Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.38877

On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability

Wenjie Wang·Yuanyuan Wang·Zixiang Jiang·Shaoan Xie·Mingming Gong
View original source ↗Read source document ↗Export metadata ↓

Abstract

Physical parameter estimation from video aims to recover the parameters of a known family of governing dynamical equations from pixel observations. Existing identifiability theory for this setting has focused on linear time-invariant (LTI) second-order systems, leaving open what can be identified for nonlinear scalar dynamics. We develop an identifiability theory for nonlinear scalar second-order ODEs, organized by how their velocity dependence interacts with changes of the learned state coordinate. Under a shared non-collapsed state map and explicit same-state velocity-coverage conditions, we show that parameter identifiability depends on the ODE family: some parameters are uniquely identifiable, while in other families only invariant parameter combinations are identifiable or external physical calibration is required. For laws that are at most linear in velocity, compatibility forces affine coordinate alignment, yielding explicit parameter relations, invariants, and calibration conditions. This affine conclusion extends to broader finite velocity-feature families when coordinate curvature can be separated from the declared velocity dependence. For families admitting a squared-velocity term, nonlinear coordinate ambiguity can remain; a law-derived normalization instead enables affine comparison between canonical laws. Experiments on synthetic systems and real pendulum and free-fall videos support the predicted parameter relations, coverage effects, and calibration requirements.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Wenjie Wang, Yuanyuan Wang, Zixiang Jiang, Shaoan Xie, Mingming Gong. 2026-09-30. On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability. https://arxiv.org/abs/2609.38877

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Best-of-Majority: Minimax-Optimal Strategy for Pass@$k$ Inference Scaling

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@$k$: the agent may submit up to $k$ responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@$k$ inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with $k$ and the sampling budget $N$. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the $N$ samples before selecting the top-$k$ rewards. We prove that when the sampling budget is $N=\tildeΩ(C^*)$, the regret of BoM is $O(ε_{\mathrm{opt}}+\sqrt{ε_{\mathrm{RM}}^2C^*/k})$, where $C^*$ is the coverage coefficient, $ε_{\mathrm{RM}}$ is the estimation error of the reward model, and $ε_{\mathrm{opt}}$ is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing $N$. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

cs.LG↗
arXiv2026

PepEVOLVE: Position-Aware Dynamic Peptide Optimization via Group-Relative Advantage

Macrocyclic peptides are an emerging modality that combines biologics-like affinity with small-molecule-like developability, yet their vast combinatorial space and multi-parameter objectives make lead optimization slow and challenging. Prior generative approaches for peptide lead optimization (e.g., PepINVENT) require chemists to pre-specify mutable positions for optimization, choices that are not always known a priori, and rely on static pretraining and optimization algorithms that limit the model's ability to generalize and effectively optimize peptide sequences. We introduce PepEVOLVE, a position-aware, dynamic framework that learns both where to edit and how to dynamically optimize peptides for multi-parameter improvement. PepEVOLVE (i) augments pretraining with dynamic masking and CHUCKLES shifting to improve generalization, (ii) uses a context-free multi-armed-bandit router that discovers high-reward residues, and (iii) couples a novel evolving optimization algorithm with group-relative advantage to stabilize reinforcement updates. During in silico evaluations, the router policy reliably learns and concentrates probability on chemically tractable sites that influence the desired peptide's properties. On a therapeutically motivated Rev-binding macrocycle benchmark, PepEVOLVE outperformed PepINVENT by reaching higher averaged permeability-weighted optimization scores of approximately 0.8 vs. 0.6, achieving best candidates with score of 0.97 (vs. 0.89), and converging in fewer steps under the task of optimizing permeability and lipophilicity with structure constraints. Overall, PepEVOLVE offers a practical, reproducible path to linear and macrocyclic peptide lead optimization when optimal edit sites are unknown, enabling more efficient chemical space exploration and improving design quality across multiple objectives to accelerate the design cycles.

cs.LG↗
arXiv2026

Beyond the Dirac Delta: Mitigating Diversity Collapse in Reinforcement Fine-Tuning for Versatile Image Generation

Reinforcement learning (RL) has emerged as a paradigm for fine-tuning large-scale generative models, such as diffusion and flow models, to align with complex human preferences and user-specified tasks. A fundamental limitation remains \textit{the curse of diversity collapse}, where the objective formulation and optimization landscape inherently collapse the policy to a Dirac delta distribution. To address this challenge, we propose \textbf{DRIFT} (\textbf{D}ive\textbf{R}sity-\textbf{I}ncentivized Reinforcement \textbf{F}ine-\textbf{T}uning for Versatile Image Generation), an innovative framework that systematically incentivizes output diversity throughout the on-policy fine-tuning process, reconciling strong task alignment with high generation diversity to enhance versatility essential for applications that demand diverse candidate generations. We approach the problem across three representative perspectives: i) \textbf{sampling} a reward-concentrated subset that filters out reward outliers to prevent premature collapse; ii) \textbf{prompting} with stochastic variations to expand the conditioning space, and iii) \textbf{optimization} of the intra-group diversity with a potential-based reward shaping mechanism. Experimental results show that DRIFT exhibits clear Pareto dominance in task alignment and generation diversity, achieving 3.88\%$\sim$81.42\% higher diversity at matched alignment and 14.38\%$\sim$56.45\% higher alignment at matched diversity. Our code is available at \textcolor{magenta}{\href{https://github.com/NJU-RL/DRIFT}{https://github.com/NJU-RL/DRIFT}}.

cs.LG↗