Related papers: Neural Group Actions
Modeling crowds has many important applications in games and computer animation. Inspired by the emergent following effect in real-life crowd scenarios, in this work, we develop a method for implicitly grouping moving agents. We achieve…
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…
We show the universality of depth-2 group convolutional neural networks (GCNNs) in a unified and constructive manner based on the ridgelet theory. Despite widespread use in applications, the approximation property of (G)CNNs has not been…
Collective, especially group-based, managerial decision making is crucial in organizations. Using an evolutionary theoretic approach to collective decision making, agent-based simulations were conducted to investigate how human collective…
We introduce a novel approach that exploits the intersection of quantum computing, machine learning and reduced density matrix functional theory to leverage the potential of quantum computing to improve simulations of interacting quantum…
In this work we present a principle which says that quasimorphisms can be obtained via "local data" of the group action on certain appropriate spaces. In a rough manner the principle says that instead of starting with a given group and try…
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…
Neural nets are known to be universal approximators. In particular, formal neurons implementing wavelets have been shown to build nets able to approximate any multidimensional task. Such very specialized formal neurons may be, however,…
Emerging reinforcement learning techniques using deep neural networks have shown great promise in control optimization. They harness non-local regularities of noisy control trajectories and facilitate transfer learning between tasks. To…
Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…
A deep generative model such as a GAN learns to model a rich set of semantic and physical rules about the target distribution, but up to now, it has been obscure how such rules are encoded in the network, or how a rule could be changed. In…
Many decision problems concerning cellular automata are known to be decidable in the case of algebraic cellular automata, that is, when the state set has an algebraic structure and the automaton acts as a morphism. The most studied cases…
We propose a natural quantization of a standard neural network, where the neurons correspond to qubits and the activation functions are implemented via quantum gates and measurements. The simplest quantized neural network corresponds to…
We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation…
We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on…
Let $G$ be a finite group acting transitively on a set $\Omega$. We study what it means for this action to be {\it quasirandom}, thereby generalizing Gowers' study of quasirandomness in groups. We connect this notion of quasirandomness to…
Bass-Serre theory provides a powerful framework for studying group actions on trees. While extremely effective for structural questions in group theory, it is less suited to the systematic construction of group actions with prescribed local…
Central to the field of quantum machine learning is the design of quantum perceptrons and neural network architectures. A key question in this regard is the impact of quantum effects on the way in which such models process information.…