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Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from dynamical update of weight parameters and heterogeneous activations. In this…
To understand the training dynamics of neural networks (NNs), prior studies have considered the infinite-width mean-field (MF) limit of two-layer NN, establishing theoretical guarantees of its convergence under gradient flow training as…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
We propose a new neural network framework, termed Neural Network Machine Regression (NNMR), which integrates trainable input gating and adaptive depth regularization to jointly perform feature selection and function estimation in an…
The apparent stochasticity of in-vivo neural circuits has long been hypothesized to represent a signature of ongoing stochastic inference in the brain. More recently, a theoretical framework for neural sampling has been proposed, which…
Recent works have highlighted the need for a new dynamical paradigm in the modeling of brain function and evolution. Specifically, these models should incorporate non-constant and asymmetric synaptic weights $T_{ij}$ in the neuron-neuron…
The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual…
There has been a long-standing controversy whether information in neuronal networks is carried by the firing rate code or by the firing temporal code. The current status of the rivalry between the two codes is briefly reviewed with the…
Deep Feedback Models (DFMs) are a new class of stateful neural networks that combine bottom up input with high level representations over time. This feedback mechanism introduces dynamics into otherwise static architectures, enabling DFMs…
The recent successes and spread of large neural language models (LMs) call for a thorough understanding of their computational ability. Describing their computational abilities through LMs' \emph{representational capacity} is a lively area…
Neural module networks (NMNs) are a popular approach for modeling compositionality: they achieve high accuracy when applied to problems in language and vision, while reflecting the compositional structure of the problem in the network…
Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on…
Over the last decade, next-generation neural mass models have become increasingly prominent in mathematical neuroscience. These models link microscopic dynamics with low-dimensional systems of so-called firing rate equations that exactly…
Despite the recent success of neural network models in mimicking animal performance on visual perceptual tasks, critics worry that these models fail to illuminate brain function. We take it that a central approach to explanation in systems…
We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous…
The Na\"ive Mean Field (NMF) approximation is widely employed in modern Machine Learning due to the huge computational gains it bestows on the statistician. Despite its popularity in practice, theoretical guarantees for high-dimensional…
We present design and implementation of a novel neural network potential (NNP) and its combination with an electrostatic embedding scheme, commonly used within the context of hybrid quantum-mechanical/molecular-mechanical (QM/MM)…
We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system…
Maximum entropy methods provide a principled path connecting measurements of neural activity directly to statistical physics models, and this approach has been successful for populations of $N\sim 100$ neurons. As $N$ increases in new…