Ghost Attractor Networks: Basin-Structured Dynamical Decoders for Closed-Loop Sequential Generation

2026-06-16

AI Summary

This work addresses the high computational and memory costs of conventional sequence generation models and the inability of lightweight feedforward decoders to support closed-loop control due to unstructured latent spaces. The authors propose Ghost Attractor Networks, a dynamics-inspired decoder that constructs basin attractors through learned potential and drift terms. By leveraging theoretically grounded design principles, the model establishes a stable latent structure, employs saddle-node bifurcations for multimodal switching, and decomposes the phase space hierarchically to separate convergence from fine-tuning. Requiring only a single forward pass with constant memory usage, the method achieves offline accuracy comparable to billion-parameter Diffusion Transformers at 32× lower latency using just 2.3 million parameters, and attains a 95.7% success rate on LIBERO-10 closed-loop tasks—improving performance by 13.5 percentage points.

Abstract

Sequential output generation with large-scale Transformer and diffusion decoders pays a memory cost that grows with sequence length, plus iterative per-step computation. Replacing them with small feed-forward decoders restores efficiency but produces unstructured latent representations that limit closed-loop control: phase-conditioned action generation and cross-step latent carry-over both require a latent geometry with stable basins. This article proposes Ghost Attractor Networks, a theoretically derived dynamical decoder whose latent evolves under a learned potential with drift and produces a basin-attractor structure by construction. Three desiderata (multi-modality, decoder-level single-pass switching, and constant memory) motivate the potential-drift form, and mode transitions arise as saddle-node bifurcations with ghost-attractor escape. A hierarchical phase-space decomposition separates first-order basin convergence from second-order proprioceptive refinement. Empirically, a Ghost trained end-to-end with a behavioral-cloning and contrastive objective exhibits the predicted gradient-flow contraction in its potential, with the gradient norm decaying by 67 percent across five integration steps on 1430 held-out samples. Ghost is evaluated as a robotic action decoder. A 2.3-million-parameter Ghost matches the offline accuracy of a 1.07-billion-parameter Diffusion Transformer at 462 times fewer parameters and 32 times lower latency, and beats five alternative 2M-parameter decoders (MLP, Neural ODE, CVAE, Transformer, 1-step Diffusion) on offline mean squared error by 5.9 to 29 percent. On the LIBERO-10 closed-loop benchmark, phase conditioning on Ghost's basin-structured latent yields a 13.5 percentage-point success-rate gain over a feed-forward MLP baseline, and persistent-latent ensembling reaches a 95.7 percent final success rate.

Problem

• closed-loop sequential generation
• latent representation structure
• basin-attractor dynamics
• efficient decoding
• robotic action generation

Innovation

• Ghost Attractor Networks
• basin-attractor structure
• potential-driven dynamics
• closed-loop sequential generation
• latent geometry