Some readers know to play the game of nim well, fewer play a perfect annihilation game, and nobody knows whether there exists an opening move in chess that will guarantee a win for white. These games and many more, belong to the family of combinatorial games, by which we mean the set of all two-player perfect-information games without chance moves and with outcomes lose or win (and sometimes: dynamic tie). The motivation for ONAG may have been, and perhaps was-and I would like to think that it was-the attempt to bridge the theory gap between nim-like and chess-like games. Why is there a gap? Every combinatorial game can be described as a directed graph called game-graph, whose vertices are the game positions, and (u, v) is a directed edge if and only if there is a move from position u to position v. Denote by N the set of all positions from which the Next (first) player can force a win; by P the set of all positions from which the Previous (second) player can force a win; and by T the set of all (dynamic) Tie positions, which are positions from which no player can force a win and therefore both can avoid losing. In an acyclic game-graph there cannot be any tie positions. The N, P, T classification of any game graph R = (V, E) can be determined in 0(\V\ + \E\) steps [8]. For both nim and chess, a finite game-graph can be constructed and the N, P, T classification can be determined. So both games are solvable in principle. If we play nim with n piles, each pile containing at most k tokens, then the game-graph contains (k + \) vertices. Suppose that in (generalized) chess played on an « X « board there are k different pieces. If k is about n/2, then the game-graph of chess contains O (2") vertices. So both game-graphs have exponentially many vertices, and thus both games appear intractable in the usual sense of computational complexity [1, Chapter 10], [14, Chapter 9], namely a computation appears to be required which is asymptotically exponential. From a computational efficiency standpoint, the essential difference between nim and chess is that nim can be viewed as a disjunctive compound (sum) of independent games, namely the individual piles. A disjunctive

http://ieeexplore.ieee.org/iel5/5/31266/01455274.pdf

On numbers and games

Od zarania dziejow ludzie marzyli o budowie maszyn, ktore bylyby godnymi przeciwnikami ludzi w grach logicznych. To marzenie stalo sie realne wraz z pojawieniem sie komputerow, szczegolnie ostatnio, gdy olbrzymia moc obliczeniowa jest w zasiegu reki. Spektakularnym przykladem gracza komputerowego jest system Deep Blue, ktory wygral z szachowym mistrzem świata Garrym Kasparowem. Rozwiązania uzyte w szachach to przeszukiwanie drzewa gry do pewnej glebokości i uzycie funkcji oceniającej w liściach drzewa do oceny szans wygranej. To podejście przenioslo sie na wiele innych gier pozwalając komputerom grac lepiej niz najlepsi ludzie lub wrecz rozwiązac daną gre. Jednym z nielicznych wyjątkow jest gra Go.

Modeling Go Game as a Large Decomposable Decision Process

This paper discusses one of the most challenging practical engineering problems in speaker recognition systems - the version control of models and user profiles. A typical speaker recognition system consists of two stages: the enrollment stage, where a profile is generated from user-provided enrollment audio; and the runtime stage, where the voice identity of the runtime audio is compared against the stored profiles. As technology advances, the speaker recognition system needs to be updated for better performance. However, if the stored user profiles are not updated accordingly, version mismatch will result in meaningless recognition results. In this paper, we describe different version control strategies for different types of speaker recognition systems, according to how they are deployed in the production environment.

Version Control of Speaker Recognition Systems

Neural network pruning compresses automatic speech recognition (ASR) models effectively. However, in multilingual ASR, language-agnostic pruning may lead to severe performance drops on some languages because language-agnostic pruning masks may not fit all languages and discard important language-specific parameters. In this work, we present ASR pathways, a sparse multilingual ASR model that activates language-specific sub-networks ("pathways"), such that the parameters for each language are learned explicitly. With the overlapping sub-networks, the shared parameters can also enable knowledge transfer for lower-resource languages via joint multilingual training. We propose a novel algorithm to learn ASR pathways, and evaluate the proposed method on 4 languages with a streaming RNN-T model. Our proposed ASR pathways outperform both dense models and a language-agnostically pruned model, and provide better performance on low-resource languages compared to the monolingual sparse models.

Learning ASR pathways: A sparse multilingual ASR model

This paper shows a new algorithm to calculate the mean and temperature of multi-branch combinatorial games. The algorithm expands gradually, one node at a time, the offspring of a game. After each step of expansion, the lower and upper bounds of the mean and temperature of the game are re-calculated. As the expanding process continues, the range between the lower and upper bounds is little by little narrowed. The key feature of the algorithm is its ability to generate a path of which the outcome is most likely to reduce the distance between the lower and upper bounds. 1. COMBINATORIAL GAMES Combinatorial game theory studies two-player games with perfect information. The two players are assumed to take turns alternatively, and a game is considered as a sum of local positions, where each player can choose one local position to move at each turn. This section introduces a heap game, named heap-go, for illustrating some key ideas of combinatorial game theory. Heap-go is played on a number of heaps of counters. Each counter has a weight and is coloured either blue or red. Figure 1 shows an example of heap-go setup. (Heap A and B are considered to be blue; heap E is red. Heap C and D are mixed; the top counter of C is red, the two other counters are blue.) Figure 1: An example of heap-go setup. Two players,  and , move alternatively and their legal moves are different.  When it is 's turn to move, he can choose any one of the heaps and repeatedly removes the top counter until either he removes a red counter or the heap has become empty.  When it is 's turn to move, he can choose any one of the heaps and repeatedly removes the top counter until either he removes a blue counter or the heap has become empty. 1 Department of Information Management National Penghu University, Penghu, Taiwan. Email: stone@npu.edu.tw 2 Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan. Email: icwu@csie.nctu.edu.tw, ycshan@java.csie.nctu.edu.tw. 3 Department of Computer Science & Information Engineering, National Dong Hwa University, Hualien, Taiwan. Email: sjyen@mail.ndhu.edu.tw 4 For brevity, we use ‘he’ and ‘his’ whenever ‘he or she’ and ‘his or her’ are meant. 6 C B A D E 2 5 5 5 8 3 2 1 7 8 ICGA Journal September 2012 158 The game is finished if all the counters in all the heaps are removed. The player who removed more total weights is the winner. Heap-go is a two-player game with perfect information. The heaps are the local positions, where each player can choose one local position to move at each turn. The more heaps in a setup, the more options each player has. Although the complexity of the complete minimax game tree of a heap-go game may grow up exponentially with the increase of the total number of heaps, each local position can be represented as a simpler combinatorial game tree where each node represents the state of the local position, each left branch represents a ’s move and each right branch a ’s move at the local position. Figure 2 shows the combinatorial game tree of heap  in Figure 1. The numbers at the terminal nodes are the net scores of the paths from the root to these nodes. ’s scores are counted positive and ’s negative. For example, consider the path .  gets 8 points for the first move (removed 2 counters);  gets 5 points for the second move (removed 1 counter); the net score is 3. Figure 2: The game tree of heap . To follow the terminology of combinatorial game theory, each local position is called a game. If  is a game, then  () represents the set of ’s (’s) options at the game, where each option in  () is a game after ’s (’s) move at . A game  is defined as an ordered pair of sets of games, and expressed as    (1) When  is a terminal node in a game tree, it is represented by a numerical outcome value. For example, heaps ,  and  can be expressed as                   Note that   ,   ,   ,   ,   , and       . In combinatorial game theory, the sum of two games is a game. Let  and  be two games, the sum    is defined as               . (2) When  is a game and  is a number, the sum can be simplified as          (3) -13 -9 2 5 5

http://par.cse.nsysu.edu.tw/~algo/paper/paper12/B3_2.pdf

Selection Search for Mean and Temperature of Multi-Branch Combinatorial Games

Reducing the latency and model size has always been a significant research problem for live Automatic Speech Recognition (ASR) application scenarios. Along this direction, model quantization has become an increasingly popular approach to compress neural networks and reduce computation cost. Most of the existing practical ASR systems apply post-training 8-bit quantization. To achieve a higher compression rate without introducing additional performance regression, in this study, we propose to develop 4-bit ASR models with native quantization aware training, which leverages native integer operations to effectively optimize both training and inference. We conducted two experiments on state-of-the-art Conformer-based ASR models to evaluate our proposed quantization technique. First, we explored the impact of different precisions for both weight and activation quantization on the LibriSpeech dataset, and obtained a lossless 4-bit Conformer model with 5.8x size reduction compared to the float32 model. Following this, we for the first time investigated and revealed the viability of 4-bit quantization on a practical ASR system that is trained with large-scale datasets, and produced a lossless Conformer ASR model with mixed 4-bit and 8-bit weights that has 5x size reduction compared to the float32 model.

4-bit Conformer with Native Quantization Aware Training for Speech Recognition

Monte-Carlo Tree Search is a very successful game playing algorithm. Unfortunately it su ers from the horizon e ect: some important tactical sequences may be delayed beyond the depth of the search tree, causing evaluation errors. Temporal-di erence search with a function approximation is a method that was proposed to overcome these weaknesses, by adaptively changing the simulation policy outside the tree. In this paper we present an experimental evidence demonstrating that a temporal di erence search may fail to nd an optimal policy, even in very simple game positions. Classical temporal di erence algorithms try to evaluate a local situation with a numerical value, but, as it appears, a single number is not enough to model the dynamics of a partial two-player game state. As a solution we propose to replace numerical values by approximate thermographs. With this richer representation of partial states, reinforcement-learning algorithms converge and accurately represent dynamics of states, allowing to nd an optimal policy.

/pdf/simulation-based-search-of-combinatorial-games-52ui98yrt7.pdf

Simulation-based search of combinatorial games

The rapid scaling of language models is motivating research using low-bitwidth quantization. In this work, we propose a novel binarization technique for Transformers applied to machine translation (BMT), the first of its kind. We identify and address the problem of inflated dot-product variance when using one-bit weights and activations. Specifically, BMT leverages additional LayerNorms and residual connections to improve binarization quality. Experiments on the WMT dataset show that a one-bit weight-only Transformer can achieve the same quality as a float one, while being 16x smaller in size. One-bit activations incur varying degrees of quality drop, but mitigated by the proposed architectural changes. We further conduct a scaling law study using production-scale translation datasets, which shows that one-bit weight Transformers scale and generalize well in both in-domain and out-of-domain settings. Implementation in JAX/Flax will be open sourced.

Lukasz Lew

Papers

4-bit Conformer with Native Quantization Aware Training for Speech Recognition

Simulation-based search of combinatorial games

Binarized Neural Machine Translation