A mean-field kinetic theory derivation produces a closed-form U-shaped token retrieval profile that explains the lost-in-the-middle phenomenon in Transformers.
hub
A unified perspective on the dynamics of deep transformers.arXiv preprint arXiv:2501.18322
11 Pith papers cite this work. Polarity classification is still indexing.
11
Pith papers citing it
hub tools
citation-role summary
background 3
citation-polarity summary
roles
background 3polarities
background 3representative citing papers
Derives transformer-like dual-filter inference layers from first-principles optimal control on nonlinear discrete and linear Gaussian sequence models.
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.
Symmetric self-attention dynamics select the dominant eigendirection of V, producing homogeneous alignment when one positive eigenvalue dominates or sign-split polarization when V is negative definite.
A preconditioned regularized Wasserstein proximal sampling algorithm is introduced for particle-based approximation of Gibbs distributions, featuring a PDE-derived kernel formulation and non-asymptotic convergence analysis for quadratic potentials.
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.
Models multi-head transformer data flow as time-dependent Wasserstein gradient flows of an attention-capturing interaction energy, with proofs on omega-limit stationary points and stability under weight and input perturbations.
In the low-temperature regime, the token distribution in mean-field transformers concentrates onto the push-forward under a key-query-value projection with Wasserstein distance scaling as √(log(β+1)/β) exp(Ct) + exp(-ct).
Gradient descent on wide shallow models with bounded nonlinearities converges globally in the mean-field limit as non-global critical points are unstable under the dynamics.
Mean-field transformer models synchronize to a Dirac point mass exponentially fast with explicit quantitative rates under suitable parameter assumptions.
citing papers explorer
-
Kinetic theory for Transformers and the lost-in-the-middle phenomenon
A mean-field kinetic theory derivation produces a closed-form U-shaped token retrieval profile that explains the lost-in-the-middle phenomenon in Transformers.
-
Transformer-like Inference from Optimal Control
Derives transformer-like dual-filter inference layers from first-principles optimal control on nonlinear discrete and linear Gaussian sequence models.
-
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.
-
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.
-
Spectral Selection in Symmetric Self-Attention Dynamics
Symmetric self-attention dynamics select the dominant eigendirection of V, producing homogeneous alignment when one positive eigenvalue dominates or sign-split polarization when V is negative definite.
-
Preconditioned Regularized Wasserstein Proximal Sampling
A preconditioned regularized Wasserstein proximal sampling algorithm is introduced for particle-based approximation of Gibbs distributions, featuring a PDE-derived kernel formulation and non-asymptotic convergence analysis for quadratic potentials.
-
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.
-
Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows
Models multi-head transformer data flow as time-dependent Wasserstein gradient flows of an attention-capturing interaction energy, with proofs on omega-limit stationary points and stability under weight and input perturbations.
-
Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regime
In the low-temperature regime, the token distribution in mean-field transformers concentrates onto the push-forward under a key-query-value projection with Wasserstein distance scaling as √(log(β+1)/β) exp(Ct) + exp(-ct).
-
On the global convergence of gradient descent for wide shallow models with bounded nonlinearities
Gradient descent on wide shallow models with bounded nonlinearities converges globally in the mean-field limit as non-global critical points are unstable under the dynamics.
-
Quantitative Clustering in Mean-Field Transformer Models
Mean-field transformer models synchronize to a Dirac point mass exponentially fast with explicit quantitative rates under suitable parameter assumptions.