CrossBFM: Distilling a Shared Latent Behavior Space Across Humanoid Embodiments

AI summary

Overview

Research area: Robotics — reinforcement learning for humanoid whole-body control, cross-embodiment transfer, and behavior foundation models (BFMs).

Technical level: Advanced. The paper assumes familiarity with unsupervised RL, successor measures, Forward–Backward representations, PPO, and motion retargeting. The summary below explains the ideas without that background.

Scope: CrossBFM distills the latent behavior space of one pretrained humanoid behavior foundation model onto multiple new humanoid robots using a single shared encoder trained in under an hour, so that all three BFM prompting modes (motion tracking, goal reaching, reward optimization) transfer to the new embodiments.

What This Paper Is About

Behavior Foundation Models give a humanoid a single latent vector that can be prompted to imitate a motion, reach a pose, or maximize a reward, but producing that latent space costs hundreds of GPU-hours for one robot. Repeating the training for a second robot produces a second latent space that is geometrically similar but semantically unrelated to the first, so nothing transfers between embodiments. CrossBFM addresses both problems by treating the latent space itself as the transferable asset and distilling a frozen source BFM's space onto new robots through supervised regression.

Key Contributions

1. A unified encoder for BFM distillation. A robot-independent encoder architecture with no robot-specific parameters that distills the behavior space onto multiple robots in a single training run, matching the accuracy of separate per-robot encoders while producing more consistent latents across robots and generalizing to unseen embodiments of similar morphology.
2. Retargeting as a correspondence oracle. The paper shows that latent transfer across humanoid embodiments reduces to supervised regression from a frozen source BFM latent, because retargeted datasets provide frame-level correspondence along a shared timeline. This removes the simulator, the RL training, and the adversarial objective from the target robot side.
3. Latent-conditioned whole-body control. Trackers conditioned on [z | proprio] are evaluated on three distinct humanoids, covering all three BFM-Zero prompting modes, plus a flow-based latent generator that produces latents from behavior modes. The pipeline is also verified on real robots.

Main Findings

• Motion tracking transfers with a small gap. Across all three robots the latent-conditioned policy stays within 0.025 rad of the joint-conditioned TWIST2 baseline. Per-robot joint MAE: M3 0.1777 ± 0.0033 (joint) vs 0.2024 ± 0.0067 (latent), Δ +0.0247; T1 0.1844 ± 0.0043 vs 0.1901 ± 0.0032, Δ +0.0057; N1 0.1362 ± 0.0032 vs 0.1391 ± 0.0038, Δ +0.0029.
• Goal reaching works only for latent-conditioned policies. Interpolating in the latent space gives smooth transitions at a cost of at most 0.032 rad relative to tracking. Goal MAE is 0.2345 ± 0.0011 (M3, Δ +0.0321), 0.1967 ± 0.0012 (T1, Δ +0.0066) and 0.1512 ± 0.0023 (N1, Δ +0.0121). Joint-conditioned policies are not reported for goal reaching because discontinuous joint targets cause large torques and early termination.
• Reward optimization improves over the source latent. Computing z_rew on the G1 with the true backward map B_S gives normalized returns of 0.145 (M3), 0.228 (T1) and 0.177 (N1), versus 0.508, 0.261 and 0.523 for the target-side computation — gains of 3.50×, 1.14× and 2.95×, with a mean of 0.183 vs 0.431 (2.35×). The paper reports all 41 reward prompts.
• Unseen motion generalizes. On validation clips the encoder's inferred latent costs 1.4–6.7 mm of key-body error. Closed-loop key-body error (×10⁻² m): M3 training oracle 8.14 vs inferred 8.02, validation oracle 6.40 vs inferred 7.07; T1 5.70/5.43 and 5.26/5.60; N1 5.58/5.57 and 5.46/5.60. On training clips the predicted latent is marginally better than the oracle latent.
• A quarter of the corpus is enough. Shrinking the distillation data from 100% to 25% raises joint MAE only from 0.2132 to 0.2241, a 5% degradation for four times less data. Performance starts to break down at 10% (0.2706), against a random-latent control at 0.4411.
• Cross-embodiment generalization depends on morphological proximity. Training the encoder on two robots and evaluating on the third recovers 89.3% ± 3.5 of tracking performance for unseen M3 (cosine 0.6251 ± 0.0196; MAE 0.1829 ± 0.0054 vs 0.1645 with the 3-robot encoder), 55.5% ± 3.2 for unseen N1 (cosine 0.5861 ± 0.0100; MAE 0.2237 ± 0.0048 vs 0.1370), and only 12.8% ± 10.3 for unseen T1 (cosine 0.2533 ± 0.0168; MAE 0.2886 ± 0.0138 vs 0.1679).
• Cosine similarity does not fully capture policy performance. Latents of unseen robots can lie far from ground truth — 0.625 cosine for the best case — yet still drive policies that recover 89.3% of oracle-tracker performance, provided the inferred latents land inside the correct behavior cluster.
• Real-robot results on M3. Motion tracking with joint reference (5 clips): 0.1985 real vs 0.1777 sim. Tracking with latent (5 clips): 0.2206 real vs 0.2024 sim. Goal reaching (9 poses): 0.2675 real vs 0.2345 sim. Reward optimization (3 tasks): 0.562 real vs 0.508 sim.

Methodology in Plain English

The pipeline has two stages built on a frozen source model, a BFM pretrained on the Unitree G1 whose backward map B_S is kept fixed. The source latent has dimension d = 256 and lives on a sphere of radius √d.

Stage 1: distilling the latent space. Because the same motion clips are retargeted onto every robot on the same timeline at the same frequency, frame t of a target robot's retargeted data corresponds to the same behavior as frame t of the source. The authors attach the source model's latent for each frame to the retargeted data as a ground-truth label, turning cross-embodiment latent transfer into plain supervised regression with a frame-wise cosine objective.

The regression is performed by one encoder shared by all robots. Each robot's proprioception is mapped into a fixed-width input of 163 dimensions built from two morphologically meaningful components: 8 key-body indices ({left, right} × {knee, foot, elbow, arm tip}, with the root deliberately excluded because key-body positions are already relative to it) and 33 canonical joint indices (12 leg, 3 waist (yaw/roll/pitch), 16 arm, 2 head). The vocabulary intentionally includes indices no robot in the experiments has, so it can cover a wide range of humanoids. Missing joints are flagged and zero-padded, letting the network distinguish "this joint is at zero" from "this joint does not exist." A robot pelvis proprioception (global height, orientation, linear velocity) anchors the other key bodies. The encoder uses a linear embedding, positional encoding, and pre-LayerNorm transformer blocks with causal attention (an upper-triangular mask), so frame t attends only to frames ≤ t — a requirement for real-world control, unlike a bidirectional version that sees about one second of future reference.

Stage 2: latent-conditioned trackers. For each robot, PPO trains a tracker that receives only the behavior latent and proprioception (base angular velocity, IMU roll and pitch, joint positions and velocities, previous action), with no explicit reference trajectory in the actor's observations. The critic stays asymmetric and keeps privileged reference observations in simulation so value estimation stays accurate without leaking unavailable information into the policy. A single rectified-flow model trained over latent chunks generates latents, broadening the prompts beyond robot-specific joint-space references.

Deployment. Motion tracking and goal reaching transfer directly through the encoder. Reward optimization needs extra work because the closed-form latent requires the backward map and the state distribution ρ over which the expectation is taken, and the target robot never ran unsupervised RL. The authors approximate ρ with the target's retargeted dataset, keep only key-body reward features (root height and velocity, uprightness, angular velocity, arm-tip and knee heights) and discard joint-configuration terms, encode each cached frame once, score it, and take a reward-weighted average (ω = softmax(τ r_{1:M})) projected back onto the sphere. To handle robots of different proportions, reward thresholds are transported between robots by percentile: θ^(r) = Φ_r⁻¹(Φ_S(θ)). A "raise arm" task at 1.0 m hand height on a medium robot converts to 0.820 m on a smaller robot and 1.157 m on a larger one.

Cost. The source backward map required on the order of 10² GPU-hours of online unsupervised RL with a replay buffer, a discriminator, and domain randomization. The encoder trains in just under an hour on a single consumer GPU, and the full pipeline needs around 10 GPU-hours on an RTX4090.

Experimental setup. The source is a frozen BFM trained on the Unitree G1 (29 DoF, 32 bodies, 3-DoF waist, 3-DoF wrists). Targets are Inhouse M3 (27 DoF, 30 bodies, 27/33 indices filled, nearest to the source, waist yaw only), Booster T1 (23 DoF, 24 bodies, 21/33, wrist-less, 4-DoF arms, 2-DoF head) and Fourier N1 (23 DoF, 29 bodies, 23/33, one wrist DoF per arm, waist yaw only). Experiments use the LAFAN dataset, with 40 motions and eight behaviors.

Why This Matters

The distinctive claim is that the latent behavior space, not the policy, is the transferable asset. Prior cross-embodiment work either conditions a single policy on an embodiment description (encoding morphology rather than task-conditioned behavior) or learns descriptive unified latents from scratch (which lack the closed form that turns a reward into a latent). CrossBFM's distilled latent is inherited from a frozen Forward–Backward model, so it retains value-functional prompting semantics — "the reward I want maximized" or "the pose I want reached" — on the new embodiment. That also collapses a five-figure-GPU-hour training problem into a regression that fits in under an hour.

Real-world applications:

• Commanding humanoid robots through behavioral intent rather than per-frame joint targets, which the authors describe as substantially more natural for complex long-horizon loco-manipulation.
• Fleet deployment: a single distilled behavior space that can be prompted across a heterogeneous set of humanoid platforms.
• Text-to-motion-to-control interfaces, using the flow-based latent generator to accept prompts such as text instead of robot-specific joint-space references.
• Rapid onboarding of new hardware, since a new robot's encoder can in principle be trained from retargeted data rather than from a fresh unsupervised RL run.

Industry relevance: the work targets the practical bottleneck in commercial humanoid deployment — that every new platform currently demands its own expensive foundation-model training run and produces a latent space incompatible with existing ones.

Future Directions

• Scaling laws along two axes: richer training data for a finer-grained behavior space, and a larger robot training set for better generalization to unseen robots. The authors suggest that with enough embodiments — where every new robot has a close relative — generalization becomes interpolation rather than extrapolation.
• Text-instruction prompting for long-horizon loco-manipulation tasks, building on the shared latent space and the flow-based generator.
• Closing the morphology gap. T1, which is smaller and morphologically distinct, recovers only 12.8% of seen-robot tracking performance, so extending the encoder to morphologically dissimilar robots remains open.
• Reconciling latent similarity with policy success. Cosine similarity as low as 0.625 still yields 89.3% recovery, so better metrics for latent quality are needed.

Target Audience

Robotics and RL researchers working on humanoid whole-body control, cross-embodiment transfer, and unsupervised skill discovery; engineers building behavior foundation models or deploying a single control stack across multiple humanoid platforms; and practitioners interested in distillation pipelines that replace expensive RL training with supervised regression. Readers without a background in Forward–Backward representations, successor measures, or PPO will find the theoretical framing dense.

Authors’ abstract

Behavior Foundation Models (BFMs) give humanoids a promptable policy over a latent behavior space, enabling one single vector to represent a motion to imitate, a pose to reach, or a reward to maximize. Forward-Backward representations successfully produce such spaces, but at the cost of hundreds of GPU-hours for a single robot. Moreover, when the training process is repeated for a second robot, it produces a second space unrelated to the first, resulting in embodiment-specific latents that do not unify or transfer. We address these problems with CrossBFM, treating the latent space as the transferable asset for various embodiments. As retargeting provides frame-level cross-embodiment correspondence, we propose a unified encoder architecture with no robot-specific parameters for distilling the behavior space to address all training embodiments simultaneously in less than a GPU-hour. Following this encoder, latent-conditioned trackers turn the distilled latent into whole-body control in a conventional PPO training manner in just 10 more GPU-hours. On three distilled humanoids, all three prompting modes transfer: motion tracking with latent-conditioned policy losing only $0.025$ rad to its joint-conditioned counterpart, smooth goal reaching between poses with no falls, and reward optimization for all $41$ reward prompts. Our experiments further reveal that 1) regressing the encoder on a quarter of the motion corpus costs only $5\%$ of tracking performance and 2) training the encoder on a subset of robots and evaluating on an unseen one recovers up to $89\%$ of the tracking performance of seen robots, demonstrating cross-embodiment generalization to morphologically similar robots. We also verify the pipeline on real robots across all three prompting modes and with flow-based generated latents. Project website: https://dotandung.github.io/crossbfm/