Tianshan Zhang

Classical mechanics can be organized around force, action, or energy. The Hamiltonian—energy on phase space—turns out to be the object that survives into quantum theory as the generator of time evolution on Hilbert space, while the action reappears as the phase weighting every path in the path integral. Following these two threads, together with the Poisson-bracket-to-commutator correspondence and the symmetry–conservation link, leads through quantization, the harmonic oscillator, statistical mechanics, quantum field theory, renormalization, and effective field theory.

Vision-Language-Action models are transforming robot learning from a collection of task-specific controllers into general-purpose embodied agents. Rather than treating VLA as a single model architecture, we examine it as a sequence of responses to increasingly difficult questions: how robots understand tasks, how semantic knowledge becomes continuous action, how policies operate over long horizons, and how they improve beyond static demonstrations.

A mathematical walkthrough of sequence modeling, tracing the evolution from recurrent neural networks and LSTM gating mechanisms to self-attention, FlashAttention, KV-cache optimization, RoPE, state space models, Mamba, RWKV, and hybrid long-context architectures.