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Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions Improved Baselines with Representation Autoencoders Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent A Two-Parameter Weibull Framework for Diagnosing Transformer Weight Distributions Calibeating for general proper losses: A Bregman divergence approach Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space Sample-efficient inductive matrix completion with noise and inexact side-information Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety XAI and Statistical Analysis for Reliable Intrusion Detection in the UAVIDS-2025 Dataset: From Tree to Hybrid and Tabular DNN Ensembles Reasoning Models Don't Just Think Longer, They Move Differently TabPFN-3: Technical Report Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: A large-scale benchmark of operator-adaptive PLS and Ridge models Towards a holistic understanding of Selection Bias for Causal Effect Identification Adaptive Kernel Density Estimation with Pre-training Coreset-Induced Conditional Velocity Flow Matching RISED: A Pre-Deployment Evaluation Framework for High-Stakes AI Decision-Support Systems, with Application to Healthcare ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage Model-based Bootstrap of Controlled Markov Chains Online Learning-to-Defer with Varying Experts Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification Keeping Score: Efficiency Improvements in Neural Likelihood Surrogate Training via Score-Augmented Loss Functions One-Step Generative Modeling via Wasserstein Gradient Flows Exact Stiefel Optimization for Probabilistic PLS: Closed-Form Updates, Error Bounds, and Calibrated Uncertainty A Composite Activation Function for Learning Stable Binary Representations Adaptive Calibration in Non-Stationary Environments Real vs. Semi-Simulated: Rethinking Evaluation for Treatment Effect Estimation Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage On Variance Reduction in Learning Mean Flows When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models Robust and Fast Training via Per-Sample Clipping Efficient Preference Poisoning Attack on Offline RLHF Joint Energy Management and Coordinated AIGC Workload Scheduling for Distributed Data Centers: A Diffusion-Aided Reward Shaping Approach Distributional Causal Mediation via Conditional Generative Modeling A Theory of Saddle Escape in Deep Nonlinear Networks Adaptive Querying with AI Persona Priors Optimal Spatio-Temporal Decoupling for Bayesian Conformal Prediction Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback Electricity price forecasting across Norway's five bidding zones in the post-crisis era Adversarial Robustness of NTK Neural Networks Identifiability and Stability of Generative Drifting with Companion-Elliptic Kernel Families A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws Conditional Score-Based Modeling of Effective Langevin Dynamics Inference of Online Newton Methods with Nesterov's Accelerated Sketching ProEval: Proactive Failure Discovery and Efficient Performance Estimation for Generative AI Evaluation Score-Repellent Monte Carlo: Toward Efficient Non-Markovian Sampler with Constant Memory in General State Spaces Learning to Emulate Chaos: Adversarial Optimal Transport Regularization Geometric Layer-wise Approximation Rates for Deep Networks S2MAM: Semi-supervised Meta Additive Model for Robust Estimation and Variable Selection Beyond Coefficients: Forecast-Necessity Testing for Interpretable Causal Discovery in Nonlinear Time-Series Models Curiosity-Critic: Cumulative Prediction Error Improvement as a Tractable Intrinsic Reward for World Model Training Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoning Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction Zeroth-Order Optimization at the Edge of Stability Generative Augmented Inference Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression Rare Event Analysis via Stochastic Optimal Control Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables Beyond Augmented-Action Surrogates for Multi-Expert Learning-to-Defer Spatio-temporal probabilistic forecast using MMAF-guided learning Conformal Policy Control The Implicit Curriculum: Learning Dynamics in RL with Verifiable Rewards Probabilistic NDVI Forecasting from Sparse Satellite Time Series and Weather Covariates Constrained Policy Optimization with Cantelli-Bounded Value-at-Risk Factorizable joint shift revisited Feature Learning Dynamics in Infinite-Depth Neural Networks Statistically-Guided Meta-Learning for Cross-Deployment Activity Recognition in Distributed Fiber-Optic Sensing DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions Neural ARFIMA model for forecasting BRIC exchange rates with long memory Neural Stochastic Differential Equations on Compact State Spaces: Theory, Methods, and Application to Suicide Risk Modeling BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization Random Walk Learning and the Pac-Man Attack Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models Post-Training Augmentation Invariance Optimizing LLM Inference: Fluid-Guided Online Scheduling with Memory Constraints Dataset-Driven Channel Masks in Transformers for Multivariate Time Series
DiffusionBlocks: Block-wise Neural Network Training via Diffusion Interpretation
Makoto Shing, Masanori Koyama, Takuya Akiba · 2025-06-17 · via stat updates on arXiv.org

End-to-end backpropagation requires storing activations throughout all layers, creating memory bottlenecks that limit model scalability. Existing block-wise training methods offer means to alleviate this problem, but they rely on ad-hoc local objectives and remain largely unexplored beyond classification tasks. We propose $\textit{DiffusionBlocks}$, a principled framework for transforming transformer-based networks into genuinely independent trainable blocks that maintain competitive performance with end-to-end training. Our key insight leverages the fact that residual connections naturally correspond to updates in a dynamical system. With minimal modifications to this system, we can convert the updates to those of a denoising process, where each block can be learned independently by leveraging the score matching objective. This independence enables training with gradients for only one block at a time, thereby reducing memory requirements in proportion to the number of blocks. Our experiments on a range of transformer architectures (vision, diffusion, autoregressive, recurrent-depth, and masked diffusion) demonstrate that DiffusionBlocks training matches the performance of end-to-end training while enabling scalable block-wise training on practical tasks beyond small-scale classification. DiffusionBlocks provides a theoretically grounded approach that successfully scales to modern generative tasks across diverse architectures. Code is available at https://github.com/SakanaAI/DiffusionBlocks .