Related papers: Note: On the memory kernel and the reduced system …

Transformer-based models show their effectiveness across multiple domains and tasks. The self-attention allows to combine information from all sequence elements into context-aware representations. However, global and local information has…

We derive the divergence-kernel formula for the scores of random dynamical systems, then formally pass to the continuous-time limit of SDEs. Our formula works for multiplicative noise systems over any period of time; it does not require…

Memory-(in)efficiency is a crucial consideration that oftentimes prevents deployment of state-of-the-art distributed algorithms in real-life modern networks. In the context of the MST problem, roughly speaking, there are three types of…

Reservoir computing is a promising neuromorphic paradigm, and its quantum implementation using spin networks has shown some advantage when entanglement is present. Here, we consider a distributed scenario in which two distinct input time…

A new collective behavior of resonant synchronization is discovered and the ability to retrieve information from brain memory is proposed based on this mechanism. We use modified Kuramoto phase oscillator to simulate the dynamics of a…

Selecting optimal kernels for regression in physical systems remains a challenge, often relying on trial-and-error with standard functions. In this work, we establish a mathematical correspondence between support vector machine kernels and…

Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques…

In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert…

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…

In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions…

Memory systems often organize user-agent interactions as retrievable external memory and are crucial for long-running agents by overcoming the limited context windows of LLMs. However, existing memory systems invoke LLMs to process every…

We present a generalized Einstein relation for the friction coefficients associated with an underlying memory kernel in terms of observable time correlation functions. There is considerable freedom in the correlations involved, and this…

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

We introduce an incremental processing scheme for convolutional neural network (CNN) inference, targeted at embedded applications with limited memory budgets. Instead of processing layers one by one, individual input pixels are propagated…

Transformers suffer from a high computational cost that grows with sequence length for self-attention, making inference in long streams prohibited by memory consumption. Constant-memory alternatives such as RNNs and SSMs compress history…

Quantum repeaters, which are indispensable for long-distance quantum communication, are necessary for extending the entanglement from short distance to long distance; however, high-rate entanglement distribution, even between adjacent…

A semilinear parabolic problem of second order with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is…

While Transformer-based neural machine translation (NMT) is very effective in high-resource settings, many languages lack the necessary large parallel corpora to benefit from it. In the context of low-resource (LR) MT between two…

Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…

In the last decade, Convolutional Neural Network with a multi-layer architecture has advanced rapidly. However, training its complex network is very space-consuming, since a lot of intermediate data are preserved across layers, especially…