A deep neural network is a good task solver, but it is difficult to make sense of its operation. People have different ideas about how to interpret its operation. We look at this problem from a new perspective where the interpretation of task solving is synthesized by quantifying how much and what previously unused information is exploited in addition to the information used to solve previous tasks. First, after learning several tasks, the network acquires several information partitions related to each task. We propose that the network then learns the minimal information partition that supplements previously learned information partitions to more accurately represent the input. This extra partition is associated with unconceptualized information that has not been used in previous tasks. We manage to identify what unconceptualized information is used and quantify the amount. To interpret how the network solves a new task, we quantify as meta-information how much information from each partition is extracted. We implement this framework with the variational information bottleneck technique. We test the framework with the MNIST and the CLEVR data set. The framework is shown to be able to compose information partitions and synthesize experience-dependent interpretation in the form of meta-information. This system progressively improves the resolution of interpretation upon new experience by converting a part of the unconceptualized information partition to a task-related partition. It can also provide a visual interpretation by imaging what is the part of previously unconceptualized information that is needed to solve a new task.

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world data that involve nonlinear source mixtures. This work theoretically validates that a cascade of linear PCA and ICA can solve a nonlinear BSS problem accurately—when the sensory inputs are generated from hidden sources via nonlinear mappings with sufficient dimensionality. Our proposed theorem, termed the asymptotic linearization theorem, theoretically guarantees that applying linear PCA to the inputs can reliably extract a subspace spanned by the linear projections from every hidden source as the major components—and thus projecting the inputs onto their major eigenspace can effectively recover a linear transformation of the hidden sources. Then subsequent application of linear ICA can separate all the true independent hidden sources accurately. Zero-element-wise-error nonlinear BSS is asymptotically attained when the source dimensionality is large and the input dimensionality is sufficiently larger than the source dimensionality. Our proposed theorem is validated analytically and numerically. Moreover, the same computation can be performed by using Hebbian-like plasticity rules, implying the biological plausibility of this nonlinear BSS strategy. Our results highlight the utility of linear PCA and ICA for accurately and reliably recovering nonlinearly mixed sources and suggest the importance of employing sensors with sufficient dimensionality to identify true hidden sources of real-world data.

Many cognitive processes rely on the ability of the brain to hold sequences of events in short-term memory. Recent studies have revealed that such memory can be read out from the transient dynamics of a network of neurons. However, the memory performance of such a network in buffering past information has been rigorously estimated only in networks of linear neurons. When signal gain is kept low, so that neurons operate primarily in the linear part of their response nonlinearity, the memory lifetime is bounded by the square root of the network size. In this work, I demonstrate that it is possible to achieve a memory lifetime almost proportional to the network size, “an extensive memory lifetime,” when the nonlinearity of neurons is appropriately used. The analysis of neural activity revealed that nonlinear dynamics prevented the accumulation of noise by partially removing noise in each time step. With this error-correcting mechanism, I demonstrate that a memory lifetime of order can be achieved.

There has recently been a great deal of interest in inferring network connectivity from the spike trains in populations of neurons. One class of useful models that can be fit easily to spiking data is based on generalized linear point process models from statistics. Once the parameters for these models are fit, the analyst is left with a nonlinear spiking network model with delays, which in general may be very difficult to understand analytically. Here we develop mean-field methods for approximating the stimulus-driven firing rates (in both the time-varying and steady-state cases), auto- and cross-correlations, and stimulus-dependent filtering properties of these networks. These approximations are valid when the contributions of individual network coupling terms are small and, hence, the total input to a neuron is approximately gaussian. These approximations lead to deterministic ordinary differential equations that are much easier to solve and analyze than direct Monte Carlo simulation of the network activity. These approximations also provide an analytical way to evaluate the linear input-output filter of neurons and how the filters are modulated by network interactions and some stimulus feature. Finally, in the case of strong refractory effects, the mean-field approximations in the generalized linear model become inaccurate; therefore, we introduce a model that captures strong refractoriness, retains all of the easy fitting properties of the standard generalized linear model, and leads to much more accurate approximations of mean firing rates and cross-correlations that retain fine temporal behaviors.

We study a computational model of audiovisual integration by setting a Bayesian observer that localizes visual and auditory stimuli without presuming the binding of audiovisual information. The observer adopts the maximum a posteriori approach to estimate the physically delivered position or timing of presented stimuli, simultaneously judging whether they are from the same source or not. Several experimental results on the perception of spatial unity and the ventriloquism effect can be explained comprehensively if the subjects in the experiments are regarded as Bayesian observers who try to accurately locate the stimulus. Moreover, by adaptively changing the inner representation of the Bayesian observer in terms of experience, we show that our model reproduces perceived spatial frame shifts due to the audiovisual adaptation known as the ventriloquism aftereffect.

We studied the hypothesis that synaptic dynamics is controlled by three basic principles: (1) synapses adapt their weights so that neurons can effectively transmit information, (2) homeostatic processes stabilize the mean firing rate of the postsynaptic neuron, and (3) weak synapses adapt more slowly than strong ones, while maintenance of strong synapses is costly. Our results show that a synaptic update rule derived from these principles shares features, with spike-timing-dependent plasticity, is sensitive to correlations in the input and is useful for synaptic memory. Moreover, input selectivity (sharply tuned receptive fields) of postsynaptic neurons develops only if stimuli with strong features are presented. Sharply tuned neurons can coexist with unselective ones, and the distribution of synaptic weights can be unimodal or bimodal. The formulation of synaptic dynamics through an optimality criterion provides a simple graphical argument for the stability of synapses, necessary for synaptic memory.

In timing-based neural codes, neurons have to emit action potentials at precise moments in time. We use a supervised learning paradigm to derive a synaptic update rule that optimizes by gradient ascent the likelihood of postsynaptic firing at one or several desired firing times. We find that the optimal strategy of up- and downregulating synaptic efficacies depends on the relative timing between presynaptic spike arrival and desired postsynaptic firing. If the presynaptic spike arrives before the desired postsynaptic spike timing, our optimal learning rule predicts that the synapse should become potentiated. The dependence of the potentiation on spike timing directly reflects the time course of an excitatory postsynaptic potential. However, our approach gives no unique reason for synaptic depression under reversed spike timing. In fact, the presence and amplitude of depression of synaptic efficacies for reversed spike timing depend on how constraints are implemented in the optimization problem. Two different constraints, control of postsynaptic rates and control of temporal locality, are studied. The relation of our results to spike-timing-dependent plasticity and reinforcement learning is discussed.