Accumulating evidence suggests stochastic cortical circuits can perform sampling-based Bayesian inference to compute the latent stimulus posterior. Canonical cortical circuits consist of excitatory (E) neurons and types of inhibitory (I) interneurons. Nevertheless, nearly no sampling neural circuit models consider the diversity of interneurons, and thus how interneurons contribute to sampling remains poorly understood. To provide theoretical insight, we build a nonlinear canonical circuit model consisting of recurrently connected E neurons and two types of I neurons including Parvalbumin (PV) and Somatostatin (SOM) neurons. The E neurons are modeled as a canonical ring (attractor) model, receiving global inhibition from PV neurons, and locally tuning-dependent inhibition from SOM neurons.We theoretically analyze the nonlinear circuit dynamics and analytically identify the Bayesian sampling algorithm performed by the circuit dynamics. We found a reduced circuit with only E and PV neurons performs Langevin sampling, and the inclusion of SOM neurons with tuning-dependent inhibition speeds up the sampling via upgrading the Langevin into Hamiltonian sampling. Moreover, the Hamiltonian framework requires SOM neurons to receive no direct feedforward connections, consistent with neuroanatomy. Our work provides overarching connections between nonlinear circuits with various types of interneurons and sampling algorithms, deepening our understanding of circuit implementation of Bayesian inference.

Visual processing in the retina has been studied in great detail at all levels such that a comprehensive picture of the retina's cell types and the many neural circuits they form is emerging. However, the currently best performing models of retinal function are black-box CNN models which are agnostic to such biological knowledge.

It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural networks with Kronecker products and hybrid tensor neural networks with MPO factorization and fully-connected layers. Nonetheless, the generalization power and robustness of the fully-connected layers are not as outstanding as circuit models in quantum computing. In this paper, we propose a novel tensor circuit neural network (TCNN) that takes advantage of the characteristics of tensor neural networks and residual circuit models to achieve generalization ability and robustness with low complexity. The proposed activation operation and parallelism of the circuit in complex number field improves its non-linearity and efficiency for feature learning. Moreover, since the feature information exists in the parameters in both the real and imaginary parts in TCNN, an information fusion layer is proposed for merging features stored in those parameters to enhance the generalization capability. Experimental results confirm that TCNN showcases more outstanding generalization and robustness with its average accuracies on various datasets 2\%-3\% higher than those of the state-of-the-art compared models. More significantly, while other models fail to learn features under noise parameter attacking, TCNN still showcases prominent learning capability owing to its ability to prevent gradient explosion. Furthermore, it is comparable to the compared models on the number of trainable parameters and the CPU running time. An ablation study also indicates the advantage of the activation operation, the parallelism architecture and the information fusion layer.

Accurate and efficient circuit behavior modeling is a cornerstone of modern electronic design automation. Among different types of circuits, stiff circuits are challenging to model using previous frameworks. In this work, we propose a new approach using Crossformer, which is a current state-of-the-art Transformer model for time-series prediction tasks, combined with Kolmogorov-Arnold Networks (KANs), to model stiff circuit transient behavior. By leveraging the Crossformer's temporal representation capabilities and the enhanced feature extraction of KANs, our method achieves improved fidelity in predicting circuit responses to a wide range of input conditions. Experimental evaluations on datasets generated through SPICE simulations of analog-to-digital converter (ADC) circuits demonstrate the effectiveness of our approach, with significant reductions in training time and error rates.

Accumulating evidence suggests stochastic cortical circuits can perform sampling-based Bayesian inference to compute the latent stimulus posterior. Canonical cortical circuits consist of excitatory (E) neurons and types of inhibitory (I) in-terneurons. Nevertheless, nearly no sampling neural circuit models consider the diversity of interneurons, and thus how interneurons contribute to sampling remains poorly understood.

The present study investigates how brain's neural circuits search group operators