533 citations · 605 across the 21 of their papers we have counts for
15 papers · 1 filter
Variational Continuation for Double Pendulum Periodic Orbits
Leo Yao, Ziming Liu, Max Tegmark
We present a Hessian-based approach to numerically continue periodic orbits in dynamical systems. A loop (periodic orbit candidate) is parametrized as a Fourier series; a loss func…
Neural Thermodynamic Laws for Large Language Model Training
Ziming Liu, Yizhou Liu, Jeff Gore +1
Beyond neural scaling laws, little is known about the laws underlying large language models (LLMs). We introduce Neural Thermodynamic Laws (NTL) -- a new framework that offers fres…
Harmonic Loss Trains Interpretable AI Models
David D. Baek, Ziming Liu, Riya Tyagi +1
In this paper, we introduce harmonic loss as an alternative supervisory signal for training neural networks and large language models (LLMs). Harmonic loss differs from standard cr…
Physics of Skill Learning
Ziming Liu, Yizhou Liu, Eric J. Michaud +2
We aim to understand physics of skill learning, i.e., how skills are learned in neural networks during training. We start by observing the Domino effect, i.e., skills are learned s…
KAN 2.0: Kolmogorov-Arnold Networks Meet Science
Ziming Liu, Pingchuan Ma, Yixuan Wang +2
A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worl…
Survival of the Fittest Representation: A Case Study with Modular Addition
Xiaoman Delores Ding, Zifan Carl Guo, Eric J. Michaud +2
When a neural network can learn multiple distinct algorithms to solve a task, how does it "choose" between them during training? To approach this question, we take inspiration from…
How Do Transformers "Do" Physics? Investigating the Simple Harmonic Oscillator
Subhash Kantamneni, Ziming Liu, Max Tegmark
How do transformers model physics? Do transformers model systems with interpretable analytical solutions, or do they create "alien physics" that are difficult for humans to deciphe…
OptPDE: Discovering Novel Integrable Systems via AI-Human Collaboration
Subhash Kantamneni, Ziming Liu, Max Tegmark
Integrable partial differential equation (PDE) systems are of great interest in natural science, but are exceedingly rare and difficult to discover. To solve this, we introduce Opt…
KAN: Kolmogorov-Arnold Networks
Ziming Liu, Yixuan Wang, Sachin Vaidya +5
Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have…
Opening the AI black box: program synthesis via mechanistic interpretability
Eric J. Michaud, Isaac Liao, Vedang Lad +7
We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the le…
GenEFT: Understanding Statics and Dynamics of Model Generalization via Effective Theory
David D. Baek, Ziming Liu, Max Tegmark
We present GenEFT: an effective theory framework for shedding light on the statics and dynamics of neural network generalization, and illustrate it with graph learning examples. We…
A Resource Model For Neural Scaling Law
Jinyeop Song, Ziming Liu, Max Tegmark +1
Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A…
Generating Interpretable Networks using Hypernetworks
Isaac Liao, Ziming Liu, Max Tegmark
An essential goal in mechanistic interpretability to decode a network, i.e., to convert a neural network's raw weights to an interpretable algorithm. Given the difficulty of the de…
Grokking as Compression: A Nonlinear Complexity Perspective
Ziming Liu, Ziqian Zhong, Max Tegmark
We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network co…
A Neural Scaling Law from Lottery Ticket Ensembling
Ziming Liu, Max Tegmark
Neural scaling laws (NSL) refer to the phenomenon where model performance improves with scale. Sharma & Kaplan analyzed NSL using approximation theory and predict that MSE losses d…