K-level Reasoning for Zero-Shot Coordination in Hanabi

The standard problem setting in cooperative multi-agent settings is self-play (SP), where the goal is to train a team of agents that works well together. However, optimal SP policies commonly contain arbitrary conventions ("handshakes") and are not compatible with other, independently trained agents or humans. This latter desiderata was recently formalized by Hu et al. 2020 as the zero-shot coordination (ZSC) setting and partially addressed with their Other-Play (OP) algorithm, which showed improved ZSC and human-AI performance in the card game Hanabi. OP assumes access to the symmetries of the environment and prevents agents from breaking these in a mutually incompatible way during training. However, as the authors point out, discovering symmetries for a given environment is a computationally hard problem. Instead, we show that through a simple adaption of k-level reasoning (KLR) Costa Gomes et al. 2006, synchronously training all levels, we can obtain competitive ZSC and ad-hoc teamplay performance in Hanabi, including when paired with a human-like proxy bot. We also introduce a new method, synchronous-k-level reasoning with a best response (SyKLRBR), which further improves performance on our synchronous KLR by co-training a best response.Comment: Neurips 2021. 15 pages. 2 figure

Learning Symmetric Rules with SATNet

SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has been successfully applied to learn, among others, the rules of a complex logical puzzle, such as Sudoku, just from input and output pairs where inputs are given as images. In this paper, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSATNet, a variant of SATNet that translates the given symmetries of the target rules to a condition on the parameters of SATNet and requires that the parameters should have a particular parametric form that guarantees the condition. The requirement dramatically reduces the number of parameters to learn for the rules with enough symmetries, and makes the parameter learning of SymSATNet much easier than that of SATNet. We also describe a technique for automatically discovering symmetries of the target rules from examples. Our experiments with Sudoku and Rubik's cube show the substantial improvement of SymSATNet over the baseline SATNet.Comment: 27 pages, 10 figures, the first two authors contributed equally to this work, accepted at NeurIPS'2

AI Feynman: a Physics-Inspired Method for Symbolic Regression

A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult test set, we improve the state of the art success rate from 15% to 90%.Comment: 15 pages, 2 figs. Our code is available at https://github.com/SJ001/AI-Feynman and our Feynman Symbolic Regression Database for benchmarking can be downloaded at https://space.mit.edu/home/tegmark/aifeynman.htm

Into a New World of Physics and Symmetry

CERN theorist John Ellis charts the LHC’s voyage to a New World of discovery, exploring physics at the TeV scale with the capacity to create new forms of matter

A layout algorithm for signaling pathways

Cataloged from PDF version of article.Visualization is crucial to the effective analysis of biological pathways. A poorly laid out pathway confuses the user, while a well laid out one improves the user's comprehension of the underlying biological phenomenon. We present a new, elegant algorithm for layout of biological signaling pathways. Our algorithm uses a force-directed layout scheme, taking into account directional and rectangular regional constraints enforced by different molecular interaction types and subcellular locations in a cell. The algorithm has been successfully implemented as part of a pathway visualization and analysis toolkit named PATIKA, and results with respect to computational complexity and quality of the layout have been found satisfactory. The algorithm may be easily adapted to be used in other applications with similar conventions and constraints as well. PATIKA version 1.0 beta is available upon request at http://www.patika.org. (C) 2004 Elsevier Inc. All rights reserved

A Unified Framework for Discovering Discrete Symmetries

We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear and tensor-valued functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the tensor-valued functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the tensor-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach

Interlacing mathematics and culture: symmetry in traditional pavements and crafts

In this paper, the authors interlace the work they have been developing in the last years, namely the classification of the Portuguese pavement patterns in the Azores islands (Teixeira, 2015; Teixeira, Costa & Moniz, 2015), with the exploration of symmetries in patchwork and ceramics within a set of professional development courses for mathematics teachers held in Aveiro, in the north of mainland Portugal (Hall, 2016). This paper focuses on rosette groups which in spite of being the simplest symmetry groups with only rotational and/or reflection symmetries, are rich enough to describe an endless variety of patterns/designs found in practice.publishe