Serial dependence reflects how recent sensory history shapes current perception, producing two opposing biases: repulsion, where perception is repelled from recent stimuli, and attraction, where perception is drawn toward them. Repulsion typically occurs at the sensory perception stage, while attraction arises at the post-perception stage. To uncover the neural basis of these effects, we developed a two-layer continuous attractor neural network model incorporating synaptic short-term plasticity (STP). The lower layer, dominated by synaptic depression, models sensory processing and drives repulsion due to sustained neurotransmitter depletion. The higher layer, dominated by synaptic facilitation, models post-perception processing and drives attraction by sustained high neurotransmitter release probability. Our model successfully explains the serial dependence phenomena observed in the visual orientation judgment experiments, highlighting STP as the critical mechanism, with its time constants defining the temporal windows of repulsion and attraction. Furthermore, the model provides a neural foundation for the Bayesian interpretation of serial dependence. This study advances our understanding of how the neural system leverages STP to balance sensitivity in sensory perception with stability in post-perceptual cognition.

Out-of-distribution (OOD) problems commonly occur when models process data with a distribution significantly deviates from the in-distribution (InD) training data. In this paper, we hypothesize that a field or potential more essential than features exists, and features are not the ultimate essence of the data but rather manifestations of them during training. With this in mind, we first treat the output of the feature extractor as charged particles and investigate their collective behavior dynamics within a self-consistent electric field. Then, to characterize the relationship between OOD problems and dynamical equations, we introduce the basin of attraction and prove that its boundary can be represented as the zero level set of a differentiable function of the potential, i.e., the spatial integral of field. We further demonstrate that: i) InD and OOD inputs can be effectively separated based on whether they are steady state solutions for specific field conditions, enabling robust OOD detection and outperforming prior methods over three benchmarks.

Serial dependence reflects how recent sensory history shapes current perception, producing two opposing biases: repulsion, where perception is repelled from recent stimuli, and attraction, where perception is drawn toward them. Repulsion typically occurs at the sensory perception stage, while attraction arises at the post-perception stage. To uncover the neural basis of these effects, we developed a two-layer continuous attractor neural network model incorporating synaptic short-term plasticity (STP). The lower layer, dominated by synaptic depression, models sensory processing and drives repulsion due to sustained neurotransmitter depletion. The higher layer, dominated by synaptic facilitation, models post-perception processing and drives attraction by sustained high neurotransmitter release probability. Our model successfully explains the serial dependence phenomena observed in the visual orientation judgment experiments, highlighting STP as the critical mechanism, with its time constants defining the temporal windows of repulsion and attraction. Furthermore, the model provides a neural foundation for the Bayesian interpretation of serial dependence. This study advances our understanding of how the neural system leverages STP to balance sensitivity in sensory perception with stability in post-perceptual cognition.

Out-of-distribution (OOD) problems commonly occur when models process data with a distribution significantly deviates from the in-distribution (InD) training data. In this paper, we hypothesize that a $\textit{field}$ or $\textit{potential}$ more essential than features exists, and features are not the ultimate essence of the data but rather manifestations of them during training.

Learning-based neural network (NN) control policies have shown impressive empirical performance. However, obtaining stability guarantees and estimates of the region of attraction of these learned neural controllers is challenging due to the lack of stable and scalable training and verification algorithms. Although previous works in this area have achieved great success, much conservatism remains in their frameworks. In this work, we propose a novel two-stage training framework to jointly synthesize a controller and a Lyapunov function for continuous-time systems. By leveraging a Zubov inspired region of attraction characterization to directly estimate stability boundaries, we propose a novel training-data sampling strategy and a domain-updating mechanism that significantly reduces the conservatism in training. Moreover, unlike existing works on continuous-time systems that rely on an SMT solver to formally verify the Lyapunov condition, we extend state-of-the-art neural network verifier $\alpha,\beta$-CROWN with the capability of performing automatic bound propagation through the Jacobian of dynamical systems and a novel verification scheme that avoids expensive bisection. To demonstrate the effectiveness of our approach, we conduct numerical experiments by synthesizing and verifying controllers on several challenging nonlinear systems across multiple dimensions. We show that our training can yield region of attractions with volume $5 - 1.5\cdot 10^{5}$ times larger compared to the baselines, and our verification on continuous systems can be up to $40-10{,}000$ times faster compared to the traditional SMT solver dReal.

While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy. However, finding Lyapunov functions for general nonlinear systems is a challenging task. To address this challenge, several methods have been proposed that represent Lyapunov functions using neural networks. However, such approaches either focus on continuous-time systems, or highly restricted classes of nonlinear dynamics.

Nico (right) and Matteo Mucchetti pose with their homemade dark ride vehicle. We may earn revenue from the products available on this page and participate in affiliate programs. When 12-year-old Matteo Mucchetti mapped out an amusement-style attraction that he wanted to create in his family's basement and then showed it to his older brother Nico, the high-school sophomore was immediately sold. "This is amazing," said Nico. "Let's make it!" Matteo had sketched on paper a top-down view of the multi-room space in Bear, Delaware, where they live.

If the memory state can be addressed by its content, itisfurthermore called content-addressable.