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The memory model for RISC-V, a newly developed open source ISA, has not been finalized yet and thus, offers an opportunity to evaluate existing memory models. We believe RISC-V should not adopt the memory models of POWER or ARM, because…

Traditional memory writing operations proceed one bit at a time, where e.g. an individual magnetic domain is force-flipped by a localized external field. One way to increase material storage capacity would be to write several bits at a time…

The exponential moving average (EMA) is a commonly used statistic for providing stable estimates of stochastic quantities in deep learning optimization. Recently, EMA has seen considerable use in generative models, where it is computed with…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…

Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its…

Deep neural networks have excelled on a wide range of problems, from vision to language and game playing. Neural networks very gradually incorporate information into weights as they process data, requiring very low learning rates. If the…

We characterize how memorization is represented in transformer models and show that it can be disentangled in the weights of both language models (LMs) and vision transformers (ViTs) using a decomposition based on the loss landscape…

Large language model agents increasingly depend on memory to sustain long horizon interaction, but existing frameworks remain limited. Most expose only a few basic primitives such as encode, retrieve, and delete, while higher order…

We consider the model equation arising in the theory of viscoelasticity $$\partial_{tt} u-h_t(0)\Delta u -\int_{0}^\infty h_t'(s)\Delta u(t-s)d s+ f(u) = g.$$ Here, the main feature is that the memory kernel $h_t(\cdot)$ depends on time,…

We study episodic reinforcement learning in non-stationary linear (a.k.a. low-rank) Markov Decision Processes (MDPs), i.e, both the reward and transition kernel are linear with respect to a given feature map and are allowed to evolve either…

This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown…

Hierarchical Vision-Language-Action (VLA) models have rapidly become a dominant paradigm for robotic manipulation. It typically comprising a Vision-Language backbone for perception and understanding, together with a generative policy for…

Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve…

The Multiplicative Weights Exponential Mechanism (MWEM) is a fundamental iterative framework for private data analysis, with broad applications such as answering $m$ linear queries, or privately solving systems of $m$ linear constraints.…

Let $\alpha,\beta$ be orientation-preserving diffeomorphism (shifts) of $\mathbb{R}_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$ and $U_\alpha,U_\beta$ be the isometric shift operators on $L^p(\mathbb{R}_+)$ given…

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…

A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via…

Foundation models are transitioning from offline predictors to deployed systems expected to operate over long time horizons. In real deployments, objectives are not fixed: domains drift, user preferences evolve, and new tasks appear after…

Accelerators with power-law memory are proposed in the framework of the discrete time approach. To describe discrete accelerators we use the capital stock adjustment principle, which has been suggested by Matthews.The suggested discrete…