stochastic dynamics and bifurcation

Últimos artículos

• Is Grokking a Loss of Normal Hyperbolicity of the Interpolation Manifold?

  Suvinava Basak · 18 de agosto de 2026

  A recent line of work recasts the post-memorization phase of grokking as constrained optimization: once a network interpolates the training set, weight decay drives a slow drift along the zero-loss manifold toward lower norm. In the language of dynamical systems, this is a fast-slow system in which …

• Stochastic Counterdiabatic Driving via Biorthogonal Liouvillian Eigenmodes

  Sandeep Suresh Cranganore, Sebastian Lehner, Johannes Brandstetter, Max Welling · 28 de julio de 2026

  Finite-time driving of stochastic systems generates excess dissipation, causing the evolving probability distribution to lag behind the instantaneous equilibrium, and consequently degrading the convergence of nonequilibrium free energy estimators based on the Jarzynski equality. Escorted free energy…

• Attention is Just Another Name for Coupling? A Fast-Slow ODE Perspective on Hierarchical Pretraining

  Zhengyuan Gao · 7 de julio de 2026

  We re-interpret Transformer pretraining as a fast-slow, singularly perturbed flow along depth, with untied weights as its non-autonomous feature. The linearised dynamics is a depth-ordered product of layer maps. Along a token-homogeneous reference trajectory, the linearised layer factorises along th…

• Central limit theorem for the averaged Adam optimizer

  Steffen Dereich, Arnulf Jentzen · 23 de junio de 2026

  In this article, we analyse convergence of the averaged Adam optimizer to an attracting zero of the Adam vector field. We provide a central limit theorem that, in particular, quantifies exactly the speed of convergence. The order of convergence is $n^{-1/2}$ in the number of steps of the algorithm w…

• Attention is Just Another Name for Coupling?: A Fast-Slow ODE Perspective on Hierarchical Pretraining

  Zhengyuan Gao · 16 de junio de 2026

  Causal self-attention is a coupling mechanism: each token's hidden state is updated by a learned mixture of preceding tokens at the same timescale. This paper asks whether a second, temporally slower coupling-a slow sub-system operating on a temporally-downsampled view of the sequence and fed back i…

• Parity Cross-Resonance: A Multiqubit Gate

  Xuexin Xu, Siyu Wang, Radhika Joshi, Rihan Hai, Mohammad H. Ansari · 10 de junio de 2026

  We present a native three-qubit entangling gate that exploits engineered interactions to realize control-control-target and control-target-target operations in a single coherent step. Unlike conventional decompositions into multiple two-qubit gates, our hybrid optimization approach selectively ampli…

• Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models

  Andrea Agazzi, Giuseppe Bruno, Eloy Mosig Garc\'ia, Samuele Saviozzi, Marco Romito · 30 de abril de 2026

  We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the stochastic partial differential equation describing the evolu…

• A ghost mechanism: An analytical model of abrupt learning in recurrent networks

  Fatih Dinc, Ege Cirakman, Bariscan Kurtkaya, Mert Yuksekgonul, Yiqi Jiang, Mark J. Schnitzer, Hidenori Tanaka · 16 de abril de 2026

  Abrupt learning is a common phenomenon in recurrent neural networks (RNNs) trained on working memory tasks. In such cases, the networks develop transient slow regions in state space that extend the effective timescales of computation. However, the mechanisms driving sudden performance improvements a…

• Score Reversal Is Not Free for Quantum Diffusion Models

  Ammar Fayad · 20 de marzo de 2026

  Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of continuous-variable decoherence, we prove that the unrestricted in…

• Sharp Phase Boundary for Quantum Reverse Diffusion

  Ammar Fayad · 17 de marzo de 2026

  Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of continuous-variable decoherence, we prove that the unrestricted in…

• Quantum Diffusion Models: Score Reversal Is Not Free in Gaussian Dynamics

  Ammar Fayad · 9 de marzo de 2026

  Diffusion-based generative modeling suggests reversing a noising semigroup by adding a score drift. For continuous-variable Gaussian Markov dynamics, complete positivity couples drift and diffusion at the generator level. For a quantum-limited attenuator with thermal parameter $\nu$ and squeezing $r…

• Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance

  Haiqi Lu, Ying Tang · 19 de febrero de 2026

  We show that deliberately breaking detailed balance in generative diffusion processes can accelerate the reverse process without changing the stationary distribution. Considering the Ornstein--Uhlenbeck process, we decompose the dynamics into a symmetric component and a non-reversible anti-symmetric…

• Paradoxical noise preference in RNNs

  Noah Eckstein, Manoj Srinivasan · 9 de enero de 2026

  In recurrent neural networks (RNNs) used to model biological neural networks, noise is typically introduced during training to emulate biological variability and regularize learning. The expectation is that removing the noise at test time should preserve or improve performance. Contrary to this intu…

• How to explain grokking

  S. V. Kozyrev · 9 de diciembre de 2025

  Explanation of grokking (delayed generalization) in learning is given by modeling grokking by the stochastic gradient Langevin dynamics (Brownian motion) and applying the ideas of thermodynamics.…