Generative Flow on Symbolic Abstractions for Embodiment Capability Discovery

Youwei Yu; Lantao Liu

cs.ROOct 12, 2026

Generative Flow on Symbolic Abstractions for Embodiment Capability Discovery

Authors: Youwei Yu, Lantao Liu

Organizations: Indiana University Bloomington

Abstract

Achieving complex, long-horizon robot behavior remains challenging because successful execution depends on skills grounded in a robot's physical affordances. Existing training-task distributions are often handcrafted or sampled from large language models (LLMs), relying on semantic plausibility rather than embodiment-specific feasibility. This mismatch can produce curricula that are too difficult, redundant, or blind to non-obvious but learnable behaviors. We propose Generative Flow on Symbolic Abstractions (FOSA), a framework for discovering embodiment-specific capabilities by learning a grounded task generator. FOSA parameterizes an abstract policy as a Generative Flow Network that constructs symbolic task skeletons. Each skeleton is compiled into a simulation environment, where low-level policy-learning performance provides the reward signal for the abstract policy. Across heterogeneous robot platforms, FOSA discovers diverse and executable tasks near the robot's empirical capability frontier. After distilling the discovered task policies into a single language-conditioned policy, FOSA improves performance on unseen complex and long-horizon tasks. The code and demonstration videos are available at https://www.youwei-yu.com/fosa.

Figures & tables

Figure 1: FOSA learns a generative flow policy over symbolic task skeletons to discover tasks near a robot’s empirical capability frontier. Starting from the empty skeleton $\varnothing$ , the policy samples grammar-valid semantic edits with transition probability $P(\mathbf{x}^{\prime}\mid\mathbf{x})$ . Blue arrow ${\color[rgb]{0,0,1}\relbar\joinrel\blacktriangleright}$ thickness indicates sampling probability.

Figure 2: FOSA framework overview. The GFlowNet abstract policy generates symbolic task skeletons, which are compiled by an LLM into simulation environments to train task policies. Task-policy performance provides the reward signal that updates the abstract policy toward the robot’s empirical capability frontier.

Panel of Figure 3 — Figure 3: Held-out evaluation tasks for the distilled language-conditioned policy across four robots.

Figure 4: Comparison of discovered tasks along different axes: lexical diversity (Div-SB4, Div-SB5), semantic dispersion in the language-embedding space (Dist-Embed1, Dist-Embed2), exploration efficiency (Expl-Eff), and proximity to the empirical capability frontier (Frontier-Prox).

Figure 5: Simulation evaluation shows normalized cumulative reward of the distilled language-conditioned policies on the explored task suites. Each task is evaluated over

10

random seeds.

Figure 6: (a) Sensitivity to reward weights, as the change in expected frontier score of the target

P^{\star}\propto R

. (b) Sensitivity to discovery budget, as the fraction of FOSA’s final frontier tasks found after its first

n

trained tasks. (c)–(d) GFlowNet training diagnostics over discovery rounds: trajectory-balance loss (log scale) and learned

\log Z

, mean over three seeds per robot.

Panel of Figure 7 — Figure 7: Held-out evaluation tasks for the distilled language-conditioned policy across two robots.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Field	Meaning	Examples
$E_{\mathbf{x}}$	Typed entities in the task.	robot, target, object, payload, ramp, obstacle, terrain patch, door, tool
$I_{\mathbf{x}}$	Initial symbolic state induced by the reset distribution.	initial robot pose, object pose, terrain condition, contact relation, visibility condition
$G_{\mathbf{x}}$	Goal literals or success conditions.	reach target, track velocity, lift object, maintain balance, rotate object, avoid obstacle
$U_{\mathbf{x}}$	Operator or task-family schemas referenced by the skeleton.	navigate, climb, push, grasp, lift, rotate, balance, transport
$\boldsymbol{\theta}_{\mathbf{x}}$	Continuous or discrete arguments needed to instantiate the task.	slope angle, friction, object mass, target distance, velocity command, tolerance, duration
$\Phi_{\mathbf{x}}$	Feasibility, safety, and simulator constraints.	valid pose ranges, contact constraints, termination thresholds, admissible friction ranges, collision constraints

Appendix

Table A1.1: Components of a symbolic task skeleton.

Figure A2.1: Real-world vehicle trajectories for FOSA, baselines, and ablations.

Hyperparameter	Value
FOSA Abstract Policy (GFlowNet)
Maximum construction depth $T_{\max}$	$10$
State encoder	Qwen2.5-0.5B
$P_{F}$ , $P_{B}$ architecture	MLP $(256,256)$
Optimizer	Adam; lr $10^{-3}$ ( $P_{F}$ , $P_{B}$ ), $10^{-1}$ ( $\log Z$ )
Replay buffer	$1024$

Appendix

Table A2.1: Hyperparameters of the three learned components.

Figure A2.2: Simulation vehicle learning snapshots with task descriptions and reward curves.

Figure A2.3: Simulation hand learning snapshots with task descriptions and reward curves.

Figure A2.4: Simulation quadruped learning snapshots with task descriptions and reward curves.

Figure A2.5: Simulation humanoid learning snapshots with task descriptions and reward curves.

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Abstract

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