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The Exponential of Skew-Symmetric Matrices: A Nearby Inverse and Efficient Computation of Derivatives

arXiv:2506.18302v2 Announce Type: replace-cross Abstract: The matrix exponential restricted to skew-symmetric matrices has numerous applications, notably in view of its interpretation as the Lie group exponential and Riemannian exponential for the special orthogonal group. We characterize the invertibility of the derivative of the skew-restricted exponential, thereby providing a simple expression of the tangent conjugate locus of the orthogonal group. In view of the skew restriction, this...

arXiv CS 5d ago

Counterfactual Transport Flows for Offline Conservative Trajectory Refinement

Announce Type: new Abstract: Offline reinforcement learning (RL) offers a path to policy improvement from logged data alone, using historical returns or other measurable outcomes as world feedback. A key difficulty is improving observed behavior without extrapolating beyond what the offline data supports. We propose \emph{counterfactual transport flows}, a source-conditioned trajectory refinement framework for offline decision-making guided by world feedback.

arXiv CS 1d ago

Understanding Quantization-Aware Training: Gradients at Quantized Weights Bias to the Low-Loss Basin

arXiv:2606.09012v1 Announce Type: new Abstract: Post-training quantization (PTQ) converts a trained full-precision model into low-bit weights without task-level retraining, while quantization-aware training (QAT) incorporates quantization into the training loop. Although PTQ is efficient and often accurate at moderate bitwidths, it can fail sharply at aggressive bitwidths; QAT is more expensive but can often recover the lost accuracy. We propose a unified geometric framework that explains...

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