533 citations · 605 across the 21 of their papers we have counts for
21 papers
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…
The 2026 Singapore Consensus on Global AI Safety Research Priorities
Stephen Casper, Oskar Galeev, Yoshua Bengio +117
Frontier AI capabilities and autonomy are advancing rapidly. A growing number of real-world incidents make a trusted AI ecosystem essential to embracing AI with confidence. The 202…
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…
Symbolic Learning of Topological Bands in Photonic Crystals
Ali Ghorashi, Sachin Vaidya, Ziming Liu +4
Topological photonic crystals (PhCs) that support disorder-resistant modes, protected degeneracies, and robust transport have recently been explored for applications in waveguiding…
Do Two AI Scientists Agree?
Xinghong Fu, Ziming Liu, Max Tegmark
When two AI models are trained on the same scientific task, do they learn the same theory or two different theories? Throughout history of science, we have witnessed the rise and f…
Language Models Use Trigonometry to Do Addition
Subhash Kantamneni, Max Tegmark
Mathematical reasoning is an increasingly important indicator of large language model (LLM) capabilities, yet we lack understanding of how LLMs process even simple mathematical tas…
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…
Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems
David "davidad" Dalrymple, Joar Skalse, Yoshua Bengio +14
Ensuring that AI systems reliably and robustly avoid harmful or dangerous behaviours is a crucial challenge, especially for AI systems with a high degree of autonomy and general in…
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…
Growing Brains: Co-emergence of Anatomical and Functional Modularity in Recurrent Neural Networks
Ziming Liu, Mikail Khona, Ila R. Fiete +1
Recurrent neural networks (RNNs) trained on compositional tasks can exhibit functional modularity, in which neurons can be clustered by activity similarity and participation in sha…
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…