University of the Basque Country（巴斯克大学）；foldAI；Bernstein Center for Computational Neuroscience（伯恩斯坦计算神经科学中心）；Basque Center for Applied Mathematics（巴斯克应用数学中心）
Jone Uria-Albizuri, Giovanni Sirio Carmantini, Peter beim Graben, Serafim Rodrigues
Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. A particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. An interesting research direction we have pursued under this framework has been to consider mapping symbolic dynamics onto neurodynamics, represented as neural automata. This representation theory, enables us to ask questions, such as, how does the brain implement Turing computations. Specifically, in this representation theory, neural automata result from the assignment of symbols and symbol strings to numbers, known as Gödel encoding. Under this assignment symbolic computation becomes represented by trajectories of state vectors in a real phase space, that allows for statistical correlation analyses with real-world measurements and experimental data. However, these assignments are usually completely arbitrary. Hence, it makes sense to address the problem question of, which aspects of the dynamics observed under such a representation is intrinsic to the dynamics and which are not. In this study, we develop a formally rigorous mathematical framework for the investigation of symmetries and invariants of neural automata under different encodings. As a central concept we define patterns of equality for such systems. We consider different macroscopic observables, such as the mean activation level of the neural network, and ask for their invariance properties. Our main result shows that only step functions that are defined over those patterns of equality are invariant under recodings, while the mean activation is not. Our work could be of substantial importance for related regression studies of real-world measurements with neurosymbolic processors for avoiding confounding results that are dependant on a particular encoding and not intrinsic to the dynamics.
A modular architecture for transparent computation in Recurrent Neural Networks
Plymouth University（普利茅斯大学）；Bernstein Center for Computational Neuroscience Berlin（柏林伯恩斯坦计算神经科学中心）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Inria Sophia-Antipolis Méditerranée（法国国家信息与自动化研究所索菲亚-安蒂波利斯地中海研究中心）
Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are end-to-end differentiable systems where the parameters of the neural network can be learned to achieve a particular task. In this work, we used neural CA to control a cart-pole agent. The observations of the environment are transmitted in input cells, while the values of output cells are used as a readout of the system. We trained the model using deep-Q lea…
Motivated by the interaction between cells, the recently introduced concept of Neural Cellular Automata shows promising results in a variety of tasks. So far, this concept was mostly used to generate images for a single scenario. As each scenario requires a new model, this type of generation seems contradictory to the adaptability of cells in nature. To address this contradiction, we introduce a concept using different initial environments as input while using a single Neural Cellular Automata to produce several outputs. Additionally, we introduce GANCA, a novel algorithm that combines Neural …
In contrast to deep reinforcement learning agents, biological neural networks are grown through a self-organized developmental process. Here we propose a new hypernetwork approach to grow artificial neural networks based on neural cellular automata (NCA). Inspired by self-organising systems and information-theoretic approaches to developmental biology, we show that our HyperNCA method can grow neural networks capable of solving common reinforcement learning tasks. Finally, we explore how the same approach can be used to build developmental metamorphosis networks capable of transforming their w…
Inspired by cellular growth and self-organization, Neural Cellular Automata (NCAs) have been capable of "growing" artificial cells into images, 3D structures, and even functional machines. NCAs are flexible and robust computational systems but -- similarly to many other self-organizing systems -- inherently uncontrollable during and after their growth process. We present an approach to control these type of systems called Goal-Guided Neural Cellular Automata (GoalNCA), which leverages goal encodings to control cell behavior dynamically at every step of cellular growth. This approach enables th…
Forschungszentrum Jülich（于利希研究中心）；University of Cologne（科隆大学）；Helmholtz AI（亥姆霍兹人工智能）
To test generalization ability of a class of deep neural networks, we randomly generate a large number of different rule sets for 2-D cellular automata (CA), based on John Conway's Game of Life. Using these rules, we compute several trajectories for each CA instance. A deep convolutional encoder-decoder network with short and long range skip connections is trained on various generated CA trajectories to predict the next CA state given its previous states. Results show that the network is able to learn the rules of various, complex cellular automata and generalize to unseen configurations. To s…
In nature, the process of cellular growth and differentiation has lead to an amazing diversity of organisms -- algae, starfish, giant sequoia, tardigrades, and orcas are all created by the same generative process. Inspired by the incredible diversity of this biological generative process, we propose a generative model, the Variational Neural Cellular Automata (VNCA), which is loosely inspired by the biological processes of cellular growth and differentiation. Unlike previous related works, the VNCA is a proper probabilistic generative model, and we evaluate it according to best practices. We f…
Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. In this work, we show that the neural network (NN) architecture of the NCA can be encapsulated in a larger NN. This allows us to propose a new model that encodes a manifold of NCA, each of them capable of generating a distinct image. Therefore, we are effectively learning an embedding space of CA, which shows generalization capabilities. We accomplish this by introducing dynamic convolutions inside an Auto-…
KAIST（韩国科学技术院）；The University of Tokyo（东京大学）；NAVER AI Lab（NAVER人工智能实验室）；Naver Clova；University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Nvidia（英伟达）
Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism for dynamical systems subject to discrete, possibly stochastic, state jumps and multi-modal continuous-time flows. Despite the versatility and importance of SHSs across applications, a general procedure for the explicit learning of both discrete events and multi-mode continuous dynamics remains an open problem. This work introduces Neural Hybrid Automata (NHAs…
New York University（纽约大学）；University of Southern California（南加州大学）
We present a method of generating diverse collections of neural cellular automata (NCA) to design video game levels. While NCAs have so far only been trained via supervised learning, we present a quality diversity (QD) approach to generating a collection of NCA level generators. By framing the problem as a QD problem, our approach can train diverse level generators, whose output levels vary based on aesthetic or functional criteria. To efficiently generate NCAs, we train generators via Covariance Matrix Adaptation MAP-Elites (CMA-ME), a quality diversity algorithm which specializes in continuo…
Institute for Information Systems, FHNW University of Applied Sciences and Arts Northwestern Switzerland（瑞士西北应用科学与艺术大学信息系统研究所）；Chair for Philosophy, ETH Zurich（苏黎世联邦理工学院哲学教席）
Many computer models such as cellular automata and artificial neural networks have been developed and successfully applied. However, in some cases, these models might be restrictive on the possible solutions or their solutions might be difficult to interpret. To overcome this problem, we outline a new approach, the so-called allagmatic method, that automatically programs and executes models with as little limitations as possible while maintaining human interpretability. Earlier we described a metamodel and its building blocks according to the philosophical concepts of structure (spatial dimens…
Google Research（谷歌研究院）；The Ohio State University（俄亥俄州立大学）
Modeling the ability of multicellular organisms to build and maintain their bodies through local interactions between individual cells (morphogenesis) is a long-standing challenge of developmental biology. Recently, the Neural Cellular Automata (NCA) model was proposed as a way to find local system rules that produce a desired global behaviour, such as growing and persisting a predefined target pattern, by repeatedly applying the same rule over a grid starting from a single cell. In this work, we argue that the original Growing NCA model has an important limitation: anisotropy of the learned u…
IT University of Copenhagen（哥本哈根信息技术大学）；Osaka University（大阪大学）；Cross Labs, Cross Compass Ltd.（Cross Compass有限公司Cross实验室）
Morphological regeneration is an important feature that highlights the environmental adaptive capacity of biological systems. Lack of this regenerative capacity significantly limits the resilience of machines and the environments they can operate in. To aid in addressing this gap, we develop an approach for simulated soft robots to regrow parts of their morphology when being damaged. Although numerical simulations using soft robots have played an important role in their design, evolving soft robots with regenerative capabilities have so far received comparable little attention. Here we propose…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules. We explore this problem in the context of cellular automata (CA), simple dynamical systems that are intrinsically discrete and thus difficult to analyze using standard tools from dynamical systems theory. We show that any CA may readily be represented using a convolutional neural network with a network-in-network architecture. This motivates our development …
Interactive Intelligence（交互智能公司）；University of Washington（华盛顿大学）
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve self-regenerating images. This new branch of CA is called neural cellular automata [1]. The goal of this project is to use the idea of idea of neural cellular automata to grow prediction machines. We place many different convolutional neural networks in a grid. Each conv net cell outputs a prediction of what the next state will be, and minimizes predictive erro…
