arXiv subjects

Naftali Tishby

Publications and source records attributed to Naftali Tishby.

At least 19 recordsLinked to original sources

arXiv2022

Intrinsic Motivation in Dynamical Control Systems

Biological systems often choose actions without an explicit reward signal, a phenomenon known as intrinsic motivation. The computational principles underlying this behavior remain poorly understood. In this study, we investigate an information-theoretic approach to intrinsic motivation, based on maximizing an agent's empowerment (the mutual information between its past actions and future states). We show that this approach generalizes previous attempts to formalize intrinsic motivation, and we provide a computationally efficient algorithm for computing the necessary quantities. We test our approach on several benchmark control problems, and we explain its success in guiding intrinsically motivated behaviors by relating our information-theoretic control function to fundamental properties of the dynamical system representing the combined agent-environment system. This opens the door for designing practical artificial, intrinsically motivated controllers and for linking animal behaviors to their dynamical properties.

cs.AI↗

arXiv2021

Detecting chaos in lineage-trees: A deep learning approach

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in characterizing and predicting these processes. Classifying a system as chaotic usually requires estimating its largest Lyapunov exponent, which quantifies the average rate of convergence or divergence of initially close trajectories in state space, and for which a positive value is generally accepted as an operational definition of chaos. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in systems affected by dynamical noise, which is the case for many models of real-world processes, in particular models of biological systems. We describe a novel method for estimating the largest Lyapunov exponent from data, based on training Deep Learning models on synthetically generated trajectories, and demonstrate that this method yields accurate and noise-robust predictions given relatively short inputs and across a range of different dynamical systems. Our method is unique in that it can analyze tree-shaped data, a ubiquitous topology in biological settings, and specifically in dynamics over lineages of cells or organisms. We also characterize the types of input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.

cs.LG↗

arXiv2021

Critical Slowing Down Near Topological Transitions in Rate-Distortion Problems

In rate-distortion (RD) problems one seeks reduced representations of a source that meet a target distortion constraint. Such optimal representations undergo topological transitions at some critical rate values, when their cardinality or dimensionality change. We study the convergence time of the Arimoto-Blahut alternating projection algorithms, used to solve such problems, near those critical points, both for the rate-distortion and information bottleneck settings. We argue that they suffer from critical slowing down -- a diverging number of iterations for convergence -- near the critical points. This phenomenon can have theoretical and practical implications for both machine learning and data compression problems.

cs.IT↗

arXiv2020

The Dual Information Bottleneck

The Information Bottleneck (IB) framework is a general characterization of optimal representations obtained using a principled approach for balancing accuracy and complexity. Here we present a new framework, the Dual Information Bottleneck (dualIB), which resolves some of the known drawbacks of the IB. We provide a theoretical analysis of the dualIB framework; (i) solving for the structure of its solutions (ii) unraveling its superiority in optimizing the mean prediction error exponent and (iii) demonstrating its ability to preserve exponential forms of the original distribution. To approach large scale problems, we present a novel variational formulation of the dualIB for Deep Neural Networks. In experiments on several data-sets, we compare it to a variational form of the IB. This exposes superior Information Plane properties of the dualIB and its potential in improvement of the error.

cs.IT↗

arXiv2020

Non-linear Canonical Correlation Analysis: A Compressed Representation Approach

Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful in many real-world applications. Given the joint probability, the Alternating Conditional Expectation (ACE) algorithm provides an optimal solution to the non-linear CCA problem. However, it suffers from limited performance and an increasing computational burden when only a finite number of samples is available. In this work we introduce an information-theoretic compressed representation framework for the non-linear CCA problem (CRCCA), which extends the classical ACE approach. Our suggested framework seeks compact representations of the data that allow a maximal level of correlation. This way we control the trade-off between the flexibility and the complexity of the model. CRCCA provides theoretical bounds and optimality conditions, as we establish fundamental connections to rate-distortion theory, the information bottleneck and remote source coding. In addition, it allows a soft dimensionality reduction, as the compression level is determined by the mutual information between the original noisy data and the extracted signals. Finally, we introduce a simple implementation of the CRCCA framework, based on lattice quantization.

cs.LG↗

arXiv2019

Machine learning and the physical sciences

Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on the interface between machine learning and physical sciences. This includes conceptual developments in machine learning (ML) motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross-fertilization between the two fields. After giving basic notion of machine learning methods and principles, we describe examples of how statistical physics is used to understand methods in ML. We then move to describe applications of ML methods in particle physics and cosmology, quantum many body physics, quantum computing, and chemical and material physics. We also highlight research and development into novel computing architectures aimed at accelerating ML. In each of the sections we describe recent successes as well as domain-specific methodology and challenges.

physics.comp-ph↗

arXiv2019

A General Memory-Bounded Learning Algorithm

Designing bounded-memory algorithms is becoming increasingly important nowadays. Previous works studying bounded-memory algorithms focused on proving impossibility results, while the design of bounded-memory algorithms was left relatively unexplored. To remedy this situation, in this work we design a general bounded-memory learning algorithm, when the underlying distribution is known. The core idea of the algorithm is not to save the exact example received, but only a few important bits that give sufficient information. This algorithm applies to any hypothesis class that has an "anti-mixing" property. This paper complements previous works on unlearnability with bounded memory and provides a step towards a full characterization of bounded-memory learning.

cs.LG↗

arXiv2019

Semantic categories of artifacts and animals reflect efficient coding

It has been argued that semantic categories across languages reflect pressure for efficient communication. Recently, this idea has been cast in terms of a general information-theoretic principle of efficiency, the Information Bottleneck (IB) principle, and it has been shown that this principle accounts for the emergence and evolution of named color categories across languages, including soft structure and patterns of inconsistent naming. However, it is not yet clear to what extent this account generalizes to semantic domains other than color. Here we show that it generalizes to two qualitatively different semantic domains: names for containers, and for animals. First, we show that container naming in Dutch and French is near-optimal in the IB sense, and that IB broadly accounts for soft categories and inconsistent naming patterns in both languages. Second, we show that a hierarchy of animal categories derived from IB captures cross-linguistic tendencies in the growth of animal taxonomies. Taken together, these findings suggest that fundamental information-theoretic principles of efficient coding may shape semantic categories across languages and across domains.

cs.CL↗

arXiv2018

Efficient human-like semantic representations via the Information Bottleneck principle

Maintaining efficient semantic representations of the environment is a major challenge both for humans and for machines. While human languages represent useful solutions to this problem, it is not yet clear what computational principle could give rise to similar solutions in machines. In this work we propose an answer to this open question. We suggest that languages compress percepts into words by optimizing the Information Bottleneck (IB) tradeoff between the complexity and accuracy of their lexicons. We present empirical evidence that this principle may give rise to human-like semantic representations, by exploring how human languages categorize colors. We show that color naming systems across languages are near-optimal in the IB sense, and that these natural systems are similar to artificial IB color naming systems with a single tradeoff parameter controlling the cross-language variability. In addition, the IB systems evolve through a sequence of structural phase transitions, demonstrating a possible adaptation process. This work thus identifies a computational principle that characterizes human semantic systems, and that could usefully inform semantic representations in machines.

cs.CL↗

arXiv2018

Color naming reflects both perceptual structure and communicative need

Gibson et al. (2017) argued that color naming is shaped by patterns of communicative need. In support of this claim, they showed that color naming systems across languages support more precise communication about warm colors than cool colors, and that the objects we talk about tend to be warm-colored rather than cool-colored. Here, we present new analyses that alter this picture. We show that greater communicative precision for warm than for cool colors, and greater communicative need, may both be explained by perceptual structure. However, using an information-theoretic analysis, we also show that color naming across languages bears signs of communicative need beyond what would be predicted by perceptual structure alone. We conclude that color naming is shaped both by perceptual structure, as has traditionally been argued, and by patterns of communicative need, as argued by Gibson et al. - although for reasons other than those they advanced.

cs.CL↗

arXiv2018

A Unified Bellman Equation for Causal Information and Value in Markov Decision Processes

The interaction between an artificial agent and its environment is bi-directional. The agent extracts relevant information from the environment, and affects the environment by its actions in return to accumulate high expected reward. Standard reinforcement learning (RL) deals with the expected reward maximization. However, there are always information-theoretic limitations that restrict the expected reward, which are not properly considered by the standard RL. In this work we consider RL objectives with information-theoretic limitations. For the first time we derive a Bellman-type recursive equa- tion for the causal information between the environment and the agent, which is combined plausibly with the Bellman recursion for the value function. The unified equitation serves to explore the typical behavior of artificial agents in an infinite time horizon.

eess.SY↗

arXiv2017

Gaussian Lower Bound for the Information Bottleneck Limit

The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from classical parametric statistics to a broader information-theoretic sense. The IB curve defines the optimal trade-off between representation complexity and its predictive power. Specifically, it is achieved by minimizing the level of mutual information (MI) between the representation and the original variables, subject to a minimal level of MI between the representation and the target. This problem is shown to be in general NP hard. One important exception is the multivariate Gaussian case, for which the Gaussian IB (GIB) is known to obtain an analytical closed form solution, similar to Canonical Correlation Analysis (CCA). In this work we introduce a Gaussian lower bound to the IB curve; we find an embedding of the data which maximizes its "Gaussian part", on which we apply the GIB. This embedding provides an efficient (and practical) representation of any arbitrary data-set (in the IB sense), which in addition holds the favorable properties of a Gaussian distribution. Importantly, we show that the optimal Gaussian embedding is bounded from above by non-linear CCA. This allows a fundamental limit for our ability to Gaussianize arbitrary data-sets and solve complex problems by linear methods.

cs.LG↗

arXiv2017

A Simple Model of Attentional Blink

The attentional blink (AB) effect is the reduced ability of subjects to report a second target stimuli (T2) among a rapidly presented series of non-target stimuli, when it appears within a time window of about 200-500 ms after a first target (T1). We present a simple dynamical systems model explaining the AB as resulting from the temporal response dynamics of a stochastic, linear system with threshold, whose output represents the amount of attentional resources allocated to the incoming sensory stimuli. The model postulates that the available attention capacity is limited by activity of the default mode network (DMN), a correlated set of brain regions related to task irrelevant processing which is known to exhibit reduced activation following mental training such as mindfulness meditation. The model provides a parsimonious account relating key findings from the AB, DMN and meditation research literature, and suggests some new testable predictions.

q-bio.NC↗

arXiv2017

Opening the Black Box of Deep Neural Networks via Information

Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the \textit{Information Plane}; i.e., the plane of the Mutual Information values that each layer preserves on the input and output variables. They suggested that the goal of the network is to optimize the Information Bottleneck (IB) tradeoff between compression and prediction, successively, for each layer. In this work we follow up on this idea and demonstrate the effectiveness of the Information-Plane visualization of DNNs. Our main results are: (i) most of the training epochs in standard DL are spent on {\emph compression} of the input to efficient representation and not on fitting the training labels. (ii) The representation compression phase begins when the training errors becomes small and the Stochastic Gradient Decent (SGD) epochs change from a fast drift to smaller training error into a stochastic relaxation, or random diffusion, constrained by the training error value. (iii) The converged layers lie on or very close to the Information Bottleneck (IB) theoretical bound, and the maps from the input to any hidden layer and from this hidden layer to the output satisfy the IB self-consistent equations. This generalization through noise mechanism is unique to Deep Neural Networks and absent in one layer networks. (iv) The training time is dramatically reduced when adding more hidden layers. Thus the main advantage of the hidden layers is computational. This can be explained by the reduced relaxation time, as this it scales super-linearly (exponentially for simple diffusion) with the information compression from the previous layer.

cs.LG↗

arXiv2017

Taming the Noise in Reinforcement Learning via Soft Updates

Model-free reinforcement learning algorithms, such as Q-learning, perform poorly in the early stages of learning in noisy environments, because much effort is spent unlearning biased estimates of the state-action value function. The bias results from selecting, among several noisy estimates, the apparent optimum, which may actually be suboptimal. We propose G-learning, a new off-policy learning algorithm that regularizes the value estimates by penalizing deterministic policies in the beginning of the learning process. We show that this method reduces the bias of the value-function estimation, leading to faster convergence to the optimal value and the optimal policy. Moreover, G-learning enables the natural incorporation of prior domain knowledge, when available. The stochastic nature of G-learning also makes it avoid some exploration costs, a property usually attributed only to on-policy algorithms. We illustrate these ideas in several examples, where G-learning results in significant improvements of the convergence rate and the cost of the learning process.

cs.LG↗

arXiv2017

Minimum-Information LQG Control - Part I: Memoryless Controllers

With the increased demand for power efficiency in feedback-control systems, communication is becoming a limiting factor, raising the need to trade off the external cost that they incur with the capacity of the controller's communication channels. With a proper design of the channels, this translates into a sequential rate-distortion problem, where we minimize the rate of information required for the controller's operation under a constraint on its external cost. Memoryless controllers are of particular interest both for the simplicity and frugality of their implementation and as a basis for studying more complex controllers. In this paper we present the optimality principle for memoryless linear controllers that utilize minimal information rates to achieve a guaranteed external-cost level. We also study the interesting and useful phenomenology of the optimal controller, such as the principled reduction of its order.

eess.SY↗

arXiv2017

Minimum-Information LQG Control - Part II: Retentive Controllers

Retentive (memory-utilizing) sensing-acting agents may operate under limitations on the communication between their sensing, memory and acting components, requiring them to trade off the external cost that they incur with the capacity of their communication channels. In this paper we formulate this problem as a sequential rate-distortion problem of minimizing the rate of information required for the controller's operation under a constraint on its external cost. We reduce this bounded retentive control problem to the memoryless one, studied in Part I of this work, by viewing the memory reader as one more sensor and the memory writer as one more actuator. We further investigate the structure of the resulting optimal solution and demonstrate its interesting phenomenology.

eess.SY↗

arXiv2017

Principled Option Learning in Markov Decision Processes

It is well known that options can make planning more efficient, among their many benefits. Thus far, algorithms for autonomously discovering a set of useful options were heuristic. Naturally, a principled way of finding a set of useful options may be more promising and insightful. In this paper we suggest a mathematical characterization of good sets of options using tools from information theory. This characterization enables us to find conditions for a set of options to be optimal and an algorithm that outputs a useful set of options and illustrate the proposed algorithm in simulation.

cs.LG↗