The success of over-parameterized neural networks trained to near-zero training error has caused great interest in the phenomenon of benign overfitting, where estimators are statistically consistent even though they interpolate noisy training data. While benign overfitting in fixed dimension has been established for some learning methods, current literature suggests that for regression with typical kernel methods and wide neural networks, benign overfitting requires a high-dimensional setting, where the dimension grows with the sample size. In this paper, we show that the smoothness of the estimators, and not the dimension, is the key: benign overfitting is possible if and only if the estimator's derivatives are large enough. We generalize existing inconsistency results to non-interpolating models and more kernels to show that benign overfitting with moderate derivatives is impossible in fixed dimension. Conversely, we show that benign overfitting is possible for regression with a sequence of spiky-smooth kernels with large derivatives. Using neural tangent kernels, we translate our results to wide neural networks. We prove that while infinite-width networks do not overfit benignly with the ReLU activation, this can be fixed by adding small high-frequency fluctuations to the activation function. Our experiments verify that such neural networks, while overfitting, can indeed generalize well even on low-dimensional data sets.

The practical success of overparameterized neural networks has motivated the recent scientific study of \emph{interpolating methods}-- learning methods which are able fit their training data perfectly. Empirically, certain interpolating methods can fit noisy training data without catastrophically bad test performance, which defies standard intuitions from statistical learning theory. Aiming to explain this, a large body of recent work has studied \emph{benign overfitting}, a behavior seen in certain asymptotic settings under which interpolating methods approach Bayes-optimality, even in the presence of noise. In this work, we argue that, while benign overfitting has been instructive to study, real interpolating methods like deep networks do not fit benignly. That is, noise in the train set leads to suboptimal generalization, suggesting that these methods fall in an intermediate regime between benign and catastrophic overfitting, in which asymptotic risk is neither is neither Bayes-optimal nor unbounded, with the confounding effect of the noise being ``tempered but non-negligible. We call this behavior \textit{tempered overfitting}. We first provide broad empirical evidence for our three-part taxonomy, demonstrating that deep neural networks and kernel machines fit to noisy data can be reasonably well classified as benign, tempered, or catastrophic. We then specialize to kernel (ridge) regression (KR), obtaining conditions on the ridge parameter and kernel eigenspectrum under which KR exhibits each of the three behaviors, demonstrating the consequences for KR with common kernels and trained neural networks of infinite width using experiments on natural and synthetic datasets.

The success of over-parameterized neural networks trained to near-zero training error has caused great interest in the phenomenon of benign overfitting, where estimators are statistically consistent even though they interpolate noisy training data. While benign overfitting in fixed dimension has been established for some learning methods, current literature suggests that for regression with typical kernel methods and wide neural networks, benign overfitting requires a high-dimensional setting, where the dimension grows with the sample size. In this paper, we show that the smoothness of the estimators, and not the dimension, is the key: benign overfitting is possible if and only if the estimator's derivatives are large enough. We generalize existing inconsistency results to non-interpolating models and more kernels to show that benign overfitting with moderate derivatives is impossible in fixed dimension. Conversely, we show that benign overfitting is possible for regression with a sequence of spiky-smooth kernels with large derivatives.

The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two-layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data which can be decomposed into the sum of a common signal and a random noise component, which lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign, or harmful, overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non-benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property.

Accurate detection of breast cancer from high-resolution mammograms is crucial for early diagnosis and effective treatment planning. Previous studies have shown the potential of using single-view mammograms for breast cancer detection. However, incorporating multi-view data can provide more comprehensive insights. Multi-view classification, especially in medical imaging, presents unique challenges, particularly when dealing with large-scale, high-resolution data. In this work, we propose a novel Multi-view Visual Prompt Tuning Network (MVPT-NET) for analyzing multiple screening mammograms. We first pretrain a robust single-view classification model on high-resolution mammograms and then innovatively adapt multi-view feature learning into a task-specific prompt tuning process. This technique selectively tunes a minimal set of trainable parameters (7\%) while retaining the robustness of the pre-trained single-view model, enabling efficient integration of multi-view data without the need for aggressive downsampling. Our approach offers an efficient alternative to traditional feature fusion methods, providing a more robust, scalable, and efficient solution for high-resolution mammogram analysis. Experimental results on a large multi-institution dataset demonstrate that our method outperforms conventional approaches while maintaining detection efficiency, achieving an AUROC of 0.852 for distinguishing between Benign, DCIS, and Invasive classes. This work highlights the potential of MVPT-NET for medical imaging tasks and provides a scalable solution for integrating multi-view data in breast cancer detection.

Background: Automated classification of thyroid Fine Needle Aspiration Biopsy (FNAB) images faces challenges in limited data, inter-observer variability, and computational cost. Efficient, interpretable models are crucial for clinical support. Objective: To develop and externally validate a deep learning system for multi-class thyroid FNAB image classification into three key categories directly guiding post-biopsy treatment in Vietnam: Benign (Bethesda II), Indeterminate/Suspicious (BI, III, IV, V), and Malignant (BVI), achieving high diagnostic accuracy with low computational overhead. Methods: Our pipeline features: (1) YOLOv10 cell cluster detection for informative sub-region extraction/noise reduction; (2) curriculum learning sequencing localized crops to full images for multi-scale capture; (3) adaptive lightweight EfficientNetB0 (4M parameters) balancing performance/efficiency; and (4) a Transformer-inspired module for multi-scale/multi-region analysis. External validation used 1,015 independent FNAB images. Results: ThyroidEffi Basic achieved macro F1 of 89.19% and AUCs of 0.98 (Benign), 0.95 (Indeterminate/Suspicious), 0.96 (Malignant) on the internal test set. External validation yielded AUCs of 0.9495 (Benign), 0.7436 (Indeterminate/Suspicious), 0.8396 (Malignant). ThyroidEffi Premium improved macro F1 to 89.77%. Grad-CAM highlighted key diagnostic regions, confirming interpretability. The system processed 1000 cases in 30 seconds, demonstrating feasibility on widely accessible hardware. Conclusions: This work demonstrates that high-accuracy, interpretable thyroid FNAB image classification is achievable with minimal computational demands.

Large Language Model (LLM) based judges form the underpinnings of key safety evaluation processes such as offline benchmarking, automated red-teaming, and online guardrailing. This widespread requirement raises the crucial question: can we trust the evaluations of these evaluators? In this paper, we highlight two critical challenges that are typically overlooked: (i) evaluations in the wild where factors like prompt sensitivity and distribution shifts can affect performance and (ii) adversarial attacks that target the judge. We highlight the importance of these through a study of commonly used safety judges, showing that small changes such as the style of the model output can lead to jumps of up to 0.24 in the false negative rate on the same dataset, whereas adversarial attacks on the model generation can fool some judges into misclassifying 100% of harmful generations as safe ones. These findings reveal gaps in commonly used meta-evaluation benchmarks and weaknesses in the robustness of current LLM judges, indicating that low attack success under certain judges could create a false sense of security. Well-known jailbreak attacks on widely used Large Language Models (LLMs) such as ChatGPT have raised concerns about the robustness of these systems to safety violations. As a result, organizations deploying them typically rely on a two-pronged approach to safety: 1) offline benchmarking and red-teaming (Mazeika et al., 2024; Perez et al., 2022; Ganguli et al., 2022), and 2) online guardrails designed to minimize the risk from attacks (Mu et al., 2024; Manczak et al., 2024; Neill et al., 2024).

Transformers serve as the foundational architecture for many successful large-scale models, demonstrating the ability to overfit the training data while maintaining strong generalization on unseen data, a phenomenon known as benign overfitting. However, research on how the training dynamics influence error bounds within the context of benign overfitting has been limited. This paper addresses this gap by developing a generalization theory for a two-layer transformer with labeled flip noise. Specifically, we present generalization error bounds for both benign and harmful overfitting under varying signal-to-noise ratios (SNR), where the training dynamics are categorized into three distinct stages, each with its corresponding error bounds. Additionally, we conduct extensive experiments to identify key factors that influence test errors in transformers. Our experimental results align closely with the theoretical predictions, validating our findings.

The success of over-parameterized neural networks trained to near-zero training error has caused great interest in the phenomenon of benign overfitting, where estimators are statistically consistent even though they interpolate noisy training data. While benign overfitting in fixed dimension has been established for some learning methods, current literature suggests that for regression with typical kernel methods and wide neural networks, benign overfitting requires a high-dimensional setting, where the dimension grows with the sample size. In this paper, we show that the smoothness of the estimators, and not the dimension, is the key: benign overfitting is possible if and only if the estimator's derivatives are large enough. We generalize existing inconsistency results to non-interpolating models and more kernels to show that benign overfitting with moderate derivatives is impossible in fixed dimension. Conversely, we show that benign overfitting is possible for regression with a sequence of spiky-smooth kernels with large derivatives.

The practical success of overparameterized neural networks has motivated the recent scientific study of \emph{interpolating methods}-- learning methods which are able fit their training data perfectly. Empirically, certain interpolating methods can fit noisy training data without catastrophically bad test performance, which defies standard intuitions from statistical learning theory. Aiming to explain this, a large body of recent work has studied \emph{benign overfitting}, a behavior seen in certain asymptotic settings under which interpolating methods approach Bayes-optimality, even in the presence of noise. In this work, we argue that, while benign overfitting has been instructive to study, real interpolating methods like deep networks do not fit benignly. That is, noise in the train set leads to suboptimal generalization, suggesting that these methods fall in an intermediate regime between benign and catastrophic overfitting, in which asymptotic risk is neither is neither Bayes-optimal nor unbounded, with the confounding effect of the noise being tempered" but non-negligible.