Related papers: Discovering interpretable low-dimensional dynamics…

Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; however, based on the sparsity-of-effect principle one may…

Any coarse-grained description of a nonequilibrium system should faithfully represent its latent irreversible degrees of freedom. However, standard dimensionality reduction methods typically prioritize accurate reconstruction over physical…

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

Snapshot back-ended reduced basis methods for dynamical systems commonly rely on the singular value decomposition of a matrix whose columns are high-fidelity solution vectors. An alternative basis generation framework is developed here. The…

Social scientists are increasingly turning to unstructured datasets to unlock new empirical insights, e.g., estimating descriptive statistics of or causal effects on quantitative measures derived from text, audio, or video data. In many…

In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

The energy paradigm, exemplified by Hopfield networks, offers a principled framework for memory in neural systems by interpreting dynamics as descent on an energy surface. While powerful for static associative memories, it falls short in…

Understanding internal representations of neural models is a core interest of mechanistic interpretability. Due to its large dimensionality, the representation space can encode various aspects about inputs. To what extent are different…

Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…

Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited,…

Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…

A major challenge in the study of dynamical systems is that of model discovery: turning data into models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. This…

Industrial financial systems operate on temporal event sequences such as transactions, user actions, and system logs. While recent research emphasizes representation learning and large language models, production systems continue to rely…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

Recently several deep learning based models have been proposed for end-to-end learning of dialogs. While these models can be trained from data without the need for any additional annotations, it is hard to interpret them. On the other hand,…

This study proposes a novel approach that combines theory and data-driven choice models using Artificial Neural Networks (ANNs). In particular, we use continuous vector representations, called embeddings, for encoding categorical or…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…