The double descent (DD) paradox, where over-parameterized models see generalization improve past the interpolation point, remains largely unexplored in the non-stationary domain of Deep Reinforcement Learning (DRL). We present preliminary evidence that DD exists in model-free DRL, investigating it systematically across varying model capacity using the Actor-Critic framework. We rely on an information-theoretic metric, Policy Entropy, to measure policy uncertainty throughout training. Preliminary results show a clear epoch-wise DD curve; the policy's entrance into the second descent region correlates with a sustained, significant reduction in Policy Entropy. This entropic decay suggests that over-parameterization acts as an implicit regularizer, guiding the policy towards robust, flatter minima in the loss landscape. These findings establish DD as a factor in DRL and provide an information-based mechanism for designing agents that are more general, transferable, and robust.

Accuracy curves of model trained using ERM. Figure 7: Accuracy curves of model trained on noisy CIFAR10 training set with 80% noise rate. For training, we use initial learning rate of 0.1, batch size of 128, 100 training epochs. We split the training set into two portions: 1) Untouched portion, i.e., the elements in the training set which were left untouched; 2) Corrupted portion, i.e., the elements in The learning rate is linearly increased from 0.0003 Following common practice, we use random resizing, cropping and flipping augmentation during training. However, they only analyzed the generalization errors in the presence of corrupted labels. This occurs around the epochs between underfitting and overfitting.

Double descent is a phenomenon of over-parameterized statistical models. Our goal is to view double descent from a Bayesian perspective. Over-parameterized models such as deep neural networks have an interesting re-descending property in their risk characteristics. This is a recent phenomenon in machine learning and has been the subject of many studies. As the complexity of the model increases, there is a U-shaped region corresponding to the traditional bias-variance trade-off, but then as the number of parameters equals the number of observations and the model becomes one of interpolation, the risk can become infinite and then, in the over-parameterized region, it re-descends -- the double descent effect. We show that this has a natural Bayesian interpretation. Moreover, we show that it is not in conflict with the traditional Occam's razor that Bayesian models possess, in that they tend to prefer simpler models when possible. We illustrate the approach with an example of Bayesian model selection in neural networks. Finally, we conclude with directions for future research.

The double descent phenomenon, which deviates from the traditional bias-variance trade-off theory, attracts considerable research attention; however, the mechanism of its occurrence is not fully understood. On the other hand, in the study of convolutional neural networks (CNNs) for image recognition, methods are proposed to quantify the bias on shape features versus texture features in images, determining which features the CNN focuses on more. In this work, we hypothesize that there is a relationship between the shape/texture bias in the learning process of CNNs and epoch-wise double descent, and we conduct verification. As a result, we discover double descent/ascent of shape/texture bias synchronized with double descent of test error under conditions where epoch-wise double descent is observed. Quantitative evaluations confirm this correlation between the test errors and the bias values from the initial decrease to the full increase in test error. Interestingly, double descent/ascent of shape/texture bias is observed in some cases even in conditions without label noise, where double descent is thought not to occur. These experimental results are considered to contribute to the understanding of the mechanisms behind the double descent phenomenon and the learning process of CNNs in image recognition.

We propose a first near complete (that will make explicit sense in the main text) nonasymptotic generalization theory for multilayer neural networks with arbitrary Lipschitz activations and general Lipschitz loss functions (with some very mild conditions). In particular, it doens't require the boundness of loss function, as commonly assumed in the literature. Our theory goes beyond the bias-variance tradeoff, aligned with phenomenon typically encountered in deep learning. It is therefore sharp different with other existing nonasymptotic generalization error bounds for neural networks. More explicitly, we propose an explicit generalization error upper bound for multilayer neural networks with arbitrary Lipschitz activations $\sigma$ with $\sigma(0)=0$ and broad enough Lipschitz loss functions, without requiring either the width, depth or other hyperparameters of the neural network approaching infinity, a specific neural network architect (e.g. sparsity, boundness of some norms), a particular activation function, a particular optimization algorithm or boundness of the loss function, and with taking the approximation error into consideration. General Lipschitz activation can also be accommodated into our framework. A feature of our theory is that it also considers approximation errors. Furthermore, we show the near minimax optimality of our theory for multilayer ReLU networks for regression problems. Notably, our upper bound exhibits the famous double descent phenomenon for such networks, which is the most distinguished characteristic compared with other existing results. This work emphasizes a view that many classical results should be improved to embrace the unintuitive characteristics of deep learning to get a better understanding of it.

Large Language Models (LLMs) have achieved remarkable success in natural language processing, but their full fine-tuning remains resource-intensive. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have emerged as a practical solution by approximating parameter updates with low-rank matrices. However, LoRA often exhibits a "double descent" phenomenon during fine-tuning, where model performance degrades due to overfitting and limited expressiveness caused by low-rank constraints. To address this issue, we propose LoRA-GGPO (Gradient-Guided Perturbation Optimization), a novel method that leverages gradient and weight norms to generate targeted perturbations. By optimizing the sharpness of the loss landscape, LoRA-GGPO guides the model toward flatter minima, mitigating the double descent problem and improving generalization. Extensive experiments on natural language understanding (NLU) and generation (NLG) tasks demonstrate that LoRA-GGPO outperforms LoRA and its state-of-the-art variants. Furthermore, extended experiments specifically designed to analyze the double descent phenomenon confirm that LoRA-GGPO effectively alleviates this issue, producing more robust and generalizable models. Our work provides a robust and efficient solution for fine-tuning LLMs, with broad applicability in real-world scenarios. The code is available at https://github.com/llm172/LoRA-GGPO.

While overparameterization is known to benefit generalization, its impact on Out-Of-Distribution (OOD) detection is less understood. This paper investigates the influence of model complexity in OOD detection. We propose an expected OOD risk metric to evaluate classifiers confidence on both training and OOD samples. Leveraging Random Matrix Theory, we derive bounds for the expected OOD risk of binary least-squares classifiers applied to Gaussian data. We show that the OOD risk depicts an infinite peak, when the number of parameters is equal to the number of samples, which we associate with the double descent phenomenon. Our experimental study on different OOD detection methods across multiple neural architectures extends our theoretical insights and highlights a double descent curve. Our observations suggest that overparameterization does not necessarily lead to better OOD detection. Using the Neural Collapse framework, we provide insights to better understand this behavior. To facilitate reproducibility, our code will be made publicly available upon publication.

Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon in specific contexts, an accepted theory for its occurring mechanism in deep learning remains yet to be established. In this study, we revisited the phenomenon of double descent and discussed the conditions of its occurrence. This paper introduces the concept of class-activation matrices and a methodology for estimating the effective complexity of functions, on which we unveil that over-parameterized models exhibit more distinct and simpler class patterns in hidden activations compared to under-parameterized ones. We further looked into the interpolation of noisy labelled data among clean representations and demonstrated overfitting w.r.t. expressive capacity. By comprehensively analysing hypotheses and presenting corresponding empirical evidence that either validates or contradicts these hypotheses, we aim to provide fresh insights into the phenomenon of double descent and benign over-parameterization and facilitate future explorations. By comprehensively studying different hypotheses and the corresponding empirical evidence either supports or challenges these hypotheses, our goal is to offer new insights into the phenomena of double descent and benign over-parameterization, thereby enabling further explorations in the field. The source code is available at https://github.com/Yufei-Gu-451/sparse-generalization.git.

This paper investigates the double descent phenomenon in two-layer neural networks, focusing on the role of L1 regularization and representation dimensions. It explores an alternative double descent phenomenon, named'sparse double descent'. The study emphasizes the complex relationship between model complexity, sparsity, and generalization, and suggests further research into more diverse models and datasets. The findings contribute to a deeper understanding of neural network training and optimization.

Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon in specific contexts, an accepted theory for its occurrence in deep learning remains yet to be established. In this study, we revisit the phenomenon of double descent and demonstrate that its occurrence is strongly influenced by the presence of noisy data. Through conducting a comprehensive analysis of the feature space of learned representations, we unveil that double descent arises in imperfect models trained with noisy data. We argue that double descent is a consequence of the model first learning the noisy data until interpolation and then adding implicit regularization via over-parameterization acquiring therefore capability to separate the information from the noise. As a well-known property of machine learning, the bias-variance trade-off suggested that the variance of the parameter estimated across samples can be reduced by increasing the bias in the estimated parameters (Geman et al., 1992). When a model is under-parameterized, there exists a combination of high bias and low variance. Under this circumstance, the model becomes trapped in under-fitting, signifying its inability to grasp the fundamental underlying structures present in the data. When a model is over-parameterized, there exists a combination of low bias and high variance. This is usually due to the model over-fitting noisy and unrepresentative data in the training set.