Quantum chaos and dynamical systems

Latest papers

• Learning-Induced Dynamical Transition in Recurrent Neural Networks

  Varun Vaidya · 18 September 2026

  Learning in recurrent neural networks can fundamentally reshape their underlying dynamics, transforming initially chaotic activity into stable task-dependent behavior. We develop a non-equilibrium dynamical mean-field theory(DMFT) to describe this transition during learning. We show that a slow feed…

• Self-Attention Dynamics with Rotary Position Embeddings: Twisted States and Explicit Consensus Rates on the Sphere

  Hao Ye (Xi'an Institute of Optics,Precision Mechanics, Chinese Academy of Sciences, University of Chinese Academy of Sciences) · 28 July 2026

  Rotary position embeddings (RoPE) modify attention scores through position-dependent rotations, but their effect on normalized token dynamics is not captured by the vanilla spherical self-attention model. We study the continuous-time dynamics obtained when queries and keys are rotated while values r…

• Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching

  Peiyan Hu, Jian Zhang, Jiashu Pan, Ruiqi Feng, Tao Zhang, Zhi-Ming Ma, Yuan-Sen Ting, Gongjie Li, Tailin Wu · 24 June 2026

  Modeling chaotic systems is crucial yet challenging. Inverse problems in chaotic dynamics, namely inferring initial conditions from final states, remain largely unsolved because of ill-posedness, non-uniqueness, instability, and potentially chaotic time-reverse dynamics. We address this open problem…

• Activation Saturation and Floquet Spectrum Collapse in Neural ODEs

  Nikolaos M. Matzakos · 2 April 2026

  We prove that activation saturation imposes a structural dynamical limitation on autonomous Neural ODEs $\dot{h}=f_\theta(h)$ with saturating activations ($\tanh$, sigmoid, etc.): if $q$ hidden layers of the MLP $f_\theta$ satisfy $|\sigma'|\le\delta$ on a region~$U$, the input Jacobian is attenuate…

• Precise Dynamics of Diagonal Linear Networks: A Unifying Analysis by Dynamical Mean-Field Theory

  Sota Nishiyama, Masaaki Imaizumi · 16 March 2026

  Diagonal linear networks (DLNs) are a tractable model that captures several nontrivial behaviors in neural network training, such as initialization-dependent solutions and incremental learning. These phenomena are typically studied in isolation, leaving the overall dynamics insufficiently understood…

• Double projection for reconstructing dynamical systems: between stochastic and deterministic regimes

  Viktor Sip, Martin Breyton, Spase Petkoski, Viktor Jirsa · 10 March 2026

  Learning stochastic models of dynamical systems from observed data is of interest in many scientific fields. Here, we propose a new method for this task within the family of dynamical variational autoencoders. The proposed double projection method estimates both the system state trajectories and the…

• Exponential time differencing for matrix-valued dynamical systems

  Nayef Shkeir, Tobias Grafke · 12 February 2026

  Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many such problems, the dominant stability restriction is imposed by a stiff linear term, making …