formed We create a dataset containing 5 million such tensor-factorization pairs Each element in the factors is sampled independently and identically distributed (i.i.d.) from a given categorical distribution over F (all possible values that can be taken) We discarded instances whose decompositions were clearly suboptimal (contained a factor with u = 0 In addition to these synthetic demonstrations we further add to the demonstration buffer previous games that have achieved large scores to reinforce the good moves made by the agent in these games The rank of a bilinear operation does not depend on the basis in which the tensor representing it is expressed B and C we have ${\rm{Rank}}\,({\mathscr{T}})={\rm{Rank}}\,({{\mathscr{T}}}^{({\bf{A}},{\bf{B}},{\bf{C}})})$ where ${{\mathscr{T}}}^{({\bf{A}},{\bf{B}},{\bf{C}})}$ is the tensor after change of basis given by We leverage this observation by expressing the matrix multiplication tensor ${{\mathscr{T}}}_{n}$ in a large number of randomly generated bases (typically 100,000) in addition to the canonical basis and letting AlphaTensor play games in all bases in parallel This approach has three appealing properties: (1) it provides a natural exploration mechanism as playing games in different bases automatically injects diversity into the games played by the agent; (2) it exploits properties of the problem as the agent need not succeed in all bases—it is sufficient to find a low-rank decomposition in any of the bases; (3) it enlarges coverage of the algorithm space because a decomposition with entries in a finite set F = {−2 2} found in a different basis need not have entries in the same set when converted back into the canonical basis a basis change for a 3D tensor of size S × S × S is specified by three invertible S × S matrices A we sample bases at random and impose two restrictions: (1) A = B = C as this performed better in early experiments and (2) unimodularity ($\det {\bf{A}}\in \{-1,+1\}$) which ensures that after converting an integral factorization into the canonical basis it still contains integer entries only (this is for representational convenience and numerical stability of the resulting algorithm) See Supplementary Information for the exact algorithm we apply a randomly chosen signed permutation to both the input and the policy targets and train the network on this transformed triplet we sample 100 signed permutations at the beginning of an experiment w) are equivalent because they lead to the same rank-one tensor (λ1u) ⊗ (λ2v) ⊗ (λ3w) = u ⊗ v ⊗ w To prevent the network from wasting capacity on predicting multiple equivalent actions during training we always present targets (u w) for the policy head in a canonical form defined as having the first non-zero element of u and the first non-zero element of v strictly positive This is well defined because u or v cannot be all zeros (if they are to be part of a minimal rank decomposition) +1} (with λ1λ2λ3 = 1) that transform it into canonical form In case the network predicts multiple equivalent actions anyway we merge them together (summing their empirical policy probabilities) before inserting them into the MCTS tree the procedure takes a week to converge The architecture is composed of a torso, followed by a policy head that predicts a distribution over actions, and a value head that predicts a distribution of the returns from the current state (see Extended Data Fig. 3) The input to the network contains all the relevant information of the current state and is composed of a list of tensors and a list of scalars The most important piece of information is the current 3D tensor ${{\mathscr{S}}}_{t}$ of size S × S × S in the description here we assume that all the three dimensions of the tensor are equal in size The generalization to different sizes is straightforward.) In addition the model is given access to the last h actions (h being a hyperparameter usually set to 7) represented as h rank-1 tensors that are concatenated to the input The list of scalars includes the time index t of the current action (where 0 ≤ t < Rlimit) and its main signature is that it operates over three S × S grids projected from the S × S × S input tensors Each grid represents two out of the three modes of the tensor Defining the modes of the tensor as ${\mathcal{U}},{\mathcal{V}},{\mathcal{W}}$ the rows and columns of the first grid are associated to ${\mathcal{U}}$ and ${\mathcal{V}}$ the rows and columns of the second grid are associated to ${\mathcal{W}}$ and ${\mathcal{U}}$ and the rows and columns of the third grid are associated to ${\mathcal{V}}$ and ${\mathcal{W}}$ Each element of each grid is a feature vector and its initial value is given by the elements of the input tensors along the grid’s missing mode These feature vectors are enriched by concatenating an S × S × 1 linear projection from the scalars This is followed by a linear layer projecting these feature vectors into a 512-dimensional space We see writing a custom low-level implementation of a given algorithm to be distinct from the focus of this paper—developing new efficient algorithms—and we believe that the algorithms we discovered can further benefit from a more efficient implementation by experts The data used to train the system were generated synthetically according to the procedures explained in the paper. 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Preprint at https://arxiv.org/abs/2104.14516 (2021) Deep reinforcement learning for de novo drug design Optimization of molecules via deep reinforcement learning Planning chemical syntheses with deep neural networks and symbolic AI Global optimization of quantum dynamics with AlphaZero deep exploration Fast matrix multiplication algorithms catalogue. Université de Lille https://fmm.univ-lille.fr/ (2021) Download references Wigderson for the inspiring discussions on the use of machine learning for maths; A Ronneberger for their advice on early drafts of the paper; A Winckler for participating in a hackathon at the early stages of the project; D Noury for sharing their expertise on TPUs; P Zhao for their help on benchmarking algorithms; G Meyer for assistance coordinating the research; and our colleagues at DeepMind for encouragement and support These authors contributed equally: Alhussein Fawzi Thomas Hubert and Bernardino Romera-Paredes developed an early supervised network prototype designed the network architecture used in the paper developed the tensor decomposition environment and data generation pipeline analysed the experimental results and algorithms discovered by AlphaTensor developed the benchmarking pipeline and experiments extended the approach to structured tensors and are listed alphabetically by last name after the corresponding author: A.F. and are listed alphabetically by last name: M The authors of the paper are planning to file a patent application relating to subject matter contained in this paper in the name of DeepMind Technologies Limited reviewer(s) for their contribution to the peer review of this work Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations This outperforms the two-level Strassen’s algorithm This outperforms the previously best known algorithm The network takes as input the list of tensors containing the current state and previous history of actions such as the time index of the current action It produces two kinds of outputs: one representing the value and the other inducing a distribution over the action space from which we can sample from The architecture of the network is accordingly designed to have a common torso We refer to Algorithms A.1-A.11 in Supplementary Information for the details of each component Download citation DOI: https://doi.org/10.1038/s41586-022-05172-4 Anyone you share the following link with will be able to read this content: a shareable link is not currently available for this article Computational Optimization and Applications (2025) Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research First extension of AlphaZero to mathematics unlocks new possibilities for research Algorithms have helped mathematicians perform fundamental operations for thousands of years The ancient Egyptians created an algorithm to multiply two numbers without requiring a multiplication table and Greek mathematician Euclid described an algorithm to compute the greatest common divisor During the Islamic Golden Age, Persian mathematician Muhammad ibn Musa al-Khwarizmi designed new algorithms to solve linear and quadratic equations despite the familiarity with algorithms today – used throughout society from classroom algebra to cutting edge scientific research – the process of discovering new algorithms is incredibly difficult and an example of the amazing reasoning abilities of the human mind In our paper the first artificial intelligence (AI) system for discovering novel and provably correct algorithms for fundamental tasks such as matrix multiplication This sheds light on a 50-year-old open question in mathematics about finding the fastest way to multiply two matrices This paper is a stepping stone in DeepMind’s mission to advance science and unlock the most fundamental problems using AI. Our system, AlphaTensor, builds upon AlphaZero, an agent that has shown superhuman performance on board games, like chess, Go and shogi and this work shows the journey of AlphaZero from playing games to tackling unsolved mathematical problems for the first time Matrix multiplication is one of the simplest operations in algebra commonly taught in high school maths classes this humble mathematical operation has enormous influence in the contemporary digital world and is ubiquitous in modern computing Example of the process of multiplying two 3x3 matrices This operation is used for processing images on smartphones running simulations to predict the weather compressing data and videos for sharing on the internet Companies around the world spend large amounts of time and money developing computing hardware to efficiently multiply matrices even minor improvements to the efficiency of matrix multiplication can have a widespread impact For centuries, mathematicians believed that the standard matrix multiplication algorithm was the best one could achieve in terms of efficiency. But in 1969, German mathematician Volker Strassen shocked the mathematical community by showing that better algorithms do exist Standard algorithm compared to Strassen’s algorithm which uses one less scalar multiplication (7 instead of 8) for multiplying 2x2 matrices Multiplications matter much more than additions for overall efficiency Through studying very small matrices (size 2x2) he discovered an ingenious way of combining the entries of the matrices to yield a faster algorithm Despite decades of research following Strassen’s breakthrough larger versions of this problem have remained unsolved – to the extent that it’s not known how efficiently it’s possible to multiply two matrices that are as small as 3x3 we explored how modern AI techniques could advance the automatic discovery of new matrix multiplication algorithms Building on the progress of human intuition AlphaTensor discovered algorithms that are more efficient than the state of the art for many matrix sizes Our AI-designed algorithms outperform human-designed ones which is a major step forward in the field of algorithmic discovery we converted the problem of finding efficient algorithms for matrix multiplication into a single-player game the board is a three-dimensional tensor (array of numbers) capturing how far from correct the current algorithm is the player attempts to modify the tensor and zero out its entries this results in a provably correct matrix multiplication algorithm for any pair of matrices and its efficiency is captured by the number of steps taken to zero out the tensor This game is incredibly challenging – the number of possible algorithms to consider is much greater than the number of atoms in the universe, even for small cases of matrix multiplication. Compared to the game of Go, which remained a challenge for AI for decades the number of possible moves at each step of our game is 30 orders of magnitude larger (above 1033 for one of the settings we consider) one needs to identify the tiniest of needles in a gigantic haystack of possibilities which significantly departs from traditional games we developed multiple crucial components including a novel neural network architecture that incorporates problem-specific inductive biases a procedure to generate useful synthetic data and a recipe to leverage symmetries of the problem We then trained an AlphaTensor agent using reinforcement learning to play the game starting without any knowledge about existing matrix multiplication algorithms re-discovering historical fast matrix multiplication algorithms such as Strassen’s eventually surpassing the realm of human intuition and discovering algorithms faster than previously known where the goal is to find a correct matrix multiplication algorithm The state of the game is a cubic array of numbers (shown as grey for 0 representing the remaining work to be done if the traditional algorithm taught in school multiplies a 4x5 by 5x5 matrix using 100 multiplications and this number was reduced to 80 with human ingenuity AlphaTensor has found algorithms that do the same operation using just 76 multiplications Algorithm discovered by AlphaTensor using 76 multiplications an improvement over state-of-the-art algorithms AlphaTensor’s algorithm improves on Strassen’s two-level algorithm in a finite field for the first time since its discovery 50 years ago These algorithms for multiplying small matrices can be used as primitives to multiply much larger matrices of arbitrary size AlphaTensor also discovers a diverse set of algorithms with state-of-the-art complexity – up to thousands of matrix multiplication algorithms for each size showing that the space of matrix multiplication algorithms is richer than previously thought Algorithms in this rich space have different mathematical and practical properties we adapted AlphaTensor to specifically find algorithms that are fast on a given hardware These algorithms multiply large matrices 10-20% faster than the commonly used algorithms on the same hardware which showcases AlphaTensor’s flexibility in optimising arbitrary objectives AlphaTensor with an objective corresponding to the runtime of the algorithm When a correct matrix multiplication algorithm is discovered in order to learn more efficient algorithms on the target hardware Because matrix multiplication is a core component in many computational tasks AlphaTensor-discovered algorithms could make computations in these fields significantly more efficient AlphaTensor’s flexibility to consider any kind of objective could also spur new applications for designing algorithms that optimise metrics such as energy usage and numerical stability helping prevent small rounding errors from snowballing as an algorithm works While we focused here on the particular problem of matrix multiplication we hope that our paper will inspire others in using AI to guide algorithmic discovery for other fundamental computational tasks Our research also shows that AlphaZero is a powerful algorithm that can be extended well beyond the domain of traditional games to help solve open problems in mathematics we hope to spur on a greater body of work – applying AI to help society solve some of the most important challenges in mathematics and across the sciences You can find more information in AlphaTensor's GitHub repository Max Barnett for their help with text and figures This work was done by a team with contributions from Alhussein Fawzi Exploring the beauty of pure mathematics in novel ways Srinivasa Ramanujan shocked the mathematical world with his extraordinary ability to see remarkable patterns in numbers that no one else could see I accept Google's Terms and Conditions and acknowledge that my information will be used in accordance with Google's Privacy Policy According to recent reports from the Grand Ducal Fire and Rescue Corps (CGDIS) a pedestrian was struck by a car on Chaussée Blanche in Strassen at 5pm on Saturday They communicated that one person was injured Shortly after 10.30pm, a rubbish bin fire in Strassen on Saturday night led to a gas bottle explosion, causing damage to a nearby school. Myriam Campelo and Juan Ramón Manzanaro live with their three children in this house they designed with Dlinea - Architecture & Design. Photo: Nader Ghavami The Manzanaro-Campelo family built their home in Strassen with a touch of Spain, their country of origin. On the ground floor, the living room, dining room and kitchen have been designed as a single unit that wraps around the central, sculptural staircase. “We love to entertain, so having a large open space was very important to us, as was the island in the kitchen and the fireplace in the living room,” continues Campelo, who worked with Claudia de Sousa on the interior design. Upstairs are the bedrooms and bathrooms for the three children. The top floor is reserved for the parents, who have installed a home office, a walk-in closet, a bedroom and a bathroom. Everywhere the colours are calm and light, with lots of beige and off-white to evoke the light of their native country. “For the garden, we called in the Spanish landscaper Innova Paisaxes, who brought all the plants from Spain. And for the façade, we chose Valencian stone for the base, which shines a little in the sun,” Manzanaro points out. Upstairs, the children have their own bedrooms, each decorated in a different way. Photo: Nader Ghavami In the kitchen, the family was keen to have an island so that they and their friends could meet up in a relaxed, convivial atmosphere. The table at the back is used for daily meals. Photo: Nader Ghavami The living room, the heart of the house, is double-height and has large bay windows, which open up the space both vertically and horizontally for a heightened sense of well-being. Photo: Nader Ghavami The architectural firm Dlinea designed this sculptural open concrete staircase and proposed installing a small indoor garden underneath. Photo: Nader Ghavami This article was written in for the magazine, published on 29 January. The content of the magazine is produced exclusively for the magazine. It is published on the website as a contribution to the complete Paperjam archive. . Is your company a member of the Paperjam Club? You can request a subscription in your name. Let us know via 30 Mar 2025 14:00:00 GMT?.css-1txiau5-AnswerContainer{color:var(--GlobalColorScheme-Text-secondaryText2);}US Mondorf les Bains won 3–1 over Una Strassen on Sun The current head to head record for the teams are Una Strassen 10 win(s) Have scored 5 goals in their last 5 matches Who won between Una Strassen and US Mondorf les Bains on Sun 30 Mar 2025 14:00:00 GMT?US Mondorf les Bains won 3–1 over Una Strassen on Sun 30 Mar 2025 14:00:00 GMT.InsightsHave scored 12 goals in their last 5 matches Una Strassen is playing home against US Mondorf les Bains on Sun The restaurant is named after its two co-owners, Vito Marinelli and Tom Weber. "It creates a new offer for Strassen,” said Strassen Mayor Nico Pundel. “There were already a few restaurants in the municipality, but this one offers a place to just have a drink, not just eat.” The opening of ViTo's is the culmination of a long process. "We launched a call for tenders to determine who would take over the restaurant,” Pundel said. “Once that was done, we were able to renovate the restaurant.” The building is owned by the local authority. "We're happy to be taking over a sophisticated address, which has been L'Épinard, Lion d'Or and now ViTo's," said Marinelli. "We've been working on this since 2020. So we're all the more pleased to have been able to open, despite the obstacles and delays encountered on site.” He knows the area very well as he lives in Strassen and is originally from the municipality. He ran his first restaurant, An der Broutgaass, in Strassen between 2007 and 2014 before moving to Mamer to run Toussaint. At the same time, he was the manager of the Habitat shop in the Belle Étoile shopping centre. Marinelli explains why ‘Aperitivo & Ristorante’ was added to the restaurant name: "We want to create a meeting place for the local residents and also for the many workers who work in the surrounding offices. To achieve this, the venue offers a non-stop service, from 11am to 11pm on weekdays and until 1am on Friday and Saturday. It was something that was missing in Strassen.” The à la carte menu includes a number of starters and dishes to share. Suggestions include homemade foie gras, Pinsa (similar to a pizza) with tomato, bruschetta with pata negra ham, Iberian tacos, ravioli, homemade taglioni. The restaurant has 90 seats inside and could be open to more people in the coming months. "We're planning to use the terrace to offer 80 extra seats outside", Marinelli added. Table Talk‘Buddik BanLieue’: where street food meets haute cuisine in TrierAnyone feeling peckish on their next shopping trip through Trier should make a detour to this not-so-secret insider tip Food wasteLeftlovers, the made in Luxembourg app that fights food wasteLaunched by five high school students, the platform enables users to combat food waste while enjoying discounted prices at partner retailers World ExpoPremiumHow hotel school students are serving up Luxembourg flavours in Osaka The students of the hotel management school are responsible for the catering and the shop in the Luxembourg pavilion EU breakfast guidelinesHow EU rules are changing your breakfastNew origin labelling for honey, less sugar in fruit juice and more fruit in jam WellbeingFrom food fads to dangerous diets: the risks of social media trendsSeeking advice online can have a negative long-term impact, dietician warns, as untrained food gurus can spread misinformation unchecked Light bites Taste Spanish tapas on these terraces in LuxembourgFrom Cantabrian anchovies and Galician octopus to Iberian ham and Rubia Gallegan beef – share some tapas at these Spanish eateries Famous recipeThe Luxembourger who invented McDonald's chicken nuggetsAs the fast-food chain prepares to celebrate its 40th anniversary in the Grand Duchy, a look at the famous recipe developed by René Arend from Wiltz ©2025 Mediahuis Group. All rights reserved A four-way tie from yesterday’s qualifying which saw Denmark’s Mathias Fullerton and Stephan Hansen, France’s Nicolas Girard and USA’s James Lutz all drop 599 at the typical 18-metre indoor distance meant that any compound men archer who could shoot all 60 of their arrows into the 10-ring would become the top seed heading into matchplay Asian Games silver medallist Verma did just that at the Guillaume Tell Archery Club, the host of the second stage of the 2025 Indoor World Series, which kicked off a fortnight ago in Lausanne, Switzerland “It’s my first perfect score ever,” the Indian said I guess this setup is good for me and I’m able to shoot again.” “I am more focusing on the elimination and will try to do the same.” As he has never won a medal in the premier international indoor circuit, world number nine Verma’s pole position is a surprise, but for 2020 Indoor World Series silver medallist Hansen it was little shock he found himself as one of the top seeds Guillaume Tell is one of the 29-year-old’s favourite ranges having won three medals (two silver, one bronze) there in 2018, 2019 and 2023 and would have felt confident ahead of the matches especially coming off the back of his victory at the annual Kings of Archery tournament last weekend But there would be no repeat of 2017 World Games Hansen’s past successes this year as Antoine Le Bars knocked him out via shoot-off in the second round with the Frenchman’s 10 measured closest to the X spot (centre of target) It was a much more memorable opening to the tournament for Luxembourg’s very own Mariya Klein in the compound women as she finished as the ninth seed easily within the required top 32 to qualify for matches her score of 591 setting a new national record Klein admitted though her new record was unexpected “Extremely happy with the record,” said the 27-year-old “I honestly didn’t have it in my mind until somebody told me now because I never know how many points exactly it was.” “So when I was told it was a record, I was very, very happy and surprised,” she added before facing Spain’s Maria Pitarch and world number one Ella Gibson in matches the latter beating her in the second round 150-149. The most convincing display in the qualifying rounds was by Nicholas D’Amour in the recurve men’s event, who shot an impressive 594 in Strassen to become the number one seed, with his closest competitor in qualifications, Croatian Alen Remar The 23-year-old who represented the Virgin Islands at both Tokyo 2020 and Paris 2024 failed to get himself carried away by his sharp shooting and praised the quality of his fellow archers at the GT Open 93 of which entered in this year’s recurve men’s field down from last year’s 105 strong contingent “We’ll see if it holds and there’s still a lot of other sessions to go and a lot of other good archers,” said Nicholas something much better than my other competitions so far this year.” Much like Hansen though, D’Amour’s form came to a sudden shocking end as he lost also via shoot-off to two-time Olympian Ziga Ravnikar Meanwhile, Lim Duna (590) and Lim Hana (587) came top two in the recurve women’s rankings and both reached the quarterfinals, the duo offering a glimpse into the future of Korea’s women’s team who won their tenth straight Olympic recurve team gold last summer. The final three rounds of matches are scheduled for tomorrow with medals and world ranking points up for grabs to conclude the weekend’s action in Strassen. Not just for seniors though, with there also being competitive matches held in the under-21 compound and recurve categories. A bus crashed into a drive-in ATM outside of a bank on Route d'Arlon in Strassen at around 4am on Saturday According to preliminary information from the police the bus was not carrying any passengers at the time of the spectacular collision which is currently believed to have been an accident and then came to a halt in the middle of the street Police have confirmed that no money was stolen from the damaged ATM which was later recovered by a security firm An investigation into the exact circumstances of the accident has been opened Read also: Luxembourg police confirm no money stolen in all three ATM blast attempts L to r: Ben Boulanger, Luiza Noculak, Martine Dieschburg-Nickels and Iurii Skobel told Paperjam about the upcoming Bridges of Solidarity forum and the work that the Ukrainescht Haus is doing in Strassen. Photo: Lydia Linna/Maison Moderne The ‘Bridges of Solidarity’ forum, which will be held in Strassen on 13 November 2024, will feature discussions on how to implement social and humanitarian projects to support Ukrainians. Paperjam got a preview of the conference from the organisation team. Managed by Iurii Skobel and thanks to the help of volunteers, the house now also provides art and dance lessons, language classes and other programmes for the community. But the Ukrainescht Haus also works with other local groups, added Luiza Noculak, who’s in charge of intercultural living together at the municipality of Strassen. An association of seniors who produce handicrafts, for instance, donates part of the money to the Ukraine House. “You can always get a cup of coffee, have a discussion and meet people,” said Dieschburg-Nickels. “It has really become a social centre where locals and Ukrainians meet.” It’s a big project, but “I think we are a real model for other cities in other countries.” When the war started, governments began to provide aid to the people of Ukraine. “But very quickly, it was clear that this aid is also based on several pillars, and one of the major pillars is that of the local communities,” said Dieschburg-Nickels, who will moderate a panel on the role of local communities and humanitarian aid centres. “So our forum is about: how can the local communities interact? How can we--as local communities from other countries--help the local communities of Ukraine?” The topic of the ‘Bridges of Solidarity’ forum, which is organised by the commune of Strassen and will take place in the Centre Culturel Paul Barblé on 13 November, aims to help cities exchange ideas about humanitarian and social initiatives. The programme includes discussions on the role of local communities, rehabilitation projects as an integral part of recovery and new challenges in the humanitarian aid sector, with speakers coming from cities and associations both in Ukraine and Luxembourg. The conference will also feature presentations from students--to give them a voice and an opportunity to speak about their “vision of the future,” said Noculak--and school directors on how schools can get involved. “It’s a very good opportunity to make them aware of what they could do for Ukrainian youths,” added Dieschburg-Nickels. Find out more about the forum and register . 22 Feb 2025 16:00:00 GMT?.css-1txiau5-AnswerContainer{color:var(--GlobalColorScheme-Text-secondaryText2);}Una Strassen won 1–0 over Racing FC Union Luxembourg on Sat The current head to head record for the teams are Racing FC Union Luxembourg 9 win(s) Haven't scored in their last 2 matches Have scored 18 goals in their last 5 matches Who won between Racing FC Union Luxembourg and Una Strassen on Sat 22 Feb 2025 16:00:00 GMT?Una Strassen won 1–0 over Racing FC Union Luxembourg on Sat 22 Feb 2025 16:00:00 GMT.InsightsHave scored 4 goals in their last 5 matches Racing FC Union Luxembourg is playing home against Una Strassen on Sat A rubbish bin on Rue du Cimetière in Strassen caught fire at around 10.30pm Saturday evening with the flames eventually triggering a nearby gas bottle to explode The blast damaged a fence and part of the nearby primary school building According to initial reports from police and firefighters at the scene the gas bottle had likely been stolen from a garden shed not far from the scene of the fire An investigation has been launched to determine the exact circumstances of the incident which is not thought to have resulted in any injuries Police officers on Saturday night also intervened on the A13 motorway when a patrol spotted a motorist driving at 196km/h instead of the 110km/h permitted at this location The vehicle was caught and intercepted at the Biff roundabout where the driver immediately received a provisional driving ban a fire broke out in an apartment on Rue de l'Église in Strassen prompting a swift response from the Grand Ducal Fire and Rescue Corps (CGDIS) emergency service teams were despatched to the scene two individuals sustained minor injuries and were treated on-site by the SAMU doctor and paramedics from Luxembourg City abandoning previous criteria which sometimes led to an overwhelming amount of artwork on display for the first time the art exhibition has a theme - sustainability Thirty artists were chosen for the exhibition The variety of media and range of techniques - sculptures and the use of materials including reclaimed wood make for a varied yet structured collection The 2022 Strassen Biennial was marred somewhat by accusations of plagiarism by photographer Jingna Zhang against Jeff Dieschburg’s painting Turandot, which had won a sponsorship award. Zhang recently won an appeal on the matter. This time, in addition to adding a specific theme, the jury is also composed only from experts and respected figures from the Luxembourg art world (and no politicians are among its members), to encourage authentic and original selection, and to highlight the diversity of artistic expression. This year’s prize winner, Tanja Kremer-Sossong, has three artworks that transform what we see in every day life into art. A backdrop of photographs showing stickers and graffiti found in public toilets or on signposts, might in their original state be considered as vandalism. Kremer-Sossong invites us to see the messages left by their authors. She also reuses waste materials, asking us to reflect on the life of these objects from our disposable society. She fuses embroidery and stickers with photography in a collage style, to make us reconsider reusing materials and what constitutes resources and what is waste. The Prix d’Encouragement goes to a young artist living in Luxembourg, Daniel Mac Lloyd. His grand-scale portrait of a hummingbird uses acrylic with aerosol on a composition of recycled wood and catches the eye as soon as you enter the exhibition, producing an almost 3D effect on closer inspection. Entitled “Unbreakable” perhaps because this bird is so very fragile, Mac Lloyd has even made a sculpture from the aerosol cans that he used, which he has called “Blue Gem”. He explained that the artworks reflect on our relationship with our resources and our outlook for the future. “One of the symbols that the hummingbird carries for me is the ephemerality of the moment. How each moment is precious, and how we must appreciate and make the most of what we have,” he said of his work. Prize-winners aside there is plenty of variety among the 90 works on display. Astrid Breuer’s sculptures entitled “Still alive…” are realistic renditions of a purple harlequin toad, a Chinese pangolin and a long-eared jerboa, staring with mournful eyes as if in recognition of their plight. There are some quirky pieces, including upcycled ancient Miele vacuum cleaners turned into little racing cars by Nico Hames, or the bicycle inner tubes turned into human-like sculptures by Rafael Springer. There’s even a sort of nod to Jean-Marie Biwer in the close up of tree trunks, beautifully rendered in oil on aluminium by Jhan Lamborelle. The Strassen Biennial of Contemporary Art seeks to make art accessible to all and to showcase the creative talents working in Luxembourg and the Greater Region. The exhibition is housed at the Cultural Centre Paul Barblé, at 50 Rue des Romains, and is open daily from 10:00 to 20:00 until 26 May 2024. Preview‘This Is a Scam’ offers satirical take on modern feminismWhether playing by the book or faking it to the top, this play performed in Luxembourg looks at how we measure success Art and moneyArtists in Luxembourg find inspiration and financial support in their day jobsTwo Luxembourg artists share how their day job helps fund and inspire their creative careers Venice BiennaleAt Biennale Architettura, Luxembourg entry is a sight to be heard‘Sonic Investigations’ invites visitors to this year’s Venice exhibition to perceive architecture with their ears Eat, Drink, DiscoverSign up for the Luxembourg Times lifestyle and culture newsletterReceive weekend events, reviews and more information about what to eat, see, drink and do in Luxembourg straight to your inbox ExhibitionsFrom florals to tigers: two exhibitions open at MudamTwo new exhibitions share a common thread: a willingness to experiment with both old and new technologies CultureLuxembourg’s government looks to add to growing art collection Art galleries invited to propose works for the state’s collection that could end up being displayed in ministries, embassies Art restoration Claire’s mission to preserve Luxembourg’s old paintings Ahead of the Antiques & Art Fair at Luxexpo, one of the Grand Duchy’s qualified painting restorers explains how she conserves artworks for future generations Museum of Modern ArtMudam chairman Patrick Majerus resigns with immediate effectNo reason given for departure of Majerus, who was mid-way through six-year term as chair of Luxembourg modern art museum US Mondorf travelled to Strassen on Sunday with the aim of closing the gap to the top six and solidifying their place in upper mid-table. The task was arduous: Strassen had been unbeaten for 12 games in all competition before the clash, winning four of their previous five outings. The underdogs took the lead after a little over a quarter of an hour through Hatim Far’s header, from a Lilian Fournier assist. Strassen created several dangerous chances across the first half, and their form showed no major regression, but João Machado did well to keep their attackers at bay. It is no wonder FC Differdange are cruising towards a successful title defence – they have a plethora of quality options for every position. The attack is no different. Last season’s best player Guillaume Trani is helped by the dynamic Artur Abreu, the most valuable player in the division in Fede Varela, winter signing André Mendy, talented loanee Gustavo Simões, and proven goal-getter Andreas Buch. So far, he has been afforded a single start in the BGL Ligue, and one in the domestic cup (recording a hat-trick against amateurs Colmar-Berg). He started three of FCD’s four European matches on the bench, missing one entirely through an ankle injury. When he is on the pitch, though, El Idrissi does contribute to his team’s successes: over the month of October, for example, he scored two goals and registered an assist in 21 minutes of game time spread out over three separate cameos. In two of those three games, he was subbed on in stoppage time and still managed to find the net both times. When you see the striker play, his condition seems ideal: agile, sharp and hungry for success. And yet, even after top scorer Jorginho was sold in the summer, the club looked for a new signing instead of solving the problem internally, turning to either one of Buch, El Idrissi or Gustavo (or a rotation of the three). Having three extremely prolific strikers on the bench at all times (Buch has 5 goal contributions over 164 minutes, or one every 32.8 minutes) seems like an incredible luxury. Differdange will likely play Champions League qualifiers next season, and Trani is expected to be sold for a hefty transfer fee, but based on past evidence, we might see a new replacement cast from abroad instead of promoting one of the existing options (though Fede Varela’s signing looks like the perfect succession plan). As for El Idrissi, it might be worth taking a step back in order to make two steps forward in the future. His qualities are wasted warming the bench for 85 minutes or more each weekend, and while his numbers still look impressive, his best years are ahead of him and could be spent at a team where he could play an important role. In the meantime, Differdange can be happy with their 15-point lead at the top of the table, and it’s a matter of time before they mathematically secure the title. Thanks to El Idrissi, among others – as the striker scored again this Sunday, completing the 4-0 rout of Mondercange in the 85th minute. Fast forward to February, and the picture is different altogether. Since the restart, RFCUL won only two of their seven games, and rank 11th in the form table. They are still only two points away from a place in Europe, and can also look forward to a Luxembourgish Cup quarter-final against fourth-tier Minerva Lintgen soon. But the club are fast approaching a turning point. Their current squad is still top-half by BGL Ligue standards, and by committing to further signings in the winter, they are clearly making steps towards risking it all for a place on the podium, and the windfall that comes with it. These ambitions took a huge dent on Saturday, when the team came out second-best again, this time at home against Niederkorn. After a 2-0 losing position at half-time, a penalty from Yann Mabella provided a glimmer of hope in a comeback, but they ended up conceding a third and suffering yet another defeat. Niederkorn have now overtaken Racing, who find themselves joint-sixth. They are facing Union Titus Pétange next week, the team whose form has only been topped by leaders Differdange since the restart. After that, it’s third-place Hesperange at home, another tricky fixture before they visit struggling Mondercange. The next two games can tip the scales in either direction, and it is undoubtedly still not too late to make a late surge for the continental qualifier spots. But this month will certainly be crucial. Hostert sorely missed first-choice goalkeeper Dorian Chiotti, who was still on international duty with Mauritius. His deputy Théo Sardou conceded 3 goals in a surprising loss to Bettembourg, who find themselves only one point away from crawling out of the relegation play-off places. Hesperange keep proving how underrated they are since their financial problems and personnel changes escalated in December. They beat a resilient Rodange team and made their way back to the podium – but UEFA’s investigation is still underway, potentially costing Hesper their European licence for next year. F91 Dudelange took the lead early on against Fola, resulting in a rather eventless encounter. Tim Flick scored against his former team from a direct free-kick to set the 2-0 scoreline and inflict their ninth consecutive defeat on Fola Esch. Victoria Rosport have made it five draws in a row, this time with a 1-1 against 10-man Jeunesse Esch. Both teams found the net in quick succession, in the opening minutes of the second half. This stretches Rosport’s unbeaten streak to six matches in total, and their survival seems all but guaranteed. Union Titus Pétange won in eye-catching fashion, dismantling Wiltz 0-3 by scoring two goals in added time. UTP’s defence kept a clean sheet for the fourth time in six games, boasting the best defensive metrics after champions-elect Differdange, while Wiltz continue to languish dangerously close to the relegation zone. Braden Gellenthien, new cadet world record holder Casey Kaufhold, and Steve Wijler – who tied on points with Cedric Rieger – also took top seedings You’re never really happy unless it’s a perfect score,” said Prieels being the first big shoot of the season and dropping only five points Hopefully it’s going to be a good start and I’ll have another shot at breaking the world record soon.” The 595-point compound women’s world record was set by Erika Jones in 2014 Braden Gellenthien dropped just three points to finish ahead of a talented compound men’s field. The world number three was one up on Dutch pair Peter Elzinga and world ranking leader Mike Schloesser was almost enough to take pole in the recurve men’s competition But world number two Steve Wijler shot a blistering back straight and dropped just one point in 30 arrows to match Rieger’s 594 and take the top spot in a coin toss “I expected high scores on top,” said Rieger. “I knew there was Steve Wijler, Patrick Huston, Rick van der Ven and many others The first-session score of 589 points from 14-year-old Casey Kaufhold, which was ratified as a new cadet world record held strong to lead all recurve women in Strassen Only the top-32 qualifiers advance to matchplay at indoor tournaments compound men’s at 586 and compound women’s at 560 All four top seeds survived the first round of eliminations shot on Saturday evening However, recent winner of the Kings of Archery Series: JVD Open and number four compound men’s seed Paul Tedford did not, upset by a perfect 15-arrow match from 29th-ranked David Etienne Competition in Strassen continues with the remaining elimination matches on Sunday The medal matches will be streamed live on World Archery platforms from 15h00 local time The GT Open is the first stage of the 2019 Indoor Archery World Series. The Grand Ducal Fire and Rescue Corps (CGDIS) reports that one person was injured in a fire on Monday evening. The incident happened on Route d'Arlon in Strassen, though no further details are known at this stage. Emergency services also report that three people sustained injuries in a car crash on the B7 near Fridhaff at 9.40pm, and another person suffered smoke-related injuries in an incident on Rue Dante in Hollerich. Luxembourg when the GT Open holds the first Indoor Archery World Series 250 competition There are over 300 archers – some travelling from as far afield as Trinidad and Tobago Every single person that competes in the Indoor Archery World Series will be listed in the circuit’s new open ranking while the top-16 finishers in each of the four competition divisions receive points towards the elite ranking. It’s the elite ranking that decides who is invited to the Indoor Archery World Series Final in Las Vegas in February Friday 23 November: qualification (two sessions) Saturday 24 November: qualification (two sessions) Sunday 25 November: second chance tournament eliminations and finals (medal matches starts at 14h00 GMT/15h00 CET) Photo courtesy Dubravko Buden The name of world number two Steve Wijler jumps out of the recurve men’s entry list, although teammate and world medallist Rick van der Ven could challenge if in form Another archer flying Dutch colours in Gabriela Bayardo and the most renowned of her former teammates from the country in which she was born (Mexico), Aida Roman, have a shot in the women’s event. Casey Kaufhold the 14-year-old from the US who’s been breaking senior national records is one to watch in her first adult event overseas Marcella Tonioli, Tanja Jensen, Sarah Prieels and Toja Ellison are all compound women with proven winning records The compound men’s line in Strassen is stacked. Headlined by world number one Mike Schloesser, it also features world number two Stephan Hansen, number three Braden Gellenthien and number four Seb Peineau And then there’s Sergio Pagni, Peter Elzinga, Evren Cagiran, Kings of Archery winner Paul Tedford, and three-time junior world indoor champion Viktor Orosz We recommend that you check the links in this article as food trucks often change their weekly whereabouts so if we've missed a new one or one has closed but still has an active website let us know and we'll add or delete it from our list If you want to take a tour of food truck cuisine head to the Food Truck Festival at Weiler-de-la-tour on 17-18 May There’s also a Street Food Festival on Remich Esplanade from 20-23 June and a Food & Music Festival in Petange park on 12-13 July Felix and Pol can be found serving up 100% beef patties at various locations in Luxembourg, including their restaurant in Ettelbruck In addition to the house burger, you can try out Black Angus steak or vegan and veggie varieties The author notes it is a shame their motorway driving isn’t as courteous as their service You'll find them daily at 120 route d'Arlon in Strassen from 11.00 to 22.00. You can check the exact location of their other food trucks here Pizza rolls including the Spider Pig which features tomato, mozzarella, porchetta and cream of peppers, are newly launched, but this food truck also does burgers, including the Matrix, which comes with egg and fries. You can find their weekly locations on social media but they include Capellen A new truck offering some carefully crafted Indian street food, curries and wraps, lovingly prepared by Jagruti Devasthali. You can find her and the food every Tuesday at Bertrange and Wednesdays in Weimershof Fancy a crepe stuffed with savoury or sweet fillings for lunch? You can even get gluten-free varities of galettes which include teryaki chicken and emmental or a veggie version with baked pumpkin, cabbage pickle and onion compote. The sweet varieties include apple compote with caramel or quince and chestnut. You’ll find them at Cloche d’Or on Monday Bertrange on Wednesday and Capellen on Thursday Serving a huge variety burgers the much-loved So Food truck started by Greggory Hell You can catch them currently find them in Cessange, Leudelange, Senningerberg and Cloche d’Or, so check this page for exact details Empanadas, burgers and of course, hot dogs, all with a Latin flavour are this truck’s speciality These aren’t just any old sausage in a bun try the Mercury which comes with Andalouse sauce or the Martian which pairs a Merguez sausage with Samurai sauce and peppers and the Sole Mio where your Italian sausage will come with black olives and pepper sauce You’ll find them at the airport, Kirchberg, Schuttrange, Garnich and Senningerberg. You can check the exact schedule plus any specials here Offering forty different types of fresh pasta you can cook with at home, but also hot pasta lunch boxes, you’ll find this popular truck in Mondercange on Monday lunchtime at Place Guillaume II on Wednesday lunchtime Traditional Polish food including Pierogi dumplings with cheese and potato all the way to XL which gives you 20 dumplings to share You can also sample Kluski (home-made noodles) with Hungarian goulash You’ll find this food truck in Strassen and Kirchberg on a regular weekly basis but it does deliver to a wider area. You can find more details on their Facebook page Noodles galore in so many styles from Sao Kao (BBQ) to sweet and sour, coconut, Sichuan, spicy Indian, Thai or house specialities. Chef Guo is pretty busy too You’ll find the truck at Findel and Garnich but it also visits Bissen, Hamm, Leudelange, Alzingen, Cloche d’Or and Schuttrange. To check where Chef Guo will be look at their Facebook page Offering home-made empanadas either with meat and Argentinian sausage in bread topped with criolla sauce or a beef Milanesa sandwich You can get a side of fries or chimichurri sauce You'll find them at Strassen Kirchberg and Bettembourg on a regular basis serving up Arepas - a gluten-free corn bread with different fillings including beef They also have chilli con carne and lasagne Since their social media pages are not up to date it’s difficult to know exactly where to find them but in the past they have been at the Garnich on Mondays and Wednesdays and at the city Whatever the weather, says their website, they'll be serving up chicken satay, spring rolls, Panang curry and pad Thai plus many more regional specialities Lunchtimes from 11.30 to 14.00 you’ll find them at Schuttrange, Kirchberg, Cloche d’Or and Strassen, with details of times and exact locations here Apparently travelling through Luxembourg and to be found at several locations (so check this page for where they will be), this street pizza outfit has tomato bases but also a green and a pistachio sauce base The latter comes with mozzarella and stracciatella cheese Tahsin grew up in Aleppo, cooking for friends and family, and this inspired him to open his food truck in Bertrange Open Monday to Friday 10.30 to 14.30 at 10 rue des Merovingiens and serving up Syrian food including falafel and shish wraps sujuk paninis and manakish with spicy cheese For a taste of Lebanese food, this truck serves up falafel kafta meat sandwiches made with Lebanese bread and Kirchberg at lunchtimes (Monday to Thursday) from 11.30 to 14.00 The first Indonesian food truck in Luxembourg, De'Reiskocher was opened by Tita and Sylvian in August 2020 and serves up fried tofu filled with bean sprouts and of course You'll find them at Heiderscheid on Tuesday and Thursday from 11.30 to 14.00 Ever tried any Georgian food This food truck dishes up minced meat Georgian dumplings (Khikhali) There are also cheese-filled bread Khachapuri served with egg on top There are also Greek dishes including halal chicken or pork Souvlaki skewers If you don't fancy these, they also serve up Greek food including Souvlaki chicken, gyro and club pita. You'll find them at lunchtimes 11.30 to 14.00 at Kirchberg, Findel, Cessange, Gasperich and Munsbach, and in the evenings from 17.00 to 21.00 at Bertrange and Strassen. You can check details here Grab a piled-high burger with an extra hunk of steak or pork from Nuno's truck which stops for lunchtimes (11.30 to 14.00) in Luxembourg City, Schuttrange, Steinsel, Contern and Leudelange, and in the evenings from 18.00 in Biwer (Thursday) and Grevenmacher (Friday). Details about exact locations can be found here Sandwiches, burgers, salads, hot sandwiches, and filled tortillas are served up by Burger and Co at Capellen's West Side Village and or outside the Ivy building You can also catch them in Clemency on Wednesday nights Beef burgers, home-made skin-on fries and onion rings, FoodRiders also offers a vegan burger (filled with fried soy slices Foodriders start their annual season in March This Moroccan food truck serves lunch at Kirchberg chicken or vegetarian (with the option to add a side of fries) are super value at €8 Serving up burgers and sausages with fries, chilli con carne, Thai green curry and seasonal soups, you’ll find this food truck at Cessange, Capellen and Dommeldange with exact locations details and the menu found here The restaurant L’Atelier del Gusto in Bonnevoie also has a food truck which will be serving Italian fare in Kirchberg on Wednesdays and Fridays. Food safetyPremiumEU food safety chief warns on bird flu threat to pigsBernhard Url says Europe’s swine herds could become a ‘dangerous virus laboratory’ Green transitionOver 8,600 solar panel subsidy requests pending in LuxembourgEnvironment administration hiring staff and training workers to cut down delays HealthcareLuxembourg to offer new homegrown midwifery qualificationUniversity of Luxembourg is launching four-year degree to train more midwives State financesLuxembourg recorded budget surplus in Q1Gilles Roth presented state of national economy report to parliament’s finance committees on Tuesday PoliticsHow much do Luxembourg ministers really earn?In addition to basic salary, ministers are entitled to monthly allowances of up to €8,000 and end-of-year bonuses EvacuationWeapon used in Kirchberg scare was fakeMan armed with fake gun caused commotion at bank branch on Monday Schengen AreaLuxembourg hopes for dialogue with Germany over border checksTens of thousands of people commute to work in Luxembourg every day Job searchBeen job-hunting unsuccessfully for more than six months? If you’ve had several months of rejection letters or never made it beyond first interviews, here’s what you might be doing wrong Financial scandalSpuerkeess rejects blame in Caritas embezzlement case Representatives tell parliament that the bank followed all internal procedures with its client The world’s leading publication for data science In the previous post we learned the maths behind the Strassen algorithm and wrote a Python code to run-test it against different matrices sizes we’ve learned that the Holy Grail of linear algebra is an optimization algorithm for matrix multiplication we would think of a matrix multiplication code as three for-loops: Thus the computational complexity is O(n³) This algorithm is applied to block matrices and the total complexity is reduced to O(n²·⁸⁰⁸) Although 2.808 may seem a very little improvement we saw that for square matrices of size 4096 the standard numpy matmult takes about 454.37 +/- 6.27 s which is a difference of about one order of magnitude We saw that the matrix multiplication problem can be reduced to a tensor product Fig.2 reports exactly the matrix multiplication, expressed as a triad, namely three elements. The minimal number of triads defines the minimal number of operations to compute the product matrix. This minimal number is the tensor’s rank R(t). Working on the tensor rank is an efficient way to find new multiplication algorithms, as explained in the Deepmind papers DeepMind has shown in these years how mathematical problems can be tackled with a machine learning approach using the reinforcement learning (RL) approach Also during this time they’ve adapted AlphaZero to find the best strategy for multiplying matrices I think it’s worth defining right now what we can appreciate in this paper: Luckily for us, DeepMind provides on its GitHub the implementation for AlphaTensor, ready to be tested and all written in JAX. The code is tailored for multiplying 4 x 4 block matrices, with a total of 47 multiplications, already reported in the tensor notations, as you can see here The benchmark is run on a TPU and V100 GPU and they’re testing matrices multiplications for the following sizes: 8192 20480 for the standard jax.numpy.dotmultiplication the Strassen algorithm and the AlphaTensor one I forked the code and added two tiny modifications: Having free access to the Google Cloud Console (still relying on $300 credits) I have created a Virtual Machine in GCP Compute Engine to test AlphaTensor The total cost is $1.94 per hour – so be careful and do not let this machine run indefinitely you can directly access with SSH and download the repo with git clone https://github.com/Steboss/alphatensor.git You’ll have to set up the Python environment and install jax with pip3 install -r alphatensor/benchmarking/requirements.txt -f [https://storage.googleapis.com/jax-releases/jax_cuda_releases.html](https://storage.googleapis.com/jax-releases/jax_cuda_releases.html) you can run the test with python alphatensor.benchmarking.run_gpu_benchmark Fig.3 reports the performance time with respect to the matrix size for each algorithm the Strassen achieves an improvement of about 6.5% with respect to standard JAX comparable with the AlphaTensor improvement of about 8.5% Excellent results are achieved for bigger matrices so that for 18432 square matrices Strassen improves the calculation by 15% (7.37 +/- 0.01) and AlphaTensor achieves an improvement of the 16% (7.31 +/- 0.01) compared to JAX (8.53 +/- 0.01) Another test I’ve done was on Google Colab. In this case, we can rely on a Tesla T4 GPU. Although the algorithm has been tested on V100, it’s worth investigating its transferability and comparing the results. Similarly to the V100 test, I’ve replicated these calculations on a Google Colab notebook, removing these lines As you can see we have more variability in the results especially for matrices of size 16384 we can see that all the algorithms achieve the same performance timings as it may be due to some downtime that we can’t manage on Google Colab Tab.1 summarises all the findings on Tesla T4: where we don’t have a real improvement with respect to JAX standard multiplication we can see that we have an improvement for very large matrices at 18432 Strassen achieves a 20% speedup and Alphatensor 22% In this paper the authors showed the technique they found to further improve matrix multiplications the core part of the technique is to start from known schemes for matrix multiplications and group them in a graph: We define a graph whose vertices are correct matrix multiplication schemes and where there is an edge from one scheme to another if the second can be obtained from the first by some kind of transformation One is called a flip and turns a given scheme to a different one with the same number of multiplications and the other is called a reduction and turns a given scheme to one with a smaller number of multiplications The navigation across all the matrix multiplication schemes is done through a random walk the flip can be done using the following idea: The idea is to subtract something from one rank-one tensor and add it to one of the others where the authors have depicted all the known schemes and how they are interlinked with each other through flip and reduction transformations but it’s another great starting point which will bring more and more efficient algorithms for matrix multiplication Today we’ve concluded the review of the DeepMind paper "Discovering faster matrix multiplication algorithms with Reinforcement Learning" This paper has brought a lot of interest in the matrix multiplication field and We defined 4 main points that we can draw from the paper: we run AlphaTensor on an NVIDIA V100 GPU and Tesla T4 we can see that overall AlphaTensor improves the calculation with an improvement of up to 16% on V100 and 22% on Tesla T4 – although the algorithm is not optimized for such a GPU Finally, we saw that this is not the end of the story, but a beautiful start for a new store. An example is given by the FBHHRBNRSSSHK-Algorithm which proves how the DeepMind solution can be further exploited with a pure mathematical formalism to find new and more efficient matrix multiplication techniques Join Medium with my referral link – Stefano Bosisio Please, feel free to send me an email for questions or comments at: [email protected] or directly here in Medium Step-by-step code guide to building a Convolutional Neural Network A beginner’s guide to forecast reconciliation Here’s how to use Autoencoders to detect signals with anomalies in a few lines of… An illustrated guide on essential machine learning concepts Derivation and practical examples of this powerful concept Columns on TDS are carefully curated collections of posts on a particular idea or category… The world’s leading publication for data science Matrix multiplication is at the heart of many computational tasks, including neural networks, 3D graphics... DeepMind recently introduced AlphaTensor a deep reinforcement learning approach based on AlphaZero efficient and provably correct algorithms" for fundamental tasks such as matrix multiplication The research team published their work in the article "Discovering faster matrix multiplication algorithms with reinforcement learning" in early October in the journal Nature commonly taught in high school math classes it underlies many processes in computing and the digital world By studying very small matrices (size 2x2) Volker Strassen discovered an ingenious way to combine the matrix entries to produce a faster algorithm experts have not found the optimal algorithm for multiplying two 3 × 3 matrices nor have they managed to outperform Strassen's two-level approach in a finite body The figure below illustrates a matrix multiplication tensor and algorithms The strategy provides a distribution over potential actions AlphaTensor has led to the discovery of a diverse set of algorithms with state-of-the-art complexity: up to thousands of matrix multiplication algorithms for each size demonstrating that the space of matrix multiplication algorithms is richer than previously thought These multiply large matrices 10-20% faster than commonly used algorithms on the same hardware highlighting AlphaTensor's flexibility in optimizing arbitrary objectives "Discovering faster matrix multiplication algorithms with reinforcement learning".Nature 610 https://doi.org/10.1038/s41586-022-05172-4 Authors: Alhussein Fawzi, Matej Balog, Aja Huang, Thomas Hubert, Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Francisco J. R. Ruiz, Julian Schrittwieser, Grzegorz Swirszcz, David Silver, Demis Hassabis & Pushmeet Kohli Translated from DeepMind accélère la découverte d'algorithmes de multiplication matricielle avec AlphaTensor Votre source d'information sur l'intelligence artificielle et ses avancées Matrix multiplication is an intense research area in mathematics [2–10] Although matrix multiplication is a simple problem the computational implementation has some hurdles to solve If we are considering only square matrices the first idea is to compute the product as a triple for-loop : Such a simple calculation has a computational complexity of O(n³) This means that the time for running such a computation increases as the third power of the matrix size as in AI and ML we deal with huge matrices for every model’s step – neural networks are tons of matrix multiplications we need more and more time to run all our AI calculations DeepMind has brought the matrix multiplication problem to a more concrete step. However, before digging into this paper, let’s have a look at the matrix multiplication problem and what algorithms can help us in lowering the computational power. In particular, we’ll take a look at Strassen’s algorithm and we’ll then implement it in Python and Jax _Remember that for the rest of the paper the size of matrices will be N>>1000. All the algorithms are to be applied to block matrices._ is given by the sum over the rows and the columns of matrices A and B As we saw in the introduction, the computational complexity for the standard matrix multiplication product is O(n³). In 1969 Volker Strassen reducing the matrix multiplication to 7 multiplications and 18 additions It’s worth noticing a few things about this algorithm: therefore the matrix multiplication can be treated as a polynomial problem From these points we can translate the matrix multiplication to a polynomial problem Each operation in fig.4 can be written as a linear combination Here α and β are the linear combinations from matrices A and B’s elements while H denotes a one-hot encoded matrix for addition/subtraction operations It’s then possible to define the product matrix C elements as a linear combination and write: As you can see the entire algorithm has been reduced to a linear combination the left-hand side of the equation Strassenin fig.7 can be denoted by the matrices sizes and p – which means a multiplication between _m_xp and _n_xp matrices: Fig.8 describes the matrix multiplication as a linear combination or a tensor – that’s why sometimes the Strassen algorithm is called "tensoring" Following DeepMind’s paper convention the triad can be expressed as: This triad establishes the objective of finding the best algorithm for minimizing the computational complexity of the matrix multiplication operation the minimal number of triads defines the minimal number of operations to compute the product matrix This minimal number is the tensor’s rank R(t) Working on the tensor rank we’ll help us in finding new and more efficient matrix multiplication algorithms – and that’s what DeepMind people have done between 1969 and today there’s been a continual creation of new algorithms to solve the matrix multiplication complexity problem (tab.1) How did Pan, Bini, Schonage, and all the researchers get to these brilliant results? One way to solve a computer science problem is to start with the definition of an algebraic problem P. For the matrix multiplication problem, for example, the algebraic problem P can be: "find a mathematical model to evaluate a set of polynomials". From here scientists start to reduce the problem and "convert" it to a matrix multiplication problem – here is a good explanation of this approach scientists were able to prove theorems as well as steps that could decompose the polynomial evaluation to a matrix multiplication algorithm they all got a theoretical algorithm that can be more powerful than the Strassen algorithm (tab.1) these theoretical algorithms can’t be coded up unless there are some heavy and strong mathematical assumptions and restrictions that could affect the algorithm’s efficiency Let’s now see how powerful Strassen’s algorithm is and how we can implement it in Python and JAX Here is the repo with all the following codes In the main code we can follow these steps: The core part of the script is the recursivestrassen function: the product matrix is reconstructed from all the computed sub-elements ( C11 Fig.10 compares the standard numpy.matmul and strassen algorithm As you can see for a dimension < 2000 ( Matrix Size < 2000 ) Strassen can be outperformed by the standard matrix multiplication The real improvement can be seen on bigger matrices Strassen completes the matrix multiplication for a 2048×2048 matrix in 8.16 +/- 1.56 s while the standard methods required 63.89 +/- 2.48 s while the standard matrix multiplication takes 454.37 +/- 6.27 s According to the equation in fig.9 we can further decompose the Strassen algorithm in a tensor form v and w can then be applied to the matrices’ blocks to obtain the final product matrix Johnson published a little paper to show how to derive the tensor version of Strassen [18] followed by another formulation in 1994 [19] where they explicitly wrote Strassen’s u For the detailed calculations you can check [18] This is a good starting point for working with JAX and comparing Strassen to the standard jax.numpy.matmul. For the JAX script I have followed closely DeepMind’s implementation The script deals with 4×4 block matrices all the A and B block matrices are multiplied by the _u_and v tensors the algorithm was tested on the following matrices’ dimensions: 8192 in the very last step the product matrix is reconstructed by concatenating and reshaping the product matrix from f function (fig.14) 15 compares JAX numpy matrix multiplication with the Strassen implementation as 8192×8192 matrices multiplication can be run in 12 s (on average) For dimensinos under 12000×12000 there is no real improvement and JAX standard method takes an average computational time of 60s on my laptop – while I am running some other things Above that dimensions we can see an impressive 20% improvement the Strassen algorithm runs in 142.31+/-14.41 s and 186.07+/-12.80 s respectively – and this was done by running on a CPU A good homework could be trying this code adding the device_put option and running on Colab’s GPU Today we made a little step forward to get a complete understanding of DeepMind’s publication "Discovering faster matrix multiplication algorithms with Reinforcement Learning" [1] This paper proposes new ways to tackle the matrix multiplication problem we started to scratch the surface of matrix multiplication We learned what’s the computational cost for this operation and we saw the Strassen algorithm From here we defined how the Strassen algorithm is made and what are its mathematical implications researchers have found better and better solutions to the matrix multiplication problem not all of these methods can be implemented in code we played a bit with Python and JAX to find out how powerful the algorithm is We learned that Strassen is a great tool to use when we have to deal with very big matrices We saw the power of JAX in handling big matrix multiplications and how easy is to implement such a solution without using GPUs or further memory options we’ll see more details from DeepMind’s paper we’ll tackle the deep reinforcement algorithm we’ll implement the new DeepMind algorithms and run them in JAX on a GPU instance I hope you enjoyed this article 🙂 and thanks for reading it Please, feel free to send me an email for questions or comments at: [email protected] or directly here in Medium SIDE-LINE Fresh news from the experimental neofolk and martial industrial act Rome aka Jérôme Reuter of Luxembourg the first being a limited vinyl edition of “Gärten und Straßen“ This represents the second instalment in a series of releases featuring exclusively martial ambient material and industrial collages partially reminiscent of earlier Rome works such as “Hate us and see if we mind” (2013) “House of Stone” (2014) or parts of the “Die Aesthetik der Herrschaftsfreiheit” trilogy (2011) Whereas Rome’s oeuvre usually features lots of guitar work “Gärten und Strassen” focuses on complex industrial loops unconventional bruitist arrangements and instrumental ambient collages This release comes in a black 180g 12″ vinyl hand-numbered and personally signed by Jérôme Reuter Baby!’ which is the teaser single from the upcoming new album “The lone furrow” (which will feature a range of guest appearances) Baby!” is a tongue-in-cheek reference to U2’s 1991 hit album “Achtung Baby” The single features Alan Averill (Primordial) and an exclusive bonus track “Any Other Grey“ The single is strictly limited to 500 copies More people are reading Side-Line Magazine than ever but advertising revenues across the media are falling fast we haven’t put up a paywall – we want to keep our journalism as open as we can - and we refuse to add annoying advertising So you can see why we need to ask for your help Side-Line’s independent journalism takes a lot of time But we do it because we want to push the artists we like and who are equally fighting to survive you can support Side-Line Magazine – and it only takes a minute The donations are safely powered by Paypal Electronic Bodies - Nightside Sessions by Shane Aungst Electronic Bodies - Session 1 by Various Artists Electronic Resistance - Reconstruction by Various Artists Electronic Resistance - A Darkwave / Post-Punk Compilation From The Ukrainian Underground by Various Artists a major police operation took place on Route d'Arlon near the municipal border between Luxembourg City and Strassen The intervention was prompted by a "suspicious report," leading authorities to inspect the reception centre for asylum seekers located next to the local Delhaize supermarket the authorities confirmed that the operation had concluded as the report was determined to be a "false alarm." They also said that “nothing suspicious” had been found on site “Several police patrols and teams” took part in the operation wrote the police on Tuesday afternoon in a statement sent to the press approximately 100 people were evacuated from the area Route d'Arlon was partially closed in both directions A team of mathematicians from the University of New South Wales in Australia and the L’École Polytechnique in France has solved a decades-old maths riddle that allows multiplication of large numbers in a much faster time. The team’s paper was published in the multi-disciplinary open access archive HAL Harvey & van der Hoeven cracked a maths problem that has stood for almost half a century which will enable computers to multiply huge numbers together much more quickly “More technically, we have proved a 1971 conjecture of Schönhage and Strassen about the complexity of integer multiplication,” said Dr. David Harvey from the School of Mathematics and Statistics at the University of New South Wales “They predicted that there should exist an algorithm that multiplies n-digit numbers using essentially n * log(n) basic operations.” “Our paper gives the first known example of an algorithm that achieves this.” if we were to multiply the numbers 314 by 159 with the usual primary school method we would need to calculate 9 digit-by-digit products.” if n represents the number of digits in each number the answer can be arrived at in n2 operations.” Schönhage and Strassen themselves invented an algorithm needing fewer than n2 operations but were unable to get it down to n * log(n) “The Schönhage-Strassen algorithm is already quite fast: a computer using the primary school method would take months to multiply two numbers with a billion digits but can do it in under 30 seconds using the Schönhage-Strassen algorithm,” Dr But for numbers with enough digits — billion, trillions or even gazillions — the new algorithm, developed by Dr. Harvey and Dr. Joris van der Hoeven from the Laboratoire d’informatique at the L’École Polytechnique would outrun even Schönhage and Strassen’s algorithm Schönhage and Strassen also predicted that n * log(n) is the ‘best possible’ result — that no-one will ever find a faster multiplication algorithm our work is expected to be the end of the road for this problem although we don’t know yet how to prove this rigorously,” Dr this breakthrough has an enormous number of consequences.” “It means you can do all sorts of arithmetic more efficiently You could also calculate digits of pi more efficiently than before It even has applications to problems involving huge prime numbers.” a batch of baguettes is baking in a Hein oven Fours Hein has delivered its “Rolls Royce of bakers” to Grande Boulangerie and several million rolls of bread will come out of a Luxembourg oven every day during the Olympic Games in Paris this summer It’s an example of the need for the public innovation agency and the state to support these winning SMEs At 80 degrees when it comes out of the oven in the industrial hall of Fours Hein in Strassen it would have been a shame not to bite into it The only thing missing is the comforting smell of good bread but the ventilation system instantly swallows up any metal dust the fifth generation to head this family-run SME leads a tailor-made tour for economy for minister (DP) The company has just delivered to the Grande Boulangerie the oven that will bake several million rolls a day during the Paris Olympics a modern oven heated with pellets and/or an oven powered by green electricity Fours Hein has seized the opportunity to get help from the public innovation agency Luxinnovation “Innovation is a fundamental added value in the life of a company especially in the economic context that we have experienced in recent years particularly for small and medium-sized businesses with limited financial and human resources It’s clear that the financial support from the economy ministry and the backing from Luxinnovation are invaluable to us and without them we’d be stuck in a cupboard for some time,” says Guillaume “The Hein group has always wanted to devote a few percent of its annual sales excluding personnel costs [5% this year editor’s note] to its development division This has been all the more true since the energy crisis hit Europe It’s not that we didn’t previously have innovative solutions for reducing energy consumption but the trend towards greater electrification and a significant reduction in CO2 emissions is not sparing the bakery sector after planning several meetings with the Luxinnovation teams we were able to submit two projects for support from the ministry of the economy: two zero fossil energy ovens,” he continues This is particularly important for the Luxembourg company Luxinnovation CEO Sasha Baillie honoured with a heart-shaped baguette Luxembourg’s economy minister Lex Delles (DP) being shown how the ovens work by the fifth generation of the Hein family Ferdinand Hein--the family’s fifth generation--explains the robotised operation of his oven Luxinnovation presents annual reportOn Thursday 4 July in Strassen economy minister Delles also presented the annual report of the public innovation agency Fit4Start will be overhauled to make it simpler and therefore more accessible to businesses and a new Fit4AI programme will “enable businesses to understand the opportunities available to them or how to improve their productivity.” Delles also announced assistance accompanied by a new strand of the SME Package: the SMP Package AI “to start something concrete carry out analysis or raise awareness.” Administrative simplification is also meant to support these schemes Delles added that 325 businesses had received support by 2023 although it was not clear how this figure should be qualified: businesses have very different needs in this area different ways of embarking on the dual transition and different and varied financial and human resources “to help companies--whatever their level of maturity--to take advantage of the many tools available” but also “to detect loopholes and solutions in the ecosystem.” “We also need to know the companies and the challenges they face “With 86 companies taking part in the Fit4 Performance programme “The support given to companies seeking to obtain European subsidies enabled 126 of them to obtain almost €61m last year,” she said while 335 companies were supported within the framework of the clusters A further 28 seized the opportunity to benefit from the Luxembourg Digital Innovation Hub (L-DIH the Chamber of Commerce and the National Research Fund) the Luxembourg Institute of Science and Technology (List) the University of Luxembourg and the university’s Competence Centre Luxinnovation also coordinates the National Supercomputing Competence Centre (with the university and Luxpovide) and runs the Sustainability Innovation Hub and the Klimakt fir Betriber Of the 387 new contacts with companies from 41 countries who might be interested in setting up in Luxembourg 53 have been supported and eight have actually arrived Forty-five start-ups were created with the agency’s support and the construction waste recycling unit project will continue in 2024 New projects include initial discussions with the agricultural sector and Luxinnovation’s contribution to defence efforts in the Nato budget: 91 companies in Luxembourg have been identified as potential participants in this dynamic Other subjects “in the oven” include the development of a “scale-up” strike force for fast-growing innovative companies that need much greater financial resources to continue to develop at cruising speed Following the success of the first Luxembourg Ventures Days in October This article was first published in French on It has been translated and edited for Delano Google’s DeepMind research group recently developed "Alphatensor." the first AI system for discovering novel algorithms to perform fundamental tasks such as matrix multiplication This application has brought innovations to the 50-year-old mathematical challenge of finding the fastest ways to multiply two matrices Let’s decompose the significance of this discovery Most of us first encountered matrix multiplication in middle or high school It consists of a series of multiplication and additions in a pre-defined order used to find the product of two nth-degree tensors The most famously taught mechanism for multiplying two matrices is using the dot product (Figure 1) of rows and columns this mathematical operation influences modern computing and is a cornerstone of digital systems Almost any data type that can be tokenized or encoded into a multi-dimensional representation of numbers will require some matrix multiplication Image processing and computer vision applications benefit tremendously from efficient matrix operations In a convolutional neural network (Figure 2) discrete convolutions are equivalent to taking a dot product between the filter weights and the values underneath the filter – in short mathematicians believed that the standard dot product was the best and most efficient method for multiplying matrices That was until Colker Strassen introduced Strassen’s Algorithm (Figure 3) and shocked the world by demonstrating that more efficient algorithms exist Strassen’s Algorithm utilized one less scalar multiplication than the traditional method Although Strassen’s Algorithm contains fewer arithmetic operations it’s essential to consider that for current-generation CPUs a multiplier can produce a result every machine cycle The multiplier takes more gates and has a longer latency to get the first result Multiplication has a higher "big O" complexity than addition (Figure 4) Strassen was more efficient because he performed one less multiplication step AlphaTensor takes this further by using AI techniques to discover new matrix multiplication algorithms by optimizing through self-play and reinforcement learning Deep Reinforcement Learning (Deep RL) leverages the power of deep neural networks to optimize the solution to a particular problem and rewards as models of real-world systems where the goal is for an agent to maximize its reward in a particular environment Suppose you consider the game of chess (Figure 5) where the objective is to capture your opponent’s pieces and checkmate their king there exist a set of optimum moves for every possible scenario on the board that will maximize the odds of success the RL schema could be defined as follows: We would award the appropriate reward for each move until either player is in check-mate or there is a draw (Figure 6) This process would be performed iteratively until our model scores are consistently high enough to meet our needs AlphaTensor does something very similar to uncover the most optimum combinations of mathematical operations to perform matrix multiplication in a novel and efficient manner Using the concept of self-play, the team at Deepmind built their reinforcement learning schema for optimizing the matrix multiplication problem Their schema, as described in their paper This schema results in a search space where the possible algorithms vastly outnumber the atoms in the universe the possible moves at each step in the game of Go (Figure 7) is 30 orders of magnitude less than the complexity encountered by AlphaTensor To increase the feasibility of this effort AlphaTensor employs "a novel neural network architecture that incorporates problem-specific inductive biases and a recipe to leverage symmetries of the problem." the DeepMind team observed improvements in AlphaTensor’s ability to rediscover feasible algorithms such as Strassen’s and eventually surpass the human-defined methods in favor of algorithms faster than anything explored In a test where 5×5 and 5×5 (Figure 8) matrices were multiplied using Strassen’s Algorithm and AlphaTensor we find that AlphaTensor can solve the operation in 76 multiplications versus Strassen’s 80 AlphaTensor has helped shed light on the richness of matrix multiplication algorithms These learnings will undoubtedly shape the future of the speed and efficiency of multi-dimensional data processing AlphaTensor has also proven that machine learning techniques can be used to discover mathematical innovation that surpasses human ingenuity. This flavor of deep Reinforcement Learning is in its early days and the AlphaTensor work serves more as proof of feasibility than an immediate solution This is an exciting step forward in computational optimization and self-optimizing AGI DeepMind’s GitHub includes a few of the algorithms that AlphaTensor has discovered and a jupyter notebook with instructions for loading and testing them Don’t forget to follow my profile for more articles like this A deep dive on the meaning of understanding and how it applies to LLMs Solving the resource constrained project scheduling problem (RCPSP) with D-Wave’s hybrid constrained quadratic model (CQM) The Ministry of Health has announced that the On-Call Medical Centre (Maison médicale) will be relocating from Val Fleuri to Strassen the centre will open its new doors at 5 rue des Primeurs The operating days remain unchanged (7 days out of 7) with the centre open daily and no appointment necessary Monday to Friday: from 8pm to midnightSaturday Sunday and public holidays: 8am to midnight[block type="subtitle"] the new location is 100 meters from the terminus of the 22 bus line and includes a parking area for visitors arriving by car visitors should ring the barrier intercom and will be directed to a free space for the consultation For further details about medical centres in Luxembourg, visit the Health Portal. Allein im Kanton Bern kam es zu rund 70 Verkehrsunfällen In der Stadt Bern kam es wegen Schnee und Glätte vorübergehend zu Einschränkungen im Busverkehr Die Stadtberner Verkehrsbetriebe Bernmobil mussten verschiedene Linien einstellen Gegen 9 Uhr war nur noch die Buslinie nach Münsingen unterbrochen Auf den übrigen betroffenen Linien war der Betrieb noch unregelmässig Im Berner Kantonsgebiet kam es zu verschiedenen Unfällen Die meisten davon seien Selbstunfälle gewesen sagte eine Sprecherin der Berner Kantonspolizei der Nachrichtenagentur Keystone-SDA An verschiedenen Orten behinderten querstehende Lastwagen den Verkehr so etwa auf der A1 zwischen Bern Brünnen und Mühleberg Wegen umgestürzter Bäume mussten diverse Strassenabschnitte gesperrt werden etwa die Hauptstrasse zwischen Frutigen und Adelboden Auf der A3 zwischen der Verzweigung Luterbach und Solothurn Ost blockierte laut TCS ebenfalls ein querstehender Lastwagen eine Ausfahrt Aufgrund einer schneebedeckten Fahrbahn war auch die Kantonsstrasse zwischen Welschenrohr und Flumenthal im Kanton Solothurn gesperrt Im Kanton Schwyz haben sich am Sonntag und in der Nacht auf heute innert 24 Stunden rund ein Dutzend Verkehrsunfälle ereignet Verletzt wurde auf den schneebedeckten Strassen niemand Vorwiegend habe es sich um Selbstunfälle gehandelt blieben im Wiesland stecken oder kollidierten mit Leitplanken In den meisten Fällen entstand Sachschaden In Rickenbach SZ war die Strasse im Gebiet Lauenen blockiert Die Feuerwehr Schwyz wurde zur Räumung aufgeboten Neben den Unfällen gaben umgeknickte Äste oder umgestürzte Bäume Arbeit für die Einsatzleitzentrale Zwischen Andermatt und Dieni ist es nach einer Entgleisung beim Oberalppass zu einem Unterbruch der Linie R45 gekommen Nach einem Augenzeugenbericht kam es zu keinen Verletzten Es werden Verspätungen und Ausfälle bis heute Abend erwartet Für die Registrierung benötigen wir zusätzliche Angaben zu Ihrer Person {| foundExistingAccountText |} {| current_emailAddress |} Geben Sie die E-Mail-Adresse Ihres Benutzerkontos an über den Sie ein neues Passwort erstellen können Sie erhalten in Kürze eine E-Mail mit einem Link Wenn Sie nach 10 Minuten kein E-Mail erhalten haben prüfen Sie bitte Ihren SPAM Ordner und die Angabe Ihrer E-Mail-Adresse Bitte versuchen Sie es später noch ein Mal oder kontaktieren Sie unseren Kundendienst Wir senden Ihnen einen SMS-Code an die Mobilnummer Wir haben Ihnen einen SMS-Code an die Mobilnummer gesendet Bitte geben Sie den SMS-Code in das untenstehende Feld ein Bitte fordern Sie einen neuen Code an oder kontaktieren Sie unseren Kundendienst Die maximale Anzahl an Codes für die angegebene Nummer ist erreicht Es können keine weiteren Codes erstellt werden Wir haben Ihnen ein E-Mail an die Adresse {* emailAddressData *} gesendet Prüfen Sie bitte Ihr E-Mail-Postfach und bestätigen Sie Ihren Account über den erhaltenen Aktivierungslink prüfen Sie bitte Ihren SPAM-Ordner und die Angabe Ihrer E-Mail-Adresse Benutzerdaten 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revenue for 2024 attributing the growth primarily to a rise in internet subscriptions The company reported that its internet subscriptions grew by 2,600 in 2024 Eltrona emphasised its commitment to strengthening its position in the market Matrix multiplication, which involves multiplying two rectangular arrays of numbers is often found at the heart of speech recognition Graphics processing units (GPUs) are particularly good at performing matrix multiplication due to their massively parallel nature They can dice a big matrix math problem into many pieces and attack parts of it simultaneously with a special algorithm In 1969, a German mathematician named Volker Strassen discovered the previous-best algorithm for multiplying 4×4 matrices which reduces the number of steps necessary to perform a matrix calculation multiplying two 4×4 matrices together using a traditional schoolroom method would take 64 multiplications while Strassen's algorithm can perform the same feat in 49 multiplications Using a neural network called AlphaTensor, DeepMind discovered a way to reduce that count to 47 multiplications, and its researchers published a paper about the achievement in Nature last week Going from 49 steps to 47 doesn't sound like much but when you consider how many trillions of matrix calculations take place in a GPU every day even incremental improvements can translate into large efficiency gains allowing AI applications to run more quickly on existing hardware AlphaTensor is a descendant of AlphaGo (which bested world-champion Go players in 2017) and AlphaZero DeepMind calls AlphaTensor "the "first AI system for discovering novel efficient and provably correct algorithms for fundamental tasks such as matrix multiplication." To discover more efficient matrix math algorithms, DeepMind set up the problem like a single-player game. The company wrote about the process in more detail in a blog post last week: DeepMind then trained AlphaTensor using reinforcement learning to play this fictional math game—similar to how AlphaGo learned to play Go—and it gradually improved over time it rediscovered Strassen's work and those of other human mathematicians In a more complicated example, AlphaTensor discovered a new way to perform 5×5 matrix multiplication in 96 steps (versus 98 for the older method). This week, Manuel Kauers and Jakob Moosbauer of Johannes Kepler University in Linz, Austria, published a paper claiming they have reduced that count by one It's no coincidence that this apparently record-breaking new algorithm came so quickly because it built off of DeepMind's work "This solution was obtained from the scheme of [DeepMind's researchers] by applying a sequence of transformations leading to a scheme from which one multiplication could be eliminated." Tech progress builds off itself, and with AI now searching for new algorithms, it's possible that other longstanding math records could fall soon. Similar to how computer-aided design (CAD) allowed for the development of more complex and faster computers, AI may help human engineers accelerate its own rollout. The suspect was faced by the police at the scene of the crime. While searching the presumed suspect thoroughly the stolen items were found. The man was arrested as ordered by the prosecutor's office. 27 Apr 2025 14:00:00 GMT?.css-1txiau5-AnswerContainer{color:var(--GlobalColorScheme-Text-secondaryText2);}Una Strassen won 5–0 over FC Mondercange on Sun The current head to head record for the teams are Una Strassen 2 win(s) Una Strassen haven't lost to FC Mondercange in their last 5 meetings (2W Matheus is the competition's top scorer (20) Have scored 1 goals in their last 5 matches Haven't scored in their last 4 matches Haven't kept a clean sheet in 6 matches Who won between Una Strassen and FC Mondercange on Sun 27 Apr 2025 14:00:00 GMT?Una Strassen won 5–0 over FC Mondercange on Sun 27 Apr 2025 14:00:00 GMT.InsightsHave scored 10 goals in their last 5 matches Una Strassen is playing home against FC Mondercange on Sun Matrix multiplication - where two grids of numbers are multiplied together - forms the basis of many computing tasks and an improved technique discovered by an artificial intelligence could boost computation speeds by up to 20 per cent By Matthew Sparkes Multiplying numbers is a fundamental task for computers An artificial intelligence created by the firm DeepMind has discovered a new way to multiply numbers The find could boost some computation speeds by up to 20 per cent as a range of software relies on carrying out the task at great scale Matrix multiplication – where two grids of numbers are multiplied together – is a fundamental computing task used in virtually all software to some extent, but particularly so in graphics, AI and scientific simulations. Even a small improvement in the efficiency of these algorithms could bring large performance gains it was believed that the most efficient way of multiplying matrices would be proportional to the number of elements being multiplied meaning that the task becomes proportionally harder for larger and larger matrices But the mathematician Volker Strassen proved in 1969 that multiplying a matrix of two rows of two numbers with another of the same size doesn’t necessarily involve eight multiplications and that, with a clever trick, it can be reduced to seven. This approach, called the Strassen algorithm but this is acceptable because additions in a computer take far less time than multiplications The algorithm has stood as the most efficient approach on most matrix sizes for more than 50 years, although some slight improvements that aren’t easily adapted to computer code have been found But DeepMind’s AI has now discovered a faster technique that works perfectly on current hardware started with no knowledge of any solutions and was presented with the problem of creating a working algorithm that completed the task with the minimum number of steps It found an algorithm for multiplying two matrices of four rows of four numbers using just 47 multiplications which outperforms Strassen’s 49 multiplications It also developed improved techniques for multiplying matrices of other sizes AlphaTensor discovered thousands of functional algorithms for each size of matrix, including 14,000 for 4×4 matrices alone. But only a small minority were better than the state of the art. The research builds on AlphaZero Hussein Fawzi at DeepMind says the results are mathematically sound “We don’t really know why the system came up with this “Why is it the best way of multiplying matrices the neural networks get an intuition of what looks good and what looks bad I honestly can’t tell you exactly how that works I think there is some theoretical work to be done there on how exactly deep learning manages to do these kinds of things,” says Fawzi DeepMind found that the algorithms could boost computation speed by between 10 and 20 per cent on certain hardware such as an Nvidia V100 graphics processing unit (GPU) and a Google tensor processing unit (TPU) v2 but there is no guarantee that those gains would also be seen on common devices like a smartphone or laptop James Knight at the University of Sussex says that a range of software run on supercomputers and powerful hardware is effectively large-scale matrix multiplication.“If this type of approach was actually implemented there then it could be a sort of universal speed-up,” he says “If Nvidia implemented this in their CUDA library [a tool that allows GPUs to work together] it would knock some percentage off most deep-learning workloads Read more: AI translates maths problems into code to make them easier to solve Oded Lachish at Birkbeck says the new algorithms could boost the efficiency of a wide range of software because matrix multiplication is such a common problem – and more algorithms are likely to follow “I believe we’ll be seeing AI-generated results for other problems of a similar nature albeit rarely something as central as matrix multiplication There’s significant motivation for such technology since fewer operations in an algorithm doesn’t just mean faster results it also means less energy spent,” he says If a task can be completed slightly more efficiently But DeepMind’s advances don’t necessarily mean human coders are out of a job Automatic optimisation has been done for decades in the microchip design industry and this is just another important tool in the coder’s arsenal,” says Lachish Nature DOI: 10.1038/s41586-022-05172-4 landab immer wieder zu hitzigen Diskussionen Dies zeigte sich kürzlich auch bei einer Debatte im Zürcher Kantonsrat Das Parlament sprach sich gegen Temporeduktionen auf Hauptstrassen aus Ganz knapp unterstützte der Kantonsrat eine Initiative dass auf Hauptverkehrsachsen Tempo 30 nur in Ausnahmefällen möglich ist Auch die Zürcher Kantonsregierung hatte sich für die Initiative ausgesprochen In den Städten Zürich und Winterthur kam dieser Entscheid indes nicht gut an Grund: Die Städte wollen die Tempolimits auf den Strassen selbst bestimmen – auch auf Hauptstrassen will ein Drittel bis die Hälfte der Befragten eine Temporeduktion eine Sektion des Schweizerischen Städteverbands Befragt wurden über 15'000 Einwohnerinnen und Einwohner in zehn Schweizer Städten der Deutschschweiz und der Romandie Die Umfrageresultate kommen bei der Basler Bau- und Verkehrsdirektorin Esther Keller (GLP) gut an: «Wir sehen uns in der aktuellen Verkehrspolitik bestätigt dass auf nationaler Ebene all die Versuche die Städte in ihrer Autonomie zu begrenzen die auch Präsidentin der Städtekonferenz Mobilität ist «Das entspricht dem Wunsch der Bevölkerung.» Die Städte wollen sich laut Keller deshalb auf nationaler Ebene verstärkt dafür einsetzen dass sie in ihrem Handlungsspielraum nicht eingeschränkt werden dass die Resultate von Stadt zu Stadt variieren So finden in den Städten Basel und Bern 45 Prozent der Befragten Nyon oder Sion sind es dagegen nur 32 Prozent Generell sind zwei Drittel der befragten Städterinnen und Städter zufrieden mit der Verkehrssituation in ihrer Gemeinde Hauptgründe sind das gute Netz und die hohe Qualität des öffentlichen Verkehrs Am häufigsten für Kritik sorgen hingegen überlastete Strassen und Staus Während der Stosszeiten sind die Befragten in den meisten Städten denn auch mehrheitlich unzufrieden mit der Verkehrssituation the incident occurred when a car stopped next to the pedestrian An investigation into the incident has been launched a man was spotted attempting to open the doors of parked cars along Rue de Reckenthal in Strassen Police were alerted and swiftly dispatched to the scene They located the suspect at the intersection of Rue de Reckenthal and Rue de Luxembourg A report was filed on the orders of the prosecutor's office A car parked on Rue Jean Waxweiler in Pétange was stolen during the night from Sunday to Monday The thief was caught in the act by the car’s owner but managed to escape with stolen cash a man was robbed of his mobile phone near the central train station in Luxembourg City the suspect threatened the victim with violence before taking the phone and a report was issued at the prosecutor's request Cosmos » ASC Edits The latest and best news from the University of New South Wales A Sydney mathematician has cracked a maths problem that has stood for almost half a century which will enable computers to multiply huge numbers together much more quickly Associate Professor David Harvey, from UNSW’s School of Mathematics and Statistics has developed a new method for multiplying together huge numbers which is much faster than the familiar “long multiplication” method that we all learn at primary school “More technically, we have proved a 1971 conjecture of Schönhage and Strassen about the complexity of integer multiplication,” A/Professor Harvey says “They predicted that there should exist an algorithm that multiplies n-digit numbers using essentially n * log(n) basic operations “Our paper gives the first known example of an algorithm that achieves this.” we would need to calculate 9 digit-by-digit products (see video) the answer can be arrived at in n2 operations Schönhage and Strassen themselves invented an algorithm needing fewer than n2 operations Harvey says that the Schönhage-Strassen algorithm is already quite fast: a computer using the primary school method would take months to multiply two numbers with a billion digits but can do it in under 30 seconds using the Schönhage-Strassen algorithm But for numbers with enough digits – billion trillions or even gazillions – the new algorithm developed by Harvey and his collaborator Joris van der Hoeven at École Polytechnique (France) would outrun even Schönhage and Strassen’s algorithm A/Professor Harvey says that Schönhage and Strassen also predicted that n * log(n) is the ‘best possible’ result – that no-one will ever find a faster multiplication algorithm our work is expected to be the end of the road for this problem although we don’t know yet how to prove this rigorously.” A/Professor Harvey imagines that this breakthrough has an enormous number of consequences “It means you can do all sorts of arithmetic more efficiently for example division and square roots A/Professor Harvey says he was surprised that such a fast multiplication algorithm is even possible “People have been hunting for such an algorithm for almost 50 years It was not a forgone conclusion that someone would eventually be successful It might have turned out that Schönhage and Strassen were wrong The work was posted recently online at HAL This article was first published on Australia’s Science Channel the original news platform of The Royal Institution of Australia A UNSW Sydney mathematician has cracked a maths problem that has stood for almost half a century which will enable computers to multiply huge numbers together much more quickly A UNSW Sydney mathematician has helped solve a decades-old maths riddle that allows multiplication of huge numbers in a much faster time from UNSW’s School of Mathematics and Statistics has developed a new method for multiplying together huge numbers we have proved a 1971 conjecture of Schönhage and Strassen about the complexity of integer multiplication,” A/Professor Harvey says “They predicted that there should exist an algorithm that multiplies n-digit numbers using essentially n * log(n) basic operations “Our paper gives the first known example of an algorithm that achieves this.” Schönhage and Strassen themselves invented an algorithm needing fewer than n2 operations would outrun even Schönhage and Strassen’s algorithm A/Professor Harvey says that Schönhage and Strassen also predicted that n * log(n) is the ‘best possible’ result – that no-one will ever find a faster multiplication algorithm our work is expected to be the end of the road for this problem although we don't know yet how to prove this rigorously.” A/Professor Harvey imagines that this breakthrough has an enormous number of consequences “It means you can do all sorts of arithmetic more efficiently “People have been hunting for such an algorithm for almost 50 years It was not a forgone conclusion that someone would eventually be successful It might have turned out that Schönhage and Strassen were wrong The work was posted recently online at HAL UNSW respectfully acknowledges the Bidjigal clan of the Dharawal Nation on whose unceded lands we are privileged to learn and recognise the broader Nations with whom we walk together UNSW acknowledges the enduring connection of Aboriginal and Torres Strait Islander peoples to culture The Uluru Statement Due to ongoing renovations at the Robert Schuman secondary school around 250 students will be relocated to a different building after the spring half-term holiday during the carnival period Pupils will thus temporarily move into classrooms at the National Language Institute (INL) until the end of the school year in July Despite the significant renovation work inside the building registration for the next school year will proceed as usual 50 adult language courses at the INL will need to relocate to the new building of the National School for Health Professions in Strassen to make room for the Robert Schuman pupils Link: Statement (FR)