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We introduce Diffusion World Model (DWM), a conditional diffusion model capable of predicting multistep future states and rewards concurrently. As opposed to traditional one-step dynamics models, DWM offers long-horizon predictions in a…
There has been much recent, exciting work on combining the complementary strengths of latent variable models and deep learning. Latent variable modeling makes it easy to explicitly specify model constraints through conditional independence…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
We introduce PDNA (Pulse-Driven Neural Architecture), a method for augmenting continuous-time recurrent networks with learnable oscillatory dynamics that maintain internal state evolution independently of external input. Built on…
Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…
The Ott-Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of $N$ globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit $N\to \infty$, evolves, under…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…
Is the standard weight decay in AdamW truly optimal? Although AdamW decouples weight decay from adaptive gradient scaling, a fundamental conflict remains: the Radial Tug-of-War. In deep learning, gradients tend to increase parameter norms…
Learning predictive world models from raw visual observations is a central challenge in reinforcement learning (RL), especially for robotics and continuous control. Conventional model-based RL frameworks directly condition future…
Purpose: This study aims to address the challenges of controlling unstable and nonlinear systems by proposing an adaptive PID controller based on predictive reinforcement learning (PRL-PID), where the PRL-PID combines the advantages of both…
A review of recent developments of the dispersive optical model (DOM) is presented. Starting from the original work of Mahaux and Sartor, several necessary steps are developed and illustrated which increase the scope of the DOM allowing its…
The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which…
We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can…
A recent line of work has shown remarkable behaviors of the generalization error curves in simple learning models. Even the least-squares regression has shown atypical features such as the model-wise double descent, and further works have…
Recently, self-supervised contrastive learning has achieved great success on various tasks. However, its underlying working mechanism is yet unclear. In this paper, we first provide the tightest bounds based on the widely adopted assumption…
In this paper, we introduce a novel architecture to connecting adaptive learning and neural networks into an arbitrary machine's control system paradigm. Two consecutive Recurrent Neural Networks (RNNs) are used together to accurately model…
The relation between neural activity and behaviorally relevant variables is at the heart of neuroscience research. When strong, this relation is termed a neural representation. There is increasing evidence, however, for partial…
We consider the problem of learning a control policy that is robust against the parameter mismatches between the training environment and testing environment. We formulate this as a distributionally robust reinforcement learning (DR-RL)…
Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we…
In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…