ℓ₂-Boosting exhibits benign overfitting with logarithmic excess variance decay Θ(σ²/log(p/n)) under isotropic noise due to ℓ₁ bias, and a subdifferential early stopping rule recovers minimax-optimal ℓ₁ rates.
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Understanding deep learning requires rethinking generalization
23 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the model family, or to the regularization techniques used during training. Through extensive systematic experiments, we show how these traditional approaches fail to explain why large neural networks generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization, and occurs even if we replace the true images by completely unstructured random noise. We corroborate these experimental findings with a theoretical construction showing that simple depth two neural networks already have perfect finite sample expressivity as soon as the number of parameters exceeds the number of data points as it usually does in practice. We interpret our experimental findings by comparison with traditional models.
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representative citing papers
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Asymmetric Langevin Unlearning uses public data to suppress unlearning noise costs by O(1/n_pub²), enabling practical mass unlearning with preserved utility under distribution mismatch.
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Stochastic trust-region methods achieve O(ε^{-2} log(1/ε)) complexity for unconstrained problems and O(ε^{-4} log(1/ε)) for equality-constrained problems under the strong growth condition, with experiments showing stable performance comparable to tuned baselines without learning-rate scheduling.
SGD dynamics in Hilbert spaces are approximated by an SDE with cylindrical noise, with the weak error between discrete and continuous versions shown to be second order in the step size.
Deep learning generalization error follows power-law scaling with training set size across multiple domains, with model size scaling sublinearly with data size.
Linear probes demonstrate that feature separability for classification increases monotonically with network depth in Inception v3 and ResNet-50.
Rescaled ASGD recovers convergence to the true global objective by rescaling worker stepsizes proportional to computation times, matching the known time lower bound in the leading term under non-convex smoothness and bounded heterogeneity.
ASD-Bench evaluates 17 ML and deep learning models on 4,068 AQ-10 records across child, adolescent, and adult cohorts, showing high adult performance, harder adolescent classification, shifting feature importance, and dissociation between accuracy and calibration.
Optimizer choice induces distinct connected regions in the loss landscape of two-layer ReLU networks, with AdamW and Muon sometimes separated by provable barriers.
Neural networks possess a propagation field of trajectories and Jacobians whose quality can be measured and optimized independently of endpoint loss, yielding better unseen-path generalization and reduced forgetting in continual learning.
Gradient flow in energy-based models for strictly positive binary distributions produces stable data-consistent fixed points and a learning hierarchy that favors lower-order interactions first, mechanistically explaining distributional simplicity bias.
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
NTK networks achieve minimax optimal adversarial regression rates in Sobolev spaces with early stopping, but minimum-norm interpolants are vulnerable.
Semi-DPO applies semi-supervised learning to noisy preference data in diffusion DPO by training first on consensus pairs then iteratively pseudo-labeling conflicts, yielding state-of-the-art alignment with complex human preferences.
Nexus optimizer improves LLM downstream performance by converging to common minima across data sources despite identical pretraining loss.
Minimax regret is characterized for misspecified universal learning with log-loss, yielding the optimal universal learner as a unified framework for any uncertainty in the data-generating process.
DP-LAC provides a new adaptive clipping technique for DP-SGD in federated LLM fine-tuning that improves accuracy by 6.6% on average without consuming additional privacy budget or requiring new hyperparameters.
A layer-wise peeling framework creates reference bounds to diagnose under-optimized layers in trained decoder-only transformers, including low-bit and quantized versions.
WRF4CIR uses weight-regularized fine-tuning with adversarial perturbations to mitigate overfitting in composed image retrieval and narrows the generalization gap on benchmarks.
OpenCLIP-based gesture classification with linear probing controls AcoustoBot swarms at 87.8% accuracy and 3.95 s latency in controlled tests.
Shallow MLPs and dense CPGs outperform deeper MLPs and Actor-Critic RL in bounded robot control tasks with limited proprioception, with a Parameter Impact metric indicating extra RL parameters yield no performance gain over evolutionary strategies.
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Deep Learning Scaling is Predictable, Empirically
Deep learning generalization error follows power-law scaling with training set size across multiple domains, with model size scaling sublinearly with data size.