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The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…
Larger language models, such as GPT-3, have shown to be excellent in many tasks. However, we demonstrate that out-of-ordinary questions can throw the model off guard. This work focuses on finding answers to negated complementary questions…
This study presents a novel heuristic algorithm called the "Minimal Positive Negative Product Strategy" to guide the CDCL algorithm in solving the Boolean satisfiability problem. It provides a mathematical explanation for the superiority of…
Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be…
Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output…
Large Language Models (LLMs) have exhibited remarkable performance on various Natural Language Processing (NLP) tasks. However, there is a current hot debate regarding their reasoning capacity. In this paper, we examine the performance of…
Standard knowledge distillation for autoregressive models often suffers from distribution mismatch. While on-policy methods mitigate this by leveraging student-generated outputs, they rely on computationally expensive Reinforcement Learning…
Multi-modal foundation models such as CLIP have showcased impressive zero-shot capabilities. However, their applicability in resource-constrained environments is limited due to their large number of parameters and high inference time. While…
We study the non-linear extension of integer programming with greatest common divisor constraints of the form $\gcd(f,g) \sim d$, where $f$ and $g$ are linear polynomials, $d$ is a positive integer, and $\sim$ is a relation among $\leq, =,…
We propose an efficient way to output better calibrated uncertainty scores from neural networks. The Distilled Dropout Network (DDN) makes standard (non-Bayesian) neural networks more introspective by adding a new training loss which…
Dataset distillation (DD) aims to synthesize a small dataset whose test performance is comparable to a full dataset using the same model. State-of-the-art (SoTA) methods optimize synthetic datasets primarily by matching heuristic indicators…
Given a constraint satisfaction problem (CSP) predicate $P \subseteq D^r$, the non-redundancy (NRD) of $P$ is maximum-sized instance on $n$ variables such that for every clause of the instance, there is an assignment which satisfies all but…
Over the last few months, AI models including large language models have improved greatly. There are now several documented examples where they have helped professional mathematical scientists prove new results, sometimes even helping…
We provide approximation algorithms for two problems, known as NECKLACE SPLITTING and $\epsilon$-CONSENSUS SPLITTING. In the problem $\epsilon$-CONSENSUS SPLITTING, there are $n$ non-atomic probability measures on the interval $[0, 1]$ and…
Active learning algorithms propose which unlabeled objects should be queried for their labels to improve a predictive model the most. We study active learners that minimize generalization bounds and uncover relationships between these…
Dataset distillation is the technique of synthesizing smaller condensed datasets from large original datasets while retaining necessary information to persist the effect. In this paper, we approach the dataset distillation problem from a…
We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and…
Recently, contrastive learning has achieved great results in self-supervised learning, where the main idea is to push two augmentations of an image (positive pairs) closer compared to other random images (negative pairs). We argue that not…
A noisy entropy inequality for boolean functions by Samorodnitsky is applied to binary codes. It is shown that a binary code that achieves capacity on the binary erasure channel admits optimal list size for list decoding on some binary…
As a front-burner problem in incremental learning, class incremental semantic segmentation (CISS) is plagued by catastrophic forgetting and semantic drift. Although recent methods have utilized knowledge distillation to transfer knowledge…