Related papers: Deep Hankel matrices with random elements
In this paper, we consider data-driven reconstruction of unknown inputs to linear time-invariant (LTI) multiple-input multiple-output (MIMO) systems. We propose a novel autoregressive estimator based on a constrained least-squares…
Recent work on recursive architectures has shown that tiny neural networks can be surprisingly powerful on structured reasoning tasks. The trick is to model reasoning trajectories with a latent dynamical system. We argue that the…
Fine-tuning LLMs for classification typically maps inputs directly to labels. We ask whether attaching brief explanations to each label during fine-tuning yields better models. We evaluate conversational response quality along three axes:…
Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…
We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…
Recently deep neural networks have been successfully used for various classification tasks, especially for problems with massive perfectly labeled training data. However, it is often costly to have large-scale credible labels in real-world…
We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…
This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…
We propose a simulation framework for generating instance-dependent noisy labels via a pseudo-labeling paradigm. We show that the distribution of the synthetic noisy labels generated with our framework is closer to human labels compared to…
Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…
We study the problem of recovering the latent ground truth labeling of a structured instance with categorical random variables in the presence of noisy observations. We present a new approximate algorithm for graphs with categorical…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we introduce…
Recommender systems often grapple with noisy implicit feedback. Most studies alleviate the noise issues from data cleaning perspective such as data resampling and reweighting, but they are constrained by heuristic assumptions. Another…
Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
Test-time compute has emerged as a powerful paradigm for improving the performance of large language models (LLMs), where generating multiple outputs or refining individual chains can significantly boost answer accuracy. However, existing…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
Sequence models, and particularly Linear Recurrent Neural Networks (LRNNs) of the form $\mathbf{h}_{k+1} = \mathbf{W} \mathbf{h}_{k} + \mathbf{y}_k + \mathbf{b}$, are widely applicable in time-series analysis for dynamical systems, yet, as…
This note addresses the question if and why the nuclear norm heuristic can recover an impulse response generated by a stable single-real-pole system, if elements of the upper-triangle of the associated Hankel matrix were given. Since the…