A simple model of the attentional blink and its modulation by mental training.

The attentional blink (AB) effect is the reduced probability of reporting a second target (T2) that appears shortly after a first one (T1) within a rapidly presented sequence of distractors. The AB effect has been shown to be reduced following intensive mental training in the form of mindfulness meditation, with a corresponding reduction in T1-evoked P3b brain potentials. However, the mechanisms underlying these effects remain unknown. We propose a dynamical-systems model of the AB, in which attentional load is described as the response of a dynamical system to incoming impulse signals. Non-task related mental activity is represented by additive noise modulated by meditation. The model provides a parsimonious computational framework relating behavioral performance, evoked brain potentials and training through the concept of reduced mental noise.

The value-complexity trade-off for reinforcement learning based brain-computer interfaces.

OBJECTIVE: One of the recent developments in the field of brain-computer interfaces (BCI) is the reinforcement learning (RL) based BCI paradigm, which uses neural error responses as the reward feedback on the agent's action. While having several advantages over motor imagery based BCI, the reliability of RL-BCI is critically dependent on the decoding accuracy of noisy neural error signals. A principled method is needed to optimally handle this inherent noise under general conditions. APPROACH: By determining a trade-off between the expected value and the informational cost of policies, the info-RL (IRL) algorithm provides optimal low-complexity policies, which are robust under noisy reward conditions and achieve the maximal obtainable value. In this work we utilize the IRL algorithm to characterize the maximal obtainable value under different noise levels, which in turn is used to extract the optimal robust policy for each noise level. MAIN RESULTS: Our simulation results of a setting with Gaussian noise show that the complexity level of the optimal policy is dependent on the reward magnitude but not on the reward variance, whereas the variance determines whether a lower complexity solution is favorable or not. We show how this analysis can be utilized to select optimal robust policies for an RL-BCI and demonstrate its use on EEG data. SIGNIFICANCE: We propose here a principled method to determine the optimal policy complexity of an RL problem with a noisy reward, which we argue is particularly useful for RL-based BCI paradigms. This framework may be used to minimize initial training time and allow for a more dynamic and robust shared control between the agent and the operator under different conditions.

Value-complexity tradeoff explains mouse navigational learning.

We introduce a novel methodology for describing animal behavior as a tradeoff between value and complexity, using the Morris Water Maze navigation task as a concrete example. We develop a dynamical system model of the Water Maze navigation task, solve its optimal control under varying complexity constraints, and analyze the learning process in terms of the value and complexity of swimming trajectories. The value of a trajectory is related to its energetic cost and is correlated with swimming time. Complexity is a novel learning metric which measures how unlikely is a trajectory to be generated by a naive animal. Our model is analytically tractable, provides good fit to observed behavior and reveals that the learning process is characterized by early value optimization followed by complexity reduction. Furthermore, complexity sensitively characterizes behavioral differences between mouse strains.

Nonlinear 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. Nonlinear 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 nonlinear 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 nonlinear 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.

Surprise response as a probe for compressed memory states.

The limited capacity of recent memory inevitably leads to partial memory of past stimuli. There is also evidence that behavioral and neural responses to novel or rare stimuli are dependent on one's memory of past stimuli. Thus, these responses may serve as a probe of different individuals' remembering and forgetting characteristics. Here, we utilize two lossy compression models of stimulus sequences that inherently involve forgetting, which in addition to being a necessity under many conditions, also has theoretical and behavioral advantages. One model is based on a simple stimulus counter and the other on the Information Bottleneck (IB) framework which suggests a more general, theoretically justifiable principle for biological and cognitive phenomena. These models are applied to analyze a novelty-detection event-related potential commonly known as the P300. The trial-by-trial variations of the P300 response, recorded in an auditory oddball paradigm, were subjected to each model to extract two stimulus-compression parameters for each subject: memory length and representation accuracy. These parameters were then utilized to estimate the subjects' recent memory capacity limit under the task conditions. The results, along with recently published findings on single neurons and the IB model, underscore how a lossy compression framework can be utilized to account for trial-by-trial variability of neural responses at different spatial scales and in different individuals, while at the same time providing estimates of individual memory characteristics at different levels of representation using a theoretically-based parsimonious model.

Communicative need in colour naming.

Colour naming across languages has traditionally been held to reflect the structure of colour perception. At the same time, it has often, and increasingly, been suggested that colour naming may be shaped by patterns of communicative need. However, much remains unknown about the factors involved in communicative need, how need interacts with perception, and how this interaction may shape colour naming. Here, we engage these open questions by building on general information-theoretic principles. We present a systematic evaluation of several factors that may reflect need, and that have been proposed in the literature: capacity constraints, linguistic usage, and the visual environment. Our analysis suggests that communicative need in colour naming is reflected more directly by capacity constraints and linguistic usage than it is by the statistics of the visual environment.

Color Naming Reflects Both Perceptual Structure and Communicative Need.

Gibson et al. () 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.

Efficient compression in color naming and its evolution.

We derive a principled information-theoretic account of cross-language semantic variation. Specifically, we argue that languages efficiently compress ideas into words by optimizing the information bottleneck (IB) trade-off between the complexity and accuracy of the lexicon. We test this proposal in the domain of color naming and show that (i) color-naming systems across languages achieve near-optimal compression; (ii) small changes in a single trade-off parameter account to a large extent for observed cross-language variation; (iii) efficient IB color-naming systems exhibit soft rather than hard category boundaries and often leave large regions of color space inconsistently named, both of which phenomena are found empirically; and (iv) these IB systems evolve through a sequence of structural phase transitions, in a single process that captures key ideas associated with different accounts of color category evolution. These results suggest that a drive for information-theoretic efficiency may shape color-naming systems across languages. This principle is not specific to color, and so it may also apply to cross-language variation in other semantic domains.

Efficient encoding of motion is mediated by gap junctions in the fly visual system.

Understanding the computational implications of specific synaptic connectivity patterns is a fundamental goal in neuroscience. In particular, the computational role of ubiquitous electrical synapses operating via gap junctions remains elusive. In the fly visual system, the cells in the vertical-system network, which play a key role in visual processing, primarily connect to each other via axonal gap junctions. This network therefore provides a unique opportunity to explore the functional role of gap junctions in sensory information processing. Our information theoretical analysis of a realistic VS network model shows that within 10 ms following the onset of the visual input, the presence of axonal gap junctions enables the VS system to efficiently encode the axis of rotation, θ, of the fly's ego motion. This encoding efficiency, measured in bits, is near-optimal with respect to the physical limits of performance determined by the statistical structure of the visual input itself. The VS network is known to be connected to downstream pathways via a subset of triplets of the vertical system cells; we found that because of the axonal gap junctions, the efficiency of this subpopulation in encoding θ is superior to that of the whole vertical system network and is robust to a wide range of signal to noise ratios. We further demonstrate that this efficient encoding of motion by this subpopulation is necessary for the fly's visually guided behavior, such as banked turns in evasive maneuvers. Because gap junctions are formed among the axons of the vertical system cells, they only impact the system's readout, while maintaining the dendritic input intact, suggesting that the computational principles implemented by neural circuitries may be much richer than previously appreciated based on point neuron models. Our study provides new insights as to how specific network connectivity leads to efficient encoding of sensory stimuli.

The Representation of Prediction Error in Auditory Cortex.

To survive, organisms must extract information from the past that is relevant for their future. How this process is expressed at the neural level remains unclear. We address this problem by developing a novel approach from first principles. We show here how to generate low-complexity representations of the past that produce optimal predictions of future events. We then illustrate this framework by studying the coding of 'oddball' sequences in auditory cortex. We find that for many neurons in primary auditory cortex, trial-by-trial fluctuations of neuronal responses correlate with the theoretical prediction error calculated from the short-term past of the stimulation sequence, under constraints on the complexity of the representation of this past sequence. In some neurons, the effect of prediction error accounted for more than 50% of response variability. Reliable predictions often depended on a representation of the sequence of the last ten or more stimuli, although the representation kept only few details of that sequence.

Dopaminergic Balance between Reward Maximization and Policy Complexity.

Previous reinforcement-learning models of the basal ganglia network have highlighted the role of dopamine in encoding the mismatch between prediction and reality. Far less attention has been paid to the computational goals and algorithms of the main-axis (actor). Here, we construct a top-down model of the basal ganglia with emphasis on the role of dopamine as both a reinforcement learning signal and as a pseudo-temperature signal controlling the general level of basal ganglia excitability and motor vigilance of the acting agent. We argue that the basal ganglia endow the thalamic-cortical networks with the optimal dynamic tradeoff between two constraints: minimizing the policy complexity (cost) and maximizing the expected future reward (gain). We show that this multi-dimensional optimization processes results in an experience-modulated version of the softmax behavioral policy. Thus, as in classical softmax behavioral policies, probability of actions are selected according to their estimated values and the pseudo-temperature, but in addition also vary according to the frequency of previous choices of these actions. We conclude that the computational goal of the basal ganglia is not to maximize cumulative (positive and negative) reward. Rather, the basal ganglia aim at optimization of independent gain and cost functions. Unlike previously suggested single-variable maximization processes, this multi-dimensional optimization process leads naturally to a softmax-like behavioral policy. We suggest that beyond its role in the modulation of the efficacy of the cortico-striatal synapses, dopamine directly affects striatal excitability and thus provides a pseudo-temperature signal that modulates the tradeoff between gain and cost. The resulting experience and dopamine modulated softmax policy can then serve as a theoretical framework to account for the broad range of behaviors and clinical states governed by the basal ganglia and dopamine systems.

Past-future information bottleneck in dynamical systems.

Biological systems need to process information in real time and must trade off accuracy of presentation and coding costs. Here we operationalize this trade-off and develop an information-theoretic framework that selectively extracts information of the input past that is predictive about the output future, obtaining a generalized eigenvalue problem. Thereby, we unravel the input history in terms of structural phase transitions corresponding to additional dimensions of a state space. We elucidate the relation to canonical correlation analysis and give a numerical example. Altogether, this work relates information-theoretic optimization to the joint problem of system identification and model reduction.

The minimum information principle and its application to neural code analysis.

The study of complex information processing systems requires appropriate theoretical tools to help unravel their underlying design principles. Information theory is one such tool, and has been utilized extensively in the study of the neural code. Although much progress has been made in information theoretic methodology, there is still no satisfying answer to the question: "What is the information that a given property of the neural population activity (e.g., the responses of single cells within the population) carries about a set of stimuli?" Here, we answer such questions via the minimum mutual information (MinMI) principle. We quantify the information in any statistical property of the neural response by considering all hypothetical neuronal populations that have the given property and finding the one that contains the minimum information about the stimuli. All systems with higher information values necessarily contain additional information processing mechanisms and, thus, the minimum captures the information related to the given property alone. MinMI may be used to measure information in properties of the neural response, such as that conveyed by responses of small subsets of cells (e.g., singles or pairs) in a large population and cooperative effects between subunits in networks. We show how the framework can be used to study neural coding in large populations and to reveal properties that are not discovered by other information theoretic methods.

Encoding by response duration in the basal ganglia.

Several models have suggested that information transmission in the basal ganglia (BG) involves gating mechanisms, where neuronal activity modulates the extent of gate aperture and its duration. Here, we demonstrate that BG response duration is informative about a highly abstract stimulus feature and show that the duration of "gate opening" can indeed be used for information transmission through the BG. We analyzed recordings from three BG locations: the external part of the globus pallidus (GPe), the substantia nigra pars reticulata (SNr), and dopaminergic neurons from the substantia nigra pars compacta (SNc) during performance of a probabilistic visuomotor task. Most (>85%) of the neurons showed significant rate modulation following the appearance of cues predicting future reward. Trial-to-trial mutual information analysis revealed that response duration encoded reward prospects in many (42%) of the responsive SNr neurons, as well as in the SNc (26.9%), and the GPe (29.3%). Whereas the low-frequency discharge SNc neurons responded with only an increase in firing rate, SNr and GPe neurons with high-frequency tonic discharge responded with both increases and decreases. Conversely, many duration-informative neurons in SNr (68%) and GPe (50%) responded with a decreased rather than an increased rate. The response duration was more informative than the extreme (minimal or maximal) amplitude or spike count in responsive bins of duration-informative neurons. Thus response duration is not simply correlated with the discharge rate and can provide additional information to the target structures of the BG.

ProMateus--an open research approach to protein-binding sites analysis.

The development of bioinformatic tools by individual labs results in the abundance of parallel programs for the same task. For example, identification of binding site regions between interacting proteins is done using: ProMate, WHISCY, PPI-Pred, PINUP and others. All servers first identify unique properties of binding sites and then incorporate them into a predictor. Obviously, the resulting prediction would improve if the most suitable parameters from each of those predictors would be incorporated into one server. However, because of the variation in methods and databases, this is currently not feasible. Here, the protein-binding site prediction server is extended into a general protein-binding sites research tool, ProMateus. This web tool, based on ProMate's infrastructure enables the easy exploration and incorporation of new features and databases by the user, providing an evaluation of the benefit of individual features and their combination within a set framework. This transforms the individual research into a community exercise, bringing out the best from all users for optimized predictions. The analysis is demonstrated on a database of protein protein and protein-DNA interactions. This approach is basically different from that used in generating meta-servers. The implications of the open-research approach are discussed. ProMateus is available at http://bip.weizmann.ac.il/promate.

Reduction of information redundancy in the ascending auditory pathway.

Information processing by a sensory system is reflected in the changes in stimulus representation along its successive processing stages. We measured information content and stimulus-induced redundancy in the neural responses to a set of natural sounds in three successive stations of the auditory pathway-inferior colliculus (IC), auditory thalamus (MGB), and primary auditory cortex (A1). Information about stimulus identity was somewhat reduced in single A1 and MGB neurons relative to single IC neurons, when information is measured using spike counts, latency, or temporal spiking patterns. However, most of this difference was due to differences in firing rates. On the other hand, IC neurons were substantially more redundant than A1 and MGB neurons. IC redundancy was largely related to frequency selectivity. Redundancy reduction may be a generic organization principle of neural systems, allowing for easier readout of the identity of complex stimuli in A1 relative to IC.

Multivariate information bottleneck.

The information bottleneck (IB) method is an unsupervised model independent data organization technique. Given a joint distribution, p(X, Y), this method constructs a new variable, T, that extracts partitions, or clusters, over the values of X that are informative about Y. Algorithms that are motivated by the IB method have already been applied to text classification, gene expression, neural code, and spectral analysis. Here, we introduce a general principled framework for multivariate extensions of the IB method. This allows us to consider multiple systems of data partitions that are interrelated. Our approach utilizes Bayesian networks for specifying the systems of clusters and which information terms should be maintained. We show that this construction provides insights about bottleneck variations and enables us to characterize the solutions of these variations. We also present four different algorithmic approaches that allow us to construct solutions in practice and apply them to several real-world problems.

Stochastic computing with biomolecular automata.

Stochastic computing has a broad range of applications, yet electronic computers realize its basic step, stochastic choice between alternative computation paths, in a cumbersome way. Biomolecular computers use a different computational paradigm and hence afford novel designs. We constructed a stochastic molecular automaton in which stochastic choice is realized by means of competition between alternative biochemical pathways, and choice probabilities are programmed by the relative molar concentrations of the software molecules coding for the alternatives. Programmable and autonomous stochastic molecular automata have been shown to perform direct analysis of disease-related molecular indicators in vitro and may have the potential to provide in situ medical diagnosis and cure.

Efficient exact p-value computation for small sample, sparse, and surprising categorical data.

A major obstacle in applying various hypothesis testing procedures to datasets in bioinformatics is the computation of ensuing p-values. In this paper, we define a generic branch-and-bound approach to efficient exact p-value computation and enumerate the required conditions for successful application. Explicit procedures are developed for the entire Cressie-Read family of statistics, which includes the widely used Pearson and likelihood ratio statistics in a one-way frequency table goodness-of-fit test. This new formulation constitutes a first practical exact improvement over the exhaustive enumeration performed by existing statistical software. The general techniques we develop to exploit the convexity of many statistics are also shown to carry over to contingency table tests, suggesting that they are readily extendible to other tests and test statistics of interest. Our empirical results demonstrate a speed-up of orders of magnitude over the exhaustive computation, significantly extending the practical range for performing exact tests. We also show that the relative speed-up gain increases as the null hypothesis becomes sparser, that computation precision increases with increase in speed-up, and that computation time is very moderately affected by the magnitude of the computed p-value. These qualities make our algorithm especially appealing in the regimes of small samples, sparse null distributions, and rare events, compared to the alternative asymptotic approximations and Monte Carlo samplers. We discuss several established bioinformatics applications, where small sample size, small expected counts in one or more categories (sparseness), and very small p-values do occur. Our computational framework could be applied in these, and similar cases, to improve performance.