Jacobians
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Related Articles from SNS
Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography
Announce Type: replace-cross Abstract: In this work we study quantitative existence results for genus-$2$ curves over $\mathbb{Q}$ whose Jacobians have Mordell--Weil rank at least $1$ or $2$, ordering the curves by the naive height of their integral Weierstrass models. We use geometric techniques to show that asymptotically the Jacobians of almost all integral models with two rational points at infinity have rank $r \geq Since there are $\asymp X^{\frac{13}{2}}$ such models among the $X^7$...
Network Recovery from Cascade Data: A Debiased Jacobian-Based Machine Learning Approach
arXiv:2606.07483v1 Announce Type: new Abstract: Many important outcomes unfold as dynamic cascades, including product adoption, disease spread, financial distress, and information diffusion. A central challenge is to recover the hidden influence network behind these cascades.
GenPO++: Generative Policy Optimization with Jacobian-free Likelihood Ratios
arXiv:2606.06967v1 Announce Type: new Abstract: Generative policies provide expressive and multimodal action distributions, making them attractive for reinforcement learning (RL) in complex continuous-control tasks. Among them, flow-based policies are especially appealing because they generate actions through deterministic transport maps. However, applying such generative policies to likelihood-based on-policy learning remains limited by the difficulty of evaluating the probability of...
Learning Chaotic Dynamics through Second-Order Geometric Supervision
arXiv:2606.01596v1 Announce Type: new Abstract: Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics. Trajectory (zero-order) and Jacobian (first-order) matching supervise the values and tangent structure of the vector field, but neither constrains how the field bends away from its tangent plane. A model can thus match values and tangents at the supervised states yet...
Generalization in Nonlinear Least Squares via Learned Feature Geometry
arXiv:2606.08799v1 Announce Type: cross Abstract: We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual--curvature term. In the linear case, where the curvature term vanishes, this recovers the classical...
Locality-Aware Automatic Differentiation on the GPU for Mesh-Based Computations
arXiv:2509.00406v3 Announce Type: replace Abstract: We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using per-element forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs,...
Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent
arXiv:2606.04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training. When the coupled Jacobian is block-triangular, asymptotic stability is governed by the spectral radii of the diagonal blocks, yet transient amplification before convergence can be arbitrarily large due to non-normality. We develop a sharp pseudospectral theory...
Spectral Audit of In-Context Operator Networks
arXiv:2606.02427v1 Announce Type: new Abstract: Existing evaluations of neural operators and in-context operator learning rely primarily on prediction error, but accurate output prediction does not guarantee the correct local dynamical structure. A model may match solutions while exhibiting incorrect sensitivities, distorted frequency response, spurious mode coupling, or unstable tangent behavior. We introduce a Jacobian-based spectral audit for in-context operator learning.
Disentangling RNA evolution and thermodynamics in genomic language models
Genomic language models (gLMs) trained only on large-scale nucleic acid sequence data seem to capture signals of RNA structure, yet the specifics of how remain unclear. Using the categorical Jacobian (CJ) operation, a model-agnostic operation for querying pairwise dependencies, we systematically compared three flagship gLMs: RNA-FM, Evo 2, and gLM2. We found that CJ signals recover base pairs supported by evolutionary covariation analyses, consistent with findings in protein language models.
S$^3$LDBO: A Snapshot Single-Loop Algorithm for Decentralized Bilevel Optimization
arXiv:2605.31311v1 Announce Type: cross Abstract: Networked AI systems increasingly rely on multiple agents that collaboratively learn and adapt models over communication networks. In such systems, bilevel formulations naturally arise in hyperparameter optimization, data cleaning, and meta-learning, but the repeated evaluation of gradients, Jacobians, and Hessians can impose a substantial computational burden on individual agents. To address this challenge, we propose Snapshot-SLDBO...