Technical Proposal: Hamiltonian Adaptive Attractor RWKV (H-RWKV) Architecture Integrating Implicit Function Theorem (DEQ)

Counts differ because each database indexes a different set of publications. We treat OpenAlex as the canonical count; Google Scholar is not shown (no API, and crawling it violates its ToS).

H-RWKV (Hamiltonian RWKV) Constant-Memory O(1) Iterative Reasoning via Phase-Space Attractor Dynamics and Implicit Function Theorem Abstract This proposal specifies H-RWKV (Hamiltonian RWKV), an architecture that integrates Hamiltonian phase-space dynamics and Deep Equilibrium Models (DEQ / Implicit Function Theorem) into the hidden state space of pre-trained RWKV (RWKV-6/7/8) backbones. Traditional test-time compute and iterative reasoning models suffer from a BPTT (Backpropagation Through Time) memory wall, where training memory scales linearly with thinking steps K ($\mathcal{O}(K)$). H-RWKV resolves this bottleneck by treating iterative thinking loops as a search for equilibrium states (attractors) in a phase space, enabling strictly constant memory O(1) training independent of the number of reasoning steps K. The architecture introduces three mathematical and systems-level innovations: Hamiltonian Phase-Space Projection: Maps hidden state ht∈Rd into position q and momentum p coordinates under a potential field V(q;Θadapter) representing conceptual inconsistency: H(q,p)=12‖p‖2+V(q;Θadapter) dpdτ=−(∂V(q)∂q+γp),dqdτ=p Implicit Function Theorem (DEQ) Backpropagation: Computes analytical gradients directly from the converged attractor point z∗=[q∗,p∗]T via Vector-Jacobian Products (VJP) without saving intermediate computational graphs (τ=0,…,K): ∂L∂θ=−∂L∂z∗(Jf(z∗))−1∂f(z∗;θ)∂θ 100% Parameter Reuse & Zero-Distortion Adapter: Fully freezes the pre-trained RWKV backbone and attaches a lightweight Phase Engine Adapter (~0.5%–2.0% total parameters), allowing small models (1B–3B) to achieve high "intelligence density" on complex reasoning, mathematics, and code generation tasks. By harmonizing symplectic phase-space integration with implicit differentiation, H-RWKV enables deep iterative reasoning with minimal memory consumption, zero context window degradation, and stable gradient flow. (Note: This is a hobby research project focused on exploring the synergy between RWKV backbones and Hamiltonian dynamics.)Generative AI tools (Gemini 3.1 Pro) were used to brainstorm the hypothesis, refine the concepts, and generate parts of the prototype code.