Related papers: Implementations of two Algorithms for the Threshol…

Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…

Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware)…

Parameter estimation is a fundamental problem in science and engineering. In many safety-critical applications, one is not only interested in a {\it point} estimator, but also the uncertainty bound that can self-assess the accuracy of the…

How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic…

This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…

Bayesian synthetic likelihood (BSL) is now a well established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable…

We formalize the problem of prompt compression for large language models (LLMs) and present a framework to unify token-level prompt compression methods which create hard prompts for black-box models. We derive the distortion-rate function…

In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically…

In this report, we describe three encodings of the multiple constant multiplication (MCM) problem to pseudo-boolean satisfiability (PBS), and introduce an algorithm to solve the MCM problem optimally. To the best of our knowledge, the…

A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…

We explore and formalize the task of synthesizing programs over noisy data, i.e., data that may contain corrupted input-output examples. By formalizing the concept of a Noise Source, an Input Source, and a prior distribution over programs,…

Program synthesis is the task of automatically generating a program consistent with a specification. Recent years have seen proposal of a number of neural approaches for program synthesis, many of which adopt a sequence generation paradigm…

Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…

Partial Multi-label Learning (PML) is a type of weakly supervised learning where each training instance corresponds to a set of candidate labels, among which only some are true. In this paper, we introduce \our{}, a novel probabilistic…

Adapting pretrained large language models (LLMs) to code domains via supervised fine-tuning (FT) has been commonly used for code generation. However, we identify a previously underappreciated failure mode, the memorization barrier, where…

Progress in the field of machine learning has been fueled by the introduction of benchmark datasets pushing the limits of existing algorithms. Enabling the design of datasets to test specific properties and failure modes of learning…

This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system…

We introduce transductive program synthesis, a new formulation of the program synthesis task that explicitly leverages test inputs during synthesis. While prior approaches to program synthesis--whether based on natural language descriptions…

One of the central themes in Sum-Product networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs). This interpretation yields an increased syntactic or semantic structure, allows the application of the EM…

This paper considers program synthesis in the context of computational hardness, asking the question: How hard is it to determine whether a given synthesis problem has a solution or not? To answer this question, this paper studies program…