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There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used…

Recurrent connectivity in the visual cortex is believed to aid object recognition for challenging conditions such as occlusion. Here we investigate if and how artificial neural networks also benefit from recurrence. We compare architectures…

After learning a concept, humans are also able to continually generalize their learned concepts to new domains by observing only a few labeled instances without any interference with the past learned knowledge. In contrast, learning…

Spiking Neural Networks (SNNs) provide a promising framework for energy-efficient and biologically grounded computation; however, scalable learning in deep recurrent architectures with sparse connectivity remains a major challenge. In this…

Discrete normalizing flows are promising generative models with advantages such as analytical log-likelihood computation and end-to-end training. However, the architectural constraints to ensure invertibility and tractable Jacobian…

Based on the predictive coding theory in neuroscience, we designed a bi-directional and recurrent neural net, namely deep predictive coding networks (PCN). It has feedforward, feedback, and recurrent connections. Feedback connections from a…

Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polynomial functions can…

Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only…

Gradient-based neural network training traditionally enforces symmetry between forward and backward propagation, requiring activation functions to be differentiable (or sub-differentiable) and strictly monotonic in certain regions to…

Composite adaptive radial basis function neural network (RBFNN) control with a lattice distribution of hidden nodes has three inherent demerits: 1) the approximation domain of adaptive RBFNNs is difficult to be determined a priori; 2) only…

Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the dint of it feedforward networks can be used to solve or…

Diffusion Models have become a cornerstone of modern generative AI for their exceptional generation quality and controllability. However, their inherent \textit{multi-step iterations} and \textit{complex backbone networks} lead to…

The human brain is the gold standard of adaptive learning. It not only can learn and benefit from experience, but also can adapt to new situations. In contrast, deep neural networks only learn one sophisticated but fixed mapping from inputs…

This paper investigates the controllability of a broad class of recurrent neural networks widely used in theoretical neuroscience, including models of large-scale human brain dynamics. Motivated by emerging applications in non-invasive…

We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kronecker product, which provides an efficient way of…

Signal reconstruction is a challenging aspect of computational imaging as it often involves solving ill-posed inverse problems. Recently, deep feed-forward neural networks have led to state-of-the-art results in solving various inverse…

Factorized layers--operations parameterized by products of two or more matrices--occur in a variety of deep learning contexts, including compressed model training, certain types of knowledge distillation, and multi-head self-attention…

Deep Boltzmann machines (DBMs), one of the first ``deep'' learning methods ever studied, are multi-layered probabilistic models governed by a pairwise energy function that describes the likelihood of all variables/nodes in the network. In…

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…

Despite the recent popularity of deep generative state space models, few comparisons have been made between network architectures and the inference steps of the Bayesian filtering framework -- with most models simultaneously approximating…