arXiv AI
Jul 7
When is a System Discoverable from Data? Discovery Requires Chaos
arXiv:2511. 08860v2 Announce Type: replace-cross Abstract: The deep learning revolution has spurred a rise in advances of using AI in sciences.
Geometry-Agnostic Data-Driven Discovery of Extreme Scenarios
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arXiv Machine Learning
Jul 8
Statistically Meaningful Geometry and Gauge Symmetry Breaking: A Geometric Foundation for Scientific Discovery and Intelligence Emergence
arXiv:2607. 05436v1 Announce Type: new Abstract: The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers?
arXiv Machine Learning
Jul 7
Physically-Relevant Information Learning in High-Dimensional Time-Derivatives Spaces
arXiv:2607. 05127v1 Announce Type: cross Abstract: Understanding the physics of many-body complex dynamical systems is typically non-trivial.
arXiv AI
Oct 9
Beyond the Ergodic Wall: A Discrete Geometric Physics Sandbox for Analysing AI Scaling Limits and Complexity Collapse
The paper identifies a fundamental limitation in current deep learning, describing an "ergodic ceiling" that forces models to converge to statistical averages of existing human knowledge. It proposes a discrete geometric physics sandbox—built on a Holographic E8 Projection Engine and a lattice of Planck‑scale spheres—to inject non‑ergodic, path‑dependent insight and enforce thermodynamic constraints. By modeling spacetime as nested FCC lattices and using topological constraints, the sandbox aims to prevent model collapse, recover quantum mechanics via renormalisation‑group flows, and potentially collapse NP‑to‑P complexity by restricting algorithmic search to physically conserved trajectories.
arXiv Machine Learning
Jun 11
How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit
arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.
arXiv Machine Learning
Oct 2
Learning Chaos Without Seeing Chaos: Extrapolation of Global Dynamics in Autoregressive Transformers
Autoregressive transformers trained on limited trajectories of nonlinear dynamical systems can extrapolate to unseen parameter regimes, reproducing period-doubling cascades, chaotic dynamics, and attractor structures with high fidelity. In the logistic map, the model captures successive period doublings up to period 128, achieving a scaling ratio within $5 imes10^{-4}$ of the Feigenbaum constant. The study also shows how control‑parameter information is processed via attention, shaping the closed‑loop dynamics during training.
Hugging Face Trending Papers
Jun 10
How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit
Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions.
arXiv Machine Learning
Aug 3
Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks
arXiv:2607. 28977v1 Announce Type: cross Abstract: Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture.
arXiv Machine Learning
Jun 25
The Urysohn Ladder: Recursive Metric Contraction for Scalable Continual Learning
arXiv:2512. 18471v2 Announce Type: replace Abstract: Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference.
arXiv Machine Learning
Jul 22
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv AI
Jun 11
Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data
arXiv:2604. 24662v2 Announce Type: replace-cross Abstract: Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences.
arXiv Machine Learning
Aug 11
NeuralDMD: Interpretable Neural Representation of Dynamics from Sparse and Noisy Measurements
arXiv:2507. 03094v2 Announce Type: replace-cross Abstract: Many challenges in scientific imaging involve solving ill-posed inverse problems, where the goal is to recover spatio-temporal fields from indirect, noisy, and highly sparse measurements - often without access to ground truth data or reliable simulators.