Power-law statistics and universal scaling in the absence of criticality

Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates, and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.Comment: in press in Phys. Rev.

Information driven self-organization of complex robotic behaviors

Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called excess entropy or effective measure complexity, of the sensorimotor process as a driving force to generate behavior. We study nonlinear and nonstationary systems and introduce the time-local predicting information (TiPI) which allows us to derive exact results together with explicit update rules for the parameters of the controller in the dynamical systems framework. In this way the information principle, formulated at the level of behavior, is translated to the dynamics of the synapses. We underpin our results with a number of case studies with high-dimensional robotic systems. We show the spontaneous cooperativity in a complex physical system with decentralized control. Moreover, a jointly controlled humanoid robot develops a high behavioral variety depending on its physics and the environment it is dynamically embedded into. The behavior can be decomposed into a succession of low-dimensional modes that increasingly explore the behavior space. This is a promising way to avoid the curse of dimensionality which hinders learning systems to scale well.Comment: 29 pages, 12 figure

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning

Taming neuronal noise with large networks

How does reliable computation emerge from networks of noisy neurons? While individual neurons are intrinsically noisy, the collective dynamics of populations of neurons taken as a whole can be almost deterministic, supporting the hypothesis that, in the brain, computation takes place at the level of neuronal populations. Mathematical models of networks of noisy spiking neurons allow us to study the effects of neuronal noise on the dynamics of large networks. Classical mean-field models, i.e., models where all neurons are identical and where each neuron receives the average spike activity of the other neurons, offer toy examples where neuronal noise is absorbed in large networks, that is, large networks behave like deterministic systems. In particular, the dynamics of these large networks can be described by deterministic neuronal population equations. In this thesis, I first generalize classical mean-field limit proofs to a broad class of spiking neuron models that can exhibit spike-frequency adaptation and short-term synaptic plasticity, in addition to refractoriness. The mean-field limit can be exactly described by a multidimensional partial differential equation; the long time behavior of which can be rigorously studied using deterministic methods. Then, we show that there is a conceptual link between mean-field models for networks of spiking neurons and latent variable models used for the analysis of multi-neuronal recordings. More specifically, we use a recently proposed finite-size neuronal population equation, which we first mathematically clarify, to design a tractable Expectation-Maximization-type algorithm capable of inferring the latent population activities of multi-population spiking neural networks from the spike activity of a few visible neurons only, illustrating the idea that latent variable models can be seen as partially observed mean-field models. In classical mean-field models, neurons in large networks behave like independent, identically distributed processes driven by the average population activity -- a deterministic quantity, by the law of large numbers. The fact the neurons are identically distributed processes implies a form of redundancy that has not been observed in the cortex and which seems biologically implausible. To show, numerically, that the redundancy present in classical mean-field models is unnecessary for neuronal noise absorption in large networks, I construct a disordered network model where networks of spiking neurons behave like deterministic rate networks, despite the absence of redundancy. This last result suggests that the concentration of measure phenomenon, which generalizes the ``law of large numbers'' of classical mean-field models, might be an instrumental principle for understanding the emergence of noise-robust population dynamics in large networks of noisy neurons

The ecology of suffering: developmental disorders of structured stress, emotion, and chronic inflammation

'Punctuated equilibrium' models of cognitive process, adapted from the Large Deviations Program of probability theory, are applied to the interaction between immune function and emotion in the context of culturally structured psychosocial stress. The analysis suggests: (1) Chronic inflammatory diseases should be comorbid and synergistic with characteristic emotional dysfunction, and may form a collection of joint disorders most effectively treated at the individual level using multifactorial 'mind/body' strategies. (2) Culturally constructed psychosocial stress can literally write an image of itself onto the punctuated etiology and progression of such composite disorders, beginning a trajectory to disease in utero or early childhood, and continuing throughout the life course, suggesting that, when moderated by 'social exposures', these are developmental disorders. (3) At the community level of organization, strategies for prevention and control of the spectrum of emotional/inflammatory developmental disorders must include redress of cross-sectional and logitudinal (i.e. historical) patterns of inequality and injustice which generate structured psychosocial stress. Evidence further suggests that within 'Westernized' or 'market economy' societies, such stress will inevitably entrain high as well as lower stutus subopulations into a unified ecology of suffering