#01Nov 5, 2026
cs.LG
Conformal Prediction for Time-Dependent PDEs
Joshua Stiller, Annika Schneider, Eyke Hüllermeier
Uncertainty quantification is crucial in scientific machine learning, where models inform safety-critical tasks such as flood forecasting, financial risk management, and thermal control in machines. Conformal prediction provides distribution-free coverage guarantees, but in time-dependent settings common to physics and engineering, these guarantees can break down, leading to systematic undercoverage. We study this problem in the context of surrogate models for time-dependent physical systems described by partial differential equations. We prove that in a function space setting, distributions at arbitrarily close times can be mutually singular, making exact coverage guarantees impossible. We further show that in discretized settings, the total variation distance between distributions often saturates exponentially fast with the grid resolution, mandating restrictions on the spatial discretization to ensure coverage. Finally, for certain settings, we show how to use principled weighted conformal prediction to obtain finite-sample coverage guarantees over growing time horizons.
#02Nov 5, 2026
cs.LG
Spectral and Subspace Dynamics of LoRA in Supervised Fine-Tuning and Reinforcement Learning
Chenruo Liu, Zihan Wang, Yijun Dong and 1 more
Low-rank adaptation (LoRA) is commonly used in both supervised fine-tuning (SFT) and reinforcement learning (RL), often under similar optimizer settings. Yet, how the different dynamics of the two stages manifest in the low-rank increment that LoRA optimizes remains unclear. Tracking the singular spectrum and subspaces of LoRA updates on mathematical reasoning tasks, we find that RL concentrates the spectrum at every learning rate, while SFT expands it at moderate learning rates; moreover, RL rotates the singular subspaces much faster than SFT at small learning rates. Interpolating between SFT and RL one ingredient at a time, we pinpoint group-mean baseline subtraction as the source of both contrasts. A quadratic multi-index model updated via LoRA unveils the underlying mechanism: group-mean baseline subtraction tilts the balance between two competing forces, coherent fitting and gradient noise, toward spectral concentration and faster subspace rotation, while forcing the risk-favorable learning rate to be low. Guided by these dynamics, we tailor LoRA updates to each stage: in SFT, we flatten the spectrum of the full update to spread adaptation across singular directions, whereas in RL, we flatten the part of the update outside the current LoRA increment span to promote subspace rotation. Experiments on mathematical reasoning tasks across multiple models show that the respective configurations for SFT and RL yield the best performance among the compared methods in most evaluated settings.
#03Nov 5, 2026
cs.CV
SM4RT: Cascaded Feed-forward Model for 4D Reconstruction
Pang-Chi Lo, Jhao-Syun Lai, Tsung-Wei Ke
We introduce SM4RT, a multi-task cascade feed-forward model for dynamic scene reconstruction from RGB videos. While existing feed-forward approaches typically address geometry reconstruction and motion estimation separately--and often predict motions in a single coordinate frame that must account for camera movement--SM4RT solves these tasks sequentially by first reconstructing 3D geometry and then bootstrapping motion estimation from the predicted structure. By expressing each pixel's 3D motion in its corresponding camera frame, SM4RT reduces ambiguity arising from camera motion. To address the sparsity of real-world motion labels, SM4RT further incorporates a weakly supervised loss that regularizes unlabeled point motions using labeled point positions at the other time step. We evaluate motion estimation on three dynamic-scene datasets--Kubric, Waymo, and Point Odyssey--and SM4RT achieves the best performance on most metrics compared with prior baselines. We additionally benchmark geometry reconstruction on five dynamic scene datasets and show that SM4RT achieves competitive performance with state-of-the-art methods. Overall, our unified framework demonstrates that combining geometry reconstruction and motion estimation in a cascade not only avoids performance trade-offs but also enhances motion estimation through improved geometric reasoning.
#04Nov 5, 2026
cs.AI
SwarmEvolve: Latent Agent Swarms for Evolutionary Discovery and Optimization
Qile Jiang, George Em Karniadakis
LLM-guided evolutionary search uses AI agents to improve programs for mathematical and computational problems by iteratively refining solutions and combining high-scoring methods. However, the process is often slow because the LLM generates a long textual chain of thought for each round and must repeat this generation many times to maintain population diversity. We present SwarmEvolve, a framework in which hundreds of low-cost agents per round work in swarms, reason in latent space without decoding to text, and share information by passing KV caches. Each swarm studies the problem from a different angle. A novelty filter keeps the most distinct agent ideas by directly measuring the distances between the agents' hidden state vectors. Crossover of ideas happens naturally in latent space, as a summarizer agent receives the combined KV caches of all swarm members. On 21 problems in mathematical discovery and scientific computing, SwarmEvolve gets the highest average score and needs a median of only 3 to 8 minutes to reach the best scores that other state-of-the-art frameworks reach in 60 minutes. On several problems, SwarmEvolve with Qwen3 8B improves on the solutions that AlphaEvolve first found with frontier LLMs. Our work shows that agent swarms that communicate in latent space offer a fast, low-cost approach to program search for scientific problems.
#05Nov 5, 2026
cs.CV
EgoGeneralist: Unifying Egocentric Action-Video Tasks through Video-Native Modeling
Yanlin Jin, Bowen Yang, Cheng Zhang and 4 more
Modern video models possess strong visual priors, yet do not natively represent human action in metric 3D space. We present EgoGeneralist, which adapts pretrained video generators to unify action-conditioned egocentric video generation, pose estimation, and joint action-video generation. Our role-adaptive action renderer provides video-native representations for multidirectional action-video learning, making metric motion usable as both a spatial control signal and a recoverable generation target. Cross-stream action-video coupling establishes close correspondence between metric motion and visual dynamics through lightweight adaptation while preserving the pretrained visual prior. Together, these designs establish a generalist framework spanning five action-video tasks. Despite adaptation only on controlled laboratory recordings, EgoGeneralist generalizes to diverse unseen scenes and interactions with effective action control and visual quality, bridging pretrained visual knowledge and metric 3D human motion.