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We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…

Machine learning methods often need a large amount of labeled training data. Since the training data is assumed to be the ground truth, outliers can severely degrade learned representations and performance of trained models. Here we apply…

We consider a living organism as an observer of the evolution of its environment recording sensory information about the state space X of the environment in real time. Sensory information is sampled and then processed on two levels. On the…

A variational formulation is introduced for the Oseen equations written in terms of vor\-ti\-city and Bernoulli pressure. The velocity is fully decoupled using the momentum balance equation, and it is later recovered by a post-process. A…

Agent memory systems accumulate experience but currently lack a principled operational metric for memory quality governance -- deciding which memories to trust, suppress, or deprecate as the agent's task distribution shifts. Write-time…

We describe Elevator, a unifying polymorphic foundation for metaprogramming with memory management based on adjoint modalities. In this setting, we distinguish between multiple memory regions using modes where each mode has a specific set…

The framework of document spanners abstracts the task of information extraction from text as a function that maps every document (a string) into a relation over the document's spans (intervals identified by their start and end indices). For…

Training Memory-based transformers can require a large amount of memory and can be quite inefficient. We propose a novel two-phase training mechanism and a novel regularization technique to improve the training efficiency of memory-based…

We present two a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators are reliable and efficient for the $h$-, $p$-, and…

We study estimation and inference using data collected by reinforcement learning (RL) algorithms. These algorithms adaptively experiment by interacting with individual units over multiple stages, updating their strategies based on past…

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent $\beta$ of absorbing phase transitions in systems with two symmetric absorbing states. The…

While deep reinforcement learning has shown important empirical success, it tends to learn relatively slow due to slow propagation of rewards information and slow update of parametric neural networks. Non-parametric episodic memory, on the…

Value-based reinforcement-learning algorithms have shown strong results in games, robotics, and other real-world applications. Overestimation bias is a known threat to those algorithms and can sometimes lead to dramatic performance…

The concept of memory is of central importance for characterizing complex systems and phenomena. Presence of long-term memories indicates how their dynamics can be less sensitive to initial conditions compared to the chaotic cases. On the…

Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…

Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al.~PODC 2019; Ghaffari-Uitto SODA 2019),…

Quantization has significantly improved the compute and memory efficiency of Large Language Model (LLM) training. However, existing approaches still rely on accumulating their updates in high-precision: concretely, gradient updates must be…

We propose a randomized multiplicative weight update (MWU) algorithm for $\ell_{\infty}$ regression that runs in $\widetilde{O}\left(n^{2+1/22.5} \text{poly}(1/\epsilon)\right)$ time when $\omega = 2+o(1)$, improving upon the previous best…

Modern multivariate time series forecasting primarily relies on two architectures: the Transformer with attention mechanism and Mamba. In natural language processing, an approach has been used that combines local window attention for…

We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic…