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EgoLAP: Learning from Egocentric Human Data through Language-Action Reasoning

Lihan Zha, Shresth Grover, Tenny Yin, Samuel M. Bateman, Hengkai Pan, Mengchao Zhang, Aykut Onol, Allen Z. Ren, Dhruv Shah, Anirudha Majumdar

Year: 2026Venue: arXiv preprintArea: cs.ROType: PreprintEmbeddings: 106

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Abstract

Abstract:Egocentric human data offer a path to scaling robot learning beyond costly robot demonstrations, yet the embodiment gap makes raw human trajectories a poor supervisory target for control. Our key insight is that, although low-level actions are embodiment-specific, their underlying motion intent can capture task-relevant structure that transfers across humans and robots. We introduce EgoLAP, a VLA pre-training framework that jointly learns from human and robot trajectories through a shared language-based action chain-of-thought. EgoLAP expresses motion intent as structured, temporally abstracted language actions and pairs them with motion-level reasoning grounded in scene geometry, physics, and object affordances. Across extensive real-world and simulated experiments, EgoLAP transfers human experience to robot control more effectively than alternative action representations and reaches 80.1% mean real-world task progress, a 2.3x performance gain over alternative action representations. Motion-level reasoning also outperforms a composite reasoning format that combines subtask, object-box, and visual-trace reasoning.

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1]Princeton University 2]Toyota Research Institute 3]Physical Intelligence [*]Equal contribution. [† ]Equal advising. ://ego-lap.github.io/https://ego-lap.github.io EgoLAP: Learning from Egocentric Human Data through Language-Action Reasoning Lihan Zha Shresth Grover Tenny Yin Samuel M. Bateman Hengkai Pan Mengchao Zhang Aykut Onol Allen Z. Ren Dhruv Shah Anirudha Majumdar Affiliation: [ Affiliation: [ Affiliation: [ Abstract Egocentric human data offer a path to scaling robot learning beyond costly robot demonstrations, yet the embodiment gap makes raw human trajectories a poor supervisory target for control. Our key insight is that, although low-level actions are embodiment-specific, their underlying motion intent can capture task-relevant structure that transfers across humans and robots. We introduce EgoLAP, a VLA pre-training framework that jointly learns from human and robot trajectories through a shared language-based action chain-of-thought. EgoLAP expresses motion intent as structured, temporally abstracted language actions and pairs them with motion-level reasoning grounded in scene geometry, physics, and object affordances. Across extensive real-world and simulated experiments, EgoLAP transfers human experience to robot control more effectively than alternative action representations and reaches 80.1%80.1\% mean real-world task progress, a 2.3×2.3× performance gain over alternative action representations. Motion-level reasoning also outperforms a composite reasoning format that combines subtask, object-box, and visual-trace reasoning. 1 INTRODUCTION Figure 1: EgoLAP turns egocentric human experience into transferable robot control. Human hands and robots differ in embodiment and low-level execution, yet share the same underlying motion intent when performing a task. EgoLAP captures this intent through motion-level reasoning and language actions, providing a shared supervision target across both data sources and leading to a 2.3×2.3× performance gain over alternative action representations. Robot foundation models have advanced rapidly by scaling robot demonstrations across tasks, environments, and embodiments [11, 24, 19, 7, 27, 52], yet such demonstrations remain costly to collect and narrow relative to the breadth of human activity. Egocentric human video offers the scale and behavioral diversity that robot data lacks, capturing long-horizon manipulation in everyday environments and growing independently of any robot platform. To leverage human data for robot learning, prior work extracts intermediate representations through hand-engineered pipelines, such as interaction hotspots and affordances [37, 45], hand poses or image-space tracks [5, 50, 6, 42], latent plans [48, 20, 4], or visually edited embodiments [2, 30, 29]. These representations capture useful facets of human behavior, but inherit the inductive biases and failure modes of their extraction pipelines that restricts scalability. Moreover, differences in morphology, kinematics, and control create an embodiment gap that limits the direct transfer of action-level knowledge from human data to robot policies [8]. Our key insight is that humans and robots need not share low-level actions; instead, they need to share motion intent: what motion needs to be produced, and why it’s appropriate given the current physical state. We represent the what using language actions: structured, temporally abstract descriptions of changes in pose and gripper state, such as “move forward 3 cm, rotate clockwise 14 degrees, and close gripper.” Unlike embodiment-specific trajectories or non-linguistic action tokens [38, 34], language actions reuse the vocabulary and compositional structure of a vision–language model (VLM), thereby providing control-relevant supervision within its pretrained semantic space [55, 17, 16]. However, the same task may require different motions across embodiments, so specifying what motion to execute is insufficient. We therefore introduce motion-level reasoning to represent the why: local, physically grounded rationales that relate contact, geometry, and object affordances to the intended effect of the next motion. Unlike subtask plans or visual traces, which primarily specify what action to take or where to move [54, 47, 46], motion-level reasoning captures the physical relationship between the current state and the motion required to achieve the intended effect, providing a form of supervision that can connect directly to low-level actions, yet transfer across embodiments. Together, motion-level reasoning and language actions define a physically grounded “action chain-of-thought”. Statement of contributions. We introduce EgoLAP, a VLA pre-training framework that co-trains on egocentric human and robot trajectories through motion-level reasoning and language actions, achieving 44.944.9 points of real-world performance more than the strongest action representation. Unlike previous embodied reasoning methods [54, 47], EgoLAP only runs a lightweight action expert during inference time, where the textual targets provide auxiliary supervision and require no autoregressive generation. Across extensive zero-shot real-world and simulation experiments on a bimanual robot, language actions transfer human experience better than non-linguistic action representations [38, 34], and motion-level reasoning contributes 44.744.7 points of real-world task progress more to EgoLAP than the baselines. Motion-level reasoning also strongly outperforms a strong composite of subtask, object-box, and visual-trace reasoning supervision. Finally, EgoLAP adapts effectively through reinforcement learning over language actions and motion-level reasoning. 2 RELATED WORK Learning Robot Policies from Egocentric Human Data. Human data provides scalable supervision for robot learning, but leveraging them requires bridging the embodiment gap. Prior methods rely on method-specific representations: interaction hotspots and affordances [37, 45], hand poses or image-space tracks [5, 50, 6, 42], latent plans [48, 20, 4], or visually edited embodiments [2, 30, 29]. Although effective, these hand-designed interfaces require modular processing (e.g., hand-pose estimation, point tracking, or embodiment editing) and inherit its inductive biases and errors, limiting their scalability. The gap is evident in direct policy learning: despite the 3,000 hours of egocentric video available in Ego4D [15], MimicPlay and Motion Tracks train on only about 10 minutes of task-specific human video, ATM evaluates transfer from 100 human videos, and Phantom trains on 250–350 demonstrations per task [48, 42, 50, 30]. Another line directly trains policies on large-scale egocentric human datasets [39, 18] along with robot data [22, 57, 40, 31, 41, 26, 51, 35]. These systems typically retain embodiment-specific pose targets or encode trajectories with non-linguistic action tokens as training targets [38, 23, 49], which impede cross-embodiment transfer [55]. Language-Action Pre-training (LAP) [55] instead expresses motion as structured natural language, showing improved zero-shot transfer among robots. EgoLAP extends this representation to human–robot co-training and pairs it with motion-level reasoning, which provides both embodiments with shared language-based targets and improves human-to-robot transfer. Action Representations for VLAs. VLAs commonly supervise a VLM with discretized action tokens [7, 27], sometimes alongside a separate continuous action expert [19]. The discrete target is especially consequential when gradients from the action expert do not reach the VLM backbone [13]. Learned tokenizers such as FAST, OAT, ActionCodec, and X-Tokenizer optimize action compression or token structure [38, 34, 12, 21]; LAP instead describes motion in natural language to remain compatible with the VLM’s pretrained semantic space [55]. EgoLAP applies this representation to bimanual human–robot co-training and shows that motion-level reasoning yields larger gains with language actions than with non-linguistic action tokens. Reasoning for Visuomotor Control. Prior work augments visuomotor policies with textual reasoning over goals, subtask plans, and spatial cues, or with visual intermediates such as affordances and 2D point traces [54, 47, 56, 28, 53, 9, 46]. With human video, plans, reasoning labels, and dense annotations improve policy performance under distribution shift [36, 14, 25, 10]. These results establish the value of reasoning supervision, but leave unresolved which reasoning content best supports cross-embodiment motion transfer. For example, DeMiAn finds that no single annotation type performs best across tasks [25], while a large-scale study finds no benefit from conditioning actions on chain-of-thought traces [33]. This gap motivates motion-level reasoning: supervision that captures the embodiment-invariant physical rationale underlying human and robot motions, thereby bridging the two data sources. Unlike prior approaches [54, 9], EgoLAP requires neither multi-stage distillation nor text generation at inference, simplifying training and ensuring fast inference. 3 METHOD Figure 2: EgoLAP places human and robot motion in a shared, physically grounded language space. By capturing the physical relationship between the current state and the motion needed to produce the intended effect, motion-level reasoning provides supervision that connects directly to low-level actions that transfers across embodiments. EgoLAP is a VLA pre-training framework for transferring motion knowledge from large-scale egocentric human experience to robot manipulation. Its central design choice is to map human-hand and robot-end-effector trajectories to the same language-based interface. We first formalize this interface (Sec. 3.1) and describe the model architecture and training objective (Sec. 3.2). We then detail the construction of language actions (Sec. 3.3) and motion-level reasoning targets (Sec. 3.4). 3.1 Problem Formulation Let RD_R contain robot samples (ot,ℓ,st,at:t+K)(o_t, ,s_t,a_t:t+K), where oto_t contains one or more RGB observations, ℓ is the task instruction, sts_t is the proprioceptive state, and at:t+Ka_t:t+K is an action chunk of horizon K. Let HD_H contain egocentric human samples (ot,ℓ,qt:t+K)(o_t, ,q_t:t+K), where q denotes one or two tracked hand poses in the head-camera frame. For human samples, the current pose qtq_t supplies the state input sts_t, and the relative motion between successive poses defines the continuous action chunk at:t+Ka_t:t+K. Each sample provides up to three training signals. First, a deterministic canonicalizer GeG_e, specialized only by embodiment metadata e — single arm robot, bimanual robot, or human data, produces a shared discrete action-token target mtm_t: mt=Ge(qt:t+K)ormt=Ge(at:t+K,st).m_t=G_e\! (q_t:t+K ) m_t=G_e\! (a_t:t+K,s_t ). (1) In EgoLAP, mtm_t is a language action summarizing one second of hand or end-effector motion in an egocentric frame (Fig. 2; Sec. 3.3). Controlled baselines replace these discrete action tokens with FAST or OAT tokens while preserving the remaining training recipe. Second, a subset of samples includes a motion rationale rtr_t that grounds mtm_t in visible spatial relations, contact evidence, object affordances, and the intended physical effect of the motion (Fig. 2; Sec. 3.4). Third, the continuous action chunk at:t+Ka_t:t+K directly supervises real-time control. The model consists of a vision–language backbone fθf_θ and a continuous action expert vϕv_φ. The backbone predicts mtm_t and, when available, rtr_t on both human and robot data, thereby aligning their motion semantics. The action expert learns at:t+Ka_t:t+K through flow matching. We stop action-loss gradients at the backbone boundary [13], insulating the language-pretrained representation from the randomly initialized expert. At inference, only the action expert is rolled out to generate control commands; neither a language action nor a rationale is decoded. 3.2 Model Architecture Figure 3: Attention and gradient structure. Orange marks allowed attention, gray blocked attention, and blue attention whose gradients are stopped at the VLM boundary. Reasoning and language action tokens are causally masked and condition on the observation prefix; action-expert tokens never attend to them, so control requires no text generation. EgoLAP uses a Mixture-of-Transformers (MoT) architecture [32], pairing a PaliGemma-2B vision–language backbone [3] with a 300M-parameter action expert initialized from scratch. Appendix A.1 provides the full architecture diagram and tensor shapes. Inputs. The VLM receives up to three RGB images—one base-camera view and two wrist-camera views—together with the task instruction and proprioceptive state. Missing camera views are zero-padded. Following π0.5 _0.5, the normalized state is discretized into 256 uniform bins and appended to the prompt as text. For our Cartesian policies, the state encodes end-effector position, continuous 6D rotation [58], and gripper state. Attention and gradient structure. Figure 3 shows the structured attention mask used by the policy. Image, instruction, and state tokens form a bidirectional prefix. Reasoning and language action tokens attend to this prefix and are casual within themselves. The action expert attends to its own tokens and to the observation–instruction–state prefix, but it cannot attend to either reasoning or language action tokens. Consequently, during inference time, no text generation is required. Knowledge insulation stops gradients from the action expert before they enter the VLM [13]; the backbone is therefore only optimized by the textual targets, while the action expert learns to consume its representations. Training objective. Let D denote the action dimension. The action expert, parameterized by flow matching [19], predicts at:t+K∈ℝK×Da_t:t+K ^K× D in delta end-effector pose space, and is optimized by a flow matching loss ℒFML_FM. Let ℒtextL_text denote the expected masked token-level objective for language action and motion-level reasoning, and let λtext _text weight the two objectives. The complete training loss is ℒ=(xt,at:t+K,mt,rt)∼pmix[λtextℒtext+ℒFM]L=E_(x_t,a_t:t+K,m_t,r_t) p_mix [ _textL_text+L_FM ] (2) where pmixp_mix is the fixed human–robot sampling distribution. In our model, K=30K=30 is the action horizon. We set λtext=0.8 _text=0.8, slightly downweighting the autoregressive VLM objective relative to continuous flow matching to align their convergence speed. At inference, the action expert starts from Gaussian noise at τ=1τ=1 and integrates its learned velocity field to τ=0τ=0, conditioned only on the current observation, instruction, and state. Because the textual targets are absent from the expert’s attention context, EgoLAP retains real-time continuous control without test-time language generation. Appendix A.3 gives the complete flow-matching and inference specification, while Appendix A.4 defines the cross-entropy loss ℒtextL_text. 3.3 Language Actions Following LAP [55], we supervise the VLM backbone with language actions: deterministic natural-language descriptions of hand or end-effector motion over a fixed horizon. Any trajectory with known Cartesian poses can be converted automatically; this conversion requires no manual labeling, VLM labeling, or learned action tokenizer. Egocentric canonicalization. Raw trajectories cannot share a representation unless their coordinate conventions are aligned. For each sample, we define an egocentric action frame Ft=(RtF,ptF)F_t=(R_t^F,p_t^F) at the start of the prediction window. We use the end-effector frame for single-arm robots with a wrist camera, the base frame for bimanual robots and single-arm robots without a wrist camera, and the head-mounted camera frame for egocentric human data. Each action frame is thus approximately aligned with its corresponding egocentric image frame—the wrist camera for single-arm robots, the base camera for bimanual robots, and the head-mounted camera for humans. Because these camera-centric frames follow broadly similar viewing conventions, motion directions are more consistent across embodiments than they would be in embodiment-specific world coordinates. For an end-effector or hand pose (Rτ,pτ)(R_τ,p_τ), we express the pose in this frame as p¯τ=(RtF)⊤(pτ−ptF),R¯τ=(RtF)⊤Rτ. p_τ=(R_t^F) (p_τ-p_t^F), R_τ=(R_t^F) R_τ. (3) We compute the net translation Δp=p¯t+1s−p¯t p= p_t+1s- p_t and relative rotation ΔR=R¯t⊤R¯t+1s R= R_t R_t+1s over a one-second window. For bimanual samples, we apply the same procedure independently to the left and right trajectories and retain arm identity. Rotations are converted to extrinsic XYZ Euler angles before serialization. Deterministic language actions. We serialize (Δp,ΔR,Δc)( p, R, c)—where Δc c denotes a gripper or hand-state transition—using the structured grammar from LAP: mtlang=“⟨verb⟩⟨direction⟩⟨magnitude⟩⟨unit⟩”.m_t^lang=`` \; \; \; ′. (4) Here, move denotes translation, tilt denotes roll or pitch, and rotate denotes yaw. Translational magnitudes are rounded to integer centimeters and rotational magnitudes to multiples of five degrees; components that round to zero are omitted. We append an open, close, or maintain-state phrase for the gripper or hand and use explicit left arm and right arm clauses for bimanual motion. For example: “Left arm: move forward 5 cm, move left 2 cm, tilt left 10 degrees, rotate clockwise 10 degrees, close gripper. Right arm: move down 10 cm, tilt forward 15 degrees, open gripper.” Reinforcement learning on language actions. Because GeG_e is deterministic and the grammar is machine-parseable, a language action is a verifiable target: any sampled completion can be parsed and scored against the demonstrated motion with no learned reward model. We use this to post-train EgoLAP with GRPO [44], updating only the language backbone while the vision encoder and action expert stay frozen. Appendix A.9 gives the reward and full protocol, and results are presented in Sec.4.5. 3.4 Motion-Level Reasoning A language action specifies what motion occurs, but not why that motion is appropriate in the current physical state. We therefore annotate subsets of human and robot trajectories with a motion rationale rtr_t. Given the task instruction, ordered trajectory frames, recent action history, and the ground-truth language action at the current frame, we produce a rationale that identifies a concrete end-effector–object relation, relevant contact or affordance evidence, and the immediate physical effect of the labeled motion. For example, a rationale for kneading dough might read: The dough mass rests at the base of the metal bowl, with both palms directly contacting the top and sides of the dough. Kneading requires deforming the dough against the bowl surface. Both hands translate dominantly backward while tilting wrists up and opening fingers, pulling across the compliant dough toward the body before the next pressing stroke. Motion-level reasoning is deliberately local and physics-focused. It differs from the high-level task or subtask reasoning studied in prior work [54, 9, 46, 47]: it lives on a lower hierarchy and directly connects to low-level actions, describing the underlying motion intent shared between embodiments. Appendix A.5 describes the annotation procedure, and Appendix D provides generated robot and human examples together with the labeling prompt. We apply reasoning dropout and reasoning loss dropout during training, which is discussed in Appendix A.4. 4 EXPERIMENTS We organize the evaluation around four questions: 1. Which action representation is most effective when co-training with human data? 2. Does motion-level reasoning improve transfer from human data to robots, and are motion-level reasoning and language actions mutually reinforcing? 3. How does motion-level reasoning compare to established reasoning formats? 4. Can EgoLAP be effectively adapted to downstream tasks using reinforcement learning? 4.1 Experimental Design Zero-shot evaluation. In the real world, we evaluate our models and baselines on a customized bimanual YAM robot (Fig. 4 (b)) whose arm placement (e.g., distance between the two arms) and camera configuration differ from every training embodiment. We test five behaviors spanning rigid, articulated, and deformable manipulation: Pick Place (Simple), Fold Pants, Handover & Place, Wipe Object, and Pick Place (Complex). We run 10 trials per task, except Pick Place (Complex), for which we run 12 trials, and report mean task progress. Appendix B describes each task and gives the complete scoring rubric. Error bar is reported as ±1± 1 SEMSEM. We complement the real-world experiments with a bimanual simulation benchmark built upon ABC [1], including 14 tasks that span picking, placing, open-ended language following, and cloth folding. Representative tasks are visualized in Fig. 4 (a). Notably, none of our models is trained on simulation data, so this is a zero-shot simulation evaluation. We evaluate each model for 100 episodes per task, 1,400 episodes in total, and report the mean success rate for each task group. Appendix B reports the suite composition and full evaluation protocol. Baselines. We instantiate three policy families differing only in action representation. EgoLAP uses language actions and motion-level reasoning; EgoFAST replaces language actions with FAST tokens [38] and uses the same motion-level reasoning; and EgoOAT instead uses OAT tokens [34] plus motion-level reasoning. We re-train the OAT tokenizer on our data mixture. In addition, we compare to LAP [55], which is EgoLAP trained without reasoning and without human data, as shown in Fig. 5. In Sec.4.4, we compare EgoLAP with our reimplemented ECoT baselines, which replaces motion-level reasoning with subtask plan, bounding box and visual trace reasoning. Appendix A.8 discusses the implementation details for baselines. Unless stated otherwise, all variants share everything except the action representation — same backbone, same architecture, same data mixture, same data pre-processing (e.g., egocentric canonicalization in Sec. 3.3), same optimization budget, and same evaluation protocol. All action representations correspond to the same one-second action chunk. We train every variant for 40k steps and select its checkpoint with the same validation procedure before the final evaluation; the only exception is EgoLAP, which converges faster and we train it up to 30k steps (Appendix C). Appendix A reports the shared training recipe and data mixture. Notably, within our matched implementation, EgoFAST reproduces the discrete action-token interface of π0.5 _0.5 [19], differing primarily in its training mixture. We also compare with the released checkpoint for ABC-VLA [1], which is trained directly on the ABC YAM platform. No publicly released multi-task world-action model supports the bimanual YAM platform used in our evaluation, so we do not include WAMs in the zero-shot comparison. Figure 4: Zero-shot evaluation on bimanual YAM robots. EgoLAP achieves 80.1% mean progress on real-world tasks—a 2.3×2.3× gain over alternative action representations—and a 38.3% success rate on simulated tasks, outperforming ABC-VLA [1] by 1.8×1.8×. When paired with language actions, motion-level reasoning yields a 35.6-point improvement, substantially greater than the gains achieved with other action representations. 4.2 Language Actions Transfer Human Experience Most Effectively Figure 5: Human data helps with EgoLAP. Adding egocentric human data more than doubles simulation success for the same language action policy. We first show that EgoLAP benefits from human data. Holding the representation fixed, we compare EgoLAP (no reasoning) trained on human plus robot data against the same policy trained on robot data alone, i.e., LAP [55] trained on our data mixture. Adding human data lifts simulation success from 7.2%7.2\% to 16.4%16.4\%, a 2.3×2.3× gain (Fig. 5) The simulation suite is the harder test of transfer, since neither policy has ever seen the simulator, and it is there that human data pays off most. Appendix A.8 specifies the matched robot-only training setup. We next compare action representations. Changing only the action representation and using no reasoning, EgoLAP reaches 16.4%16.4\% success in simulation and 44.5%44.5\% progress in the real world, against 1.6%1.6\% and 35.2%35.2\% for EgoFAST and 2.7%2.7\% and 18.0%18.0\% for EgoOAT. The margin is largest exactly where the domain gap is biggest: on the unseen simulator, language actions are an order of magnitude better than FAST and OAT. This strongly suggests that language actions transfer human experience to robot tasks better than non-linguistic action tokenizers do, even without any reasoning supervision. We believe this is because language actions align with the VLM’s pre-training distribution, so human and robot motions that share an intent are described by the same words and land in the same region of a representation space the backbone already understands. The full EgoLAP policy also beats ABC-VLA, which is trained directly on the data from the same simulation environment, by 16.916.9 points in simulation and 54.554.5 points in the real world. This strongly suggests EgoLAP overcomes an in-domain data advantage and generalizes better by transferring human data knowledge. 4.3 Motion-Level Reasoning and Language Actions Are Mutually Reinforcing We further compare each EgoX (no reasoning) policy with its reasoning-supervised counterpart. Motion-level reasoning raises EgoLAP from 44.5%44.5\% to 80.1%80.1\% mean progress in the real world, a 35.635.6-point gain that holds on every one of the five tasks (Fig. 4 (b)), and from 16.4%16.4\% to 38.3%38.3\% in simulation, a 21.921.9-point gain that holds on every task family (Fig. 4 (a)). This first suggests that motion-level reasoning is very helpful on its own. The same supervision, however, adds only 7.17.1 points to EgoFAST in simulation and in fact hurts it in the real world, dropping it from 35.2%35.2\% to 26.1%26.1\%. EgoOAT benefits more modestly, gaining 0.70.7 points in simulation and 7.67.6 points in the real world. This gap strongly suggests a synergy between language actions and motion-level reasoning. As shown in Fig. 2, the two form a single textual “action chain-of-thought”, moving from reasoning about why a motion is appropriate, grounded in visuals and physics, to the actual motion to execute. Non-linguistic action tokens like FAST and OAT lack this semantic correspondence, leaving the backbone to infer the correlation from co-occurrence alone, without transferring the knowledge already in the VLM backbone. Table 1: Human data strengthens reasoning. Zero-shot success (%) on the 14-task simulation suite. Training data No reasoning Reasoning Robot only 7.2 18.4 Robot + human 16.4 38.3 Human data strengthens reasoning. To test whether robot-side rationale supervision alone explains the gain, we compare language-action policies trained with and without human data on the same 14-task simulation suite (Table 1). Reasoning improves robot-only success from 7.2%7.2\% to 18.4%18.4\% (+11.2+11.2 points), versus 16.4%16.4\% to 38.3%38.3\% (+21.9+21.9 points) with human data. Adding human data therefore yields 9.29.2 points without reasoning and 19.919.9 points with reasoning: robot-side rationale supervision alone does not explain the full gain. 4.4 Motion-Level Reasoning Outperforms Established Reasoning Formats Figure 6: Motion-level reasoning is what carries the gain. Motion-level reasoning outperforms ECoT-style reasoning [54], and augments it by a large margin. We next ask whether the benefit comes from motion-level reasoning specifically or from reasoning tokens in general. We compare against a strong composite target in the style of ECoT [54], which predicts the current subtask, visible-object bounding boxes, and a visual trace before the language action. Motion-level reasoning helps every target we tried (Fig. 6): it adds 7.17.1 points to FAST, 9.19.1 points to the ECoT composite, and 21.921.9 points to plain language actions. The composite itself, however, does not help. On its own it reaches 5.3%5.3\%, well below the 16.4%16.4\% of language actions with no reasoning at all, and stacking it in front of motion-level reasoning caps the policy at 14.4%14.4\%, less than half of the 38.3%38.3\% obtained by motion-level reasoning alone. Because all action-representation variants are trained on the same trajectories with identical action-conditioned rationales, and the ECoT-style control retains the same language-action target while adding subtask, box, and future-trace supervision, EgoLAP’s substantially larger gain cannot be attributed to privileged action information or merely to additional auxiliary supervision; it specifically demonstrates the effectiveness of pairing motion-level rationales with a language-based action interface. 4.5 Adapting EgoLAP to Downstream Tasks Figure 7: GRPO over language actions over simulation tasks. Following Sec. 3.4, we post-train EgoLAP with GRPO [44] over the language actions on ABC [1], keeping the vision and action expert frozen. We construct the language action reward by summing the negative squared translation, geodesic rotation, and a binary gripper error of the parsed language action. This can be seen as an indirect behavior cloning alignment reward of the language actions. We test three variations: reasoning pre-training without reasoning generation (i.e., only generates language actions during sampling), reasoning pre-training with reasoning generation, and the non-reasoning baseline (w/o reasoning). Appendix A.9 gives the reward, objective, and full protocol. Even with a frozen expert, RL improves simulation success in all three arms (Fig. 7). Comparing the orange bar and the blue bar suggests reasoning pre-training supplies a stronger initialization for a stronger post-RL policy. Secondly, generating reasoning during RL sampling hurts performance relative to only sampling language actions (+12.7%+12.7\% vs. +19.4%+19.4\%): ABC rationales were never seen in training, so the sampled rationales are out of distribution, which makes the subsequent language actions generation also worse. We leave investigating how to better leverage motion-level reasoning for RL in future works. 4.6 Reasoning Aligns Skill Structure Across Embodiments Table 2: Motion-level reasoning improves cross-embodiment skill retrieval. All values are percentages. Retrieval w/o EgoLAP Δ R→ ⋅· 3w R@1 51 76 ++25 H→ ⋅· 3w R@1 42 63 ++21 R→ ⋅· 2w R@1 69 92 ++23 R→ ⋅· 3w MRR 61 80 ++19 We test matched checkpoints differing only in reasoning supervision. We mean-pool final-layer features from 1,0021,002 balanced human and robot frames, subtract each embodiment mean, and perform cross-embodiment cosine retrieval. In Tab. 2, R→ means a robot query ranks human frames; H→ is the reverse. “3w” and “2w” denote three- and two-skill splits; R@1 is the fraction whose nearest frame has the same skill; MRR is the mean reciprocal rank of the first same-skill match; “w/o” is the matched checkpoint without reasoning; and Δ is the absolute gain from reasoning in percentage points. We report paired task-bootstrap confidence intervals. Robot-to-human R@1 rises from 51% to 76% (+25 points, 95% CI [16,39][16,39], p<.005p<.005), while the reverse direction rises from 42% to 63% (+21 points, p=.04p=.04). The two-skill split improves from 69% to 92% (+23 points, 95% CI [16,30][16,30]), and MRR from 61% to 80% (Tab. 2). Because the embodiments remain linearly separable, reasoning preserves domain identity but gives both domains the same internal organization—fold near fold, place near place. 5 CONCLUSION We introduce EgoLAP, a VLA pre-training framework that transfers egocentric human experience to robots through a shared language of motion. By pairing language actions that describe what motion to produce with physically grounded reasoning that explains why, EgoLAP reaches 80.1%80.1\% real-world task progress and 38.3%38.3\% simulation success on bimanual manipulation, substantially outperforming alternative action representations and reasoning formats. Beyond policy performance, motion-level reasoning improves cross-embodiment skill retrieval by up to 2525 points, suggesting that it organizes human and robot experience by shared skill structure without erasing embodiment identity. EgoLAP also adapts effectively through reinforcement learning, while its textual targets remain training-only and add no generation cost during control. Limitations and future work. Language actions currently summarize fixed one-second windows with quantized translation and rotation, which may miss the dynamics or precision required for fast, contact-rich manipulation. Their linguistic form, however, can naturally support adaptive precision: future representations could combine coarse, long-horizon descriptions with fine, high-frequency corrections, while tolerating approximate labels from pose tracking, UMI, or internet video. Our evaluation remains focused on bimanual tabletop tasks. Finally, our reinforcement-learning study is confined to simulation and optimizes a motion-matching proxy rather than task reward; future work should jointly post-train motion-level reasoning and the action expert using task-level feedback. Acknowledgments Toyota Research Institute (TRI) provided funds to assist the authors with their research; this article solely reflects the opinions and conclusions of its authors, and not TRI nor any other Toyota entity. We thank Google’s TPU Research Cloud (TRC) for providing access to Cloud TPUs. We also thank Tim Chu and Asher J. Hancock for their valuable feedback on this project. Samuel M. Bateman is supported by the National Science Foundation CISE Graduate Fellowships under Grant No. 2313998. The authors were partially supported by the Office of Naval Research under Grant N00014-23-1-2148, the Army Research Laboratory under DCIST CRA W911NF-17-2-0181, and Gemini Academic Program. AI Use Statement We used large language models to edit and polish the manuscript. We also used Google Gemini to generate offline motion-level reasoning labels: gemini-3.5-flash for DROID and gemini-3.7-flash for MECKA. These labels serve as training targets for the reasoning-enabled policies; Appendix A.5 documents the inputs and annotation procedure, and Appendix D provides the prompts and representative outputs. The authors designed and checked the labeling pipeline, reviewed the AI-assisted manuscript edits, and take responsibility for all content, claims, results, and AI-assisted artifacts in this work. Reproducibility Statement We provide the methodological and experimental details needed to reproduce our results. Section 3 specifies the model, objectives, shared motion representation, and motion-level reasoning formulation, while Section 4.1 describes the matched comparison protocol. Appendix A documents the architecture, prompt and action serialization, flow-matching objective, reasoning-annotation pipeline, training hyperparameters, data mixture, and baseline implementations. 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Lin (2025) CoT-vla: visual chain-of-thought reasoning for vision-language-action models. External Links: 2503.22020, Link Cited by: §2. [57] R. Zheng, D. Niu, Y. Xie, J. Wang, M. Xu, Y. Jiang, F. Castañeda, F. Hu, Y. L. Tan, L. Fu, T. Darrell, F. Huang, Y. Zhu, D. Xu, and L. Fan (2026) EgoScale: scaling dexterous manipulation with diverse egocentric human data. External Links: 2602.16710, Link Cited by: §2. [58] Y. Zhou, C. Barnes, J. Lu, J. Yang, and H. Li (2020) On the continuity of rotation representations in neural networks. External Links: 1812.07035, Link Cited by: §3.2. Appendix A Training Details A.1 Model Architecture and Tensor Shapes Figure 8: Detailed EgoLAP architecture. A shared SigLIP encoder maps each camera view to visual tokens. The 2B VLM branch predicts motion-level reasoning and the language action; the 300M action expert maps a noisy action chunk to its flow velocity. The two branches hold separate parameters but join the same masked-attention operation at every transformer layer. Action tokens attend to the observation, instruction, and discretized state, never to the textual targets, and gradients through the VLM keys and values are stopped. Let B be the batch size and V the number of enabled camera slots. Before tokenization, a sample contains RGB observations ot∈ℝB×V×224×224×3o_t ^B× V× 224× 224× 3, a task instruction, a normalized proprioceptive state st∈ℝB×20s_t ^B× 20, and a continuous target at:t+30∈ℝB×30×14a_t:t+30 ^B× 30× 14. The 20 state values comprise ten values per arm: end-effector position, a continuous 6D rotation, and gripper state. The 14 action values comprise seven Cartesian-control values per arm; single-arm samples occupy one seven-dimensional block and pad the other. For samples with fewer than three views, absent views are zero-filled and masked. Each 224×224224× 224 image produces 256 SigLIP patch tokens. The normalized state is discretized into 256 uniform bins and serialized with the instruction, so it is part of the text prefix rather than a separate action-expert token. For EgoLAP, the padded text tensor has shape B×320B× 320. Thus, with three views, the maximum VLM prefix has shape B×(3⋅256+320)×2048B×(3· 256+320)× 2048. Padding and absent-image tokens are removed by the attention mask. The VLM has 18 transformer blocks, width 2048, an FFN width of 16,384, eight query heads, and one key–value head. The action expert receives at:t+30τ∈ℝB×30×14a_t:t+30^τ ^B× 30× 14 and projects it to B×30×1024B× 30× 1024. A sinusoidal embedding of τ produces one B×1024B× 1024 conditioning vector used by adaptive RMS normalization in all 18 expert blocks. The expert has FFN width 4096, eight query heads, and one key–value head. Its velocity head returns vϕ∈ℝB×30×14v_φ ^B× 30× 14, exactly matching the target action-chunk shape. The tied VLM head produces token logits of shape B×L×257,152B× L× 257,152; only reasoning and action-target positions receive text loss. At inference, ten Euler steps integrate a noise tensor of shape B×30×14B× 30× 14 to the final action chunk of the same shape. Text is not decoded for control. A.2 Prompt and Language-Action Format Prompt serialization. The observation images are followed by a single text sequence with the literal format Task: [instruction], predict the robot’s action in the egocentric frame; State: [b1b_1 … bdb_d]; Answer: The instruction is stripped of a trailing period, and underscores and line breaks are replaced by spaces. Each bi∈0,…,255b_i∈\0,…,255\ is a uniformly discretized normalized state value. Trailing zero-padded state dimensions are omitted, leaving d=10d=10 values for a single arm and d=20d=20 for bimanual robot and human samples. The reference run reuses the exacting phrase egocentric frame and robot’s action for all embodiments, including human samples. For a sample without motion-level reasoning, the language action mtm_t immediately follows Answer:. When a rationale is included, the complete target is Answer: [rtr_t] Concrete actions to take are: [mtm_t] The boundary phrase is fixed and separates the optional rationale from the language action, allowing their losses to be masked independently while retaining one causal target sequence. At inference, the policy receives the same observation–instruction–state prefix, but the continuous action expert does not decode either textual field. Language-action grammar. Each arm is represented by an ordered, comma-separated clause. Translation is emitted in the order longitudinal, vertical, then lateral; rotation follows as roll, pitch, then yaw; and the clause always ends with the final gripper state. Table 3 gives the exact vocabulary. Table 3: Canonical component vocabulary for language actions. Here n is an integer number of centimeters and θ is an integer multiple of 55 degrees. A component is omitted when its rounded magnitude is zero. Component Positive direction Negative direction Translation x move forward n cm move back n cm Translation z move up n cm move down n cm Translation y move left n cm move right n cm Roll tilt left θ degrees tilt right θ degrees Pitch tilt back θ degrees tilt forward θ degrees Yaw rotate counterclockwise θ degrees rotate clockwise θ degrees Gripper state open gripper close gripper Translational displacement is rounded to integer centimeters, and each Euler-angle component is rounded to the nearest 55 degrees. The open/close token describes the final aperture state rather than a displacement and is therefore retained even when all pose components are omitted. The embodiment-specific serializations are as follows. Single-arm robot. One clause is emitted, with its arm prefix sampled uniformly during training: [Left∣ ] arm: [motion components], [open∣ ] gripper For example, a DROID sample in the reference run is serialized as Left arm: move forward 8 cm, move down 6 cm, move right 7 cm, tilt forward 10 degrees, rotate counterclockwise 10 degrees, close gripper. Bimanual robot. Both clauses are emitted in a fixed order and separated by a period: Left arm: [left components]. Right arm: [right components] Egocentric human. Human hand trajectories use the same bimanual template rather than a separate human-only vocabulary. Left arm and Right arm identify the tracked hands, while open gripper and close gripper encode the corresponding binary hand-aperture state. This shared serialization provides a common interface through which human and robot motion supervise the same VLM tokens. A.3 Flow-Matching Objective For a continuous action chunk at:t+K∈ℝK×Da_t:t+K ^K× D, Gaussian noise ϵ∼⁡(0,I)ε (0,I), and interpolation time τ=0.001+0.999zτ=0.001+0.999z with z∼Beta⁡(1.5,1)z (1.5,1), define the interpolated state and target velocity: at:t+Kτ=(1−τ)at:t+K+τϵ,ut=ϵ−at:t+K.a_t:t+K^τ=(1-τ)a_t:t+K+τε, u_t=ε-a_t:t+K. (5) The action expert vϕv_φ is trained to recover this velocity: ℒFM=τ,ϵ[1KD‖vϕ(at:t+Kτ,τ,sg[hθ(xt)])−ut‖F2],L_FM=E_τ,ε [ 1KD \|v_φ\! (a_t:t+K^τ,τ,sg[h_θ(x_t)] )-u_t \|_F^2 ], (6) where xt=(ot,ℓ,st)x_t=(o_t, ,s_t) is the multimodal prefix, hθh_θ is the backbone prefix representation and sgsg denotes stop-gradient, implementing the knowledge-insulation boundary [13] that prevents continuous-action gradients from eroding VLM’s pretrained representation. At inference, actions are generated by integrating the learned velocity field from τ=1τ=1 (noise) to τ=0τ=0 (action) using a fixed-step ODE solver. A.4 Stochastic supervision To avoid VLMs overfitting to reasoning, we stochastically vary whether reasoning appears in the target and whether it receives loss. For rationale tokens rt=(rt,1,…,rt,M)r_t=(r_t,1,…,r_t,M) and discrete action tokens mt=(mt,1,…,mt,N)m_t=(m_t,1,…,m_t,N), draw two independent variables B∼Bernoulli⁡(pctx),C∼Bernoulli⁡(psup).B (p_ctx), C (p_sup). (7) If B=1B=1, the rationale is inserted as a teacher-forced causal prefix before mtm_t; otherwise, the VLM predicts mtm_t directly. Write rt(B)=rtr_t^(B)=r_t when B=1B=1 and rt(B)=∅r_t^(B)= otherwise. Conditional on the rationale’s presence, C determines whether its tokens receive language-modeling loss. The masked per-sample objective is ℓtext(B,C)=−1N+BCM[ _text(B,C)=- 1N+BCM [ BC∑j=1Mlog⁡pθ(rt,j∣xt,rt,<j) BC _j=1^M p_θ\! (r_t,j x_t,r_t,<j ) +∑i=1Nlogpθ(mt,i∣xt,rt(B),mt,<i)]. + _i=1^N p_θ\! (m_t,i x_t,r_t^(B),m_t,<i ) ]. (8) The text term in Eq. 2 is ℒtext=B,C[ℓtext(B,C)]L_text=E_B,C[ _text(B,C)]. We use pctx=psup=0.5p_ctx=p_sup=0.5; for samples without a rationale, we set B=C=0B=C=0. Thus, among labeled samples, half train direct language action prediction, one quarter use reasoning only as causal context, and one quarter both condition on and supervise the rationale. The discrete action tokens are supervised in every case. A.5 Motion-Level Reasoning Annotation Coverage. Motion-level reasoning labels exist for only two of the datasets in our mixture: the MECKA subset of EgoVerse [39], which supplies all of our egocentric human reasoning, and DROID [24], which supplies all of our robot reasoning. Together they account for 32%32\% of each training batch (Fig. 9). Every other dataset — ABC YAM, the remaining bimanual robot datasets, the Scale and Aria subsets of EgoVerse, and the remaining OXE datasets — contributes language actions and continuous actions but no rationale. Those samples take B=C=0B=C=0 in Eq. 8 and are therefore trained exactly as in the no-reasoning variants. The same two annotated sources are used for every reasoning policy we report, including EgoFAST and EgoOAT, so reasoning coverage is never a confound between action representations. Annotation procedure. We generate the annotations offline with gemini-3.5-flash for DROID and gemini-3.7-flash for MECKA. Both runs use temperature 0. Gemini is given the task instruction and a temporally ordered set of action anchors. The target language action is an input to the annotation procedure to provide Gemini with the action context, which we empirically find to lead to more grounded reasoning labels compared to only providing images. Appendix D shows representative DROID and MECKA annotations together with the labeling prompt. For DROID, anchors are formed from adaptive action segments with a nominal stride of 15 filtered steps (approximately one second). A segment can end early at a persistent gripper-state change or a large change in translational direction. At each anchor, Gemini receives the current primary and wrist-camera images, the current gripper and transition metadata, the language action computed from the numeric actions over that segment, and a compact text-only summary of up to five seconds of preceding actions. The prompt distinguishes the state visible at the anchor from the command to be executed over the following segment, which prevents a future grasp, release, or contact event from being described as already complete. For MECKA, subsequences belonging to the same high-level recording are first concatenated in their recorded order. Then, adaptive anchors are selected with a separation of 15–30 frames at 30 Hz. Each anchor contains the head-mounted egocentric image, the high-level instruction and stitched subtask context, the segment-level bimanual language action, and the same compact action history. Since MECKA records human manipulation, the prompt maps the shared action vocabulary to left and right hands, fingers, contact, support, and release rather than robot grippers. Gemini outputs a trajectory summary, a subtask plan, and, for every requested anchor, the completed, current, and next subtasks; observation–action grounding; the main rationale; a visual-relation sentence; a motion-effect sentence; and an alternative-motion diagnostic. However, during training, we only use the main motion-level reasoning rationale. A.6 Training Hyperparameters Table 4 summarizes the pre-training hyperparameters. We train all policy variants for 40k steps with the same hyperparameter settings. This includes EgoLAP, EgoFAST, and EgoOAT, each with and without reasoning, as well as the robot-data-only ablation. The language action loss weight is set below 1.0 because the discrete token loss objective converges faster than the flow-matching expert; slightly downweighting this loss prevents the backbone from overfitting early in training. Appendix A.8 reports additional observations under varying training budgets. Table 4: Shared policy pre-training hyperparameters. Hyperparameter Value Batch size 2048 Hardware 64 × TPU v6e Training steps 40k Learning-rate schedule 2500-step linear warmup, then constant Peak learning rate 5×10−55× 10^-5 Optimizer Adam (β1=0.9 _1=0.9, β2=0.95 _2=0.95, ϵ=10−8ε=10^-8) Weight decay 1×10−41× 10^-4 Gradient clipping norm 1.0 EMA decay 0.999 Language-action loss weight 0.8 Flow-matching loss weight 1.0 Action chunk length 30 steps Action dimension 14 State dimension 20 Image resolution 224×224224× 224 Numeric precision bfloat16 Action/state normalization per-category 1st–99th percentile bounds Flow-time distribution 0.001+0.999Beta⁡(1.5,1)0.001+0.999Beta(1.5,1) Inference integration steps 10 Wrist-image dropout 0.1 Random camera masking 0.2 Validation/checkpoint interval 1000 steps Random seed 0 Image pre-processing and augmentation. Input images are resized with aspect-ratio-preserving symmetric padding to a fixed resolution (224×224 in the default configuration). During training, image augmentation is enabled by default for each model-facing camera view. Images are mapped from [−1,1][-1,1] to [0,1][0,1] and transformed using a random crop of ⌊0.95W⌋×⌊0.95H⌋ 0.95W × 0.95H , resizing back to the target resolution, a random in-plane rotation sampled uniformly from [−5∘,5∘][-5 ,5 ], and Augmax color jitter configured with brightness, contrast, and saturation strengths of 0.2. The augmented images are then mapped back to [−1,1][-1,1]. Random seeds are independent across batch elements but shared across camera views for a given element. A.7 Data Mixture Figure 9 shows the training data mixture reflecting the composition of each training batch. The mixture spans four groups: ABC robot data [1] (30%, from the ABC YAM platform), egocentric human data from EgoVerse [39] (25%, drawn from the MECKA, Scale, and Aria subsets), additional bimanual robot data (25%, including AgiBot, Galaxea R1 Lite, and MolmoAct2 YAM), and single-arm OXE robot datasets [11] (20%, predominantly DROID [24] at 12%). Of these, only MECKA and DROID carry motion-level reasoning labels, as described in Appendix A.5. The total raw data amounts to around 10k hours. Figure 9: Training data mixture. Inner ring: group weights; outer ring: individual dataset contributions within each group. Only MECKA (20%20\%) and DROID (12%12\%) carry motion-level reasoning labels; the remaining samples are supervised with language actions and continuous actions alone. A.8 Baseline Implementation Details All matched policies use the architecture in Fig. 8, the continuous 30×1430× 14 flow-matching target, the data mixture in Fig. 9, and the optimization settings in Table 4. FAST and OAT change only the autoregressive action target. Their action tokens supervise the VLM branch; they do not replace the continuous action expert. The expert therefore receives the same observations and continuous targets for every representation. FAST. We use the released FAST tokenizer [38] to encode each normalized 30×1430× 14 action chunk. In the no-reasoning policy, the FAST tokens directly follow the observation–instruction–state prefix. In the reasoning policy, the motion rationale is placed before the codes. The tokenizer is fixed while the policy is trained. OAT. We separately train the OAT codec [34] on normalized 30×1430× 14 action chunks sampled from the same mixture used for policy pretraining, and freeze it during policy training. In our configuration, the codec represents each action chunk with a maximum-length sequence of 16 ordered discrete tokens. Since OAT is trained with power-of-two prefix dropout, any prefix of 11, 22, 44, 88, or 1616 tokens can reconstruct the complete action chunk, with later tokens progressively refining the reconstruction. The encoder and decoder have hidden width 256, eight attention heads, and six Transformer blocks each, with dropout 0.1. Each latent is quantized using finite scalar quantization with levels (8,8,6,5)(8,8,6,5), yielding 8×8×6×5=1,9208× 8× 6× 5=1,920 possible codes per token. We train the codec for 100,000 updates and use the same frozen checkpoint for both OAT policy variants. In the reasoning variant, reasoning tokens precede the OAT action tokens; the no-reasoning variant predicts the OAT action tokens directly. ECoT-style reasoning [54]. We implement the composite baseline in Sec. 4.4 as an ordered prefix containing subtask context, visible-object boxes, and a visual trace, followed by the same language action used by EgoLAP. The subtask context is reused from the offline Gemini annotations of Appendix A.5: for DROID, we extract the standardized full-plan and current-subtask sentences from each annotated segment; for MECKA, we read the corresponding structured fields after stitching subsequences from the same recording. We obtain object boxes in a separate offline grounding pass: given an anchor image, the task instruction, and the current subtask, gemini-3.5-flash at temperature 0 returns task-relevant visible objects and their normalized boxes. We ground every second annotated anchor and do not propagate boxes to intervening frames. We map the boxes through the same aspect-preserving resize and symmetric padding as the input image, quantize them into the 1,024 PaliGemma location bins, and serialize each box in (ymin,xmin,ymax,xmax)(y_ ,x_ ,y_ ,x_ ) order. The visual traces are computed from trajectories and camera parameters directly, rather than generated by Gemini. For DROID, we project the recorded end-effector positions into the calibrated exterior camera using its intrinsics and camera-to-base extrinsics; for MECKA, we project the left- and right-palm positions into the head-camera view using the synchronized head pose and camera intrinsics. In both cases, the target contains five future image-space positions sampled at 5 Hz over the next second. Each (y,x)(y,x) position is quantized into the same 1,024 location-token bins. A box or trace is attached only when its source annotation or complete future projection is valid; otherwise that component is omitted without removing the training sample. The resulting target has the form Full subtask plan is ... Current subtask is ... Visible objects: ... Visual motion plan ... Concrete actions to take are: .... It deliberately excludes the motion-level rationale, so the comparison isolates ECoT-style what/where supervision from our physical why supervision. We retain loss on the ECoT-prefix tokens with probability 0.5 per sample while supervising the language-action tokens in every case. For the ECoT + motion-level reasoning baseline, we additionally appends motion-level reasoning after the visual traces. Reasoning and no-reasoning variants. The no-reasoning variants remove the rationale from the target and retain the action target on every sample. For reasoning variants, a rationale is included with probability 0.5. EgoLAP and EgoFAST retain rationale-token loss with probability 0.5 when the rationale is present. Language-action, FAST, or OAT action-target tokens receive loss in every case. Robot-only ablation. The robot-only baseline removes EgoVerse data while preserving the relative weights of every robot dataset in the full mixture; the remaining weights are renormalized. It is otherwise identical to the main model in architecture, hyperparameters, and compute budget. Checkpoint selection. All policies train for the same 40k-step budget, and we select one checkpoint per variant with a single validation procedure applied identically to every variant — taking checkpoint with the lowest offline validation loss on the held out split.. The reported comparison point is therefore around 40k steps, except for EgoLAP, which we train for 30k steps only due to faster convergence. A.9 Reinforcement Learning Experiment Details This section specifies the language-action GRPO post-training reported in Sec. 4.5. All three methods share the reward, the objective, the optimizer, the data pipeline, and the compute budget; they differ only in the SFT checkpoint they start from and in how rollouts are sampled. Datasets. Training draws from the ABC YAM dataset [1], from which we use the 1% validation held out split from pre-training. Each eligible episode contributes exactly one observation per run. Reward. For arm b∈left,rightb∈\left,right\, let pbp_b be the parsed translation in centimeters, RbR_b the rotation reconstructed from the parsed XYZ Euler angles, and gbg_b the binary gripper command, with ⋆ denoting the target. Writing the target-relative rotation vector as ωb=Log⁡((Rb⋆)−1Rb)∨∈ℝ3 _b=Log\! ((R_b )^-1R_b ) ^3 in radians, the cost and reward are C=∑b[∥pb−pb⋆∥22(2cm)2+∥ωb∥22(π/18)2+[gb≠gb⋆]],r=−C.C= _b [ p_b-p_b _2^2(2\,cm)^2+ _b _2^2(π/18)^2+1\! [g_b≠ g_b ] ], r=-C. (9) Terms are summed over arms, not averaged, so a 22 cm single-axis translation error, a 10∘10 relative orientation error, and one wrong gripper each cost one unit. Rotation error is the SO(3)SO(3) residual rather than a difference of Euler angles, and the gripper term is a discrete mismatch penalty rather than a cross-entropy. Valid rewards are non-positive and uncapped; an exact match scores zero. A completion is valid only if the parser recovers exactly one clause for each arm with finite motion values; missing, duplicated, or non-finite clauses are rejected. Unspecified axes take the parser’s zero default and an unspecified or “maintain” gripper takes its closed-state default. Within each group, an invalid completion receives rinvalid=−max⁡(1001, 1+maxjvalid⁡Cj)r_invalid=- \! (1001,\,1+ _j\,validC_j ), which ranks it below every valid completion in the same group; a group in which all completions are invalid therefore yields zero reward-derived advantage. There is no reward term for rationale quality, response length, entropy, or simulator success. GRPO objective. Each update samples 32 observations and 64 completions per observation, and all 2,048 completions enter the gradient: the group is used for group-relative advantage estimation, not for selecting a single best response to imitate. Rewards and advantages are computed on the host without differentiating through the parser. For observation i and completion j, Aij=clip⁡(rij−r¯imax⁡(σi,10−4),−4, 4),A_ij=clip\! ( r_ij- r_i ( _i,10^-4),\,-4,\,4 ), (10) where r¯i r_i and σi _i are the mean and population standard deviation within the group; groups whose reward range is at most 10−610^-6 receive zero advantage. Let PθP_θ denote the policy’s sequence distribution. For each retained response token, define the importance ratio ρijt _ijt against the sampling policy PoldP_old and the reference log-ratio δijt=log⁡Pref−log⁡Pθ _ijt= P_ref- P_θ. The minimized loss averages over tokens within a response and then over responses, ℒRL=12048∑i,j1Lij∑t=1Lij[−min⁡(ρijtAij,clip⁡(ρijt,1−ε,1+ε)Aij)+β⁡(eδijt−1−δijt)],L_RL= 12048 _i,j 1L_ij _t=1^L_ij [- \! ( _ijtA_ij,\ clip( _ijt,1- ,1+ )A_ij )+β (e _ijt-1- _ijt ) ], (11) with ε=0.2 =0.2 for the clipped surrogate [43] and a non-negative sampled (“k3k_3”) penalty of weight β=0.02β=0.02 against the frozen SFT reference. The complete continuation — any rationale, the language action, and the first EOS — carries the same response-level advantage; prompt and post-EOS tokens are masked. Only VLM backbone (excluding the vision encoder) is updated; the vision encoder and the action expert are frozen. There is no auxiliary flow-matching, SFT, rationale, or entropy term. Optimization and compute. Table 5 lists the settings shared by all three runs. Table 5: Shared language-action GRPO settings. Setting Value Observations per update 32 Completions per observation 64 (2,048 responses per update) Gradient accumulation 16 microbatches of 128 responses, one step per rollout bank Optimizer AdamW (β1=0.9 _1=0.9, β2=0.95 _2=0.95, ϵ=10−8ε=10^-8), weight decay 0 Learning rate linear warmup 5×10−8→10−65× 10^-8\!→\!10^-6 over 20 updates, then constant Gradient clipping global norm 1.0, after accumulation PPO clip range ε 0.2 Reference penalty β 0.02, against the frozen SFT reference Advantage group-normalized, clipped to [−4,4][-4,4] Rollout sampling categorical, temperature 1, no top-k or top-p Generation buffer 211 response tokens (including any seeded prefix) Retained response through the first EOS, within the 320-token text buffer Trainable parameters language backbone and tied embeddings only Hardware eight TPU v4 hosts (v4-64), 32 devices, FSDP size 32 Precision bfloat16 model; float32 log-softmax and optimizer moments Validation and checkpoint selection. Every 20 updates, and at initialization and termination, we evaluate on a fixed development set of 224 observations drawn from 28 held-out ABC dataset episodes (eight stratified temporal bins per episode), disjoint from the RL training episodes. We log (i) a language-action metric — eight temperature-1 samples plus one greedy decode per observation, scored with the same reward of Eq. 9, including invalid penalties — and (i) a continuous action-chunk metric from the flow-matching action expert: four action chunks per observation, scored as normalized MSE against the recorded command chunk. We manually choose the checkpoint that roughly minimizes both metrics. Appendix B Evaluation Details Simulation (Fig. 4 (a)). The bimanual simulation benchmark contains 14 tasks grouped into three object-picking, eight object-placement, two color-selection, and one cloth-manipulation task categories. Picking covers colored blocks and fruit in isolated and cluttered scenes. Placement requires depositing fruit or blocks into bins or positioning them on plates and trays, including variants with distractors. Color tasks include selecting an object from an color-based instruction, and stacking one colored block on another. The cloth task requires folding a towel. Each task contains 100 episodes per checkpoint, yielding 1,400 episodes for a complete evaluation. Real robot (Fig. 4 (b)). We evaluate on five real-world tasks on a custom bimanual YAM platform: two YAMs are mounted on the table, separated by around 0.8m. We use realsense D435 as the base camera and realsense D405 for the two wrist cameras. Each task is decomposed into ordered stages, and a trial is scored by how many stages it completes: if task i has KiK_i stages, its normalized progress is pi=Ki−1∑k=1Kisikp_i=K_i^-1 _k=1^K_is_ik with sik∈0,1s_ik∈\0,1\. We report the mean of pip_i over trials. Object and container poses are randomized on the table between trials, and every policy sees the same initial configurations. • Pick Place (Simple): place a toy banana into a bowl, with the banana and the bowl randomly positioned on the table. Three stages: pick up the banana, move it to the bowl, and release it into the bowl. 10 trials, split over two different objects. • Pick Place (Complex): a cluttered tabletop holds several candidate objects and several candidate containers, and the instruction names one of each. The instructed pair may fall across the two arms’ workspaces, in which case the task additionally requires a handover. Four stages: approach the instructed object, acquire and lift it, transport it to the instructed container, and place it. 12 trials, split over four different objects. • Fold Pants: fold a pair of pants in half. Five stages: grasp one end of the garment, grasp both ends, manipulate or lift the ends, produce a partial overlap, and complete the fold. 10 trials. • Handover & Place: one arm picks up an object, transfers it to the other arm, and that arm places it into a container. The task is only solvable bimanually, since the object starts outside the placing arm’s reachable workspace. Four stages: pick up the object, approach the handover configuration, complete the handover, and place the object. 10 trials, split over two different objects. • Wipe Object — pick up a cloth and wipe a target surface with it. Four stages: pick up the cloth, align it with the target surface, wipe part of the surface, and cover the full area. Wiping appears in our egocentric human data but in none of the robot pre-training corpora. 10 trials. Appendix C Additional Results C.1 Should the Action Expert Learn from Human Actions? EgoLAP applies the flow-matching loss to human and robot action chunks alike, so the continuous action expert is trained on human hand motion as well as on robot end-effector motion. This is not an obvious choice: human motion is faster, noisier, and kinematically unlike anything the robot can execute, and one might expect it to corrupt an expert whose only job is real-time control. We therefore train a matched variant that masks the action-expert loss on every human sample while keeping the human language actions and motion-level reasoning that supervise the backbone. The variant isolates a single question: is human data useful only as language supervision for the VLM, or also as motion supervision for the expert? Masking the loss is the worse choice overall (Fig. 10). The masked variant loses 4.44.4 points of overall success, and the loss is concentrated in the language-conditioned tasks, where it falls from 26.0%26.0\% to 10.0%10.0\%; it is roughly on par on picking and placing and slightly better on cloth folding, the one task family whose dynamics are least like anything in the human corpus. We read this as evidence that the two roles of human data are not separable. Once the backbone is supervised with an action representation that already transfers across embodiments, the features the expert consumes are embodiment-agnostic enough that additional, noisier human motion acts as useful augmentation rather than as distribution shift. Figure 10: Masking the action-expert loss on human samples hurts. Simulation success over the 14-task suite for EgoLAP (“no human mask”, the main model) and for a matched variant that withholds the flow-matching loss on human samples (“use human mask”). Both variants receive identical language action and motion-level reasoning supervision; they differ only in whether the continuous action expert is trained on human motion. We compare the 25k step checkpoint for both models. Error bars are one binomial standard error. C.2 Per-Task Simulation Results Figure 11 expands the aggregate simulation results in Fig. 4 (a) into the 14 individual tasks and additionally includes the EgoOAT reasoning and no-reasoning variants. The aggregate gains are broadly distributed rather than driven by one task: EgoLAP outperforms its no-reasoning counterpart on 13 of 14 tasks, with especially large gains on cluttered fruit picking, Lego placement, colored-Lego selection, and towel folding. The task-level view also reveals complementary strengths that are hidden by the group means. For example, ABC-VLA is strongest on placing fruit in a bin and on a tray, whereas EgoLAP leads on most of the remaining placement tasks. EgoOAT reaches 3.3%3.3\% mean success with reasoning and 2.7%2.7\% without; its clearest reasoning gain is on towel folding (15.6%15.6\% versus 2.1%2.1\%). Figure 11: Per-task zero-shot simulation success. Rows expand the same 14-task suite summarized in Fig. 4 (a), grouped as Pick, Place, Color, and Fold. Columns show ABC-VLA and the reasoning and no-reasoning variants of EgoLAP, EgoFAST, and EgoOAT. Each cell reports the empirical task success rate, with darker shading indicating higher success. C.3 Do language actions benefit more from human data? Higher performance under human–robot co-training could reflect a stronger robot-only policy rather than a greater benefit from human data. To distinguish these explanations, Table 6 compares robot-only and joint human–robot training for language actions and FAST. We measure the human-data gain as the absolute change in zero-shot simulation success when adding egocentric human data. Table 6: Language actions benefit more from human data under motion-level reasoning supervision. Zero-shot success on the 14-task simulation suite. Human-data gains are absolute percentage-point differences. Reasoning denotes motion-level reasoning supervision. Representation Reasoning Robot only Robot + human Human-data gain Language No 7.2% 16.4% +9.2 p Language Yes 18.4% 38.3% +19.9 p FAST Yes 1.4% 8.7% +7.3 p With motion-level reasoning, adding human data improves language actions from 18.4% to 38.3%, a 19.9-point gain, whereas FAST improves from 1.4% to 8.7%, a 7.3-point gain. Thus, although language actions already provide a stronger robot-only baseline, their advantage widens under human–robot co-training: the gap over FAST increases from 17.0 to 29.6 points. This 12.6-point difference in human-data gains supports the conclusion that the advantage of language actions is not explained solely by stronger robot-only performance. Within the language-action policies, human data also provides a larger improvement with reasoning than without it (19.9 versus 9.2 points), consistent with the interaction observed in Section 4.3 (Table 1). Together, these results support the effectiveness of pairing language actions with motion-level reasoning for human-to-robot transfer under our training recipe. Appendix D Generated Motion-Level Reasoning Examples and Prompt Following the annotation procedure in Appendix A.5, we randomly show some motion-level reasoning labels from robot trajectories in DROID and egocentric human trajectories in MECKA, paired with the corresponding language actions, which form the complete textual supervision targets of the backbone. Each card places the unprocessed model observation on the left and the reasoning and language action on the right. Task headings are lightly normalized for readability. D.1 DROID and MECKA Examples Primary Wrist DROID Push the pump of the blue bottle down Motion-level reasoning The gripper has successfully grasped the pump nozzle. The robot now needs to push the pump down to fulfill the task instruction. The proposed motion moves the arm forward and down to begin depressing the pump mechanism. This downward motion must be controlled to avoid tipping the bottle. Language action Left arm: move forward 1 cm, move down 2 cm, close gripper. Primary Wrist DROID Hang the wire on the cabinet door Motion-level reasoning With the hanger secured, the robot must lift it off the countertop to transport it to the cabinet. The next motion should lift the gripper upward and backward to clear the countertop and any obstacles. This begins the transport phase of the task. Language action Left arm: move back 7 cm, move up 8 cm, move right 3 cm, tilt right 20 degrees, tilt forward 20 degrees, close gripper. Primary Wrist DROID Put the sunglasses on the tray Motion-level reasoning The gripper jaws are perfectly positioned around the sunglasses. The robot should move down slightly to ensure the jaws are fully surrounding the target, then close the gripper to secure the sunglasses. This action will establish a firm hold on the object. Language action Left arm: move forward 2 cm, move down 4 cm, move right 2 cm, tilt back 10 degrees, rotate clockwise 10 degrees, close gripper. Primary Wrist DROID Put the stick of glue in the mug Motion-level reasoning The glue stick is now securely grasped. The robot needs to lift it to clear the table and the rim of the cup. The next motion should raise the gripper and move it toward the left where the cup is located. Language action Right arm: move forward 1 cm, move up 14 cm, move left 25 cm, tilt right 10 degrees, tilt forward 10 degrees, rotate counterclockwise 20 degrees, close gripper. Primary Wrist DROID Put the white object on the top shelf inside the grey toolbox Motion-level reasoning The robot has successfully grasped and lifted the white USB adapter cable. The next step is to transport it toward the grey storage bin. The next motion should move the gripper forward and left while rotating to align with the bin. Language action Left arm: move forward 4 cm, move left 8 cm, tilt forward 10 degrees, rotate clockwise 30 degrees, close gripper. MECKA Reposition the grip and continue brushing the metal component Motion-level reasoning The left hand rests open across the metal disk, shifting slightly forward to maintain stability. Simultaneously, the right hand pulls the brushing tool upward and toward the torso, lifting the brush stroke clear to reposition for the next motion. Language action Left arm: move forward 1 cm, move right 1 cm, move down 1 cm, tilt left 5 degrees, rotate counterclockwise 5 degrees, open gripper. Right arm: move backward 5 cm, move up 2 cm, tilt left 5 degrees, tilt backward 15 degrees, close gripper. MECKA Insert small components into electronic device Motion-level reasoning The left hand is directly above the open blue container. It should descend into the blue bin to target a small component. Translating down and forward aligns the fingers inside the container. The right hand should maintain its grip on the fixture. Language action Left arm: move forward 6 cm, move down 11 cm, move right 12 cm, tilt right 10 degrees, tilt back 10 degrees, rotate clockwise 70 degrees, open gripper. Right arm: move back 4 cm, tilt left 10 degrees, tilt forward 10 degrees, rotate clockwise 20 degrees, close gripper. MECKA Fill bottle with liquid from syringe Motion-level reasoning The left hand supports the bottle firmly on the mat. The right hand shifts forward, up, and right while opening fingers to disengage from the plunger. This finishes the current stroke and allows resetting. Language action Left arm: move back 2 cm, rotate counterclockwise 10 degrees, close gripper. Right arm: move forward 1 cm, move up 1 cm, move right 2 cm, tilt left 10 degrees, rotate clockwise 10 degrees, open gripper. MECKA Cut red fabric into strips with scissors Motion-level reasoning The left hand advances the held fabric over the table pile. The right hand keeps the scissors ready with fingers open. This repositions the active cutting zone conveniently. Language action Left arm: move forward 5 cm, move down 1 cm, tilt right 10 degrees, tilt forward 10 degrees, rotate clockwise 10 degrees, close gripper. Right arm: move forward 4 cm, tilt forward 10 degrees, rotate counterclockwise 10 degrees, open gripper. MECKA Open the bottle Motion-level reasoning The right hand advances, lowers, closes fingers and rotates clockwise, securing a new contact point. The left hand shifts back and up slightly. This repositions the right hand for secondary stabilization. Closing the fingers provides firm support. Language action Left arm: move back 1 cm, move up 2 cm, tilt right 10 degrees, tilt forward 10 degrees, rotate clockwise 10 degrees, open gripper. Right arm: move forward 2 cm, move down 2 cm, move right 5 cm, tilt right 50 degrees, rotate clockwise 40 degrees, close gripper. D.2 Annotation Prompt We use separate prompts for MECKA and DROID. Below we retain the operative labeling instructions and show placeholders for per-step text, structured-action metadata, and images. MECKA Gemini Prompt You label egocentric human bimanual hand-manipulation trajectories for training a vision-language action model. The model will be trained to predict a reasoning bridge first, then the provided language action. Generate concise, observable, action-grounded rationales. These are MECKA first-person human manipulation videos. The primary image is the head-mounted egocentric camera view; there is no wrist camera. The action formatter is shared with robot data and may say “Left arm,” “Right arm,” and “gripper.” Interpret these as the human left and right hands or palms and the corresponding fingers. In generated reasoning, prefer human terms such as left hand, right hand, fingers, grasp, pinch, contact, support, and release. A MECKA trajectory may be one subsequence cut from a longer high-level recording. Unless explicit stitched context is provided, treat the supplied instruction as the scope of the visible segment and do not invent unseen earlier or later subtasks. Build a concise trajectory summary, instruction-target checklist, and ordered subtask plan that cover all requested objects, receptacles, quantities, and spatial constraints. Mark requested but unseen entities as unresolved rather than substituting a different object. For each requested step, use the current observations, task instruction, proposed language action, and compact past-action history when supplied. The requested steps are adaptive trajectory segments and may end early at a persistent finger-state change or major motion transition. Treat each image as the state before its segment action. Do not backdate the expected result of the current action or use later images as evidence that it succeeded. Interpret finger opening and closing separately for the two hands. A commanded finger state does not by itself prove a grasp, release, or object support. Keep each hand’s contact and role distinct, ground grasp or release claims in visible evidence, and respect the stated order between arm motion and a finger transition. Cross-check every directional word in the rationale against the supplied action; do not describe upward motion as lowering or downward motion as lifting. The reasoning must connect visible task progress, the active hand–object relation, and the physical purpose of the next motion without copying action magnitudes or merely paraphrasing the command. State concrete relations to the target, receptacle, support surface, opening, rim, or obstacle. Explain relevant contact, support, stability, alignment, grasp choice, and clearance. If visibility is ambiguous, describe only what is supported by the image. Return a trajectory summary, checklist, subtask plan, instruction paraphrases, and one label per requested step. Each step contains completed, current, and next subtasks; observation–action grounding; the main reasoning; a visual-relation sentence; a motion-rationale sentence; and an alternative-motion diagnostic. Return strict JSON only. Trajectory and per-step input template Task instruction: [TASK INSTRUCTION] Number of requested steps: [N] Step [STEP INDEX]: filtered trajectory index [INDEX], original frame [FRAME], segment frames [START]--[END] ([TERMINATION REASON]), duration [SECONDS]s, action-summary horizon [SECONDS]s. Target language action in [ACTION FRAME]: [LANGUAGE ACTION] Past 5s action history: [OPTIONAL HISTORY ITEMS] Structured-action metadata: ‘step_index’: [STEP INDEX], ‘trajectory_step_index’: [TRAJECTORY STEP INDEX], ‘segment_start’: [START], ‘segment_end’: [END], ‘action_frame’: ‘egocentric frame’, ‘language_action’: ‘[LANGUAGE ACTION]’, ‘gripper_open_signal’: [LEFT/RIGHT FINGER STATE], ‘history_5s’: [OPTIONAL COMPACT ACTION HISTORY] Primary camera image follows. [[PRIMARY EGOCENTRIC IMAGE]] [REPEAT TEXT, PAYLOAD, AND IMAGE FOR EACH REQUESTED STEP] DROID Gemini Prompt You label robot manipulation trajectories for training a vision-language action model. The model will be trained to predict a reasoning bridge first, then the provided language action. Generate concise, observable, action-grounded rationales. Use the task instruction and the temporally ordered primary- and wrist-camera observations to build a concise trajectory summary, instruction-target checklist, and ordered subtask plan. The plan must reflect the visible execution rather than a default grasp-and-drop script. Preserve every requested object, receptacle, quantity, color, order, and spatial constraint; mark a requested but unseen entity as unresolved rather than replacing or dropping it. For each step, use the current observations and proposed target language action. Steps are adaptive trajectory segments and may end early at a persistent gripper-state change or a major motion transition. The prompt separates the current observation state from the future segment command. Describe the visible scene from the images and current sensor state, and use the future command only to explain what should happen next. Never describe a future grasp, release, contact, or placement as already complete. Treat the raw gripper-open signal as an auxiliary cue; visible jaw contact and object support remain authoritative. An open or closed command is not by itself proof that an object is held or released. Respect whether the gripper transition occurs before, after, or concurrently with arm motion, and keep current-state wording distinct from the future transition. For each step, audit that the rationale agrees with the commanded translation, rotation, and gripper behavior. In particular, never reverse the commanded vertical direction in the explanation. Use compact past-action history only to establish relevant progress; do not let history override the current images. Completed subtasks must precede the current step, the current subtask must name the phase advanced by the present low-level action, and the next subtask is only a preview. Do not claim that the whole task is complete while later object-directed actions remain. The reasoning must connect visible progress, the gripper–object geometry, and the physical purpose of the next motion without copying action magnitudes or reciting the command. State concrete relations to the target, receptacle, support surface, opening, rim, table, or obstacle. Explain relevant contact, support, stability, alignment, grasp choice, and clearance. Prefer conservative descriptions when the primary and wrist views do not resolve a state. Return a trajectory summary, checklist, subtask plan, instruction paraphrases, and one label per requested step. Each step contains completed, current, and next subtasks; observation–action grounding; the main reasoning; a visual-relation sentence; a motion-rationale sentence; and an alternative-motion diagnostic. Return strict JSON only. Trajectory and per-step input template Task instruction: [TASK INSTRUCTION] Number of requested steps: [N] Step [STEP INDEX]: filtered trajectory index [INDEX], original frame [FRAME], segment frames [START]--[END] ([TERMINATION REASON]), horizon [SECONDS]s. Current observation state: [GRIPPER SENSOR STATE AND TRANSITION TIMING]. Future segment command in [ACTION FRAME]: [LANGUAGE ACTION] Ordered action phases: [MOTION/GRIPPER PHASE SUMMARY] Past 5s action history: [OPTIONAL HISTORY ITEMS] Structured-action metadata: ‘step_index’: [STEP INDEX], ‘trajectory_step_index’: [TRAJECTORY STEP INDEX], ‘segment_start’: [START], ‘segment_end’: [END], ‘action_frame’: ‘egocentric frame’, ‘current_observation_state’: ‘[STATE SUMMARY]’, ‘future_segment_command’: ‘[LANGUAGE ACTION]’, ‘gripper_transition_timing’: ‘[START/END/CONCURRENT/NONE]’, ‘history_5s’: [OPTIONAL COMPACT ACTION HISTORY] Primary camera image follows, then wrist camera image follows. [[PRIMARY CAMERA IMAGE]] [[WRIST CAMERA IMAGE]] [REPEAT TEXT, PAYLOAD, AND IMAGES FOR EACH REQUESTED STEP]

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