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We introduce sparse autoencoder neural operators (SAE-NOs), a new class of sparse autoencoders that operate in function spaces rather than fixed-dimensional Euclidean representations. We formalize the functional representation hypothesis,…

Machine Learning · Computer Science 2026-05-11 Bahareh Tolooshams , Ailsa Shen , Anima Anandkumar

Sparse autoencoders (SAEs) have become a standard tool for mechanistic interpretability in autoregressive large language models (LLMs), enabling researchers to extract sparse, human-interpretable features and intervene on model behavior.…

Machine Learning · Computer Science 2026-02-06 Xu Wang , Bingqing Jiang , Yu Wan , Baosong Yang , Lingpeng Kong , Difan Zou

Deep learning has been extended to a number of new domains with critical success, though some traditional orienteering problems such as the Travelling Salesman Problem (TSP) and its variants are not commonly solved using such techniques.…

Machine Learning · Computer Science 2019-03-11 Wei Shao , Flora D. Salim , Jeffrey Chan , Sean Morrison , Fabio Zambetta

Understanding the internal representations of large language models (LLMs) remains a central challenge for interpretability research. Sparse autoencoders (SAEs) offer a promising solution by decomposing activations into interpretable…

Machine Learning · Computer Science 2025-10-10 Yifei Yao , Mengnan Du

As AI models achieve remarkable capabilities across diverse domains, understanding what representations they learn and how they encode concepts has become increasingly important for both scientific progress and trustworthy deployment.…

Machine Learning · Computer Science 2026-05-05 Yiming Tang , Harshvardhan Saini , Zhaoqian Yao , Zheng Lin , Yizhen Liao , Jingyi Cui , Yisen Wang , Mengnan Du , Dianbo Liu

Deep neural networks have demonstrated remarkable performance across various domains, yet their decision-making processes remain opaque. Although many explanation methods are dedicated to bringing the obscurity of DNNs to light, they…

Computer Vision and Pattern Recognition · Computer Science 2025-12-17 Kanglong Fan , Yunqiao Yang , Chen Ma

Mechanistic interpretability seeks to reverse engineer a trained neural network by identifying the minimal subset of internal components. We perform a mechanistic interpretability analysis of the Particle Transformer architecture, trained…

High Energy Physics - Phenomenology · Physics 2026-05-12 Saurabh Rai , Sanmay Ganguly

Sum-Product Networks (SPNs) are recently introduced deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. Up to now, they have been largely used as black box density…

Machine Learning · Computer Science 2018-08-27 Antonio Vergari , Nicola Di Mauro , Floriana Esposito

We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says…

Data Structures and Algorithms · Computer Science 2011-07-07 Sylvia Boyd , René Sitters , Suzanne van der Ster , Leen Stougie

TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…

Data Structures and Algorithms · Computer Science 2019-11-12 Yang Li , Junbin Gao , Mingyuan Bai , Chengjun Li , Gang Liu

The traveling salesman (or salesperson) problem, short TSP, is a problem of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application…

Data Structures and Algorithms · Computer Science 2025-11-10 Sophia Saller , Jana Koehler , Andreas Karrenbauer

In the Traveling Salesman Problem (TSP), a list of cities and the distances between them are given. The goal is to find the shortest possible route that visits each city exactly once and returns to the original city. The TSP has a wide…

Optimization and Control · Mathematics 2019-06-17 Johnny Seay , Edwin Gonzalez , Stephen Lowe , Jesse Crawford , Bryant Wyatt

The travelling salesman problem (TSP) is one of the well-studied NP-hard problems in the literature. The state-of-the art inexact TSP solvers are the Lin-Kernighan-Helsgaun (LKH) heuristic and Edge Assembly crossover (EAX). A recent study…

Artificial Intelligence · Computer Science 2023-09-14 Swetha Varadarajan , Darrell Whitley

The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc. Although the…

Computational Complexity · Computer Science 2021-02-26 Omar Cheikhrouhou , Ines Khoufi

Sparse Autoencoders (SAEs) have shown promise in improving the interpretability of neural network activations, but can learn features that are not features of the input, limiting their effectiveness. We propose \textsc{Mutual Feature…

Machine Learning · Computer Science 2024-11-07 Luke Marks , Alasdair Paren , David Krueger , Fazl Barez

Sparse autoencoders (SAEs) have shown promise in extracting interpretable features from complex neural networks. We present one of the first applications of SAEs to dense text embeddings from large language models, demonstrating their…

Machine Learning · Computer Science 2024-08-06 Charles O'Neill , Christine Ye , Kartheik Iyer , John F. Wu

In data-driven applications relying on tabular data, where interpretability is key, machine learning models such as decision trees and linear regression are applied. Although neural networks can provide higher predictive performance, they…

Machine Learning · Computer Science 2026-03-30 Khawla Elhadri , Jörg Schlötterer , Christin Seifert

Mechanistic interpretability aims to reverse engineer neural networks by uncovering which high-level algorithms they implement. Causal abstraction provides a precise notion of when a network implements an algorithm, i.e., a causal model of…

Machine Learning · Computer Science 2025-03-17 Theodora-Mara Pîslar , Sara Magliacane , Atticus Geiger

The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the…

Robotics · Computer Science 2026-03-24 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

To tackle interpretability in deep learning, we present a novel framework to jointly learn a predictive model and its associated interpretation model. The interpreter provides both local and global interpretability about the predictive…

Machine Learning · Computer Science 2022-02-24 Jayneel Parekh , Pavlo Mozharovskyi , Florence d'Alché-Buc