Statistical Physics and Representations in Real and Artificial Neural Networks

This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we consider the neural representations of space (maps) in the hippocampus. We introduce an extension of the Hopfield model, able to store multiple spatial maps as continuous, finite-dimensional attractors. The phase diagram and dynamical properties of the model are analyzed. We then show how spatial representations can be dynamically decoded using an effective Ising model capturing the correlation structure in the neural data, and compare applications to data obtained from hippocampal multi-electrode recordings and by (sub)sampling our attractor model. In a second part, we focus on the problem of learning data representations in machine learning, in particular with artificial neural networks. We start by introducing data representations through some illustrations. We then analyze two important algorithms, Principal Component Analysis and Restricted Boltzmann Machines, with tools from statistical physics

SOM-VAE: Interpretable Discrete Representation Learning on Time Series

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model in terms of clustering performance and interpretability on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on Learning Representations (ICLR 2019

Motion Switching with Sensory and Instruction Signals by designing Dynamical Systems using Deep Neural Network

To ensure that a robot is able to accomplish an extensive range of tasks, it is necessary to achieve a flexible combination of multiple behaviors. This is because the design of task motions suited to each situation would become increasingly difficult as the number of situations and the types of tasks performed by them increase. To handle the switching and combination of multiple behaviors, we propose a method to design dynamical systems based on point attractors that accept (i) "instruction signals" for instruction-driven switching. We incorporate the (ii) "instruction phase" to form a point attractor and divide the target task into multiple subtasks. By forming an instruction phase that consists of point attractors, the model embeds a subtask in the form of trajectory dynamics that can be manipulated using sensory and instruction signals. Our model comprises two deep neural networks: a convolutional autoencoder and a multiple time-scale recurrent neural network. In this study, we apply the proposed method to manipulate soft materials. To evaluate our model, we design a cloth-folding task that consists of four subtasks and three patterns of instruction signals, which indicate the direction of motion. The results depict that the robot can perform the required task by combining subtasks based on sensory and instruction signals. And, our model determined the relations among these signals using its internal dynamics.Comment: 8 pages, 6 figures, accepted for publication in RA-L. An accompanied video is available at this https://youtu.be/a73KFtOOB5

How active perception and attractor dynamics shape perceptual categorization: A computational model

We propose a computational model of perceptual categorization that fuses elements of grounded and sensorimotor theories of cognition with dynamic models of decision-making. We assume that category information consists in anticipated patterns of agent–environment interactions that can be elicited through overt or covert (simulated) eye movements, object manipulation, etc. This information is firstly encoded when category information is acquired, and then re-enacted during perceptual categorization. The perceptual categorization consists in a dynamic competition between attractors that encode the sensorimotor patterns typical of each category; action prediction success counts as ‘‘evidence’’ for a given category and contributes to falling into the corresponding attractor. The evidence accumulation process is guided by an active perception loop, and the active exploration of objects (e.g., visual exploration) aims at eliciting expected sensorimotor patterns that count as evidence for the object category. We present a computational model incorporating these elements and describing action prediction, active perception, and attractor dynamics as key elements of perceptual categorizations. We test the model in three simulated perceptual categorization tasks, and we discuss its relevance for grounded and sensorimotor theories of cognition.Peer reviewe

Mammalian Brain As a Network of Networks

Acknowledgements AZ, SG and AL acknowledge support from the Russian Science Foundation (16-12-00077). Authors thank T. Kuznetsova for Fig. 6.Peer reviewedPublisher PD