Recurrent Neural Networks (RNN) are commonly used models to study neural computation. However, a comprehensive understanding of how dynamics in RNN emerge from the underlying connectivity is largely lacking. Previous work derived such an understanding for RNN fulfilling very specific constraints on their connectivity, but it is unclear whether the resulting insights apply more generally. Here we study how network dynamics are related to network connectivity in RNN trained without any specific constraints on several tasks previously employed in neuroscience. Despite the apparent high-dimensional connectivity of these RNN, we show that a low-dimensional, functionally relevant subspace of the weight matrix can be found through the identification of \textit{operative} dimensions, which we define as components of the connectivity whose removal has a large influence on local RNN dynamics. We find that a weight matrix built from only a few operative dimensions is sufficient for the RNN to operate with the original performance, implying that much of the high-dimensional structure of the trained connectivity is functionally irrelevant. The existence of a low-dimensional, operative subspace in the weight matrix simplifies the challenge of linking connectivity to network dynamics and suggests that independent network functions may be placed in specific, separate subspaces of the weight matrix to avoid catastrophic forgetting in continual learning.

This letter addresses the problem of separating two speakers from a single microphone recording. Three linear methods are tested for source separation, all of which operate directly on sound spectrograms: (1) eigenmode analysis of covariance difference to identify spectro-temporal features associated with large variance for one source and small variance for the other source; (2) maximum likelihood demixing in which the mixture is modeled as the sum of two gaussian signals and maximum likelihood is used to identify the most likely sources; and (3) suppression-regression, in which autoregressive models are trained to reproduce one source and suppress the other. These linear approaches are tested on the problem of separating a known male from a known female speaker. The performance of these algorithms is assessed in terms of the residual error of estimated source spectrograms, waveform signal-to-noise ratio, and perceptual evaluation of speech quality scores. This work shows that the algorithms compare favorably to nonlinear approaches such as nonnegative sparse coding in terms of simplicity, performance, and suitability for real-time implementations, and they provide benchmark solutions for monaural source separation tasks.

Recently, there have been remarkable advances in modeling the relationships between the sensory environment, neuronal responses, and behavior. However, most models cannot encompass variable stimulus-response relationships such as varying response latencies and state or context dependence of the neural code. Here, we consider response modeling as a dynamic alignment problem and model stimulus and response jointly by a mixed pair hidden Markov model (MPH). In MPHs, multiple stimulus-response relationships (e.g., receptive fields) are represented by different states or groups of states in a Markov chain. Each stimulus-response relationship features temporal flexibility, allowing modeling of variable response latencies, including noisy ones. We derive algorithms for learning of MPH parameters and for inference of spike response probabilities. We show that some linear-nonlinear Poisson cascade (LNP) models are a special case of MPHs. We demonstrate the efficiency and usefulness of MPHs in simulations of both jittered and switching spike responses to white noise and natural stimuli. Furthermore, we apply MPHs to extracellular single and multi-unit data recorded in cortical brain areas of singing birds to showcase a novel method for estimating response lag distributions. MPHs allow simultaneous estimation of receptive fields, latency statistics, and hidden state dynamics and so can help to uncover complex stimulus response relationships that are subject to variable timing and involve diverse neural codes.

Visual attention is thought to be driven by the interplay between low-level visual features and task dependent information content of local image regions, as well as by spatial viewing biases. Though dependent on experimental paradigms and model assumptions, this idea has given rise to varying claims that either bottom-up or top-down mechanisms dominate visual attention. To contribute toward a resolution of this discussion, here we quantify the influence of these factors and their relative importance in a set of classification tasks. Our stimuli consist of individual image patches (bubbles). For each bubble we derive three measures: a measure of salience based on low-level stimulus features, a measure of salience based on the task dependent information content derived from our subjects' classification responses and a measure of salience based on spatial viewing biases. Furthermore, we measure the empirical salience of each bubble based on our subjects' measured eye gazes thus characterizing the overt visual attention each bubble receives. A multivariate linear model relates the three salience measures to overt visual attention. It reveals that all three salience measures contribute significantly. The effect of spatial viewing biases is highest and rather constant in different tasks. The contribution of task dependent information is a close runner-up. Specifically, in a standardized task of judging facial expressions it scores highly. The contribution of low-level features is, on average, somewhat lower. However, in a prototypical search task, without an available template, it makes a strong contribution on par with the two other measures. Finally, the contributions of the three factors are only slightly redundant, and the semi-partial correlation coefficients are only slightly lower than the coefficients for full correlations. These data provide evidence that all three measures make significant and independent contributions and that none can be neglected in a model of human overt visual attention.