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Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformers
The discovery of conservation laws is a cornerstone of scientific progress. However, identifying these invariants from observational data remains a significant challenge. We propose a hybrid framework to automate the discovery of conserved quantities from noisy trajectory data. Our approach integrates three components: (1) a Neural Ordinary Differential Equation (Neural ODE) that learns a continuous model of the system's dynamics, (2) a Transformer that generates symbolic candidate invariants conditioned on the learned vector field, and (3) a symbolic-numeric verifier that provides a strong numerical certificate for the validity of these candidates. We test our framework on canonical physical systems and show that it significantly outperforms baselines that operate directly on trajectory data. This work demonstrates the robustness of a decoupled learn-then-search approach for discovering mathematical principles from imperfect data.
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ZEBRA: Towards Zero-Shot Cross-Subject Generalization for Universal Brain Visual Decoding
Wang, Haonan, Lu, Jingyu, Li, Hongrui, Li, Xiaomeng
Recent advances in neural decoding have enabled the reconstruction of visual experiences from brain activity, positioning fMRI-to-image reconstruction as a promising bridge between neuroscience and computer vision. However, current methods predominantly rely on subject-specific models or require subject-specific fine-tuning, limiting their scalability and real-world applicability. In this work, we introduce ZEBRA, the first zero-shot brain visual decoding framework that eliminates the need for subject-specific adaptation. ZEBRA is built on the key insight that fMRI representations can be decomposed into subject-related and semantic-related components. By leveraging adversarial training, our method explicitly disentangles these components to isolate subject-invariant, semantic-specific representations. This disentanglement allows ZEBRA to generalize to unseen subjects without any additional fMRI data or retraining. Extensive experiments show that ZEBRA significantly outperforms zero-shot baselines and achieves performance comparable to fully finetuned models on several metrics. Our work represents a scalable and practical step toward universal neural decoding. Code and model weights are available at: https://github.com/xmed-lab/ZEBRA.
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Noise, Adaptation, and Strategy: Assessing LLM Fidelity in Decision-Making
Feng, Yuanjun, Choudhary, Vivek, Shrestha, Yash Raj
Large language models (LLMs) are increasingly used in social science simulations. While their performance on reasoning and optimization tasks has been extensively evaluated, less attention has been paid to their ability to simulate human decision-making's variability and adaptability. We propose a process-oriented evaluation framework with progressive interventions (Intrinsicality, Instruction, and Imitation) to examine how LLM agents adapt under different levels of external guidance and human-derived noise. We validate the framework on two classic economics tasks, irrationality in the second-price auction and decision bias in the newsvendor problem, showing behavioral gaps between LLMs and humans. We find that LLMs, by default, converge on stable and conservative strategies that diverge from observed human behaviors. Risk-framed instructions impact LLM behavior predictably but do not replicate human-like diversity. Incorporating human data through in-context learning narrows the gap but fails to reach human subjects' strategic variability. These results highlight a persistent alignment gap in behavioral fidelity and suggest that future LLM evaluations should consider more process-level realism. We present a process-oriented approach for assessing LLMs in dynamic decision-making tasks, offering guidance for their application in synthetic data for social science research.
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