gautam6599123's Feed

Numerical Integration at the Intersection of Probability Theory, Number Theory and Dynamical Systems

This paper is devoted to the study of uniformly distributed (u.d.) sequences on general non-compact topological spaces. Convergence-determining classes and the equivalent characterizations of u.d. sequences on $T_4$ spaces are discussed. For Polish spaces endowed with regular probability measures, the existence of a countable convergence-determining class for u.d. sequences is proved by virtue of the tightness of Borel probability measures. It... Read more ›

📊Optimization arxiv.org·

A Link between Shock-wave Theory and Symmetry-reduced Stochastic Gradient Descent for Artificial Neural Networks

We develop a mathematically explicit link between shock-wave theory and the symmetry-quotiented learning dynamics of stochastic gradient descent, drawing on differential geometry, Lie group theory, and fluid mechanics. Specifically, after quotienting parameter symmetries and applying local-entropy coarse-graining, the effective dynamics satisfy a viscous Hamilton--Jacobi equation on the quotient manifold. Moreover, under the assumption that the ... Read more ›

🎮Reinforcement Learning lesswrong.com·

Reinforcement learning towards broadly and persistently beneficial models

This is an unofficial We find that reinforcement learning on realistic scenarios targeting beneficial traits can produce broad improvements across dozens of benchmarks measuring aligned and beneficial behavior. These alignment gains generalize beyond the domains used for training and persist under adversarial pressure. As AI systems become more capable and autonomous in high-stakes settings like health, science, education, and coding, they will need to remain helpful, honest, transparent, and... Read more ›

Covers Reinforcement learning towards broadly and persistently beneficial models

📊Data Science GitHub·

Data Visualization from the Comfort of Your Terminal

The CSV magician. Contribute to medialab/xan development by creating an account on GitHub. Read more ›

Covers Zipf's Law

Discussed on Hacker News and Lobsters

🕸️Graph Theory arxiv.org·

Graph Instance Landscapes: When Structural Similarity Does (Not) Reflect Shortest-Path Performance

Benchmarking shortest-path algorithms is commonly based on aggregate performance over heterogeneous graph sets, which limits insight into how different search paradigms react to instance structure. We adopt an instance-landscape view of graph benchmarking by embedding graphs into a low-cost structural feature space and clustering them into regions of similar structure. Three benchmark suites are studied: weighted Erd\H{o}s--R\'enyi graphs, rando... Read more ›

📐Linear Algebra GitHub·

RunEdgeAI/turboquant.cpp: Near-optimal online vector quantization in C++23 — 1-4 bits per coordinate, no training, no codebooks

Near-optimal online vector quantization in C++23 — 1-4 bits per coordinate, no training, no codebooks - RunEdgeAI/turboquant.cpp Read more ›

Covers TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate

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🔢Mathematics Simons Foundation·

Solved, Unsolved and Unsolvable: The Status of Hilbert’s 23 Problems in Mathematics

More than a century after David Hilbert presented a list of 23 mathematical challenges to the 1900 ICM, mathematicians have made significant progress, but there’s still much work to do. Read more ›

Discussed on Hacker News

🗣️Large Language Models MIT Technology Review·

A startup claims it broke through a bottleneck that's holding back LLMs

Subquadratic has now shared more details about its new model. But some are still skeptical. Read more ›

Covers Attention is all you need (2017)

Covered by Techrights, Singularity Hub

Discussed on Hacker News

🌐Distributed Systems hackernoon.com·

Let AI Models Fight Over Your Architecture

Asking a single AI to design your system is a mistake. Single prompts yield generic, happy-path answers. Instead, developers should build multi-agent workflows where specialized AIs—like an Architect, Red-Team, and Evaluator, actively debate the architecture. By forcing LLMs to propose, critique, and score tradeoffs against simpler baselines, you avoid brittle chatbot responses. The result is an automated architecture review board that outputs production-ready Decision Records. Read more ›

🔢Discrete Mathematics arxiv.org·

Structural Lemmas on Temporal Connectivity

This paper presents several lemmas on the structure of temporal connectivity in temporal graphs. Some of these lemmas are adapted from the literature on gossip from the 70-90's and reformulated in the context of temporal graph theory. Many others are original. For ease of presentation and for avoiding lengthy case distinctions, we formulate all the lemmas in the setting of simple and proper (a.k.a, happy) temporal graphs, discussing occasionally... Read more ›

🔢Numerical Methods arxiv.org·

A uniform-in-time weakly convergent explicit numerical method for the underdamped Langevin equation with polynomial potentials

The underdamped Langevin equation is a fundamental model in statistical mechanics for sampling Gibbs measures and simulating molecular dynamics, for which numerical methods with uniform-in-time weak convergence are essential for accurately reproducing long-time statistical observables and invariant measures of the underlying dynamics. Currently, such uniform-in-time weak convergence is established for implicit schemes, but remains unknown for ex... Read more ›

🧠Deep Learning GitHub·

GPU Puzzles (2021)

Solve puzzles. Learn CUDA. Contribute to srush/GPU-Puzzles development by creating an account on GitHub. Read more ›

Discussed on Hacker News

🐍Python GitHub·

My symbolic regression engine rediscovered Kepler's Third Law from raw data

Régression symbolique par programmation génétique — lois interprétables en pur Python - ariel95500-create/gp-elite Read more ›

Discussed on Hacker News

💻Computer Science Hacker News·

Show HN: Memento – Self-hosted agentic search and LLM wiki over your email

Our email inboxes carry multiple decades of messages (100K-500K). This is a good proxy for all the important things that happened in your life, the projects you have done and the people that you have connected with. With the chronological view of messages in the inbox, these details remain hidden. What if we could turn this archive into a personal wiki that you can search and curate? That is Memento. Read more ›

Discussed on Hacker News

🎲Probability Theory arxiv.org·

A Computational Audit of Demographic Association Encoding in ClinicalBERT Language Predictions

Transformer-based clinical language models are increasingly integrated into high-stakes clinical decision support pipelines, yet the computational mechanisms through which demographic associations encoded in medical documentation propagate into model probability distributions remain empirically underspecified. We present a systematic computational audit of representational bias in ClinicalBERT (Alsentzer et al., 2019), a BERT-based model pretrai... Read more ›

🤖AI huggingface.co·

NovaVest/VN-Noxa-v1-7B-Beta-Low

We’re on a journey to advance and democratize artificial intelligence through open source and open science. Read more ›

Discussed on Hacker News

📈Statistical Learning arxiv.org·

Scalable Malware Family Classification Using Quantum Kernel Based Machine Learning

The classification of malware families is a key challenge in cybersecurity, which enables threat attribution, analysis of attack operations, and the formulation of effective defense strategies. Emerging malware samples are becoming increasingly structurally similar and obfuscated, making accurate multiclass classification challenging for traditional machine learning models, especially when deployed at scale. In this research, we propose a scalab... Read more ›

🔷Abstract Algebra arxiv.org·

Structural Preservation and the Logical Expressiveness of Graph Neural Networks

Bridges between graph neural networks (GNNs) and logical formalisms have been established by fixing architectural choices, such as the types of aggregation, combination, and activation functions. These choices define restricted classes of GNNs for which tight correspondences with logical formalisms can be obtained, by showing that logical formulae can be translated into equivalent GNNs and, conversely, that GNNs can be translated into equivalent... Read more ›

📊Optimization arxiv.org·

An Adaptive Algorithm for the Approximation of General Linear-Parametric Optimization Problems

Linear-multi-parametric optimization problems are a widely studied class of optimization problems. The objective function in such a problem is affine linear dependent on a parameter vector, and the goal is to compute a set of solutions that contains an optimal solution for every fixed parameter vector. However, this is known to be computationally challenging: The underlying non-parametric problem might be NP-hard, and, in addition, optimal sol... Read more ›

🗣️Large Language Models lector.dev·

Show HN: Evaluating Local LLMs as language translators for my app

How good are local LLMs at translation, and do you actually need the cloud? A reproducible benchmark of 24 on-device, self-hosted, and cloud models translating into English, with the low-resource case (Afrikaans) front and centre. The headline: on Afrikaans→English a local 18 GB model lands in a statistical tie with frontier cloud. Same blinded Tatoeba sentences, same prompt, greedy decoding, scored multi-reference with COMET (meaning) and chrF++ (surface). Built to pick a translation model f... Read more ›

Discussed on Hacker News