Spatial Forcing: Implicit Spatial Representation Alignment for Vision-Language-Action Model
1. Paper overview
In one sentence: Spatial Forcing transfers geometric features into a VLA during fine-tuning, improving manipulation while keeping the base inference path, but leaving the geometry-to-action explanation only partly tested. e-identitye-probleme-architecturee-alignmente-componentse-liberoe-real
| At a glance | What to know |
|---|---|
| Research problem | Author claim The authors argue that semantic competence from 2D VLM pretraining does not ensure accurate spatial control. Explicit depth inputs create sensor-quality, calibration and coverage constraints; estimated depth introduces another bottleneck. SF asks whether geometric information can instead be transferred into the policy’s existing visual representations during fine-tuning. e-problem |
| Core mechanism | Source description A training-time representation-alignment objective transfers pretrained VGGT features into intermediate VLA tokens without adding a geometry branch to deployed inference. e-architecturee-alignment |
| A key reported result | LIBERO four-suite manipulation: Spatial 99.4; Object 99.6; Goal 98.8; Long 96.0; average 98.5. Success rate (%), higher is better. OpenVLA-OFT with primary/wrist images; SF trained 150k iterations on eight H100s; 500 evaluation trials per task under random seeds. OpenVLA-OFT average 97.1; pi_0 94.2; extra-sensor GeoVLA 97.7 and 3D-CA VLA 98.1. The average gain over OFT is 1.4 percentage points. SF does not lead every column: GeoVLA has 96.6 Long and 3D-CA VLA has 99.8 Object. No uncertainty intervals are reported. e-implementatione-libero |
| Reading caution |
Core contributions
- Source description
A training-time representation-alignment objective transfers pretrained VGGT features into intermediate VLA tokens without adding a geometry branch to deployed inference. e-architecturee-alignment
- Source description
Teacher, positional-embedding and layer ablations test design choices; depth probes and manipulation evaluations provide complementary representation and execution evidence. e-probee-componentse-real
Figure 1(a). Geometry supervises an internal policy representation during training. Original paper, p. 1 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start at the image near the bottom. One arrow enters the image tokenizer; the other reaches the foundation 3D model. The snowflake identifies the frozen teacher, while the flame marks the trainable VLA. The dashed arrows converge on the alignment block from teacher features and the selected intermediate visual tokens. Read them as inputs to a training loss, consistent with Equation (3), rather than an inference-time feature-injection path. Text tokens continue through the policy alongside image tokens. Section 2.3 supplies the omitted normalization, projection and positional embedding details; Equation (4) combines alignment with action supervision. e-architecturee-alignmente-preliminariese-base-heads
What it supports. The intervention changes what the visual tokens learn while retaining the base action path. The diagram supports a separate training teacher and a supervised policy; it does not depict a learned future-world rollout or a joint future-image/action generator. This distinction explains the report’s VLA classification.
Where the evidence stops. This is a conceptual diagram. Its layered token layout does not specify every base policy’s decoder: Appendix D describes parallel action decoding for OpenVLA-OFT and a flow-matching expert for pi_0. The exact VGGT feature layer and token-resizing implementation remain unspecified.
2. Motivation
2.1 The problem and the proposed response
The authors argue that semantic competence from 2D VLM pretraining does not ensure accurate spatial control. Explicit depth inputs create sensor-quality, calibration and coverage constraints; estimated depth introduces another bottleneck. SF asks whether geometric information can instead be transferred into the policy’s existing visual representations during fine-tuning. e-problem
2.2 What this reading follows
A robot may recognize a cup yet still misjudge where to place its gripper. Spatial Forcing addresses this gap by supervising the visual representations already inside a vision-language-action policy. During training, the same camera views also enter VGGT, a pretrained geometry model; its features guide intermediate policy tokens alongside the action objective. At deployment, the policy retains its usual action-generation path. Read the evidence in three stages: locate where supervision enters, examine controlled component changes, then separate benchmark improvements from the smaller physical-robot study. This edition reviews the October 2025 arXiv v2 preprint and preserves its unresolved reporting details. e-identitye-probleme-architecturee-alignmente-componentse-liberoe-real
3. Research context
We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.
| Catalog dimension | Recorded classification |
|---|---|
| Major category | VLA |
| Architecture | Not applicable |
| Prediction paradigm | Not applicable |
| Quadrant | Not applicable |
3.1 Evidence-based assessment
Supports the recorded classification
The recorded VLA and spatially aware/post-training categories fit SF’s auxiliary geometric supervision. The post-training aspect is supported; SF is not a synthetic-data generation method. Architecture, prediction paradigm and WAM quadrant remain not applicable: a separate teacher during training does not establish a joint world/action model, future prediction or inverse-dynamics control. e-architecturee-alignmente-implementation
This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.
4. Problem formulation
4.1 Inputs and outputs
| Inputs | Outputs |
|---|---|
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4.2 Equations and their role
5. Method in detail
5.1 Trace the training target without adding a deployment sensor
First distinguish an observation from a target. The policy already receives camera images and a task instruction. During SF training, those views also enter the frozen VGGT teacher, whose cross-view features supply an additional target for selected VLA visual tokens. Batch normalization and a two-layer MLP adapt the policy features before the cosine comparison. Positional embedding is added on the target side, and the alignment loss joins the usual action loss with weight alpha. This supervision encourages a representation that is useful both for matching demonstrations and for reflecting geometry. Once training ends, Section 2.3 retains the base policy’s inference path. Reader interpretation: the geometric model contributes a prior through training, so deployment need not reconstruct depth or invoke VGGT before each action. e-architecturee-preliminariese-alignmente-weight
5.2 Use the ablation structure to narrow the mechanism
The main benchmark can show a gain without explaining it. Table 2 provides a more focused progression: even the 2D teachers SigLIP and DINOv2 improve the one-H100 baseline, so representation supervision itself matters. VGGT improves the average further, and positional embedding particularly helps the Long suite. Next compare aligned layers: layer 24 wins the tested average, while the deepest layer does worse. The authors suggest that very late features become less vision-specific; the table supports the layer preference but does not directly establish that explanation. Reader interpretation: SF needs a useful combination of target information, correspondence and intervention depth. A geometry-specific causal claim would require controls that preserve teacher feature statistics while disrupting their spatial correspondence, beyond simply switching pretrained encoders. e-componentse-preliminariese-alignment
5.3 Connect recoverable geometry to executed actions cautiously
The depth probe and robot experiment answer different questions. A DPT head trained on frozen VLA features asks whether depth structure is recoverable; selected cleaner maps motivate the representation argument. LIBERO and RoboTwin then test action success, and Figure 6 adds physical execution under lighting, object and height variation. None alone establishes the entire causal chain from feature geometry to robust control. The real study fine-tunes separate task policies and trains each across its variations, so its improvements should not be relabeled zero-shot generalization. Reader interpretation: the strongest supported conclusion is that adding SF improves several reported manipulation settings. A fuller explanation requires quantitative probes, matched controls and transparent trial aggregation, especially for the pot result whose printed percentage conflicts with a single set of 20 trials. e-probee-liberoe-robotwine-reale-collection
5.4 Training and inference
During training
Add the alignment loss to the normal supervised action loss. Appendix A sets alpha to 0.5 by default and reports degraded success at excessively large weights. The frozen-VLA DPT depth probe is a separate diagnostic, not the policy-training objective. e-alignmente-weighte-probe
The main LIBERO run uses eight NVIDIA H100s for 150k iterations; component runs use one H100. RoboTwin fine-tunes pi_0 with LoRA for 30k iterations on one H100. LIBERO has four suites, each with 500 demonstrations across ten tasks. e-implementation
During inference
SF leaves base-policy inference unchanged, with no additional architecture or computation according to Section 2.3. Images and instructions drive the inherited action expert. SF adds neither future-scene rollout nor inverse dynamics; its contribution is training supervision. e-alignmente-preliminaries
Physical execution is task-specific: camera frames and absolute joint angles are collected at 30 Hz by teleoperation, and each task receives its own fine-tuned policy. The source does not specify an SF-specific feedback or replanning schedule. e-collectione-alignment
5.5 Implementation flow
- Encode observations and instruction
The VLA converts images and language into visual and linguistic tokens. OpenVLA-OFT supplies the LIBERO base; pi_0 supplies the RoboTwin base. The paper’s generic autoregressive formulation should not override the inherited parallel-decoding or flow-matching implementations. e-preliminariese-implementatione-base-heads
- Construct a geometric target
The frozen teacher in Figure 1 is VGGT. Its backbone alternates within-frame and cross-frame attention over multiple views. SF uses spatial backbone features with added positional embedding, bypassing explicit depth/point prediction as the supervision target. e-architecturee-preliminariese-alignment
- Align corresponding visual tokens
Batch normalization and a two-layer MLP map selected intermediate VLA visual tokens into the target dimension. Negative cosine similarity rewards agreement at corresponding image locations. Layer 24 of the tested 32-layer backbone gives the highest ablation average. e-alignmente-components
6. Experiments & results
Spatial Forcing (SF) fine-tunes a vision-language-action policy with supervision from a pretrained geometry model. It aligns intermediate visual tokens with VGGT features, improving reported manipulation success while retaining the base inference path. The strongest LIBERO average is 98.5%, versus 97.1% for OpenVLA-OFT; component experiments and physical-robot tests support a useful training intervention, with unresolved efficiency and evaluation details (e-alignment, e-libero, e-components, e-real).
6.1 Read the original evidence
Table 1. SF improves the reported LIBERO average over its OpenVLA-OFT base. Original paper, p. 5 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Begin with the OpenVLA-OFT row, then compare the bottom Spatial Forcing row across the four suites and the Average column. SR means success rate, so higher is better. The main SF run uses primary and wrist camera images, eight H100 GPUs and 150k iterations; the text states 500 evaluation trials per task. The caption identifies gray rows as methods using additional depth or point-cloud sensor inputs. Bold values identify the best results among methods without those extra sensors, not universal column winners. Keep this table separate from the one-H100 component study, which has different baseline and SF averages. e-liberoe-implementation
What it supports. SF reports 98.5% average versus 97.1% for OpenVLA-OFT, a 1.4 percentage-point improvement. Its suite rates are 99.4%, 99.6%, 98.8% and 96.0%. This supports strong RGB-based manipulation in the evaluated suites, while comparison with extra-sensor methods involves a different input budget.
Where the evidence stops. Section 3.2’s best-across-all-tasks wording is broader than the table: GeoVLA scores 96.6% on Long, and 3D-CA VLA scores 99.8% on Object. Neither uncertainty intervals nor a matched-compute study of every listed baseline are supplied.
Figure 6. Physical tasks test manipulation under controlled visual and spatial variations. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the three left columns vertically: the top shows an example action sequence, the middle shows task variations, and the bottom gives orange without-SF and blue with-SF success rates. The upper right locates workspace, puppet arms/cameras and master arms; the lower right shows bimanual pot lifting. Section 4.1 specifies 40 demonstrations per single-arm task and ten evaluation trials per variation, totaling 40. Appendix C says policies are fine-tuned separately for each task, while Figure 6 says each such policy covers all its variations. Camera images and absolute joint angles are recorded by teleoperation at 30 Hz. e-reale-collection
What it supports. With SF, cups improve from 15.0% to 62.5%, vegetable grasping from 10.0% to 47.5%, and block placement from 67.5% to 85.0%. These are action-execution results on the physical platform. The lighting, object and height changes probe different demands, but the study is small and task-specific.
Where the evidence stops. The pot panel prints 42.5% with SF, while Section 4.1 states 20 evaluation trials. A single binary-trial set cannot yield that percentage; the paper leaves any averaging unresolved. Training across the task variations also does not demonstrate held-out-variation generalization.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| LIBERO four-suite manipulation OpenVLA-OFT with primary/wrist images; SF trained 150k iterations on eight H100s; 500 evaluation trials per task under random seeds. | Spatial 99.4; Object 99.6; Goal 98.8; Long 96.0; average 98.5. Success rate (%), higher is better | OpenVLA-OFT average 97.1; pi_0 94.2; extra-sensor GeoVLA 97.7 and 3D-CA VLA 98.1. The average gain over OFT is 1.4 percentage points. SF does not lead every column: GeoVLA has 96.6 Long and 3D-CA VLA has 99.8 Object. No uncertainty intervals are reported. e-implementatione-libero |
| LIBERO teacher and positional alignment ablation One H100, layer 24, 150k iterations, full data; Table 2. | VGGT with PE 96.9; without PE 94.7. Average success rate (%) | No alignment 92.7; SigLIP 94.0; DINOv2 94.1. Long improves from 84.4 without PE to 94.2 with PE. Both alignment and target choice matter. These are separate runs from Table 1; the 92.7 baseline cannot replace its 97.1 baseline. e-componentse-implementation |
| LIBERO training and data efficiency One-H100 component protocol; uniformly subsampled data uses cosine annealing. | 93.7 at 20k iterations versus 96.9 at 150k; 75.8 with 5% data at 150k iterations. Average success rate (%) and author-reported efficiency ratios | The authors report 3.8-fold iteration efficiency and 5.9-fold data efficiency in Figure 5. These ratios are author claims, not measured wall-clock speedups. Figure 5 does not state suite aggregation and its points differ from Table 2 averages; the table supplies the exact averages here. e-efficiency |
| RoboTwin 2.0 bimanual manipulation pi_0 base; in-domain easy and randomized hard settings; 100 easy/300 hard trials per task. | SF has the highest plotted mean in both settings; exact bar values are not labeled. Plotted success rate (%) | Figure 4 compares Diffusion Policy, RDT and pi_0; RDT remains stronger on some individual tasks. Supports gains under the tested randomizations, without establishing that shortcut reliance has been eliminated. e-robotwine-implementation |
| Physical single-arm variation tasks AgileX Piper; 40 demonstrations per task; four variations with ten trials each; task-specific policies. | Cups 62.5; right-side vegetable 47.5; green block 85.0. Success rate (%) | Without SF: 15.0, 10.0 and 67.5 respectively. The cups gain is 47.5 percentage points. These are executed manipulation tasks; each policy covers its task variations, rather than all tasks jointly. e-reale-collection |
| Physical bimanual lift pot 20 training demonstrations; Section 4.1 states 20 evaluation trials. | 42.5 with SF. Success rate (%) as printed | 30.0 without SF. Unresolved denominator: 42.5% cannot arise from one set of 20 binary trials. Repeated-run averaging could explain it, but the source does not specify this; no success count is inferred. e-real |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Figure 3. A frozen-feature depth probe makes the representation change visible. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read each group from the RGB image through the unaligned and aligned predictions to GT, the ground-truth depth. The upper row uses the primary camera and the lower row the wrist camera; simulation and physical scenes occupy separate halves. The source freezes the VLA and trains only a DPT prediction head, so this visualization asks what depth information a decoder can recover from the policy’s embeddings. It is separate from SF training, whose objective uses VGGT feature similarity rather than these depth maps. Compare object contours and scene structure across columns, without treating grayscale intensity as a calibrated distance scale. e-probee-alignment
What it supports. The aligned examples reveal cleaner object and surface structure, especially the real-world vessel and simulated wrist-view boundaries. They support the authors’ motivation that feature supervision can make spatial information more recoverable. The manipulation tables are still needed to establish whether the representation change accompanies useful actions.
Where the evidence stops. The paper provides no depth-error table, physical depth scale, probe training split or uncertainty here. Recoverability through a trained DPT head does not itself show that the action expert uses that information; selected images cannot establish general spatial reasoning or a causal explanation of action gains.
Table 2. Teacher features, positional embedding and layer choice each affect the result. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Treat each colored block as a separate question. The pink block changes the teacher while holding layer 24, 150k iterations and full data fixed. PE means positional embedding; compare the two VGGT rows to isolate its addition. The yellow block changes the supervised transformer layer. Green rows shorten training, and purple rows reduce the data fraction. Use the gray no-alignment row as this table’s reference, and read the rightmost average together with Long, where several changes have large effects. The caption states one H100 for these experiments; repeated VGGT rows reconnect the blocks rather than providing independent replications. e-componentse-implementatione-weight
What it supports. VGGT with PE reaches 96.9% average versus 92.7% without alignment and 94.7% for VGGT without PE. Adding PE improves Long from 84.4% to 94.2%. Layer 24 gives the highest tested average, supporting an intermediate-depth supervision choice rather than a rule that later alignment is always better.
Where the evidence stops. The target comparison also changes pretrained-model properties; it does not isolate geometry alone. One reported value per configuration cannot establish significance. The alpha sweep is elsewhere in Appendix A, whose unspecified task/budget prevents merging its scores into this table.
Figure 5(a–c). Faster learning is reported alongside a qualitative representation diagnostic. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read panels (a) and (b) before the feature plot. Blue denotes alignment and orange its absence; the horizontal labels are sampled training budgets or data fractions, so the drawn spacing is not a continuous timing measurement. Dashed arrows annotate the authors’ claimed 3.8-fold and 5.9-fold efficiency comparisons. Panel (c) uses filled dots for primary-view features and open squares for wrist-view features; gray is the teacher target, orange the unaligned policy and blue the aligned policy. Appendix B interprets similar shapes with separate centers as learning a related representation structure while retaining modality identity. That last step is the authors’ interpretation. e-efficiencye-tsne
What it supports. The curves suggest the greatest benefit before training or data saturates. For exact average rates, Table 2 reports 93.7% at 20k iterations and 75.8% with 5% data. The visualization motivates testing whether geometry supervision improves sample use, rather than only the final full-data score.
Where the evidence stops. Figure 5 does not specify suite aggregation; some points differ from Table 2 averages. Its ratios are not demonstrated wall-clock savings including VGGT. Similar t-SNE shapes and separate centers do not by themselves establish high-dimensional isomorphism, retained semantics or absence of collapse.
7. Analysis & limitations
7.1 What the evidence leaves open
Depth-probe images and t-SNE cluster shapes are suggestive diagnostics, not proof of calibrated 3D understanding, manifold equivalence or preserved semantic competence. The source provides no numerical depth evaluation or quantitative collapse test. e-probee-tsne
Table 1’s blanket best-across-all-tasks prose overstates its columns. Efficiency plots lack aggregation details and wall-clock accounting; reported trial denominators do not explain the pot percentage. Tables and figures omit uncertainty estimates, limiting small-margin conclusions. e-liberoe-efficiencye-real
The alpha sweep lacks task/suite and budget identifiers, so its 93.6% best score cannot be merged with Table 2. Real-world experiments are small, task-specific studies, leaving broad transfer and held-out-variation behavior unresolved. e-weighte-reale-collection
7.2 Questions for discussion
- Does token-correspondence preservation explain the PE benefit, or does PE mainly regularize optimization? (e-components)
- Does better frozen-feature depth prediction track action gains under genuinely held-out camera or object configurations? (e-probe, e-real)
8. Reproducibility audit
8.1 Requirements and known gaps
Reproduction requires compatible OFT/pi_0 and VGGT checkpoints, matched image preprocessing, LIBERO/RoboTwin configurations and the documented compute. The supplied text does not specify the VGGT feature layer, precise token correspondence/resizing, PE implementation, projection widths, optimizer/batch settings, LoRA rank or full real-robot policy configuration. e-alignmente-implementatione-real
Proposed checks: compare matched versus spatially shuffled VGGT targets under identical layer-24 budgets; separately measure iterations and elapsed training time to a fixed success threshold with teacher computation included. Both tests require controlled seeds, subsets and base-policy settings. e-componentse-efficiencye-alignment
8.2 Proposed reproduction checks
The following checks are proposals motivated by the paper. They have not been run as part of this reading.
Check 1: Does correct spatial correspondence carry the benefit?
Reader-proposed, not run: reproduce the one-H100 layer-24, 150k-iteration LIBERO setting with identical demonstration subsets, initialization, optimizer and evaluation seeds. Compare no alignment, VGGT with correct correspondence, and VGGT whose feature-plus-position targets are jointly shuffled across token locations within each image. Keep the projection, alpha 0.5 and teacher-feature distributions fixed in the two aligned arms; add a no-PE control. Evaluate per-suite success with seed uncertainty and an identically trained held-out DPT probe. If correct correspondence outperforms the shuffled target while improving depth recovery, that supports spatial transfer. If shuffling preserves the gains, generic regularization or optimization becomes a stronger explanation. e-alignmente-componentse-weighte-probe
Check 2: Does iteration efficiency survive full training-cost accounting?
Reader-proposed, not run: on identical H100 hardware, compare OFT with and without SF using the same global batch, data order and evaluation schedule. Predeclare a 90% four-suite average-success target and evaluate checkpoints repeatedly under common seeds. Record optimizer steps, elapsed time, peak memory and teacher-feature computation, including any preprocessing/cache time. Use the same cosine-annealing schedule in a separate matched 5%-data comparison. SF must reach the threshold earlier in elapsed time, not merely in iterations, to establish an end-to-end training speedup. Report censoring if a run never reaches it. Publish per-suite values so Figure 5-style curves can be reconciled with Table 2-style averages. e-implementatione-efficiencye-alignment
8.3 Reading coverage
Visual audit: Visually inspected the title/authors/affiliations and v2 date on p. 1; Figures 1–6; Tables 1–3; method equations and inference statement on pp. 3–4; training/evaluation descriptions on pp. 5–9; weight, t-SNE and 30 Hz collection details on p. 16; and inherited OFT decoding details on p. 17. All six final original crops were individually viewed and retained with their legends, axes and table headers. Figure 1’s arrows and freeze/train markers were checked against Section 2.3, with no claim-relevant conflict found. Every page supporting the edition’s guides, findings, cautions and proposed checks is declared here. References and the remainder of Appendix D were read in full as text; external cited papers, code and separate supplements were outside this review.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17. Appendix coverage: reviewed.
Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.
Text reading scope & known omissions
- Abstract (p. 1)
- 1 Introduction (p. 2)
- 2 Method: 2.1 Preliminaries, 2.2 Motivation, 2.3 Spatial Forcing (pp. 3–4)
- 3 Simulation Experiments: setup, comparisons, component analysis (pp. 5–8)
- 4 Real-world Experiments (pp. 8–9)
- 5 Related Work and 6 Conclusion (p. 9)
- References (pp. 10–15)
- Appendix A Weight Factor, B Explanations of t-SNE Results, C Real-world Data Collection (p. 16)
- Appendix D Details of Compared Models (pp. 16–19)
Outside the original text pass
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
- Separate supplemental material availability has not been fully verified.
- Official arXiv title and all eight authors match the catalog. Project site identifies ICLR 2026. This is an author preprint version; equivalence to the camera-ready version has not been established.
- The extraction limitation was addressed by inspecting the original PDF: Figures 1–6, Tables 1–3 and every page supporting retained scientific claims. All six supplied text chunks were read completely, including references and Appendices A–D.
- Identity notes: the inspected title and all eight authors match the catalog, allowing for title capitalization. The title-page stamp verifies arXiv:2510.12276v2, dated 17 October 2025, and labels this artifact Preprint. The catalog lists ICLR 2026; its venue record and camera-ready text were not independently inspected, and equivalence is not claimed.
- No separate supplement was supplied. Code, project website and external baseline papers were not inspected; no experiments were reproduced. Appendix D is read as this paper’s background account, not independent verification of the cited works.
- The source has no dedicated limitations section; limitations below distinguish reader analysis from author statements.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e-identityPDF p. 1, title block and arXiv margin stamp
The title matches the supplied observed title apart from typesetting/capitalization. All eight catalog authors appear in the same order. The artifact says Preprint and arXiv:2510.12276v2, 17 Oct 2025; five institutional affiliations are listed.
Go to primary source ↓e-problemPDF p. 2, Introduction, paragraphs 2–4
The authors motivate spatial supervision through noisy and heterogeneous depth sensors, missing depth in robot datasets, and limitations of estimated depth. VGGT processes robot views to provide representation supervision.
Go to primary source ↓e-architecturePDF p. 1, Figure 1(a); p. 3, Figure 2(c)
The image feeds both a foundation 3D model, marked with a snowflake, and the VLA image tokenizer. Dashed arrows bring teacher features and intermediate visual tokens into alignment. The VLA is marked trainable; Figure 2 places spatial features on the supervision side.
Go to primary source ↓e-preliminariesPDF p. 3, Section 2.1, Eqs. (1)–(2) and VGGT paragraph
Images and language become tokens, and an action expert maps action representations to supervised actions. VGGT alternates frame-wise and global attention; SF uses backbone representations rather than its 3D prediction heads.
Go to primary source ↓e-probePDF p. 4, Figure 3 and Section 2.2, Observation
Depth probing freezes the VLA and trains only a DPT head. Figure 3 compares input images, unaligned and aligned depth predictions, and ground truth for primary/wrist views in simulation and the real world; no quantitative depth metric is provided.
Go to primary source ↓e-alignmentPDF p. 4, Section 2.3, Eqs. (3)–(4) and Model Inference
Multi-view VGGT features plus positional embedding supervise corresponding VLA visual tokens after batch normalization and a two-layer MLP. Negative mean cosine similarity is weighted by alpha and added to action loss. Inference uses the unchanged base VLA structure.
Go to primary source ↓e-implementationPDF p. 5, Section 3.1 and Section 3.2, LIBERO paragraph; p. 6, Section 3.3 opening
LIBERO uses OpenVLA-OFT with primary/wrist images, 150k training iterations on eight H100s, and 500 evaluation trials per task. Each suite contains 500 demonstrations across ten tasks. RoboTwin uses pi_0 with LoRA, one H100 and 30k iterations. Component analysis uses one H100.
Go to primary source ↓e-liberoPDF p. 5, Table 1, SF, OpenVLA-OFT, pi_0, GeoVLA and 3D-CA VLA rows
SF reports Spatial/Object/Goal/Long success of 99.4/99.6/98.8/96.0%, averaging 98.5%; OpenVLA-OFT averages 97.1% and pi_0 94.2%. Extra-sensor rows GeoVLA and 3D-CA VLA average 97.7% and 98.1%. GeoVLA scores 96.6% Long; 3D-CA VLA scores 99.8% Object and 96.1% Long.
Go to primary source ↓e-robotwinPDF p. 5, Section 3.1, RoboTwin settings; p. 6, Figure 4 and RoboTwin paragraph
Easy tasks have in-domain layouts; hard tasks randomize clutter, backgrounds, lighting and table height. Evaluation uses 100 easy and 300 hard trials per task. SF has the highest plotted easy/hard averages, while RDT exceeds SF on some tasks. Bars have no exact numerical labels.
Go to primary source ↓e-componentsPDF p. 6, Section 3.3, Target Representation and Alignment at Different VLA Layers; p. 7, Table 2, first three blocks
At 150k iterations and full data, one-H100 average success is 92.7% without alignment; SigLIP 94.0%, DINOv2 94.1%, VGGT without PE 94.7%, VGGT with PE 96.9%. Adding PE raises Long from 84.4% to 94.2%. Layer 24 of 32 has the best tested average; layers 1/8/16/32 score 94.6/95.7/93.8/94.8%.
Go to primary source ↓e-efficiencyPDF p. 7, Table 2, iteration/data blocks; Figure 5(a)–(b); Training efficiency and Data efficiency paragraphs
Table 2 gives average success 93.7% at 20k, 96.5% at 50k and 96.9% at 150k iterations, and 42.3%/75.8% with 1%/5% data. The text reports 3.8-fold iteration efficiency and 5.9-fold data efficiency; subsampling is uniform and uses cosine annealing. Figure 5 does not identify suite aggregation and some plotted points differ from Table 2 averages.
Go to primary source ↓e-realPDF p. 8, Figure 6 and Section 4.1; p. 9, Section 4.2 continuation
The AgileX platform has two 6-DoF Piper arms, 1-DoF grippers, a primary camera and two wrist cameras. Single-arm training uses 40 demonstrations per task, evaluation 10 trials per variation/40 total. Figure 6 gives without/with SF rates of 15.0/62.5% cups, 10.0/47.5% vegetable, 67.5/85.0% block and 30.0/42.5% pot. Bimanual training/evaluation are each stated as 20 demonstrations/trials; no aggregation explaining 42.5% is supplied.
Go to primary source ↓e-weightPDF p. 16, Appendix A and Table 3
Alpha values 0, 0.02, 0.1, 0.5, 2.5, 12.5 yield success 73.2, 92.2, 92.8, 93.6, 86.6, 81.2%. Alpha 0.5 is the default elsewhere. The appendix warns that excessive weight can interfere with action prediction, but does not identify this sweep’s task/suite or training budget.
Go to primary source ↓e-tsnePDF p. 7, Figure 5(c); p. 8, The t-SNE visualization paragraph; p. 16, Appendix B
The plot distinguishes primary/wrist features and target/unaligned/aligned groups. Authors interpret similar cluster shapes and separated centers as relational alignment with retained modality identity. No quantitative representation-collapse test accompanies this interpretation.
Go to primary source ↓e-collectionPDF p. 16, Appendix C
Master arms teleoperate puppet arms. Camera images and absolute joint angles are recorded at 30 Hz, and a separate policy is fine-tuned for each task.
Go to primary source ↓e-base-headsPDF p. 16, Appendix D, pi_0 paragraph; p. 17, Appendix D, OpenVLA-OFT paragraph
The source describes pi_0’s flow-matching action expert and OpenVLA-OFT’s parallel decoding, action chunking, continuous actions and L1 regression. These base-policy details qualify the generic autoregressive preliminaries.
Go to primary source ↓8.5 Primary sources
Spatial Forcing: Implicit Spatial Representation Alignment for Vision-language-action Model ↗
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