Deep Double Descent: Where Bigger Models and More Data Hurt
Not on the map. Why?
Abstract (arXiv)
We show that a variety of modern deep learning tasks exhibit a "double-descent" phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the effective model complexity and conjecture a generalized double descent with respect to this measure. Furthermore, our notion of model complexity allows us to identify certain regimes where increasing (even quadrupling) the number of train samples actually hurts test performance.
Key facts. Cited by 672 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Dec 2019.
Builds on
No reference list yet.
Built on by
Citing papers per year: 2020: 1; 2021: 120; 2022: 134; 2023: 119; 2024: 122; 2025: 93; 2026: 83.
672 papers.
Sort:
By area:
- 2023A Survey of Large Language Modelscited by 2,576
- 2022In-context Learning and Induction Headscited by 964
- 2022Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasetscited by 629
- 2023Scaling Data-Constrained Language Modelscited by 403
- 2021Explaining Neural Scaling Lawscited by 363
- 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Examplecited by 295
- 2021The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networkscited by 291
- 2021Scaling Laws for Transfercited by 272
- 2022Towards Understanding Grokking: An Effective Theory of Representation Learningcited by 230
- 2021A Geometric Analysis of Neural Collapse with Unconstrained Featurescited by 227
- 2022Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Modelscited by 220
- 2023ReLoRA: High-Rank Training Through Low-Rank Updatescited by 204
38 more
- 2024Do Membership Inference Attacks Work on Large Language Models?cited by 195
- 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
- 2021The Low-Rank Simplicity Bias in Deep Networkscited by 154
- 2022Scaling Laws and Interpretability of Learning from Repeated Datacited by 152
- 2021A Universal Law of Robustness via Isoperimetrycited by 151
- 2024CycleResearcher: Improving Automated Research via Automated Reviewcited by 148
- 2022Towards Understanding Sharpness-Aware Minimizationcited by 146
- 2022Omnigrok: Grokking Beyond Algorithmic Datacited by 146
- 2023Taken out of context: On measuring situational awareness in LLMscited by 143
- 2024Rho-1: Not All Tokens Are What You Needcited by 133
- 2021Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolationcited by 132
- 2023End-to-End Speech Recognition: A Surveycited by 129
- 2023On Memorization in Diffusion Modelscited by 125
- 2024A Practical Review of Mechanistic Interpretability for Transformer-Based Language Modelscited by 118
- 2021Assessing Generalization of SGD via Disagreementcited by 117
- 2021The Devil is in the Detail: Simple Tricks Improve Systematic Generalization of Transformerscited by 117
- 2022A Solvable Model of Neural Scaling Lawscited by 116
- 2021Understanding and Improving Early Stopping for Learning with Noisy Labelscited by 113
- 2022Broken Neural Scaling Lawscited by 109
- 2022On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Featurescited by 97
- 2024RLHF Deciphered: A Critical Analysis of Reinforcement Learning from Human Feedback for LLMscited by 90
- 2021SpeechStew: Simply Mix All Available Speech Recognition Data to Train One Large Neural Networkcited by 83
- 2022Training Trajectories of Language Models Across Scalescited by 81
- 2021Pixelated Butterfly: Simple and Efficient Sparse training for Neural Network Modelscited by 76
- 2022PAC-Bayes Compression Bounds So Tight That They Can Explain Generalizationcited by 76
- 2024SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learningcited by 76
- 2021Label-Imbalanced and Group-Sensitive Classification under Overparameterizationcited by 74
- 2021On the geometry of generalization and memorization in deep neural networkscited by 73
- 2023Why Do We Need Weight Decay in Modern Deep Learning?cited by 72
- 2021Benign Overfitting of Constant-Stepsize SGD for Linear Regressioncited by 71
- 2021The Shape of Learning Curves: a Reviewcited by 70
- 2022SGD with Large Step Sizes Learns Sparse Featurescited by 68
- 2021Model Complexity of Deep Learning: A Surveycited by 65
- 2022Deep Ensembles Work, But Are They Necessary?cited by 63
- 2021Lost in Pruning: The Effects of Pruning Neural Networks beyond Test Accuracycited by 62
- 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
- 2025How much do language models memorize?cited by 61
- 2021On Memorization in Probabilistic Deep Generative Modelscited by 60
50 most cited of 672 All 672 (JSON)
- 2026Simulating Training Spikes of Deep Neural Networks by Layer-wise Random Feature Models9 Oct 2026
- 2026How to scale your HEP ML models: A recipe for robust architecture comparisons at scale5 Oct 2026
- 2026LoRA's Second Descent Extends Beyond Parameter Parity3 Oct 2026
- 2026Measuring trainable degrees of freedom in materials graph neural networks: a random-subspace intrinsic dimension analysis28 Sep 2026
- 2026Rolling Conformal Prediction in Sequential Model Training22 Sep 2026
- 2026Double Descent and Malign Overfitting in Diffusion Models22 Sep 2026
- 2026Neural Cellular Automata Learn General Features in their Hidden Channels18 Sep 2026
- 2026Double descent is the principle of least action16 Sep 2026
- 2026Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking9 Sep 2026
- 2026A Data-dependent Early Stopping Rule using Rademacher Complexity with L1-norm25 Aug 2026
- 2026From Gradient-Boosted Trees to Deep Recommenders: Practical Lessons from Migrating a Production Customer Support Recommender25 Aug 2026
- 2026Is Grokking a Loss of Normal Hyperbolicity of the Interpolation Manifold?14 Aug 2026
38 more
- 2026Adapting Vision Foundation Models with Cascaded Semantics5 Aug 2026
- 2026Double Descent in Gradient Boosting Decision Trees via Split-Candidate Scaling4 Aug 2026
- 2026Simplifying Neural Networks During Training30 Jul 2026
- 2026Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generation29 Jul 2026
- 2026Origins and mitigation of double descent in reduced order modeling29 Jul 2026
- 2026Cautious optimism for deep parameterized quantum circuits23 Jul 2026
- 2026Fisher Rank Inflation: A Spectral Signature of Memorization under Label Noise14 Jul 2026
- 2026Random Label Prediction Heads for Studying Memorization in Deep Neural Networks13 Jul 2026
- 2026Benign Overfitting Does Not Occur in Diffusion Models2 Jul 2026
- 2026World-Model Collapse as a Phase Transition30 Jun 2026
- 2026How Far Can Sharpness and Complexity Jointly Explain Generalization?27 Jun 2026
- 2026Bridging Ab Initio Symmetries and Global Nuclear Masses with Interpretable Neural Networks26 Jun 2026
- 2026Interpreting "Interpretability" and Explaining "Explainability" in Machine Learning in Physics24 Jun 2026
- 2026Knowledge Cascade: Reverse Knowledge Distillation on Nonparametric Multivariate Functional Estimation24 Jun 2026
- 2026The Generalization Spectrum: A Chromatographic Approach to Evaluating Learning Algorithms24 Jun 2026
- 2026Internal Data Repetition Destroys Language Models23 Jun 2026
- 2026Statistical Properties of Training & Generalization18 Jun 2026
- 2026The Geometry of Saturation: Effective Rank Predicts When Labels Stop Helping in Few-Shot Classification12 Jun 2026
- 2026The Weight Norm Sets the Grokking Timescale: A Causal Delay Law11 Jun 2026
- 2026GLACIER: A Multimodal Student-Teacher Foundation Model for Molecular Property Prediction9 Jun 2026
- 2026One Step Closer to Ground Truth: A Multi-Scale Residual-Aware Representation Learning Pipeline for Predicting Time Series Data9 Jun 2026
- 2026An Empirical Study of Data Scale, Model Complexity, and Input Modalities in Visual Generalization3 Jun 2026
- 2026Provable Data Scaling Law for Meta Learning via Complexity Minimization1 Jun 2026
- 2026Inconsistency-Aware Minimization: Improving Generalization with Unlabeled Data29 May 2026
- 2026Is the Last Layer Sufficient for Uncertainty Quantification?29 May 2026
- 2026Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention28 May 2026
- 2026Unveiling Multi-regime Patterns in SciML: Distinct Failure Modes and Regime-specific Optimization27 May 2026
- 2026Do Deep Networks Forget Initialization? A Forgetting-Time View of Practical Inductive Bias27 May 2026
- 2026Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks26 May 2026
- 2026Unified Neural Scaling Laws25 May 2026
- 2026Asymmetric Scaling Laws from Sparse Features22 May 2026
- 2026Understanding Goal Generalisation in Sequential Reinforcement Learning22 May 2026
- 2026A Rigorous, Tractable Measure of Model Complexity20 May 2026
- 2026Cumulative Meta-Learning from Active Learning Queries for Robustness to Spurious Correlations20 May 2026
- 2026Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise18 May 2026
- 2026Bounded-Rationality, Hedging, and Generalization14 May 2026
- 2026Slower Generalization, Faster Memorization: A Sweet Spot in Algorithmic Learning14 May 2026
- 2026Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds10 May 2026
50 newest of 672 All 672 (JSON)
- 2023On Memorization in Diffusion Modelscited by 125
- 2025Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Modelscited by 25
- 2024GenMix: Effective Data Augmentation with Generative Diffusion Model Image Editingcited by 14
- 2024Swing-by Dynamics in Concept Learning and Compositional Generalizationcited by 5
- 2026Benign Overfitting Does Not Occur in Diffusion Modelscited by 3
- 2025Understanding Generalization in Diffusion Distillation via Probability Flow Distancecited by 2
- 2026Understanding diffusion models requires rethinking (again) generalizationcited by 2
- 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Modelscited by 1
- 2025On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Modelscited by 1
- 2025Double Descent as a Lens for Sample Efficiency in Autoregressive vs. Discrete Diffusion Modelscited by 1
- 2025On the Anisotropy of Score-Based Generative Modelscited by 1
- 2026Double Descent and Malign Overfitting in Diffusion Modelscited by 1
- 2026Double Descent and Malign Overfitting in Diffusion Models22 Sep 2026
- 2026Benign Overfitting Does Not Occur in Diffusion Models2 Jul 2026
- 2026Understanding diffusion models requires rethinking (again) generalization7 May 2026
- 2025On the Anisotropy of Score-Based Generative Models27 Oct 2025
- 2025Double Descent as a Lens for Sample Efficiency in Autoregressive vs. Discrete Diffusion Models29 Sep 2025
- 2025On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models22 Aug 2025
- 2025Understanding Generalization in Diffusion Distillation via Probability Flow Distance26 May 2025
- 2025Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models22 May 2025
- 2024GenMix: Effective Data Augmentation with Generative Diffusion Model Image Editing3 Dec 2024
- 2024Swing-by Dynamics in Concept Learning and Compositional Generalization10 Oct 2024
- 2023On Memorization in Diffusion Models4 Oct 2023
- 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models16 May 2023
- 2021Teacher's pet: understanding and mitigating biases in distillationcited by 21
- 2021Even your Teacher Needs Guidance: Ground-Truth Targets Dampen Regularization Imposed by Self-Distillationcited by 11
- 2021Distilling Double Descentcited by 7
- 2024Robust Knowledge Distillation Based on Feature Variance Against Backdoored Teacher Modelcited by 2
- 2023Learn from the Past: A Proxy Guided Adversarial Defense Framework with Self Distillation Regularizationcited by 0
- 2024Dynamics of Meta-learning Representation in the Teacher-student Scenariocited by 0
- 2025Deep Probabilistic Supervision for Image Classificationcited by 0
- 2026Knowledge Cascade: Reverse Knowledge Distillation on Nonparametric Multivariate Functional Estimationcited by 0
- 2026Knowledge Cascade: Reverse Knowledge Distillation on Nonparametric Multivariate Functional Estimation24 Jun 2026
- 2025Deep Probabilistic Supervision for Image Classification30 Dec 2025
- 2024Dynamics of Meta-learning Representation in the Teacher-student Scenario22 Aug 2024
- 2024Robust Knowledge Distillation Based on Feature Variance Against Backdoored Teacher Model1 Jun 2024
- 2023Learn from the Past: A Proxy Guided Adversarial Defense Framework with Self Distillation Regularization19 Oct 2023
- 2021Teacher's pet: understanding and mitigating biases in distillation19 Jun 2021
- 2021Even your Teacher Needs Guidance: Ground-Truth Targets Dampen Regularization Imposed by Self-Distillation25 Feb 2021
- 2021Distilling Double Descent13 Feb 2021
- 2024SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learningcited by 76
- 2025All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuningcited by 59
- 2024Estimating Reaction Barriers with Deep Reinforcement Learningcited by 1
- 2025The Cake that is Intelligence and Who Gets to Bake it: An AI Analogy and its Implications for Participationcited by 1
- 2025Free Random Projection for In-Context Reinforcement Learningcited by 0
- 2025On The Presence of Double-Descent in Deep Reinforcement Learningcited by 0
- 2026Understanding Goal Generalisation in Sequential Reinforcement Learningcited by 0
- 2026Understanding Goal Generalisation in Sequential Reinforcement Learning22 May 2026
- 2025On The Presence of Double-Descent in Deep Reinforcement Learning10 Nov 2025
- 2025Free Random Projection for In-Context Reinforcement Learning9 Apr 2025
- 2025All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuning3 Mar 2025
- 2025The Cake that is Intelligence and Who Gets to Bake it: An AI Analogy and its Implications for Participation5 Feb 2025
- 2024SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learning13 Oct 2024
- 2024Estimating Reaction Barriers with Deep Reinforcement Learning17 Jul 2024
- 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Examplecited by 295
- 2024Towards Uncovering How Large Language Model Works: An Explainability Perspectivecited by 22
- 2024Take the essence and discard the dross: A Rethinking on Data Selection for Fine-Tuning Large Language Modelscited by 12
- 2025Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformerscited by 12
- 2026Outcome-Based RL Provably Leads Transformers to Reason, but Only With the Right Datacited by 6
- 2022GPT-Neo for commonsense reasoning -- a theoretical and practical lenscited by 4
- 2025Finding the Minimal Parameter Budget for Implicit Reasoning: A Data Complexity Driven Scaling Law for Language Modelscited by 3
- 2026Outcome-Based RL Provably Leads Transformers to Reason, but Only With the Right Data21 Jan 2026
- 2025Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformers29 Apr 2025
- 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Example29 Apr 2025
- 2025Finding the Minimal Parameter Budget for Implicit Reasoning: A Data Complexity Driven Scaling Law for Language Models4 Apr 2025
- 2024Take the essence and discard the dross: A Rethinking on Data Selection for Fine-Tuning Large Language Models20 Jun 2024
- 2024Towards Uncovering How Large Language Model Works: An Explainability Perspective16 Feb 2024
- 2022GPT-Neo for commonsense reasoning -- a theoretical and practical lens28 Nov 2022
- 2024Do Membership Inference Attacks Work on Large Language Models?cited by 195
- 2022A Blessing of Dimensionality in Membership Inference through Regularizationcited by 18
- 2024Trojan Cleansing with Neural Collapsecited by 1
- 2025How Does Overparameterization Affect Machine Unlearning of Deep Neural Networks?cited by 1
- 2026Beyond Passive Aggregation: Active Auditing and Topology-Aware Defense in Decentralized Federated Learningcited by 0
- 2026Beyond Passive Aggregation: Active Auditing and Topology-Aware Defense in Decentralized Federated Learning19 Mar 2026
- 2025How Does Overparameterization Affect Machine Unlearning of Deep Neural Networks?11 Mar 2025
- 2024Trojan Cleansing with Neural Collapse19 Nov 2024
- 2024Do Membership Inference Attacks Work on Large Language Models?12 Feb 2024
- 2022A Blessing of Dimensionality in Membership Inference through Regularization27 May 2022
- 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
- 2024RLHF Deciphered: A Critical Analysis of Reinforcement Learning from Human Feedback for LLMscited by 90
- 2024Dynamic Normativity: Necessary and Sufficient Conditions for Value Alignmentcited by 3
- 2024Dynamic Normativity: Necessary and Sufficient Conditions for Value Alignment16 Jun 2024
- 2024RLHF Deciphered: A Critical Analysis of Reinforcement Learning from Human Feedback for LLMs12 Apr 2024
- 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks23 Jun 2020
- 2023A Survey of Large Language Modelscited by 2,576
- 2022In-context Learning and Induction Headscited by 964
- 2022Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasetscited by 629
- 2023Scaling Data-Constrained Language Modelscited by 403
- 2021Explaining Neural Scaling Lawscited by 363
- 2021The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networkscited by 291
- 2021Scaling Laws for Transfercited by 272
- 2022Towards Understanding Grokking: An Effective Theory of Representation Learningcited by 230
- 2021A Geometric Analysis of Neural Collapse with Unconstrained Featurescited by 227
- 2022Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Modelscited by 220
- 2023ReLoRA: High-Rank Training Through Low-Rank Updatescited by 204
- 2021The Low-Rank Simplicity Bias in Deep Networkscited by 154
12 most cited of 625 All 625 (JSON)
- 2026Simulating Training Spikes of Deep Neural Networks by Layer-wise Random Feature Models9 Oct 2026
- 2026How to scale your HEP ML models: A recipe for robust architecture comparisons at scale5 Oct 2026
- 2026LoRA's Second Descent Extends Beyond Parameter Parity3 Oct 2026
- 2026Measuring trainable degrees of freedom in materials graph neural networks: a random-subspace intrinsic dimension analysis28 Sep 2026
- 2026Rolling Conformal Prediction in Sequential Model Training22 Sep 2026
- 2026Neural Cellular Automata Learn General Features in their Hidden Channels18 Sep 2026
- 2026Double descent is the principle of least action16 Sep 2026
- 2026Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking9 Sep 2026
- 2026A Data-dependent Early Stopping Rule using Rademacher Complexity with L1-norm25 Aug 2026
- 2026From Gradient-Boosted Trees to Deep Recommenders: Practical Lessons from Migrating a Production Customer Support Recommender25 Aug 2026
- 2026Is Grokking a Loss of Normal Hyperbolicity of the Interpolation Manifold?14 Aug 2026
- 2026Adapting Vision Foundation Models with Cascaded Semantics5 Aug 2026
12 newest of 625 All 625 (JSON)