Bernhard Schölkopf

Florent Draye, Abir Harrasse, Vedant Palit et al. · utoronto

Mechanistic interpretability seeks to understand how Large Language Models (LLMs) represent and process information. Recent approaches based on dictionary learning and transcoders enable representing model computation in terms of sparse, interpretable features and their interactions, giving rise to feature attribution graphs. However, these graphs are often large and redundant, limiting their interpretability in practice. Cross-Layer Transcoders (CLTs) address this issue by sharing features across layers while preserving layer-specific decoding, yielding more compact representations, but remain difficult to train and analyze at scale. We introduce an open-source library for end-to-end training and interpretability of CLTs. Our framework integrates scalable distributed training with model sharding and compressed activation caching, a unified automated interpretability pipeline for feature analysis and explanation, attribution graph computation using Circuit-Tracer, and a flexible visualization interface. This provides a practical and unified solution for scaling CLT-based mechanistic interpretability. Our code is available at: https://github.com/LLM-Interp/CLT-Forge.

Sirui Lu, Zhijing Jin, Terry Jingchen Zhang et al.

Large Language Models (LLMs) are rapidly advancing across diverse domains, yet their application in theoretical physics remains inadequate. While current models show competence in mathematical reasoning and code generation, we identify critical gaps in physical intuition, constraint satisfaction, and reliable reasoning that cannot be addressed through prompting alone. Physics demands approximation judgment, symmetry exploitation, and physical grounding that require AI agents specifically trained on physics reasoning patterns and equipped with physics-aware verification tools. We argue that LLM would require such domain-specialized training and tooling to be useful in real-world for physics research. We envision physics-specialized AI agents that seamlessly handle multimodal data, propose physically consistent hypotheses, and autonomously verify theoretical results. Realizing this vision requires developing physics-specific training datasets, reward signals that capture physical reasoning quality, and verification frameworks encoding fundamental principles. We call for collaborative efforts between physics and AI communities to build the specialized infrastructure necessary for AI-driven scientific discovery.

Egor Shulgin, Dimitri von Rütte, Tianyue H. Zhang et al. · mila

Hyperparameter transfer has become an important component of modern large-scale training recipes. Existing methods, such as muP, primarily focus on transfer between model sizes, with transfer across batch sizes and training horizons often relying on empirical scaling rules informed by insights from timescale preservation, quadratic proxies, and continuous-time approximations. We study hyperparameter scaling laws for modern first-order optimizers through the lens of recent convergence bounds for methods based on the Linear Minimization Oracle (LMO), a framework that includes normalized SGD, signSGD (approximating Adam), and Muon. Treating bounds in recent literature as a proxy and minimizing them across different tuning regimes yields closed-form power-law schedules for learning rate, momentum, and batch size as functions of the iteration or token budget. Our analysis, holding model size fixed, recovers most insights and observations from the literature under a unified and principled perspective, with clear directions open for future research. Our results draw particular attention to the interaction between momentum and batch-size scaling, suggesting that optimal performance may be achieved with several scaling strategies.

Maximilian Mordig, Andreas Opedal, Weiyang Liu et al.

Curriculum learning (CL), motivated by the intuition that learning in increasing order of difficulty should ease generalization, is commonly adopted both in pre-training and post-training of large language models (LLMs). The intuition of CL is particularly compelling for compositional reasoning, where complex problems are built from elementary inference rules; however, the actual impact of CL on such tasks remains largely underexplored. We present a systematic empirical study of CL for post-training of LLMs, using synthetic arithmetic and logical benchmarks where difficulty is characterized by reasoning complexity rather than surface-level proxies. Surprisingly, across multiple model families and curriculum schedules, we find no robust advantage in difficulty-based sequencing over standard random sampling in either accuracy or response length. These findings persist across both supervised fine-tuning (SFT) and reinforcement learning (RL) methods. Our study suggests that, in the context of deductive reasoning, the specific ordering of training examples plays a negligible role in achieving compositional generalization, challenging the practical utility of curriculum-based post-training.

Ricardo Olmedo, Bernhard Schölkopf, Moritz Hardt

Consider a market of competing model providers selling query access to models with varying costs and capabilities. Customers submit problem instances and are willing to pay up to a budget for a verifiable solution. An arbitrageur efficiently allocates inference budget across providers to undercut the market, thus creating a competitive offering with no model-development risk. In this work, we initiate the study of arbitrage in AI model markets, empirically demonstrating the viability of arbitrage and illustrating its economic consequences. We conduct an in-depth case study of SWE-bench GitHub issue resolution using two representative models, GPT-5 mini and DeepSeek v3.2. In this verifiable domain, simple arbitrage strategies generate net profit margins of up to 40%. Robust arbitrage strategies that generalize across different domains remain profitable. Distillation further creates strong arbitrage opportunities, potentially at the expense of the teacher model's revenue. Multiple competing arbitrageurs drive down consumer prices, reducing the marginal revenue of model providers. At the same time, arbitrage reduces market segmentation and facilitates market entry for smaller model providers by enabling earlier revenue capture. Our results suggest that arbitrage can be a powerful force in AI model markets with implications for model development, distillation, and deployment.

Jan Schneider, Mridul Mahajan, Le Chen et al.

Tendon drives paired with soft muscle actuation enable faster and safer robots while potentially accelerating skill acquisition. Still, these systems are rarely used in practice due to inherent nonlinearities, friction, and hysteresis, which complicate modeling and control. So far, these challenges have hindered policy transfer from simulation to real systems. To bridge this gap, we propose a sim-to-real pipeline that learns a neural network model of this complex actuation and leverages established rigid body simulation for the arm dynamics and interactions with the environment. Our method, called Generalized Actuator Network (GeAN), enables actuation model identification across a wide range of robots by learning directly from joint position trajectories rather than requiring torque sensors. Using GeAN on PAMY2, a tendon-driven robot powered by pneumatic artificial muscles, we successfully deploy precise goal-reaching and dynamic ball-in-a-cup policies trained entirely in simulation. To the best of our knowledge, this result constitutes the first successful sim-to-real transfer for a four-degrees-of-freedom muscle-actuated robot arm.