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How Accurate Is Accurate Enough?
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arXiv Machine Learning
Oct 2
How Accurate Is Accurate Enough?
The paper investigates how the magnitude of numerical errors in a learning system should be evaluated, arguing that error impact depends on the current learning state, the class affected, and the class weight. By analyzing softmax cross‑entropy, the authors derive exact bounds on loss changes for fixed error sets and use these to provide finite‑error guarantees for losses, probabilities, predictions, and gradients. They then invert these guarantees to certify the maximum allowable primitive error for a given learning‑level requirement, demonstrating through von Mises‑Fisher learning that identical errors can have vastly different effects across states.
arXiv Machine Learning
Oct 2
Same Loss, Different Gradients
The paper demonstrates that in differentiable learning, the scalar objective computed during the forward pass can differ from the gradient supplied in the backward pass when probabilistic objectives depend on finite special‑function recurrences, custom backward rules, and numerical clipping. This mismatch is shown in high‑dimensional von Mises‑Fisher learning, where identical forward scores can lead to different gradients and optimization paths. To address this, the authors introduce AR/FR, a fixed‑depth analytic method that jointly constructs a potential and its derivative, guaranteeing forward‑backward coherence and providing a uniform cubic‑order error bound relative to the exact Bessel ratio across all nonnegative concentration values.
arXiv Machine Learning
Aug 20
Contrasting Cost-Agnostic and Cost-Sensitive Losses under Limited Model Capacity via $\mathcal H$-consistency
The paper investigates the difference between cost‑agnostic and cost‑sensitive loss functions when model capacity is limited. It shows that, unlike in ideal infinite‑capacity settings, optimizing a cost‑sensitive objective can yield a strictly better downstream decision than post‑processing a cost‑agnostic model. The authors prove this gap under a hypothesis class that can recover the optimal decision boundary but not the optimal cost‑agnostic hypothesis, and provide a simple example and empirical evidence on UCI datasets with simple models.
arXiv Machine Learning
Oct 15
The Statistical Benefits of Multiple Responses for Learning from Demonstrations
arXiv:2609.33291v2 Announce Type: replace-cross Abstract: Many generative systems return multiple candidate responses and are evaluated according to the best one. Recent work shows that, when demonst...
arXiv Machine Learning
Jun 18
Not Just How Much, But Where: Decomposing Epistemic Uncertainty into Per-Class Contributions
arXiv:2602. 21160v3 Announce Type: replace-cross Abstract: In safety-critical classification, the cost of failure is often asymmetric, yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), that cannot distinguish whether a model's ignorance involves a benign or safety-critical class.
arXiv AI
Oct 19
Human-Centered Learning Mechanics: Observable Entropy Control under Protected-Risk Constraints
arXiv:2605.22940v2 Announce Type: replace-cross Abstract: Entropy reduction is not a safety criterion: it can leave predictions unchanged or accompany increasing risk for a protected group. We study...