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We study the Weighted Min Cut problem in the Adaptive Massively Parallel Computation (AMPC) model. In 2019, Behnezhad et al. [3] introduced the AMPC model as an extension of the Massively Parallel Computation (MPC) model. In the past…

Nonlinear model predictive control (NMPC) is typically restricted to short, finite horizons to limit the computational burden of online optimization. As a result, global planning frameworks are frequently necessary to avoid local minima…

We derive the calculation of two critical numbers predicting the behavior of perceptron networks. First, we derive the calculation of what we call the lossless memory (LM) dimension. The LM dimension is a generalization of the…

Decision-making under uncertainty is a crucial ability for autonomous systems. In its most general form, this problem can be formulated as a Partially Observable Markov Decision Process (POMDP). The solution policy of a POMDP can be…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

We propose a novel information bottleneck (IB) method named Drop-Bottleneck, which discretely drops features that are irrelevant to the target variable. Drop-Bottleneck not only enjoys a simple and tractable compression objective but also…

Scaling large language models typically involves three dimensions: depth, width, and parameter count. In this work, we explore a fourth dimension, \textbf{virtual logical depth} (VLD), which increases effective algorithmic depth without…

Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…

Reinforcement learning in partially observed Markov decision processes (POMDPs) faces two challenges. (i) It often takes the full history to predict the future, which induces a sample complexity that scales exponentially with the horizon.…

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of $K$-sparse degree-$d$ PTFs on $\mathbb{R}^n$, where any such concept depends only on…

Concept-bottleneck models (CBMs) are neural classifiers that compute predictions from high-level concepts extracted from the input. CBMs ensure stakeholders can understand the concepts -- and the predictions they entail -- by learning these…

Deep learning can accurately represent sub-grid-scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality,…

Instance-based learning techniques typically handle continuous and linear input values well, but often do not handle nominal input attributes appropriately. The Value Difference Metric (VDM) was designed to find reasonable distance values…

Model counting of Disjunctive Normal Form (DNF) formulas is a critical problem in applications such as probabilistic inference and network reliability. For example, it is often used for query evaluation in probabilistic databases. Due to…

Bounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such "VC dimensions" exist for models taking…

A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008].…

Practical and pervasive needs for robustness and privacy in algorithms have inspired the design of online adversarial and differentially private learning algorithms. The primary quantity that characterizes learnability in these settings is…

Clustering algorithms have significantly improved along with Deep Neural Networks which provide effective representation of data. Existing methods are built upon deep autoencoder and self-training process that leverages the distribution of…

Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus…

Open-ended grading is central to equitable and personalized education, yet manual grading remains time-consuming and costly, underscoring the need for automated grading systems. Although recent neural and large language model (LLM) based…