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Adaptive multi-fidelity optimization with fast learning rates Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction Sample Complexity Bounds for Stochastic Shortest Path with a Generative Model The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback Stylistic-STORM (ST-STORM) : Perceiving the Semantic Nature of Appearance Collective Kernel EFT for Pre-activation ResNets PRIM-cipal components analysis One-Shot Generative Flows: Existence and Obstructions Structural interpretability in SVMs with truncated orthogonal polynomial kernels Amortized Optimal Transport from Sliced Potentials MinShap: A Modified Shapley Value Approach for Feature Selection Unsupervised feature selection using Bayesian Tucker decomposition Multi-User mmWave Beam and Rate Adaptation via Combinatorial Satisficing Bandits Best of both worlds: Stochastic & adversarial best-arm identification Scalable Model-Based Clustering with Sequential Monte Carlo Expert-Guided Class-Conditional Goodness-of-Fit Scores for Interpretable Classification with Informative Missingness: An Application to Seismic Monitoring Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks Gating Enables Curvature: A Geometric Expressivity Gap in Attention Zeroth-Order Optimization at the Edge of Stability Differentially Private Conformal Prediction CLion: Efficient Cautious Lion Optimizer with Enhanced Generalization Generative Augmented Inference Improving Machine Learning Performance with Synthetic Augmentation PAC-MCTS: Bias-Aware Pruning for Robust LLM-Guided Search and Planning Path-Sampled Integrated Gradients Heat and Matérn Kernels on Matchings Doubly Outlier-Robust Online Infinite Hidden Markov Model Momentum Further Constrains Sharpness at the Edge of Stochastic Stability Multistage Conditional Compositional Optimization BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization Sandpile Economics: Theory, Identification, and Evidence Online learning with noisy side observations Spectral Thompson sampling Covariance-adapting algorithm for semi-bandits with application to sparse rewards Ordinary Least Squares is a Special Case of Transformer Metric-Aware Principal Component Analysis (MAPCA):A Unified Framework for Scale-Invariant Representation Learning Robust Low-Rank Tensor Completion based on M-product with Weighted Correlated Total Variation and Sparse Regularization Joint Representation Learning and Clustering via Gradient-Based Manifold Optimization Universality of Gaussian-Mixture Reverse Kernels in Conditional Diffusion Interpretable and Explainable Surrogate Modeling for Simulations: A State-of-the-Art Survey and Perspectives on Explainable AI for Decision-Making Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression A short proof of near-linear convergence of adaptive gradient descent under fourth-order growth and convexity Some Theoretical Limitations of t-SNE Bias-Corrected Adaptive Conformal Inference for Multi-Horizon Time Series Forecasting Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing Rare Event Analysis via Stochastic Optimal Control Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. 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The Devil Is in Gradient Entanglement: Energy-Aware Gradient Coordinator for Robust Generalized Category Discovery A Tutorial Review of Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches Certified and accurate computation of function space norms of deep neural networks Mini-Batch Covariance, Diffusion Limits, and Oracle Complexity in Stochastic Gradient Descent: A Sampling-Design Perspective Conformal Policy Control Diagnostics for Individual-Level Prediction Instability in Machine Learning for Healthcare Neural Networks With Dense Weights Are Not Universal Approximators Continuous-time reinforcement learning: ellipticity enables model-free value function approximation Scalable spatial point process models for forensic footwear analysis A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios Active Learning with Selective Time-Step Acquisition for PDEs Joint Score-Threshold Optimization for Interpretable Risk Assessment Revisiting Entropy Regularization: Adaptive Coefficient Unlocks Its Potential for LLM Reinforcement Learning Discrete Guidance Matching: Exact Guidance for Discrete Flow Matching PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problems Online Distributionally Robust LLM Alignment via Regression to Relative Reward Heavy-Tailed Class-Conditional Priors for Long-Tailed Generative Modeling Random Walk Learning and the Pac-Man Attack Sequential Regression Learning with Randomized Algorithms Diagnosing and Improving Diffusion Models by Estimating the Optimal Loss Value Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models Scalable Spatiotemporal Inference with Biased Scan Attention Transformer Neural Processes Towards AI-assisted Neutrino Flavor Theory Design Towards Reasonable Concept Bottleneck Models Practical estimation of the optimal classification error with soft labels and calibration Flow-based Generative Modeling of Potential Outcomes and Counterfactuals The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach FSPO: Few-Shot Optimization of Synthetic Preferences Personalizes to Real Users Identifying Information from Observations with Uncertainty and Novelty A ghost mechanism: An analytical model of abrupt learning in recurrent networks A Multiparty Homomorphic Encryption Approach to Confidential Federated Kaplan Meier Survival Analysis Large Language Models for Market Research: A Data-augmentation Approach Transformer Neural Processes - Kernel Regression FIT-GNN: Faster Inference Time for GNNs that 'FIT' in Memory Using Coarsening Estimating Joint Interventional Distributions from Marginal Interventional Data Nonparametric Sparse Online Learning of the Koopman Operator
Symbolic Pregression: Discovering Physical Laws from Distorted Video
2020-05-20 · via stat.ML updates on arXiv.org

We present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled video. We first train an autoencoder that maps each video frame into a low-dimensional latent space where the laws of motion are as simple as possible, by minimizing a combination of non-linearity, acceleration and prediction error. Differential equations describing the motion are then discovered using Pareto-optimal symbolic regression. We find that our pre-regression ("pregression") step is able to rediscover Cartesian coordinates of unlabeled moving objects even when the video is distorted by a generalized lens. Using intuition from multidimensional knot-theory, we find that the pregression step is facilitated by first adding extra latent space dimensions to avoid topological problems during training and then removing these extra dimensions via principal component analysis.

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