The mean field theory of multilayer neural networks centers around a particular infinite-width scaling, in which the learning dynamics is shown to be closely tracked by the mean field limit. A random fluctuation around this infinite-width limit is expected from a large-width expansion to the next order. This fluctuation has been studied only in the case of shallow networks, where previous works employ heavily technical notions or additional formulation ideas amenable only to that case. Treatment of the multilayer case has been missing, with the chief difficulty in finding a formulation that must capture the stochastic dependency across not only time but also depth. In this work, we initiate the study of the fluctuation in the case of multilayer networks, at any network depth.

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex.These models learn a shared set of nonlinear basis functions, which are linearly combined via a learned weight vector to represent a neuron's function.Such weight vectors, which can be thought as embeddings of neuronal function, have been proposed to define functional cell types via unsupervised clustering.However, as deep models are usually highly overparameterized, the learning problem is unlikely to have a unique solution, which raises the question if such embeddings can be used in a meaningful way for downstream analysis.In this paper, we investigate how stable neuronal embeddings are with respect to changes in model architecture and initialization. We find that $L_1$ regularization to be an important ingredient for structured embeddings and develop an adaptive regularization that adjusts the strength of regularization per neuron. This regularization improves both predictive performance and how consistently neuronal embeddings cluster across model fits compared to uniform regularization.To overcome overparametrization, we propose an iterative feature pruning strategy which reduces the dimensionality of performance-optimized models by half without loss of performance and improves the consistency of neuronal embeddings with respect to clustering neurons.Our results suggest that to achieve an objective taxonomy of cell types or a compact representation of the functional landscape, we need novel architectures or learning techniques that improve identifiability.

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex.

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex.These models learn a shared set of nonlinear basis functions, which are linearly combined via a learned weight vector to represent a neuron's function.Such weight vectors, which can be thought as embeddings of neuronal function, have been proposed to define functional cell types via unsupervised clustering.However, as deep models are usually highly overparameterized, the learning problem is unlikely to have a unique solution, which raises the question if such embeddings can be used in a meaningful way for downstream analysis.In this paper, we investigate how stable neuronal embeddings are with respect to changes in model architecture and initialization. We find that L_1 regularization to be an important ingredient for structured embeddings and develop an adaptive regularization that adjusts the strength of regularization per neuron. This regularization improves both predictive performance and how consistently neuronal embeddings cluster across model fits compared to uniform regularization.To overcome overparametrization, we propose an iterative feature pruning strategy which reduces the dimensionality of performance-optimized models by half without loss of performance and improves the consistency of neuronal embeddings with respect to clustering neurons.Our results suggest that to achieve an objective taxonomy of cell types or a compact representation of the functional landscape, we need novel architectures or learning techniques that improve identifiability.

By exploiting discrete signal processing and simulating brain neuron communication, Spiking Neural Networks (SNNs) offer a low-energy alternative to Artificial Neural Networks (ANNs). However, existing SNN models, still face high computational costs due to the numerous time steps as well as network depth and scale. The tens of billions of neurons and trillions of synapses in the human brain are developed from only 20,000 genes, which inspires us to design an efficient genetic encoding strategy that dynamic evolves to regulate large-scale deep SNNs at low cost. Therefore, we first propose a genetically scaled SNN encoding scheme that incorporates globally shared genetic interactions to indirectly optimize neuronal encoding instead of weight, which obviously brings about reductions in parameters and energy consumption. Then, a spatio-temporal evolutionary framework is designed to optimize the inherently initial wiring rules. Two dynamic regularization operators in the fitness function evolve the neuronal encoding to a suitable distribution and enhance information quality of the genetic interaction respectively, substantially accelerating evolutionary speed and improving efficiency. Experiments show that our approach compresses parameters by approximately 50\% to 80\%, while outperforming models on the same architectures by 0.21\% to 4.38\% on CIFAR-10, CIFAR-100 and ImageNet. In summary, the consistent trends of the proposed genetically encoded spatio-temporal evolution across different datasets and architectures highlight its significant enhancements in terms of efficiency, broad scalability and robustness, demonstrating the advantages of the brain-inspired evolutionary genetic coding for SNN optimization.

We focus on the online-based active learning (OAL) setting where an agent operates over a stream of observations and trades-off between the costly acquisition of information (labelled observations) and the cost of prediction errors. We propose a novel foundation for OAL tasks based on partial monitoring, a theoretical framework specialized in online learning from partially informative actions. We show that previously studied binary and multi-class OAL tasks are instances of partial monitoring. We expand the real-world potential of OAL by introducing a new class of cost-sensitive OAL tasks. We propose NeuralCBP, the first PM strategy that accounts for predictive uncertainty with deep neural networks. Our extensive empirical evaluation on open source datasets shows that NeuralCBP has favorable performance against state-of-the-art baselines on multiple binary, multi-class and cost-sensitive OAL tasks.

Conventional semiconductor-based integrated circuits are gradually approaching fundamental scaling limits. Many prospective solutions have recently emerged to supplement or replace both the technology on which basic devices are built and the architecture of data processing. Neuromorphic circuits are a promising approach to computing where techniques used by the brain to achieve high efficiency are exploited. Many existing neuromorphic circuits rely on unconventional and useful properties of novel technologies to better mimic the operation of the brain. One such technology is single flux quantum (SFQ) logic -- a cryogenic superconductive technology in which the data are represented by quanta of magnetic flux (fluxons) produced and processed by Josephson junctions embedded within inductive loops. The movement of a fluxon within a circuit produces a quantized voltage pulse (SFQ pulse), resembling a neuronal spiking event. These circuits routinely operate at clock frequencies of tens to hundreds of gigahertz, making SFQ a natural technology for processing high frequency pulse trains. Prior proposals for SFQ neural networks often require energy-expensive fluxon conversions, involve heterogeneous technologies, or exclusively focus on device level behavior. In this paper, a design methodology for deep single flux quantum neuromorphic networks is presented. Synaptic and neuronal circuits based on SFQ technology are presented and characterized. Based on these primitives, a deep neuromorphic XOR network is evaluated as a case study, both at the architectural and circuit levels, achieving wide classification margins. The proposed methodology does not employ unconventional superconductive devices or semiconductor transistors. The resulting networks are tunable by an external current, making this proposed system an effective approach for scalable cryogenic neuromorphic computing.

We analyze Elman-type Recurrent Reural Networks (RNNs) and their training in the mean-field regime. Specifically, we show convergence of gradient descent training dynamics of the RNN to the corresponding mean-field formulation in the large width limit. We also show that the fixed points of the limiting infinite-width dynamics are globally optimal, under some assumptions on the initialization of the weights. Our results establish optimality for feature-learning with wide RNNs in the mean-field regime

Researchers have found that higher visual cognitive functions can arise spontaneously in untrained neural networks. A KAIST research team led by Professor Se-Bum Paik from the Department of Bio and Brain Engineering has shown that visual selectivity of facial images can arise even in completely untrained deep neural networks. This new finding has provided revelatory insights into mechanisms underlying the development of cognitive functions in both biological and artificial neural networks, also making a significant impact on our understanding of the origin of early brain functions before sensory experiences. The study published in Nature Communications on December 16 demonstrates that neuronal activities selective to facial images are observed in randomly initialized deep neural networks in the complete absence of learning, and that they show the characteristics of those observed in biological brains. The ability to identify and recognize faces is a crucial function for social behavior, and this ability is thought to originate from neuronal tuning at the single or multi-neuronal level.