More features and data lead to better model performance in random feature regression.
problem Improving model performance in random feature regression.
method Theoretical analysis of random feature regression, demonstrating the benefits of overparameterization, overfitting, and more data.
result Infinite width RF architectures are preferable to those of any finite width, and training to near-zero training loss is obligatory for near-optimal performance.
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
Deep ResNets can achieve zero loss with enough layers and weights.
problem Finding parameters in deep ResNets that fit training data perfectly.
method Mean-field analysis and gradient descent flow to a PDE.
result Gradient descent for ResNet training converges to a zero-loss solution in the large-NN limit.
SLT reveals how grokking occurs via basin selection in training.
problem Understanding grokking in machine learning models.
method Singular Learning Theory (SLT) to analyze the loss landscape and local learning coefficient (LLC).
result LLC ranks basins by statistical preference, leading to grokking.
Transformers learn unseen tasks via prompts without fine-tuning.
problem Understanding how transformers learn unseen tasks without additional fine-tuning.
method Structured data model, gradient descent, two-phase convergence analysis.
result Transformers can learn linear function classes via in-context learning.
Two-layer ReLU networks can overfit without harm, study finds.
problem Understanding when and how two-layer ReLU networks can overfit without harming generalization.
method Established algorithm-dependent risk bounds for two-layer ReLU convolutional neural networks with label-flipping noise.
result Gradient descent-trained ReLU networks can achieve near-zero training loss and Bayes optimal test risk.
Novel oracle-type inequality for logistic loss in DNNs achieves sharp convergence rates.
problem Generalization analysis for binary classification with DNNs and logistic loss.
method Established an oracle-type inequality to handle the boundedness of the target function.
result Optimal convergence rates for fully connected ReLU DNN classifiers trained with logistic loss.
AlphaZeroBeta uses deep reinforcement learning for market-neutral portfolios, outperforming traditional methods.
problem Traditional portfolio management methods often fail during market regime shifts or when assumptions break down.
method Combines a composite reward function and CNN-GRU policy trained end-to-end via Recurrent PPO.
result Achieves higher Sharpe ratios than baselines while maintaining near-zero benchmark correlations.
Interpolating estimators in nonparametric regression become suboptimal under adversarial attacks.
problem Adversarial robustness of interpolating estimators in nonparametric regression.
method Investigation of adversarial robustness of interpolating estimators in a nonparametric regression framework.
result Interpolating estimators must be suboptimal even under a subtle future X-attack. A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient descent. This is surprising because of the large capacity demonstrated by DNNs to…
Gradient-based methods find saddle points, not critical points, in neural networks.
problem Gradient-based optimization methods converge to saddle points rather than critical points in deep neural networks.
method Critical point-finding methods used to analyze neural network losses.
result Gradient-based methods often converge to or pass through gradient-flat regions, where gradient norm has a stationary point.
Forecastability measures predictive information across horizons.
problem How much predictive information is available at each prediction horizon?
method Develops the consequences of mutual information between future observations and information set.
result Forecastability is a profile reflecting process dependence structure, with properties like compression and truncation error.
Recursive Feature Machines show grokking in modular arithmetic without neural networks.
problem Grokking in modular arithmetic tasks.
method Recursive Feature Machines (RFM) with Average Gradient Outer Product (AGOP).
result RFM and neural networks learn block-circulant features to solve modular arithmetic.
Pre-trained GPs improve Bayesian optimization efficiency.
problem Optimizing complex machine learning models requires domain knowledge but is challenging.
method Developed HyperBO framework using pre-trained Gaussian processes.
result HyperBO achieves up to 3x better efficiency in hyperparameter tuning.
Hyperfitting improves LLM generation quality by enhancing diversity, contrary to simple temperature scaling.
problem Improving open-ended generation quality of LLMs with minimal fine-tuning effort.
method Demonstrates that hyperfitting, a phenomenon where LLMs are fine-tuned to near-zero training loss, enhances generation quality and mitigates repetition.
result Hyperfitting is distinct from temperature scaling and involves a dynamic, context-dependent rank reordering mechanism in the final transformer block.
New study shows diversification can increase risk for heavy-tailed losses.
problem Diversification can increase tail risk for heavy-tailed losses.
method Comparison of diversified portfolio to a 'one-basket' benchmark.
result Diversified portfolio has larger tail probabilities than a 'one-basket' benchmark for all thresholds.
In modern supervised learning, many deep neural networks are able to interpolate the data: the empirical loss can be driven to near zero on all samples simultaneously. In this work, we explicitly exploit this interpolation property for the design of a new optimization algorithm for deep learning, which we term Adaptive…
Theory explains generalization in deep learning, reducing memorization and improving performance.
problem Understanding and improving generalization in deep learning models.
method Developed a non-asymptotic theory using the empirical neural tangent kernel.
result Generalization is possible even when the kernel evolves significantly, with coherent signal accumulation and noise suppression.
Machine learning forecasts show bias at long horizons, contrary to standard tests.
problem Forecast efficiency tests misinterpret machine learning performance.
method Theoretical and empirical analysis of regularization and measurement noise.
result Machine learning forecasts exhibit overreaction at longer horizons, not bias.
Recently, neural networks in machine learning use rectified linear units (ReLUs) in early processing layers for better performance. Training these structures sometimes results in "dying ReLU units" with near-zero outputs. We first explore this condition via simulation using the CIFAR-10 dataset and variants of two popu…
Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on test data, a phenomenon not yet fully understood. The first point of our paper is t…
New findings challenge the use of flatness measures in neural networks.
problem The validity of flatness measures in assessing generalization in neural networks.
method Analysis of Hessian-based flatness norms and their relation to generalization.
result Solutions with large weights and low loss are often sharper than expected, contradicting flatness measures.
Analyzes the Hessian of ReLU networks, proving skewed eigenvalue distribution.
problem Characterizing the Hessian at spurious minima in shallow ReLU models.
method Symmetry breaking and representation theory techniques.
result Proves skewed eigenvalue distribution of Hessian at spurious minima.
Quantizes symplectic manifolds with bounded geometry using Berezin-Toeplitz method.
problem Quantization of symplectic manifolds with bounded geometry.
method Berezin-Toeplitz quantization theory.
result Correct semiclassical limit achieved.
SGD achieves near optimal convergence rate in smooth interpolation regime.
problem Optimization of smooth convex objectives with zero noise at optimum.
method Stochastic Gradient Descent (SGD) with large stepsize analysis.
result Last iterate of SGD achieves expected excess risk of O(1/T + σ* / √T) with optimal stepsize.
A scalable PyTorch framework for non-crossing quantile regression.
problem Non-crossing quantile regression to avoid impossible negative probability densities.
method CJQR-ALM combining Augmented Lagrangian Method, differentiable pinball loss, and L-BFGS optimization.
result Achieves near-zero crossing rates on large datasets within minutes.
New research shows LLMs can't be explained by statistical generalization alone.
problem Understanding why large language models (LLMs) perform well despite statistical generalization limitations.
method Examined the non-identifiability of AR probabilistic models and their implications for LLMs.
result Non-identifiability of LLMs leads to different behaviors and requires a separate theoretical explanation.
sGPO optimizes RLVR training by balancing inference FLOPs and training efficiency.
problem RLVR training allocates rollout budget without considering query difficulty.
method sGPO trades inference FLOPs for reduced training FLOPs.
result sGPO matches or exceeds baseline performance while reducing training compute by a factor of three.
High-dimensional shrinkage risk depends on the default prior for the common scale.
problem Choosing the default prior for the common scale in high-dimensional shrinkage.
method Using radial-power benchmark to compare variance-flat and standard deviation-flat priors.
result The standard deviation-flat prior has a one-unit asymptotic risk advantage near the origin.
This paper studies the problem of learning causal structures from observational data. We reformulate the Structural Equation Model (SEM) with additive noises in a form parameterized by binary graph adjacency matrix and show that, if the original SEM is identifiable, then the binary adjacency matrix can be identified up…
We propose a max-pooling based loss function for training Long Short-Term Memory (LSTM) networks for small-footprint keyword spotting (KWS), with low CPU, memory, and latency requirements. The max-pooling loss training can be further guided by initializing with a cross-entropy loss trained network. A posterior smoothin…
Flooding prevents deep networks from achieving zero training loss, improving test performance.
problem Deep networks can achieve zero training error but often have zero training loss, leading to overconfidence and poor test performance.
method Flooding prevents training loss from reaching zero by applying gradient ascent when loss is below a preset flood level.
result Flooding improves test performance and induces a double descent curve of the test loss.
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed …
HDT improves MCMC on graphs with history-dependent sampling.
problem Efficient sampling from target distributions on general graphs with low computational overhead.
method History-driven target (HDT) framework that replaces the original target distribution with a history-dependent one.
result Near-zero variance performance and scalability to large graphs with memory-efficient implementation.
The paper predicts loss scaling across different datasets and compute scales.
problem Predicting loss scaling across different datasets and compute scales.
method Derive shifted power law relationships between train and test losses.
result Shifted power law relationships hold for various datasets and tasks, improving prediction accuracy.
Compensation methods correct overestimation of adversarial robustness in neural networks.
problem Overestimation of adversarial robustness using first-order attack methods.
method Proposed compensation methods address inaccurate gradient computation and reduce backpropagations.
result Empirical evaluation of adversarial robustness is improved with these methods.
We study the regularity of exceptional actions of groups by C1,α diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of continuity α. Let G be a finitely generated group admitting a C1,α action $ρ…
Adversarial training makes logistic regression weight loss landscapes sharper.
problem Understanding why adversarial training sharpens the weight loss landscape in logistic regression.
method Theoretical analysis of linear logistic regression model with L2 norm constraints, and experiments on ResNet18.
result Adversarial training sharpens the weight loss landscape in linear logistic regression models.
New SPS variant improves non-smooth optimization without small gradients.
problem Improving non-smooth optimization without small gradients.
method Safeguarded Stochastic Polyak Step Size (SPSsafe) for non-smooth optimization. result Rigorous convergence guarantees for non-smooth convex optimization without strong assumptions.
The study finds a trade-off between model size, test loss, and training loss for linear predictors.
problem Finding the optimal balance between model size, test loss, and training loss for linear predictors.
method Established an algorithm and distribution-independent trade-off using non-asymptotic analysis.
result Models with low test loss are either classical (close to noise level training loss) or modern (large number of parameters).
Loss-guided training accelerates node embedding methods on graphs.
problem Training efficiency in graph learning methods with implicit positive examples.
method Dynamic adjustment of training distribution based on loss values.
result Significant acceleration in training and computation over static methods.
The L2-∂∂-Lemma is extended to complete Kähler manifolds with a gap in the spectrum.
problem Extending the L2-∂∂-Lemma to non-compact Kähler manifolds. method Proving the L2-∂∂-Lemma on complete Kähler manifolds with a gap in the spectrum. result The L2-∂∂-Lemma is generalized to complete Kähler manifolds. Paper discovers simplicial complexes connecting trained models for improved ensembling.
problem Improving robustness and accuracy of deep learning ensembles.
method Identifies mode-connecting simplicial complexes on loss surfaces.
result Efficiently builds simplicial complexes for ensembling, outperforming independent ensembles.
Large learning rates improve neural network generalization, study shows.
problem Understanding why large learning rates lead to better neural network generalization.
method Visual analysis of training and testing loss landscapes, introduction of a nonlinear model.
result Extended phase with large learning rates leads to near-optimal generalization.
Modified model prevents volatility from approaching zero.
problem Volatility in the Gatheral model can approach zero, making it statistically indistinguishable.
method Proposed a modified model with Skorokhod reflection to prevent volatility from approaching zero.
result The modified model prevents volatility from approaching zero, preserving the model's flexibility.
AWP improves robustness by flattening weight loss landscape.
problem Improving robustness of deep neural networks against adversarial examples.
method Explicitly regularizes the flatness of weight loss landscape through adversarial weight perturbation.
result AWP forms a double-perturbation mechanism in adversarial training, leading to flatter weight loss landscape.
SIFT reduces training time by selecting samples with approximate losses.
problem Reducing training time by selecting samples with large approximate losses.
method Developed SIFT which uses early exiting to obtain approximate losses with intermediate layer representations for sample selection.
result SIFT achieves significant gains in training time and number of backpropagation steps without optimized implementation.
This work improves diffusion models by estimating the optimal loss value for better training diagnostics.
problem The optimal loss value of diffusion models is unknown and not indicative of absolute data-fitting quality.
method Derive the optimal loss in closed form and develop effective estimators, including a stochastic variant.
result Unlocking the optimal loss as a metric for diagnosing training quality of diffusion models.