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

arXiv: https://arxiv.org/abs/2606.18315 · HTML: https://mlsanity.com/paper/2606.18315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024)
- [RL2: Fast Reinforcement Learning via Slow Reinforcement Learning](https://mlsanity.com/paper/1611.02779/) (2016)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [In-context Reinforcement Learning with Algorithm Distillation](https://mlsanity.com/paper/2210.14215/) (2022)
- [Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation](https://mlsanity.com/paper/2405.07503/) (2024)
- [Supervised Pretraining Can Learn In-Context Reinforcement Learning](https://mlsanity.com/paper/2306.14892/) (2023)
- [ProMP: Proximal Meta-Policy Search](https://mlsanity.com/paper/1810.06784/) (2018)
- [Dream-VL & Dream-VLA: Open Vision-Language and Vision-Language-Action Models with Diffusion Language Model Backbone](https://mlsanity.com/paper/2512.22615/) (2025)
- [RoLD: Robot Latent Diffusion for Multi-task Policy Modeling](https://mlsanity.com/paper/2403.07312/) (2024)

## Abstract (arXiv)

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.