Finite-width shallow networks remain within poly(d) m^{-min(1,c/6)} of their mean-field limit uniformly in time when mean-field excess loss decays as t^{-c} under standard regularity and an integral condition on the loss.
The hidden width of deep resnets: Tight error bounds and phase diagrams
6 Pith papers cite this work. Polarity classification is still indexing.
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AdamW-trained transformer hidden states and backpropagated variables converge uniformly in L2 to a forward-backward ODE system (McKean-Vlasov when non-causal) at rate O(L^{-1}+L^{-1/3}H^{-1/2}) as depth L and heads H increase, with bounds independent of token number.
Transformers converge pathwise to a stochastic particle system and SPDE in the scaling limit, exhibiting synchronization by noise and exponential energy dissipation when common noise is coercive relative to self-attention drift.
Derives forward and backward propagation-of-chaos bounds for finite vs. infinite-context transformers modeled as contextual flow maps, achieving Wasserstein rate n^{-1/d} generally and n^{-1/2} for transformer-like cases.
Strengthens classical scaling limit theorems for correlated random walks to functional convergence in Hölder and rough Hölder topologies.
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
citing papers explorer
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Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks
Finite-width shallow networks remain within poly(d) m^{-min(1,c/6)} of their mean-field limit uniformly in time when mean-field excess loss decays as t^{-c} under standard regularity and an integral condition on the loss.
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Uniform Scaling Limits in AdamW-Trained Transformers
AdamW-trained transformer hidden states and backpropagated variables converge uniformly in L2 to a forward-backward ODE system (McKean-Vlasov when non-causal) at rate O(L^{-1}+L^{-1/3}H^{-1/2}) as depth L and heads H increase, with bounds independent of token number.
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Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models
Transformers converge pathwise to a stochastic particle system and SPDE in the scaling limit, exhibiting synchronization by noise and exponential energy dissipation when common noise is coercive relative to self-attention drift.
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Propagation of Chaos in Contextual Flow Maps
Derives forward and backward propagation-of-chaos bounds for finite vs. infinite-context transformers modeled as contextual flow maps, achieving Wasserstein rate n^{-1/d} generally and n^{-1/2} for transformer-like cases.
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Functional Scaling Limits of Interpolated Correlated Random Walks in H\"older Topology
Strengthens classical scaling limit theorems for correlated random walks to functional convergence in Hölder and rough Hölder topologies.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.