LayerRoute: Action-Conditioned Mixture-of-Layers Routing for Vision-Language-Action Policies

# LayerRoute: Action-Conditioned Mixture-of-Layers Routing for Vision-Language-Action Policies
Source: [https://arxiv.org/html/2609.06079](https://arxiv.org/html/2609.06079)
Zhisheng Chen, Yantang Qu, Meijia Chen, Tianyu Xin, Zirui Song, Yiming LiAffiliation:Tsinghua University MBZUAI Nanyang Technological University Zhejiang University Rutgers University

###### Abstract

Vision\-Language\-Action \(VLA\) policies leverage pretrained vision\-language models \(VLMs\) to guide action generation for robot control\. VLMs provide hierarchical visual\-semantic representations that evolve across layers, from local visual geometry to abstract, language\-aligned semantics; different manipulation tasks may therefore require different mixtures of layer representations\. Meanwhile, the action module maintains intermediate representations that evolve throughout action computation and may provide useful information for subsequent decisions\. However, existing VLA interfaces offer limited flexibility in representation access: VLM information is exposed through fixed layer assignments for each action layer, while intermediate action states are only propagated implicitly through residual streams without explicit reuse\. We introduce LayerRoute, an action\-conditioned representation routing interface that enables adaptive access to VLM layers and action representations\. The Layer Mixture Router dynamically forms mixtures of cached VLM representations, while Action\-State Reread reuses earlier action representations\. Across diverse simulation and real\-world benchmarks, LayerRoute consistently improves StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}, achieving up to 7\.2 gains on LIBERO Long with only 0\.31% / 3\.87% additional parameters\. Ablation studies validate the benefit of action\-conditioned layer routing, while routing analyses reveal structured allocation patterns across action layers and task settings\.

## Introduction

Vision\-Language\-Action \(VLA\) policies inherit visual and semantic priors from pretrained vision–language models \(VLMs\) and translate them into closed\-loop robot behavior through diverse action\-generation architectures\([Zitkovich et al\. 2023](https://arxiv.org/html/2609.06079#bib.bib3);[Kim et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib4);[Team et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib15);[Black et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib5);[Intelligence et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib13)\)\. Despite their differences in action representation and generation, these systems expose each action layer to predetermined VLM layers, limiting the ability to adapt layer\-wise VLM representation access to evolving action computation and diverse manipulation requirements\.

This limitation matters because VLM representations vary across layers\. Analyses of ViTs, CLIP, and multimodal language models associate earlier states with local texture, geometry, and spatial patterns, and later states with abstract or language\-aligned semantics\([Raghu et al\. 2021](https://arxiv.org/html/2609.06079#bib.bib30);[Gandelsman et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib19);[Neo et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib18)\)\. Robot manipulation requires different combinations of these cues across action tasks: grasp localization, gripper–object alignment, and contact\-sensitive placement depend more strongly on fine\-grained visual evidence, whereas instruction grounding, object\-role disambiguation, and subgoal selection rely more on abstract semantic representations\. Since different action tasks may require different mixtures of VLM layer representations, fixed layer assignments cannot dynamically adapt representation access to evolving action requirements\.

The limitation also arises within the action module\. Under standard residual propagation, earlier action states are progressively transformed and integrated into the current representation, leaving later blocks unable to revisit earlier intermediate action states\. This indirect access may hinder the retrieve of information needed for later manipulation decisions, particularly in long\-horizon manipulation\. The policy is therefore constrained at two levels: fixed VLM\-depth exposure limits access to external VLM representations, while residual\-only access limits reuse of internal action states\.

We argue that enabling adaptive access to VLM layers and earlier action states can improve control beyond fixed representation interfaces\. Motivated by this view, we introduce LayerRoute, a representation routing interface that selects VLM representations across depth and retrieves earlier action states in the action module \(Figure[1](https://arxiv.org/html/2609.06079#Sx1.F1)\)\. The Layer Mixture Router conditions layer\-wise VLM representation access on the current action state, while Action\-State Reread enables action blocks to reuse earlier action representations\.

![Refer to caption](https://arxiv.org/html/2609.06079v1/figure_1.png)Figure 1:Original standard StarVLA\-π\\piversus StarVLA\-π\\piwith LayerRoute\. The original interface uses fixed VLM context and residual\-only action\-state access, while LayerRoute enables action\-conditioned layer\-wise routing and earlier action\-state reuse\.We train LayerRoute on two representative VLA backbones, StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}\. With modest overhead, LayerRoute improves LIBERO performance, increasing Long success rates by 7\.2 and 3\.6 and Avg4by 2\.3 and 1\.3 for StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}, respectively\. These improvements transfer to SimplerEnv and RoboCasa\-GR1, where LayerRoute improves performance across robot settings, with gains of up to 5\.6 points on SimplerEnv WidowX\. The improvements generalize across VLM backbones, including Qwen3\-VL, Qwen2\.5\-VL\([Bai et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib9)\), MiMo\-Embodied, and Cosmos\-Reason2\-2B\([NVIDIA 2026](https://arxiv.org/html/2609.06079#bib.bib10)\)\. Routing ablations validate the mechanism, while routing analyses reveal layer allocation patterns across action layers and task settings\.

## Related Work

#### VLA Action Generation and Representation Interfaces\.

VLA and generalist robot policies differ in how actions are decoded\. RT\-2\([Zitkovich et al\. 2023](https://arxiv.org/html/2609.06079#bib.bib3)\)and OpenVLA\([Kim et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib4)\)map robot controls to discrete language\-model tokens, Octo\([Team et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib15)\)uses a diffusion action head, andπ0\\pi\_\{0\}/π0\.5\\pi\_\{0\.5\}\([Black et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib5);[Intelligence et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib13)\)use flow\-matching action experts, withπ0\.5\\pi\_\{0\.5\}additionally incorporating tokenized\-action pretraining\. StarVLA\([Community 2026](https://arxiv.org/html/2609.06079#bib.bib16)\)adopts a modular VLM–action architecture, while Knowledge Insulation\([Driess et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib6)\)studies the interaction between continuous action experts and VLM training\. These works primarily study action representation, decoding, or VLM–expert coupling\. We instead study how action layers access pretrained VLM representations across depth\.

#### Adaptive Representation Access and Routing\.

OTTER\([Huang et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib33)\)selects instruction\-relevant visual features, CogVLA\([Li et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib34)\)aggregates and prunes visual tokens, VLA\-Cache\([Xu et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib35)\)reuses stable visual\-token key–value states across frames, and AVA\-VLA\([Xiao et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib36)\)uses execution history to reweight current visual tokens\. FedVLA\([Miao et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib38)\)studies token and expert routing in a federated setting\. SpatialVLA\([Qu et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib12)\)introduces Ego3D position encoding and adaptive action grids\. Beyond visual selection, MiMo\-Embodied\([Hao et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib8)\)targets affordance prediction, task planning, and spatial understanding, while Causal Planner\([Lu et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib11)\)emphasizes physically grounded next\-state reasoning\. HAMLET and MemoryVLA\([Koo et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib37);[Shi et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib7)\)aggregate information across environment timesteps\. These works address visual feature selection, embodied reasoning, and cross\-timestep context aggregation, whereas LayerRoute focuses on depth\-aware access to VLM states and direct reuse of action states during action computation\.

#### Layerwise Representations and Cross\-Layer Reuse\.

Prior studies reveal layerwise structures in ViTs, CLIP, VLMs, and language models by analyzing representation evolution, attention patterns, visual\-token processing, and intermediate predictions\([Raghu et al\. 2021](https://arxiv.org/html/2609.06079#bib.bib30);[Gandelsman et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib19);[Neo et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib18);[Belrose et al\. 2023](https://arxiv.org/html/2609.06079#bib.bib20)\)\. These analyses establish layer depth as a representation axis, but do not address which VLM representations should be exposed to action computation\. Beyond representation analysis, prior architectures modify information flow: Highway Networks and stochastic depth regulate inter\-layer propagation or execution\([Srivastava et al\. 2015](https://arxiv.org/html/2609.06079#bib.bib21);[Huang et al\. 2016](https://arxiv.org/html/2609.06079#bib.bib22)\); DenseFormer and Attention Residuals aggregate or reuse earlier hidden states\([Pagliardini et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib23);[Team et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib32)\); Mixture\-of\-Depths, DeeR\-VLA, and MoLe\-VLA adapt computation depth\([Raposo et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib24);[Yue et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib25);[Zhang et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib26)\), while Hyper\-Connections learn cross\-depth pathways\([Zhu et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib31)\)\. These methods alter state propagation or computation allocation within a model, whereas LayerRoute adapts representation access across the VLM–action boundary and enables token\-wise reuse of earlier action states\. Table[1](https://arxiv.org/html/2609.06079#Sx2.T1)compares these approaches from perspective of representation access\.

InterfaceRepresentationAction\-Cond\. RoutingState ReuseMechanismFinal\-layer readoutfinal VLM representationNoNonefixed readoutFixed layer mappingpredefined VLM layersNoNonefixed cross\-attentionPrefix/suffix joint attentionsame\-layer VLM streamNoNonejoint attentionToken/expert routingvisual tokens / expertsNoNonetoken selectionDenseFormercurrent/prior hidden statesN/Abackbonehidden aggregationComputation depthtoken/layer executionNoNonedepth allocationAttention Residualsprevious layer/block statesN/Abackboneresidual aggregationLayerRoutecached VLM/action statesYesaction modulelayer routing \+ rereadTable 1:Representative interfaces for adaptive representation access and state reuse\([Pagliardini et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib23);[Raposo et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib24);[Team et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib32)\)\. Existing approaches modify VLM exposure, computation depth, or hidden\-state aggregation, while LayerRoute enables action\-conditioned routing over VLM layers together with explicit action\-state rereading\.

## Background and Formulation

#### layer\-wise VLM representation access\.

A pretrained VLM produces a hierarchy of hidden states𝐕n∈ℝB×Tv×Dv\\mathbf\{V\}\_\{n\}\\in\\mathbb\{R\}^\{B\\times T\_\{v\}\\times D\_\{v\}\}at boundariesn∈\{0,…,N\}n\\in\\\{0,\\ldots,N\\\}, wheren=0n=0denotes the embedded input\. We retain these states as a multi\-layer representation cache\. Since intermediate states preserve token correspondence across depth, they can be directly combined along the depth dimension\. At action layerss, let𝐚\(s\)∈ℝB×Ta×Da\\mathbf\{a\}^\{\(s\)\}\\in\\mathbb\{R\}^\{B\\times T\_\{a\}\\times D\_\{a\}\}denote the current action state, and let𝒞s⊆\{0,…,N\}\\mathcal\{C\}\_\{s\}\\subseteq\\\{0,\\ldots,N\\\}specify the VLM layers available at that layer\. We formulate layer routing as a readout problem: a static interface accesses fixed VLM layers, whereas our action\-conditioned readout adapts this access based on the current action state\.

𝐕~static\(s\)=Φsstatic​\(\{𝐕n\}n∈𝒞s\),𝐕~\(s\)=Φs​\(\{𝐕n\}n∈𝒞s,𝐚\(s\)\)\.\\begin\{gathered\}\\widetilde\{\\mathbf\{V\}\}\_\{\\mathrm\{static\}\}^\{\(s\)\}=\\Phi\_\{s\}^\{\\mathrm\{static\}\}\\bigl\(\\\{\\mathbf\{V\}\_\{n\}\\\}\_\{n\\in\\mathcal\{C\}\_\{s\}\}\\bigr\),\\\\ \\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}=\\Phi\_\{s\}\\bigl\(\\\{\\mathbf\{V\}\_\{n\}\\\}\_\{n\\in\\mathcal\{C\}\_\{s\}\},\\mathbf\{a\}^\{\(s\)\}\\bigr\)\.\\end\{gathered\}Here,Φsstatic\\Phi\_\{s\}^\{\\mathrm\{static\}\}andΦs\\Phi\_\{s\}denote the readout functions at action layerss\. The static readout does not depend on𝐚\(s\)\\mathbf\{a\}^\{\(s\)\}, whereas the action\-conditioned readout adapts the VLM\-layer combination according to the current action state\.

#### Action\-State Access\.

Representation access is also constrained within the action module\. Under residual propagation, earlier action states are progressively transformed and integrated into the current representation\. Later layers can therefore access earlier action states only through the residual stream rather than directly revisiting intermediate states\. LayerRoute addresses this limitation with Action\-State Reread, which reuses earlier action states from the action module\. Together with the action\-conditioned layer\-wise routing introduced above, it forms a representation routing interface for adaptive access to both VLM and action representations\.

#### Architectural Instantiations\.

We then apply this representation\-access formulation to two representative VLA architectures\. StarVLA\-π\\pi\([Community 2026](https://arxiv.org/html/2609.06079#bib.bib16)\)couples Qwen3\-VL\([Bai et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib9)\)to an action DiT through cross\-attention, whereasπ0\.5\\pi\_\{0\.5\}\([Intelligence et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib13)\)combines PaliGemma\([Beyer et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib17)\)with a flow\-matching action expert\. These architectures allow us to examine representation access under different VLA designs\.

## Method

At action blockss, Action\-Conditioned Layer Mixture Router pools current action state and cached VLM representations to predict a sample\-wise distribution over VLM depth\. It mixes same\-position VLM tokens using this distribution and uses the result as the cross\-attention context\. After attention, Action\-State Reread mixes the same action\-token position across selected earlier action blocks\. The resulting state is passed to the FFN and subsequent action blocks\.

### Action\-Conditioned Layer Mixture Router

Given the current action state and candidate VLM states, the router computes an action\-conditioned distribution over accessible VLM layers\. At a selected action layerss, let𝒞s⊆\{0,…,N\}\\mathcal\{C\}\_\{s\}\\subseteq\\\{0,\\ldots,N\\\}denote the indices of the available VLM states\. The routed VLM representation is denoted by𝐕~\(s\)\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}\.

We first obtain compact summaries of the current action state and each candidate VLM state by pooling over valid token positions:𝐩a\(s\)=Pool⁡\(𝐚\(s\)\)\\mathbf\{p\}\_\{a\}^\{\(s\)\}=\\operatorname\{Pool\}\\\!\\left\(\\mathbf\{a\}^\{\(s\)\}\\right\),𝐩V,n=Pool⁡\(𝐕n\)\\mathbf\{p\}\_\{V,n\}=\\operatorname\{Pool\}\\\!\\left\(\\mathbf\{V\}\_\{n\}\\right\),n∈𝒞sn\\in\\mathcal\{C\}\_\{s\}\. The action and VLM summaries are separately normalized and projected with layer\-specific mappings into a shared router space of dimensiondsel=256d\_\{\\mathrm\{sel\}\}=256:

𝐪\(s\)=𝐖q,d\(s\)​LayerNorma\(s\)⁡\(𝐩a\(s\)\),𝐤n\(s\)=𝐖k,d\(s\)​LayerNormV\(s\)⁡\(𝐩V,n\),𝐪\(s\),𝐤n\(s\)∈ℝdsel,n∈𝒞s\.\\begin\{gathered\}\\mathbf\{q\}^\{\(s\)\}=\\mathbf\{W\}\_\{q,d\}^\{\(s\)\}\\operatorname\{LayerNorm\}\_\{a\}^\{\(s\)\}\\\!\\left\(\\mathbf\{p\}\_\{a\}^\{\(s\)\}\\right\),\\\\ \\mathbf\{k\}\_\{n\}^\{\(s\)\}=\\mathbf\{W\}\_\{k,d\}^\{\(s\)\}\\operatorname\{LayerNorm\}\_\{V\}^\{\(s\)\}\\\!\\left\(\\mathbf\{p\}\_\{V,n\}\\right\),\\\\ \\mathbf\{q\}^\{\(s\)\},\\mathbf\{k\}\_\{n\}^\{\(s\)\}\\in\\mathbb\{R\}^\{d\_\{\\mathrm\{sel\}\}\},\\qquad n\\in\\mathcal\{C\}\_\{s\}\.\\end\{gathered\}The scaled dot\-product similarity produces routing logits, which are normalized into depth weights over the available VLM states:

ℓn\(s\)=⟨𝐪\(s\),𝐤n\(s\)⟩dsel,n∈𝒞s,αn\(s\)=exp⁡\(ℓn\(s\)\)∑m∈𝒞sexp⁡\(ℓm\(s\)\),n∈𝒞s\.\\begin\{gathered\}\\ell\_\{n\}^\{\(s\)\}=\\frac\{\\left\\langle\\mathbf\{q\}^\{\(s\)\},\\mathbf\{k\}\_\{n\}^\{\(s\)\}\\right\\rangle\}\{\\sqrt\{d\_\{\\mathrm\{sel\}\}\}\},\\qquad n\\in\\mathcal\{C\}\_\{s\},\\\\ \\alpha\_\{n\}^\{\(s\)\}=\\frac\{\\exp\\\!\\left\(\\ell\_\{n\}^\{\(s\)\}\\right\)\}\{\\sum\_\{m\\in\\mathcal\{C\}\_\{s\}\}\\exp\\\!\\left\(\\ell\_\{m\}^\{\(s\)\}\\right\)\},\\qquad n\\in\\mathcal\{C\}\_\{s\}\.\\end\{gathered\}The routed representation is obtained by aggregating candidate VLM states with these depth weights:𝐕~\(s\)=∑n∈𝒞sαn\(s\)​𝐕n\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}=\\sum\_\{n\\in\\mathcal\{C\}\_\{s\}\}\\alpha\_\{n\}^\{\(s\)\}\\,\\mathbf\{V\}\_\{n\}\.

The router predicts a single depth distribution for each selected action layer, shared across all VLM token positions\.

### Internal Action\-State Reread

Action\-State Reread enables each action token to reuse intermediate action states from earlier layers\. At a selected action layerss, the accessible source states are indexed byℐs=\{0,j1,…,jk,cur\}\\mathcal\{I\}\_\{s\}=\\\{0,j\_\{1\},\\ldots,j\_\{k\},\\mathrm\{cur\}\\\},𝐀cur=𝐚\(s\)\\mathbf\{A\}\_\{\\mathrm\{cur\}\}=\\mathbf\{a\}^\{\(s\)\}, where𝐀0\\mathbf\{A\}\_\{0\}denotes the initial action state,𝐀j1,…,𝐀jk\\mathbf\{A\}\_\{j\_\{1\}\},\\ldots,\\mathbf\{A\}\_\{j\_\{k\}\}denote states retained from earlier action layers, and𝐀cur\\mathbf\{A\}\_\{\\mathrm\{cur\}\}denotes the current state\.

Each selected action layer maintains a learned query𝐪A\(s\)∈ℝDa\\mathbf\{q\}\_\{A\}^\{\(s\)\}\\in\\mathbb\{R\}^\{D\_\{a\}\}, shared across all action tokens in that layer\. For tokentt, the learned query𝐪A\(s\)\\mathbf\{q\}\_\{A\}^\{\(s\)\}measures its compatibility with the token representation𝐀i,t\\mathbf\{A\}\_\{i,t\}from each accessible source statei∈ℐsi\\in\\mathcal\{I\}\_\{s\}:

ηt,i\(s\)=\(𝐪A\(s\)\)⊤RMSNorm\(𝐀i,t\),i∈ℐs,ρt,i\(s\)=exp⁡\(ηt,i\(s\)\)∑r∈ℐsexp⁡\(ηt,r\(s\)\),i∈ℐs\.\\begin\{gathered\}\\eta\_\{t,i\}^\{\(s\)\}=\\left\(\\mathbf\{q\}\_\{A\}^\{\(s\)\}\\right\)^\{\\top\}\\operatorname\{RMSNorm\}\\\!\\left\(\\mathbf\{A\}\_\{i,t\}\\right\),\\qquad i\\in\\mathcal\{I\}\_\{s\},\\\\ \\rho\_\{t,i\}^\{\(s\)\}=\\frac\{\\exp\\\!\\left\(\\eta\_\{t,i\}^\{\(s\)\}\\right\)\}\{\\sum\_\{r\\in\\mathcal\{I\}\_\{s\}\}\\exp\\\!\\left\(\\eta\_\{t,r\}^\{\(s\)\}\\right\)\},\\qquad i\\in\\mathcal\{I\}\_\{s\}\.\\end\{gathered\}
The reread state for tokenttis obtained by aggregating source states with these weights:𝐚^t\(s\)=∑i∈ℐsρt,i\(s\)​𝐀i,t\\widehat\{\\mathbf\{a\}\}\_\{t\}^\{\(s\)\}=\\sum\_\{i\\in\\mathcal\{I\}\_\{s\}\}\\rho\_\{t,i\}^\{\(s\)\}\\,\\mathbf\{A\}\_\{i,t\}\. Stacking token\-level outputs yields the reread action state𝐚^\(s\)\\widehat\{\\mathbf\{a\}\}^\{\(s\)\}\. Although the query is shared within each layer, source states vary across token positions, resulting in token\-specific weightsρt,i\(s\)\\rho\_\{t,i\}^\{\(s\)\}\. This differs from the VLM router, which predicts a single depth distribution for each sample and selected action layer that is shared across all VLM token positions\.

### Integration into StarVLA\-π\\pi

In StarVLA\-π\\pi, the action module is a 36\-layer DiT with 18 cross\-attention layers and 18 self\-attention layers\. We retain representations from six predefined VLM depths and expose them to all cross\-attention layers, allowing each layer to construct its depth mixture conditioned on the current action state rather than using a fixed VLM representation\. The six\-depth choice is evaluated in Supplementary Table 2\.

At cross\-attention layerss, the router uses𝐚\(s\)\\mathbf\{a\}^\{\(s\)\}to compute routing weights over the retained VLM states and obtain𝐕~\(s\)\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}, which replaces the encoder context of the original interface:𝐙\(s\)=𝐕~\(s\)\\mathbf\{Z\}^\{\(s\)\}=\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}\. The cross\-attention takes𝐚\(s\)\\mathbf\{a\}^\{\(s\)\}as the query and𝐙\(s\)\\mathbf\{Z\}^\{\(s\)\}as the key–value context, producing𝐚attn\(s\)\\mathbf\{a\}\_\{\\mathrm\{attn\}\}^\{\(s\)\}\. Applied at all 18 cross\-attention layers, the router enables action\-conditioned layer\-wise routing throughout the DiT\.

We apply Action\-State Reread to all 36 DiT blocks, including the 18 self\-attention blocks\. At each block, the attention output serves as the current action\-state source\. For cross\-attention blocks,𝐀cur=𝐚attn\(s\)\\mathbf\{A\}\_\{\\mathrm\{cur\}\}=\\mathbf\{a\}\_\{\\mathrm\{attn\}\}^\{\(s\)\}\. For self\-attention blocks,𝐀cur\\mathbf\{A\}\_\{\\mathrm\{cur\}\}is obtained analogously from the post\-self\-attention state\. The current state is then recombined with earlier action representations to produce𝐚^\(s\)\\widehat\{\\mathbf\{a\}\}^\{\(s\)\}, which is passed to the feed\-forward network\. Thus, the router provides adaptive layer\-wise VLM representation access at the 18 cross\-attention layers, while Action\-State Reread enables reuse of earlier action states throughout the 36 DiT blocks\.

We extend the same representation routing interface LayerRoute toπ0\.5\\pi\_\{0\.5\}, with its backbone\-specific implementation detailed in Supplementary Table 1\.

## Experiments

We evaluate LayerRoute on two VLA backbones across three simulation benchmarks\. We further study its generality across VLM backbones, examine the roles of the two representation reads through ablations, and analyze the learned structured routing behavior through layer\-routing analysis\.

### Setup

We evaluate StarVLA\-π\\pi\([Community 2026](https://arxiv.org/html/2609.06079#bib.bib16)\)andπ0\.5\\pi\_\{0\.5\}\([Intelligence et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib13)\)on three simulation benchmarks\([Liu et al\. 2023](https://arxiv.org/html/2609.06079#bib.bib27);[Li et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib29);[Nasiriany et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib28)\)\. LIBERO evaluates diverse tabletop manipulation across spatial, object\-conditioned, goal\-conditioned, and long\-horizon tasks\. SimplerEnv measures robustness under visual and environmental variations across different robot platforms, while RoboCasa\-GR1 extends evaluation to household manipulation with a humanoid embodiment\. Together, these benchmarks assess representation access under diverse task structures, environments, and control demands across manipulation scenarios\.

All models are trained on eight NVIDIA H200 GPUs with a per\-device batch size of 32\. The pretrained VLM, action module, router, and action\-state reread are jointly fine\-tuned\. For StarVLA\-π\\pi, the multi\-depth representation cache retains six Qwen3\-VL hidden states from layers\[5,11,17,23,29,35\]\[5,11,17,23,29,35\]\. A256256\-dimensional router operates at all 18 cross\-attention layers of the 36\-layer action DiT\. Training uses AdamW with backbone\-specific learning rates,10−810^\{\-8\}weight decay and 5K\-step warmup; for StarVLA\-π\\pi, the base parameters use2\.5×10−52\.5\\times 10^\{\-5\}, while the action and routing parameters use10−410^\{\-4\}\. Dataset, training, and benchmark\-specific evaluation settings are detailed under*Experimental Setup*and*Cross\-benchmark execution*in the Supplementary\.

### LIBERO Evaluation across Backbones

Table[6](https://arxiv.org/html/2609.06079#Sx5.T6)reports the performance of LayerRoute on StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}\. Across both backbones, LayerRoute improves LIBERO performance\. Specifically, StarVLA\-π\\pigains 2\.3 and 7\.2 percentage points on Avg4and Long, whileπ0\.5\\pi\_\{0\.5\}gains 1\.3 and 3\.6 points, respectively\. These results demonstrate that the representation\-access mechanism generalizes across VLA architectures with distinct action formulations\. The Long\-suite improvements further suggest that adaptive layer\-wise VLM representation access and earlier action\-state reuse are beneficial for long\-horizon manipulation\.

### Cross\-Benchmark Evaluation

We further evaluate LayerRoute on SimplerEnv and RoboCasa\-GR1\. Across both benchmarks, LayerRoute consistently improves the performance of StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}\. On SimplerEnv, StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}achieve gains of 1\.6/2\.5 and 2\.1/5\.6 points on Overall/WidowX success, respectively \(Table[6](https://arxiv.org/html/2609.06079#Sx5.T6)\)\. On RoboCasa\-GR1, LayerRoute improves macro\-average success by 1\.2 and 5\.5 points for StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}, respectively \(Table[6](https://arxiv.org/html/2609.06079#Sx5.T6)\)\. These improvements are achieved with modest parameter overheads of 0\.31% and 3\.87% and latency increases of 10\.03% and 25\.04%, yielding a favorable accuracy–efficiency trade\-off\. RoboCasa\-GR1 task\-level results and SimplerEnv task/task\-family breakdowns are reported in Supplementary Tables 4, 7, and 8\. Overall, these results show that LayerRoute remains effective across diverse manipulation settings, including different tasks, environments, and robot embodiments\.

### Sensitivity to the VLM Backbone

Table 2:LIBERO success rate\. Each suite contains 500 evaluation episodes; Avg4is the unweighted mean across suites\. StarVLA\-π\\piuses Qwen3\-VL\([Bai et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib9)\)\. Bold indicates the best result in each column throughout the paper\.Table 3:SimplerEnv success rate\. VM/VA denote Google Robot Visual Matching/Variant Aggregation; GR Avg\. averages VM/VA, and WidowX is reported separately\.Table 4:Macro\-average success rate over 24 RoboCasa\-GR1 tasks\. Added parameters and latency increases are relative to the corresponding backbone\.Table 5:VLM\-backbone sensitivity on LIBERO Avg4\. Gain \(pp\) is LayerRoute minus the original interface\.Table 6:Component ablations on LIBERO\. Avg4denotes the average SR \(%\) across four suites\.To assess the sensitivity of LayerRoute to the VLM backbone, we keep the StarVLA\-π\\piaction architecture and training configuration fixed while varying only the VLM backbone that provides the multi\-layer representations\.

As shown in Table[6](https://arxiv.org/html/2609.06079#Sx5.T6), LayerRoute improves Avg4relative to the corresponding static interface for all four VLM backbones, with gains ranging from 1\.2 to 3\.3 percentage points\. These consistent improvements across VLM backbones demonstrate that adaptive representation access remains effective across different VLM choices\.

### Component Ablations

Table[6](https://arxiv.org/html/2609.06079#Sx5.T6)presents controlled ablations of the two routing mechanisms\. We compare the static interface, VLM router only, action\-state reread only, and complete routing interface\.

Across both backbones, the complete routing interface achieves the best Avg4and Long performance\. Compared with the best\-performing single\-read variant, it improves Avg4/Long by 1\.6/1\.8 points on StarVLA\-π\\piand 0\.9/1\.8 points onπ0\.5\\pi\_\{0\.5\}, respectively\. These results demonstrate that adaptive access to both VLM layer representations and intermediate action states provides complementary benefits\.

## Layer\-Routing Analysis

We further examine whether the Layer Mixture Router benefits from action\-guided layer\-wise routing by comparing it with static, uniform, and fixed\-depth alternatives\. We also analyze how the learned VLM\-depth distributions evolve during training and vary across action layers and task suites\.

Table 7:StarVLA\-π\\pirouting\-policy controls\. All routed variants differ only in the layer\-wise routing rule\.ΔLong\\Delta\_\{\\mathrm\{Long\}\}is measured relative to the original static interface\.### Routing\-Policy Controls

Table[7](https://arxiv.org/html/2609.06079#Sx6.T7)examines whether conditioning layer\-wise routing on the current action state improves performance relative to uniform, fixed\-depth, and action\-independent routing alternatives\. In the action\-independent control, the pooled action representation𝐩a\(s\)\\mathbf\{p\}\_\{a\}^\{\(s\)\}is replaced with a fixed nonzero vector𝐜0\\mathbf\{c\}\_\{0\}:𝐪ind\(s\)=𝐖q,d\(s\)​LayerNorma\(s\)⁡\(𝐜0\)\\mathbf\{q\}\_\{\\mathrm\{ind\}\}^\{\(s\)\}=\\mathbf\{W\}\_\{q,d\}^\{\(s\)\}\\operatorname\{LayerNorm\}\_\{a\}^\{\(s\)\}\\\!\\left\(\\mathbf\{c\}\_\{0\}\\right\)\. The resulting query remains learned and layer\-specific, but the routing weights no longer depend on the current action state\. The action\-guided route achieves 98\.0 Avg4and 95\.6 Long, exceeding the action\-independent control by 0\.8 points on both metrics, the strongest fixed\-depth route by 1\.6/1\.4 points, and uniform routing by 3\.8/3\.4 points\. These comparisons show that conditioning layer\-wise routing on the current action representation provides an effective routing signal\.

### Routing Diagnostics

We analyze aggregate routing behavior across four LIBERO suites during training\. As shown in Figure[2](https://arxiv.org/html/2609.06079#Sx6.F2), the routing statistics largely stabilize by 20K steps; we therefore use this checkpoint for the subsequent analyses in Figures[3](https://arxiv.org/html/2609.06079#Sx6.F3)–[5](https://arxiv.org/html/2609.06079#Sx6.F5)\.

Figure 2:Routing selectivity over training\. Normalized entropyH⁡\(𝜶\)/log⁡KH\(\\boldsymbol\{\\alpha\}\)/\\log Kand entropy deficitΔH\\Delta\_\{\\mathrm\{H\}\}are complementary measures: entropy decreases asΔH\\Delta\_\{\\mathrm\{H\}\}increases\. Shaded regions indicate routing variation in late\-training window\.Figure 3:Routing selectivity across action\-layer groups\. Top: bin\-level normalized entropy deficitΔH\\Delta\_\{\\mathrm\{H\}\}\(circles\) and early/middle/late means of 0\.126/0\.205/0\.253 \(diamonds\)\. Bottom: pairwise Jensen–Shannon divergences between groups; the dashed line marks their mean,MDS=0\.205\\mathrm\{MDS\}=0\.205\.Figure 4:layer\-wise routing across action\-layer groups at 20K\. Columns E1–L2 denote six router bins and rowsV1V\_\{1\}–V6V\_\{6\}denote the six VLM layers\. Routing shifts from shallow states in early bins to middle and deeper states in later bins\.Figure 5:Suite\-specific layer\-wise routing\. Columns E1–L2 denote router bins and rowsV1V\_\{1\}–V6V\_\{6\}denote VLM layers\. Spatial favors shallow states, Object middle states, Goal deeper states, and Long a broader mixture\. Subtitles report suite\-specific margins relative to the corresponding reference distribution; 6/6 indicates positive margins across all six router bins\.To characterize how routing evolves across the action DiT, we analyze the 18 cross\-attention layers where the VLM\-depth router is applied\. Following their order in the network, we group consecutive layers into six bins of three layers each:ℬ=\{E1,E2,M1,M2,L1,L2\}\\mathcal\{B\}=\\\{\\mathrm\{E1\},\\mathrm\{E2\},\\mathrm\{M1\},\\mathrm\{M2\},\\mathrm\{L1\},\\mathrm\{L2\}\\\}\. For each binb∈ℬb\\in\\mathcal\{B\}, we first average the routing distributions of its three layers within each suite and then compute the equal\-weight mean over the four suites, obtaining an aggregate distribution𝜶¯\(b\)\\bar\{\\boldsymbol\{\\alpha\}\}^\{\(b\)\}over the six VLM depths\. The componentα¯n\(b\)\\bar\{\\alpha\}\_\{n\}^\{\(b\)\}denotes the mean routing weight assigned to VLM depthnnwithin binbb\. We quantify routing selectivity using the entropy and normalized entropy deficit:

H\(b\)=−∑n=1Kα¯n\(b\)logα¯n\(b\),ΔH\(b\)=1−H\(b\)log⁡K,K=6\.\\mathrm\{H\}^\{\(b\)\}=\-\\sum\_\{n=1\}^\{K\}\\bar\{\\alpha\}\_\{n\}^\{\(b\)\}\\log\\bar\{\\alpha\}\_\{n\}^\{\(b\)\},\\quad\\Delta\_\{\\mathrm\{H\}\}^\{\(b\)\}=1\-\\frac\{\\mathrm\{H\}^\{\(b\)\}\}\{\\log K\},\\quad K=6\.Uniform routing givesΔH\(b\)=0\\Delta\_\{\\mathrm\{H\}\}^\{\(b\)\}=0, whereas larger values indicate stronger concentration on fewer VLM layers\.

To measure routing variation across action\-computation stages, we merge adjacent bins into early, middle, and late groups:𝒢e=\{E1,E2\}\\mathcal\{G\}\_\{e\}=\\\{\\mathrm\{E1\},\\mathrm\{E2\}\\\},𝒢m=\{M1,M2\}\\mathcal\{G\}\_\{m\}=\\\{\\mathrm\{M1\},\\mathrm\{M2\}\\\}, and𝒢l=\{L1,L2\}\\mathcal\{G\}\_\{l\}=\\\{\\mathrm\{L1\},\\mathrm\{L2\}\\\}\. Forg∈\{e,m,l\}g\\in\\\{e,m,l\\\}, we average the corresponding bin\-level distributions:𝜶¯g=12​∑b∈𝒢g𝜶¯\(b\)\\bar\{\\boldsymbol\{\\alpha\}\}\_\{g\}=\\frac\{1\}\{2\}\\sum\_\{b\\in\\mathcal\{G\}\_\{g\}\}\\bar\{\\boldsymbol\{\\alpha\}\}^\{\(b\)\}\. These group\-level distributions characterize the average VLM\-depth allocation at different stages of action computation\. We measure their separation using the mean distribution separation \(MDS\), computed using Jensen–Shannon divergence:

MDS=13​\[JS⁡\(𝜶¯e,𝜶¯m\)\+JS⁡\(𝜶¯e,𝜶¯l\)\+JS⁡\(𝜶¯m,𝜶¯l\)\]\.\\mathrm\{MDS\}=\\frac\{1\}\{3\}\\Bigl\[\\operatorname\{JS\}\(\\bar\{\\boldsymbol\{\\alpha\}\}\_\{e\},\\bar\{\\boldsymbol\{\\alpha\}\}\_\{m\}\)\+\\operatorname\{JS\}\(\\bar\{\\boldsymbol\{\\alpha\}\}\_\{e\},\\bar\{\\boldsymbol\{\\alpha\}\}\_\{l\}\)\+\\operatorname\{JS\}\(\\bar\{\\boldsymbol\{\\alpha\}\}\_\{m\},\\bar\{\\boldsymbol\{\\alpha\}\}\_\{l\}\)\\Bigr\]\.LargerMDS\\mathrm\{MDS\}indicates greater variation in VLM\-depth allocation across action\-computation stages, whileMDS=0\\mathrm\{MDS\}=0corresponds to identical depth distributions\.

#### Routing becomes more selective during training\.

Figure[2](https://arxiv.org/html/2609.06079#Sx6.F2)shows that routing gradually shifts away from the uniform distribution\. The mean normalized entropy across the six bins decreases from 1\.000 at initialization to 0\.805 at 20K, while the corresponding normalized entropy deficit increases from 0\.000 to 0\.195\. Both measures stabilize near 20K\. These trends indicate that the router learns increasingly selective VLM\-depth allocation while maintaining a distributed mixture rather than collapsing to a single depth\.

#### Routing varies across the action DiT\.

The group\-averaged normalized entropy deficit increases from 0\.126 in the early layers to 0\.205 in the middle layers and 0\.253 in the late layers \(Figure[3](https://arxiv.org/html/2609.06079#Sx6.F3)\), indicating more selective depth routing in later action stages\. The early–middle, early–late, and middle–late Jensen–Shannon divergences are 0\.163, 0\.248, and 0\.205, respectively, with the largest separation between the early and late groups\. Their mean yieldsMDS=0\.205\\mathrm\{MDS\}=0\.205\. Figure[4](https://arxiv.org/html/2609.06079#Sx6.F4)reveals a shift in VLM\-depth allocation: early action layers assign more weight to shallower VLM states, whereas later layers increasingly favor middle and deeper states\.

#### Task suites exhibit distinct layer\-routing patterns\.

Figure[5](https://arxiv.org/html/2609.06079#Sx6.F5)reports routing heatmaps stratified by task suite\. Let𝜶¯\(u,b\)\\bar\{\\boldsymbol\{\\alpha\}\}^\{\(u,b\)\}denote the routing distribution for suiteuuin router binbb\. We define shallow and middle masses as the summed routing weights overV1V\_\{1\}–V2V\_\{2\}andV3V\_\{3\}–V4V\_\{4\}, and compute the expected layer index as:D\(u,b\)=∑n=1Kn​α¯n\(u,b\)D^\{\(u,b\)\}=\\sum\_\{n=1\}^\{K\}n\\,\\bar\{\\alpha\}\_\{n\}^\{\(u,b\)\}\.

The routing behaviors exhibit clear task\-dependent preferences\. Spatial tasks favor shallow layers, particularly in early routing stages, with a shallow\-mass margin of 0\.211, reflecting greater reliance on fine\-grained visual and geometric representations\. Object tasks maintain higher routing mass overV3V\_\{3\}–V4V\_\{4\}before gradually shifting toward deeper layers, yielding a middle\-mass margin of 0\.198\. Goal tasks consistently exhibit the largest expected layer index across all bins, exceeding the mean of other suites by 0\.504 on average, suggesting stronger reliance on higher\-level semantic representations\. Long\-horizon tasks maintain the broadest routing distribution across VLM layers, with normalized entropy higher by 0\.081, indicating that extended tasks benefit from integrating diverse representations across multiple visual, semantic, and action\-relevant hierarchical levels\.

## Real\-World Robot Experiments

![Refer to caption](https://arxiv.org/html/2609.06079v1/figure_6.png)Figure 6:Real\-world manipulation tasks for evaluating LayerRoute with a Franka robotic arm\. The tasks include \(a\) cube pick\-and\-place, \(b\) eraser\-based board wiping, and \(c\) broom\-based table cleaning, covering diverse grasping, contact, and tool\-use interactions\.To further evaluate LayerRoute under real\-world execution, we conduct physical robot experiments with a Franka robotic arm equipped with a gripper across three manipulation tasks\. As shown in Figure[6](https://arxiv.org/html/2609.06079#Sx7.F6), the tasks cover diverse embodied interactions: PnP requires accurate object pose estimation, stable grasping, and precise placement; Wipe board involves contact\-rich interaction and coordinated tool motion; and Clean Table requires tool use and longer\-horizon object manipulation\. Together, these tasks evaluate whether adaptive representation routing can improve real\-world manipulation performance across different physical interaction patterns\.

For each task, we collect 50 demonstration trajectories and fine\-tune bothπ0\.5\\pi\_\{0\.5\}andπ0\.5\+L​a​y​e​r​R​o​u​t​e\\pi\_\{0\.5\}\+LayerRoute\{\}for 20K steps under identical training configurations and optimization settings\. Each policy is evaluated over 50 independent physical trials per task\. As shown in Table[8](https://arxiv.org/html/2609.06079#Sx7.T8), LayerRoute consistently improves task success rates by \+8\.0, \+4\.0, and \+6\.0 percentage points on PnP, Wipe board, and Clean Table, respectively\. Detailed task definitions and training/inference configurations are provided under*Real\-World Experimental Details*in the Supplementary Material\.

Table 8:Real\-world manipulation success rates \(%\) comparingπ0\.5\\pi\_\{0\.5\}andπ0\.5\+L​a​y​e​r​R​o​u​t​e\\pi\_\{0\.5\}\+LayerRoute\{\}\. LayerRoute consistently improves performance across cube pick\-and\-place, board wiping, and table cleaning real\-world tasks\.
## Conclusion

We identify fixed representation interfaces as a limitation of current VLA action computation and introduce LayerRoute, an action\-conditioned mixture\-of\-layers routing framework with adaptive access to VLM and action representations\. By routing over cached VLM layer representations and revisiting intermediate action states, LayerRoute enables action computation to dynamically access information beyond fixed layer exposure and residual\-only propagation\. Extensive experiments across simulation and real\-world settings demonstrate consistent improvements in VLA performance with modest overhead\. Ablation studies validate the contributions of both representation routing mechanisms, while routing analyses reveal structured layer allocation patterns that vary across action layers and task settings\. These findings highlight adaptive representation routing for flexible robot policies\.

## References

- Baiet al\.\(2025\)S\. Bai, Y\. Cai, R\. Chen, K\. Chen, X\. Chen, Z\. Cheng, L\. Deng, W\. Ding, C\. Gao, C\. Ge,et al\.Qwen3\-vl technical report\.arXiv preprint arXiv:2511\.21631\.Cited by:[Table 9](https://arxiv.org/html/2609.06079#A2.T9.1.3.2.1.1),[Introduction](https://arxiv.org/html/2609.06079#Sx1.p5.1),[Architectural Instantiations\.](https://arxiv.org/html/2609.06079#Sx3.SS0.SSS0.Px3.p1.1),[Table 6](https://arxiv.org/html/2609.06079#Sx5.T6)\.
- Belroseet al\.\(2023\)N\. Belrose, I\. Ostrovsky, L\. McKinney, Z\. Furman, L\. Smith, D\. Halawi, S\. Biderman, and J\. SteinhardtEliciting latent predictions from transformers with the tuned lens\.arXiv preprint arXiv:2303\.08112\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Beyeret al\.\(2024\)L\. Beyer, A\. Steiner, A\. S\. Pinto, A\. Kolesnikov, X\. Wang, D\. Salz, M\. Neumann, I\. Alabdulmohsin, M\. Tschannen, E\. Bugliarello,et al\.Paligemma: a versatile 3b vlm for transfer\.arXiv preprint arXiv:2407\.07726\.Cited by:[Table 9](https://arxiv.org/html/2609.06079#A2.T9.1.2.2.1.1),[Architectural Instantiations\.](https://arxiv.org/html/2609.06079#Sx3.SS0.SSS0.Px3.p1.1)\.
- Blacket al\.\(2024\)K\. Black, N\. Brown, D\. Driess, A\. Esmail, M\. Equi, C\. Finn, N\. Fusai, L\. Groom, K\. Hausman, B\. Ichter,et al\.π0\\pi\_\{0\}: a vision\-language\-action flow model for general robot control\.arXiv preprint arXiv:2410\.24164\.Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p1.1),[VLA Action Generation and Representation Interfaces\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px1.p1.1)\.
- Brohanet al\.\(2022\)A\. Brohan, N\. Brown, J\. Carbajal, Y\. Chebotar, J\. Dabis, C\. Finn, K\. Gopalakrishnan, K\. Hausman, A\. Herzog, J\. Hsu,et al\.Rt\-1: robotics transformer for real\-world control at scale\.arXiv preprint arXiv:2212\.06817\.Cited by:[Appendix C](https://arxiv.org/html/2609.06079#A3.SS0.SSS0.Px1.p2.1)\.
- Community \(2026\)S\. CommunityStarVLA: a lego\-like codebase for vision\-language\-action model developing\.arXiv preprint arXiv:2604\.05014\.Cited by:[Appendix A](https://arxiv.org/html/2609.06079#A1.SS0.SSS0.Px1.p1.1),[Table 9](https://arxiv.org/html/2609.06079#A2.T9),[Appendix C](https://arxiv.org/html/2609.06079#A3.SS0.SSS0.Px1.p2.1),[VLA Action Generation and Representation Interfaces\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px1.p1.1),[Architectural Instantiations\.](https://arxiv.org/html/2609.06079#Sx3.SS0.SSS0.Px3.p1.1),[Setup](https://arxiv.org/html/2609.06079#Sx5.SSx1.p1.1)\.
- Driesset al\.\(2026\)D\. Driess, J\. Springenberg, B\. Ichter, L\. Yu, A\. Li\-Bell, K\. Pertsch, A\. Ren, H\. Walke, Q\. Vuong, L\. X\. Shi,et al\.Knowledge insulating vision\-language\-action models: train fast, run fast, generalize better\.Advances in Neural Information Processing Systems38,pp\. 102867–102888\.Cited by:[VLA Action Generation and Representation Interfaces\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px1.p1.1)\.
- Ebertet al\.\(2021\)F\. Ebert, Y\. Yang, K\. Schmeckpeper, B\. Bucher, G\. Georgakis, K\. Daniilidis, C\. Finn, and S\. LevineBridge data: boosting generalization of robotic skills with cross\-domain datasets\.arXiv preprint arXiv:2109\.13396\.Cited by:[Appendix C](https://arxiv.org/html/2609.06079#A3.SS0.SSS0.Px1.p2.1)\.
- Gandelsmanet al\.\(2024\)Y\. Gandelsman, A\. Efros, and J\. SteinhardtInterpreting clip’s image representation via text\-based decomposition\.InInternational Conference on Learning Representations,Vol\.2024,pp\. 18395–18416\.Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p2.1),[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Haoet al\.\(2025\)X\. Hao, L\. Zhou, Z\. Huang, Z\. Hou, Y\. Tang, L\. Zhang, G\. Li, Z\. Lu, S\. Ren, X\. Meng,et al\.Mimo\-embodied: x\-embodied foundation model technical report\.arXiv preprint arXiv:2511\.16518\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Huanget al\.\(2016\)G\. Huang, Y\. Sun, Z\. Liu, D\. Sedra, and K\. WeinbergerDeep networks with stochastic depth\.arXiv preprint arXiv:1603\.09382\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Huanget al\.\(2025\)H\. Huang, F\. Liu, L\. Fu, T\. Wu, M\. Mukadam, J\. Malik, K\. Goldberg, and P\. AbbeelOtter: a vision\-language\-action model with text\-aware visual feature extraction\.arXiv preprint arXiv:2503\.03734\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Intelligenceet al\.\(2025\)P\. Intelligence, K\. Black, N\. Brown, J\. Darpinian, K\. Dhabalia, D\. Driess, A\. Esmail, M\. Equi, C\. Finn, N\. Fusai,et al\.π0\.5\\pi\_\{0\.5\}: a vision\-language\-action model with open\-world generalization\.arXiv preprint arXiv:2504\.16054\.Cited by:[Table 9](https://arxiv.org/html/2609.06079#A2.T9),[Introduction](https://arxiv.org/html/2609.06079#Sx1.p1.1),[VLA Action Generation and Representation Interfaces\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px1.p1.1),[Architectural Instantiations\.](https://arxiv.org/html/2609.06079#Sx3.SS0.SSS0.Px3.p1.1),[Setup](https://arxiv.org/html/2609.06079#Sx5.SSx1.p1.1)\.
- Kimet al\.\(2024\)M\. J\. Kim, K\. Pertsch, S\. Karamcheti, T\. Xiao, A\. Balakrishna, S\. Nair, R\. Rafailov, E\. Foster, G\. Lam, P\. Sanketi,et al\.Openvla: an open\-source vision\-language\-action model\.arXiv preprint arXiv:2406\.09246\.Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p1.1),[VLA Action Generation and Representation Interfaces\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px1.p1.1)\.
- Kooet al\.\(2025\)M\. Koo, D\. Choi, T\. Kim, K\. Lee, C\. Kim, Y\. Seo, and J\. ShinHamlet: switch your vision\-language\-action model into a history\-aware policy\.arXiv preprint arXiv:2510\.00695\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Liet al\.\(2026\)W\. Li, R\. Zhang, R\. Shao, J\. He, and L\. NieCogVLA: cognition\-aligned vision\-language\-action models via instruction\-driven routing & sparsification\.Advances in neural information processing systems38,pp\. 137646–137675\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Liet al\.\(2024\)X\. Li, K\. Hsu, J\. Gu, K\. Pertsch, O\. Mees, H\. R\. Walke, C\. Fu, I\. Lunawat, I\. Sieh, S\. Kirmani,et al\.Evaluating real\-world robot manipulation policies in simulation\.arXiv preprint arXiv:2405\.05941\.Cited by:[Appendix C](https://arxiv.org/html/2609.06079#A3.SS0.SSS0.Px1.p2.1),[Setup](https://arxiv.org/html/2609.06079#Sx5.SSx1.p1.1)\.
- Liuet al\.\(2023\)B\. Liu, Y\. Zhu, C\. Gao, Y\. Feng, Q\. Liu, Y\. Zhu, and P\. StoneLibero: benchmarking knowledge transfer for lifelong robot learning\.Advances in Neural Information Processing Systems36,pp\. 44776–44791\.Cited by:[Appendix F](https://arxiv.org/html/2609.06079#A6.SSx1.p1.1),[Setup](https://arxiv.org/html/2609.06079#Sx5.SSx1.p1.1)\.
- Luet al\.\(2026\)Z\. Lu, M\. Gao, Q\. Xie, W\. Zhong, H\. Cui, H\. Cao, Z\. Song, Y\. Yang, C\. Luo, B\. Liu,et al\.Token predictors are not planners: building physically grounded causal reasoners\.arXiv preprint arXiv:2606\.01810\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Miaoet al\.\(2025\)C\. Miao, T\. Chang, M\. Wu, H\. Xu, C\. Li, M\. Li, and X\. WangFedvla: federated vision\-language\-action learning with dual gating mixture\-of\-experts for robotic manipulation\.InProceedings of the IEEE/CVF International Conference on Computer Vision,pp\. 6904–6913\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Nasirianyet al\.\(2024\)S\. Nasiriany, A\. Maddukuri, L\. Zhang, A\. Parikh, A\. Lo, A\. Joshi, A\. Mandlekar, and Y\. ZhuRobocasa: large\-scale simulation of everyday tasks for generalist robots\.arXiv preprint arXiv:2406\.02523\.Cited by:[Table 12](https://arxiv.org/html/2609.06079#A3.T12),[Setup](https://arxiv.org/html/2609.06079#Sx5.SSx1.p1.1)\.
- Neoet al\.\(2025\)C\. Neo, L\. Ong, P\. Torr, M\. Geva, D\. Krueger, and F\. BarezTowards interpreting visual information processing in vision\-language models\.InInternational Conference on Learning Representations,Vol\.2025,pp\. 57172–57189\.Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p2.1),[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- NVIDIA \(2026\)NVIDIACosmos\-Reason2\-2B\.Note:https://huggingface\.co/nvidia/Cosmos\-Reason2\-2BHugging Face model card; accessed 2026\-07\-23Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p5.1)\.
- Pagliardiniet al\.\(2024\)M\. Pagliardini, A\. Mohtashami, F\. Fleuret, and M\. JaggiDenseformer: enhancing information flow in transformers via depth weighted averaging\.Advances in neural information processing systems37,pp\. 136479–136508\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1),[Table 1](https://arxiv.org/html/2609.06079#Sx2.T1)\.
- Physical Intelligence \(2026\)Physical IntelligenceOpenPI: open\-source vision\-language\-action models\.Note:https://github\.com/Physical\-Intelligence/openpiGitHub repository, LIBERO results table; accessed 2026\-05\-14Cited by:[Appendix A](https://arxiv.org/html/2609.06079#A1.SS0.SSS0.Px1.p1.1)\.
- Quet al\.\(2025\)D\. Qu, H\. Song, Q\. Chen, Y\. Yao, X\. Ye, Y\. Ding, Z\. Wang, J\. Gu, B\. Zhao, D\. Wang,et al\.Spatialvla: exploring spatial representations for visual\-language\-action model\.arXiv preprint arXiv:2501\.15830\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Raghuet al\.\(2021\)M\. Raghu, T\. Unterthiner, S\. Kornblith, C\. Zhang, and A\. DosovitskiyDo vision transformers see like convolutional neural networks?\.Advances in neural information processing systems34,pp\. 12116–12128\.Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p2.1),[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Raposoet al\.\(2024\)D\. Raposo, S\. Ritter, B\. Richards, T\. Lillicrap, P\. C\. Humphreys, and A\. SantoroMixture\-of\-depths: dynamically allocating compute in transformer\-based language models\.arXiv preprint arXiv:2404\.02258\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1),[Table 1](https://arxiv.org/html/2609.06079#Sx2.T1)\.
- Shiet al\.\(2025\)H\. Shi, B\. Xie, Y\. Liu, L\. Sun, F\. Liu, T\. Wang, E\. Zhou, H\. Fan, X\. Zhang, and G\. HuangMemoryvla: perceptual\-cognitive memory in vision\-language\-action models for robotic manipulation\.arXiv preprint arXiv:2508\.19236\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Srivastavaet al\.\(2015\)R\. K\. Srivastava, K\. Greff, and J\. SchmidhuberTraining very deep networks\.Advances in neural information processing systems28\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Teamet al\.\(2026\)K\. Team, G\. Chen, Y\. Zhang, J\. Su, W\. Xu, S\. Pan, Y\. Wang, Y\. Wang, G\. Chen, B\. Yin,et al\.Attention residuals\.arXiv preprint arXiv:2603\.15031\.Cited by:[Appendix B](https://arxiv.org/html/2609.06079#A2.SS0.SSS0.Px1.p1.1),[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1),[Table 1](https://arxiv.org/html/2609.06079#Sx2.T1)\.
- Teamet al\.\(2024\)O\. M\. Team, D\. Ghosh, H\. Walke, K\. Pertsch, K\. Black, O\. Mees, S\. Dasari, J\. Hejna, T\. Kreiman, C\. Xu,et al\.Octo: an open\-source generalist robot policy\.arXiv preprint arXiv:2405\.12213\.Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p1.1),[VLA Action Generation and Representation Interfaces\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px1.p1.1)\.
- Xiaoet al\.\(2025\)L\. Xiao, J\. Li, J\. Gao, F\. Ye, Y\. Jin, J\. Qian, J\. Zhang, Y\. Wu, and X\. YuAVA\-vla: improving vision\-language\-action models with active visual attention\.arXiv preprint arXiv:2511\.18960\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Xuet al\.\(2026\)S\. Xu, Y\. Wang, C\. Xia, D\. Zhu, T\. Huang, and C\. XuVla\-cache: efficient vision\-language\-action manipulation via adaptive token caching\.Advances in Neural Information Processing Systems38,pp\. 164448–164473\.Cited by:[Adaptive Representation Access and Routing\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px2.p1.1)\.
- Yueet al\.\(2024\)Y\. Yue, Y\. Wang, B\. Kang, Y\. Han, S\. Wang, S\. Song, J\. Feng, and G\. HuangDeer\-vla: dynamic inference of multimodal large language models for efficient robot execution\.Advances in Neural Information Processing Systems37,pp\. 56619–56643\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Zhanget al\.\(2026\)R\. Zhang, M\. Dong, Y\. Zhang, L\. Heng, X\. Chi, G\. Dai, L\. Du, D\. Wang, Y\. Du, and S\. ZhangMole\-vla: dynamic layer\-skipping vision language action model via mixture\-of\-layers for efficient robot manipulation\.InProceedings of the AAAI Conference on Artificial Intelligence,Vol\.40,pp\. 18764–18772\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Zhuet al\.\(2025\)D\. Zhu, H\. Huang, Z\. Huang, Y\. Zeng, Y\. Mao, B\. Wu, Q\. Min, and X\. ZhouHyper\-connections\.InInternational Conference on Learning Representations,Vol\.2025,pp\. 97183–97219\.Cited by:[Layerwise Representations and Cross\-Layer Reuse\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px3.p1.1)\.
- Zitkovichet al\.\(2023\)B\. Zitkovich, T\. Yu, S\. Xu, P\. Xu, T\. Xiao, F\. Xia, J\. Wu, P\. Wohlhart, S\. Welker, A\. Wahid,et al\.Rt\-2: vision\-language\-action models transfer web knowledge to robotic control\.InConference on Robot Learning,pp\. 2165–2183\.Cited by:[Introduction](https://arxiv.org/html/2609.06079#Sx1.p1.1),[VLA Action Generation and Representation Interfaces\.](https://arxiv.org/html/2609.06079#Sx2.SS0.SSS0.Px1.p1.1)\.

## Appendix

## Appendix AExperimental Setup

This supplement provides implementation details, controlled ablations, efficiency measurements, and task\-level results\. Within each backbone, all component variants share identical training and evaluation settings\. All routed StarVLA\-π\\picontrols retain the same Action\-State Reread module and differ only in the VLM\-layer routing strategy\.

#### Training data\.

For each backbone, LayerRoute preserves the baseline datasets, mixtures, preprocessing, normalization, and sampling strategy without adding demonstrations or task\-specific samples\. The registered StarVLA\-π\\pirobot\-policy mixtures\([Community 2026](https://arxiv.org/html/2609.06079#bib.bib16)\)contain 1,693 no\-op\-filtered LIBERO trajectories \(432 Spatial, 454 Object, 428 Goal, and 379 LIBERO\-10\), 140,404 SimplerEnv trajectories \(53,192 Bridge and 87,212 RT\-1/Fractal\), and 24,000 RoboCasa\-GR1 trajectories \(1,000 per task dataset\)\. Each constituent dataset has registry weight 1\.0; these counts exclude the auxiliary VLM instruction\-data stream\. Theπ0\.5\\pi\_\{0\.5\}integration likewise preserves the original OpenPI\([Physical Intelligence 2026](https://arxiv.org/html/2609.06079#bib.bib14)\)data configuration\. Consequently, each baseline and LayerRoute pair differs only in its representation\-access interface\.

#### Training configuration\.

All models are trained on eight NVIDIA H200 GPUs with a per\-device batch size of 32\. The pretrained VLM, action module, router, and action\-state reread are jointly fine\-tuned together with the backbone\-specific fusion parameters\. All VLM parameters are updated during fine\-tuning\. For LIBERO, SimplerEnv, and RoboCasa\-GR1, we use fixed training budgets of 30K, 40K, and 100K optimization steps, respectively\. Both backbones use a 5K\-step warmup during training\. We do not perform hyperparameter sweeps\. We evaluate the corresponding endpoint checkpoints\. For the VLM\-backbone sensitivity experiments, we keep the action architecture and optimization protocol fixed while replacing the pretrained VLM backbone and jointly fine\-tuning the resulting model under the same configuration\.

#### Randomness control\.

We train three independent runs per benchmark configuration with seeds77,4242, and4141, and report the mean performance\. For each run, the global seed is used to initialize Python, NumPy, PyTorch, and CUDA random number generators before model construction\. In distributed training, each process uses a rank\-specific seed derived ass\+rs\+r, wheressis the global seed andrris the process rank\. This ensures deterministic initialization of the router, fusion modules, and Action\-State Reread across distributed workers while preserving independent stochastic streams\. Data\-loader workers additionally inherit rank\-specific generator states to ensure reproducible data sampling\.

#### Evaluation checkpoints\.

Figure 2 in the main paper tracks aggregate routing behavior across the four LIBERO suites during training\. The routing statistics largely stabilize by the 20K\-step diagnostic checkpoint, which we use for the subsequent analyses in Figures 3–5\. These routing diagnostics are separate from the benchmark\-specific endpoint evaluations\. All displayed task\-level results are obtained by reevaluating the corresponding models under the same protocols used for their reported aggregate scores\.

## Appendix BImplementation Details

Table[9](https://arxiv.org/html/2609.06079#A2.T9)summarizes the backbone\-specific implementations\. Both implementations preserve the native action objectives and insert the two representation reads at backbone\-appropriate locations\.

Table 9:Backbone\-specific implementations of LayerRoute\. Theπ0\.5\\pi\_\{0\.5\}path\([Intelligence et al\. 2025](https://arxiv.org/html/2609.06079#bib.bib13)\)reads the selected memory through a separate action\-to\-VLM cross\-attention adapter before native joint attention\. The StarVLA\-π\\pipath\([Community 2026](https://arxiv.org/html/2609.06079#bib.bib16)\)instead supplies the routed memory directly as context to native cross\-attention\. Both paths jointly fine\-tune the pretrained VLM, action module, router, action\-state reread, and backbone\-specific fusion parameters\.#### Choice of VLM\-layer granularity\.

The Layer Mixture Router operates over six cached VLM states in StarVLA\-π\\pi, retained after Qwen3\-VL layers\[5,11,17,23,29,35\]\[5,11,17,23,29,35\]\. This granularity follows the block\-level state retention used in Block Attention Residuals\([Team et al\. 2026](https://arxiv.org/html/2609.06079#bib.bib32)\)\. The same six candidates are exposed to all 18 action\-DiT cross\-attention routing sites\. Grouping these 18 sites into six consecutive three\-site bins is used only for the routing diagnostics in Figures 3–5 and does not define the VLM candidate set\.

We additionally evaluate a denser routing variant with 18 VLM\-layer candidates, where the router directly routes over individual cached VLM layers\. Although this provides finer\-grained depth access, we find that the enlarged routing space leads to less stable router optimization and does not provide consistent performance gains\. Moreover, the denser variant introduces additional router computation and inference latency\. Therefore, we use the six\-depth configuration as a practical balance between routing granularity, optimization stability, and computational overhead\.

Table 10:Effect of VLM\-layer routing granularity on StarVLA\-π\\pi\. The 6\-depth variant routes over cached Qwen3\-VL states from layers\[5,11,17,23,29,35\]\[5,11,17,23,29,35\], whereas the 18\-depth variant routes over individual cached VLM layers\. All 18 action\-DiT cross\-attention sites use the selected candidate set\. Latency overhead is measured relative to the static interface\. Bold denotes the higher Avg4success rate\.
#### Optimization details\.

Both implementations use bfloat16 mixed precision and AdamW with\(β1,β2\)=\(0\.9,0\.95\)\(\\beta\_\{1\},\\beta\_\{2\}\)=\(0\.9,0\.95\),ϵ=10−8\\epsilon=10^\{\-8\}, and gradient clipping at 1\.0\. Theπ0\.5\\pi\_\{0\.5\}run uses weight decay10−810^\{\-8\}, a per\-device batch size of 32, and gradient accumulation of 1\. The StarVLA\-π\\pirun uses DeepSpeed ZeRO\-2 through Accelerate, weight decay10−810^\{\-8\}, and a base\-parameter learning rate of×10−52\.5\\\!\\times\\\!10^\{\-5\}\.

#### Online memory inπ0\.5\\pi\_\{0\.5\}\.

The configured indices specify where VLM outputs are stored rather than the candidate states available at each routing site\. Before action\-expert layerℓ\\ell, the router reads completed boundary outputs withb<ℓb<\\elland additionally reads the layer\-ℓ\\ellinput when it does not duplicate the immediately preceding boundary\. At layer 17, the readable memory bank contains outputs after layers2,5,8,11,142,5,8,11,14and the layer\-17 input\. The layer\-17 output is stored afterward but is not available to downstream routers\. Routing does not modify VLM execution\.

#### Cross\-attention adapter inπ0\.5\\pi\_\{0\.5\}\.

At zero\-based action\-expert layers∈\{0,…,17\}s\\in\\\{0,\\ldots,17\\\}, let𝐀in\(s\)∈ℝB×Ta×Da\\mathbf\{A\}\_\{\\mathrm\{in\}\}^\{\(s\)\}\\in\\mathbb\{R\}^\{B\\times T\_\{a\}\\times D\_\{a\}\}denote the current action state and let𝐕~\(s\)∈ℝB×Tv×Dv\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}\\in\\mathbb\{R\}^\{B\\times T\_\{v\}\\times D\_\{v\}\}denote the token\-aligned mixture over causally available vlm layers, whereDa=1024D\_\{a\}=1024andDv=2048D\_\{v\}=2048\. The selected memory is not provided directly to the native joint\-attention interface\. Instead, each action\-expert layer applies an unshared action\-to\-VLM cross\-attention adapter:

𝐐\(s\)\\displaystyle\\mathbf\{Q\}^\{\(s\)\}=𝐀in\(s\)​\(𝐖q\(s\)\)⊤,\\displaystyle=\\mathbf\{A\}\_\{\\mathrm\{in\}\}^\{\(s\)\}\\left\(\\mathbf\{W\}\_\{q\}^\{\(s\)\}\\right\)^\{\\top\},\(1\)𝐊\(s\)\\displaystyle\\mathbf\{K\}^\{\(s\)\}=𝐕~\(s\)​\(𝐖k\(s\)\)⊤,\\displaystyle=\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}\\left\(\\mathbf\{W\}\_\{k\}^\{\(s\)\}\\right\)^\{\\top\},𝐔\(s\)\\displaystyle\\mathbf\{U\}^\{\(s\)\}=𝐕~\(s\)​\(𝐖v\(s\)\)⊤,\\displaystyle=\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}\\left\(\\mathbf\{W\}\_\{v\}^\{\(s\)\}\\right\)^\{\\top\},𝐒h\(s\)\\displaystyle\\mathbf\{S\}\_\{h\}^\{\(s\)\}=𝐐h\(s\)​\(𝐊h\(s\)\)⊤dh\+ℳ,\\displaystyle=\\frac\{\\mathbf\{Q\}\_\{h\}^\{\(s\)\}\\left\(\\mathbf\{K\}\_\{h\}^\{\(s\)\}\\right\)^\{\\top\}\}\{\\sqrt\{d\_\{h\}\}\}\+\\mathcal\{M\},𝐎h\(s\)\\displaystyle\\mathbf\{O\}\_\{h\}^\{\(s\)\}=softmax⁡\(𝐒h\(s\)\)​𝐔h\(s\),\\displaystyle=\\operatorname\{softmax\}\\\!\\left\(\\mathbf\{S\}\_\{h\}^\{\(s\)\}\\right\)\\mathbf\{U\}\_\{h\}^\{\(s\)\},𝐂\(s\)\\displaystyle\\mathbf\{C\}^\{\(s\)\}=Concath=1H⁡\(𝐎h\(s\)\)​\(𝐖o\(s\)\)⊤,\\displaystyle=\\operatorname\{Concat\}\_\{h=1\}^\{H\}\\\!\\left\(\\mathbf\{O\}\_\{h\}^\{\(s\)\}\\right\)\\left\(\\mathbf\{W\}\_\{o\}^\{\(s\)\}\\right\)^\{\\top\},𝐀pre\(s\)\\displaystyle\\mathbf\{A\}\_\{\\mathrm\{pre\}\}^\{\(s\)\}=𝐀in\(s\)\+𝐂\(s\)\.\\displaystyle=\\mathbf\{A\}\_\{\\mathrm\{in\}\}^\{\(s\)\}\+\\mathbf\{C\}^\{\(s\)\}\.The adapter usesH=8H=8heads withdh=Da/H=128d\_\{h\}=D\_\{a\}/H=128\. Its bias\-free matrices have dimensions𝐖q\(s\),𝐖o\(s\)∈ℝDa×Da\\mathbf\{W\}\_\{q\}^\{\(s\)\},\\mathbf\{W\}\_\{o\}^\{\(s\)\}\\in\\mathbb\{R\}^\{D\_\{a\}\\times D\_\{a\}\}and𝐖k\(s\),𝐖v\(s\)∈ℝDa×Dv\\mathbf\{W\}\_\{k\}^\{\(s\)\},\\mathbf\{W\}\_\{v\}^\{\(s\)\}\\in\\mathbb\{R\}^\{D\_\{a\}\\times D\_\{v\}\};ℳ\\mathcal\{M\}excludes invalid VLM tokens\. The attention is non\-causal and uses zero dropout\. The four matrices are initialized with the default PyTorch linear\-layer scheme,KaimingUniform⁡\(a=5\)\\operatorname\{KaimingUniform\}\(a=\\sqrt\{5\}\), and do not use biases\. The router’s action\-side depth\-query projection is zero\-initialized, so the initial depth distribution is uniform over the available causal states\. All adapter parameters are optimized during fine\-tuning\.

The updated state𝐀pre\(s\)\\mathbf\{A\}\_\{\\mathrm\{pre\}\}^\{\(s\)\}becomes the action\-suffix input to native prefix/suffix joint attention, while the adapter leaves the VLM\-prefix input unchanged at this insertion point\. After native attention, Action\-State Reread is applied before the action FFN\. Training and inference follow the same execution order\. Together, the Q/K/V/O projections, per\-site routers, normalization layers, and Action\-State Reread increase the parameter count by 3\.87% relative to the backbone\.

#### router and action\-state reread\.

The routers pool action and VLM tokens, apply separate LayerNorm operations, and use site\-specific query and key projections\. Both full and router\-only variants use the current action state𝐚\(s\)\\mathbf\{a\}^\{\(s\)\}to construct the router query\. Only the StarVLA\-π\\piinitial\-state control uses the pass\-level state𝐚init\\mathbf\{a\}\_\{\\mathrm\{init\}\}for depth selection \(pass\-level state refers to the incoming action state at the beginning of the forward/denoising pass\); the current action state at each site remains the input to native cross\-attention and its residual stream\. Each router predicts a single sample\- and site\-specific distribution shared across token positions, whereas Action\-State Reread produces token\-specific weights\. Neither read uses an auxiliary loss or an additional expert\.

For StarVLA\-π\\pi, let𝐕~\(s\)\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\}denote the routed VLM representation and let𝐚^\(s\)\\widehat\{\\mathbf\{a\}\}^\{\(s\)\}denote the token\-wise reread action state\. The outputs supplied to downstream sublayers are:

𝐙\(s\)\\displaystyle\\mathbf\{Z\}^\{\(s\)\}=𝐕~\(s\),\\displaystyle=\\widetilde\{\\mathbf\{V\}\}^\{\(s\)\},𝐚out\(s\)\\displaystyle\\mathbf\{a\}\_\{\\mathrm\{out\}\}^\{\(s\)\}=𝐚^\(s\)\.\\displaystyle=\\widehat\{\\mathbf\{a\}\}^\{\(s\)\}\.
Both backbones apply this action\-state assignment at every configured reread site\. In StarVLA\-π\\pi,𝐙\(s\)\\mathbf\{Z\}^\{\(s\)\}replaces the original encoder context, and𝐚out\(s\)\\mathbf\{a\}\_\{\\mathrm\{out\}\}^\{\(s\)\}is passed to the native FFN\. Inπ0\.5\\pi\_\{0\.5\}, the cross\-attention adapter first produces𝐀pre\(s\)\\mathbf\{A\}\_\{\\mathrm\{pre\}\}^\{\(s\)\}; after native joint attention,𝐚out\(s\)\\mathbf\{a\}\_\{\\mathrm\{out\}\}^\{\(s\)\}is likewise passed to the native action FFN\.

#### Action\-state memory locations\.

All layer indices are zero\-based\. In StarVLA\-π\\pi, post\-FFN\-residual action states are retained after the 18 odd DiT blocks\{1,3,…,35\}\\\{1,3,\\ldots,35\\\}\. The pre\-FFN reread at each blockssaccesses detached copies of the initial state, all retained states with indices belowss, and the current post\-attention\-residual state\.

Inπ0\.5\\pi\_\{0\.5\}, post\-FFN\-residual action states are retained after layers\{2,5,8,11,14,17\}\\\{2,5,8,11,14,17\\\}\. The pre\-FFN reread at each layerssaccesses the initial state, all retained states with indices belowss, and the current post\-attention\-residual state\.

## Appendix CCompute Environment

Table[11](https://arxiv.org/html/2609.06079#A3.T11)summarizes the hardware and software configurations used in our experiments\. The two backbone implementations and simulator clients run in isolated environments and communicate through the existing policy server, preserving their native training stacks without modifying optimization or evaluation protocols\.

Table 11:Hardware and software used for the controlled experiments\. For the robot\-policy training stream, both integrations use a per\-device batch size of 32 and gradient accumulation of 1, yielding a global batch size of 256\.#### Cross\-benchmark execution\.

For LIBERO endpoint evaluation, each model is evaluated on 50 episodes per task across all 40 tasks \(2,000 episodes per model\), using base evaluation seed 7\.

For SimplerEnv\([Li et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib29)\), both integrations are trained on the same LeRobot conversions of Bridge\([Ebert et al\. 2021](https://arxiv.org/html/2609.06079#bib.bib1)\)and RT\-1\([Brohan et al\. 2022](https://arxiv.org/html/2609.06079#bib.bib2)\), with equal source probability and benchmark\-specific normalization\. The evaluator preserves the public visual\-matching, variant\-aggregation, and WidowX protocols; only the policy call is replaced by WebSocket communication\. Following the official StarVLA\-π\\piprotocol\([Community 2026](https://arxiv.org/html/2609.06079#bib.bib16)\), we run the complete evaluator five times per reported setting and report the mean success rate\. All five repetitions use the same endpoint checkpoint and do not constitute independent training runs\. Each repetition uses 24 episodes per WidowX task\.

For Google Robot, the per\-repetition episode counts for Coke, Near, Drawer, and Put\-in are 300/240/216/108 under VM and 825/600/378/189 under VA, giving five\-repetition totals of 1,500/1,200/1,080/540 and 4,125/3,000/1,890/945, respectively\. Each repetition follows the same benchmark\-defined episode grid; no additional environment\-seed averaging is applied\.

For RoboCasa\-GR1, both integrations use the same 24\-dataset mixture, equal source probability, and the same 24\-task evaluator with 50 rollouts per task \(1,200 rollouts per model\), without additional environment\-seed averaging\. The StarVLA\-π\\pipath applies its registered 58\-dimensional sine/cosine state transform\. Theπ0\.5\\pi\_\{0\.5\}path concatenates the corresponding 29 raw joint values, discretizes this state into prefix tokens, and pads only the action target to its internal 32\-dimensional width\. The released code provides the training, normalization, policy\-serving, and evaluation commands in the SimplerEnv, RoboCasa\-GR1, andπ0\.5\\pi\_\{0\.5\}code directories\.

Table 12:RoboCasa\-GR1 task\-level success rates \(%\) across 24 tasks\([Nasiriany et al\. 2024](https://arxiv.org/html/2609.06079#bib.bib28)\), obtained from our reevaluation under the common benchmark protocol\. The Average row reports the macro\-average across all 24 tasks\. Bold denotes the highest macro\-average\.

## Appendix DComponent Ablations

Table[13](https://arxiv.org/html/2609.06079#A4.T13)reports additional routing and component controls for StarVLA\-π\\pi\. All variants are fine\-tuned with the same optimization protocol, including updates to the VLM parameters, and use the same data, optimization budget, and evaluation protocol\.

Table 13:Routing and component controls for StarVLA\-π\\pi\. Long gain is measured in percentage points relative to the original static interface\. The initial\-state and current\-state routes differ only in the router query state and retain the same Action\-State Reread module\. The static\-mixture row disables Action\-State Reread and therefore does not isolate routing policy\. Bold denotes the best result in each metric\.
## Appendix EAblation Details

For StarVLA\-π\\pi, letPℓP\_\{\\ell\},ℓ=0,…,17\\ell=0,\\ldots,17, denote the router at theℓ\\ell\-th DiT cross\-attention site, corresponding to zero\-based DiT blocks\{0,2,…,34\}\\\{0,2,\\ldots,34\\\}\. At the beginning of each training forward pass or inference denoising pass,P0P\_\{0\}captures its incoming action state without detachment:

𝐚init=𝐚in\(P0\)\.\\mathbf\{a\}\_\{\\mathrm\{init\}\}=\\mathbf\{a\}\_\{\\mathrm\{in\}\}^\{\(P\_\{0\}\)\}\.
Let𝐕n\\mathbf\{V\}\_\{n\},n∈𝒞=\{1,…,6\}n\\in\\mathcal\{C\}=\\\{1,\\ldots,6\\\}, denote the six token\-aligned VLM states cached after Qwen3\-VL layers\[5,11,17,23,29,35\]\[5,11,17,23,29,35\], and let𝐩V,n=Pool⁡\(𝐕n\)\\mathbf\{p\}\_\{V,n\}=\\operatorname\{Pool\}\(\\mathbf\{V\}\_\{n\}\)denote the corresponding mask\-aware pooled summary\. Every router uses the same candidate set𝒞s=𝒞\\mathcal\{C\}\_\{s\}=\\mathcal\{C\}\. The following definitions cover the controls in Table[13](https://arxiv.org/html/2609.06079#A4.T13)and Table 7 of the main paper, using router dimensiondsel=256d\_\{\\mathrm\{sel\}\}=256:

𝐙static\(s\)\\displaystyle\\mathbf\{Z\}\_\{\\mathrm\{static\}\}^\{\(s\)\}=Φs​\(\{𝐕n\}n∈𝒞s\),\\displaystyle=\\Phi\_\{s\}\\\!\\left\(\\\{\\mathbf\{V\}\_\{n\}\\\}\_\{n\\in\\mathcal\{C\}\_\{s\}\}\\right\),𝐕~mix\(s\)\\displaystyle\\widetilde\{\\mathbf\{V\}\}\_\{\\mathrm\{mix\}\}^\{\(s\)\}=∑n∈𝒞ssoftmax⁡\(𝜷\(s\)\)n​𝐕n,\\displaystyle=\\sum\_\{n\\in\\mathcal\{C\}\_\{s\}\}\\operatorname\{softmax\}\\\!\\left\(\\boldsymbol\{\\beta\}^\{\(s\)\}\\right\)\_\{n\}\\mathbf\{V\}\_\{n\},𝐪ind\(s\)\\displaystyle\\mathbf\{q\}\_\{\\mathrm\{ind\}\}^\{\(s\)\}=𝐖q,d\(s\)LayerNorma\(s\)\(𝐜0\),𝐜0≠𝟎,\\displaystyle=\\mathbf\{W\}\_\{q,d\}^\{\(s\)\}\\operatorname\{LayerNorm\}\_\{a\}^\{\(s\)\}\\\!\\left\(\\mathbf\{c\}\_\{0\}\\right\),\\qquad\\mathbf\{c\}\_\{0\}\\neq\\mathbf\{0\},𝐤n\(s\)\\displaystyle\\mathbf\{k\}\_\{n\}^\{\(s\)\}=𝐖k,d\(s\)​LayerNormV\(s\)⁡\(𝐩V,n\),\\displaystyle=\\mathbf\{W\}\_\{k,d\}^\{\(s\)\}\\operatorname\{LayerNorm\}\_\{V\}^\{\(s\)\}\\\!\\left\(\\mathbf\{p\}\_\{V,n\}\\right\),ℓn,ind\(s\)\\displaystyle\\ell\_\{n,\\mathrm\{ind\}\}^\{\(s\)\}=1dsel⟨𝐪ind\(s\),𝐤n\(s\)⟩,n∈𝒞s,\\displaystyle=\\frac\{1\}\{\\sqrt\{d\_\{\\mathrm\{sel\}\}\}\}\\langle\\mathbf\{q\}\_\{\\mathrm\{ind\}\}^\{\(s\)\},\\mathbf\{k\}\_\{n\}^\{\(s\)\}\\rangle,\\qquad n\\in\\mathcal\{C\}\_\{s\},𝐩a,init\\displaystyle\\mathbf\{p\}\_\{a,\\mathrm\{init\}\}=Pool⁡\(𝐚init\),\\displaystyle=\\operatorname\{Pool\}\\\!\\left\(\\mathbf\{a\}\_\{\\mathrm\{init\}\}\\right\),𝐪init\(s\)\\displaystyle\\mathbf\{q\}\_\{\\mathrm\{init\}\}^\{\(s\)\}=𝐖q,d\(s\)​LayerNorma\(s\)⁡\(𝐩a,init\),\\displaystyle=\\mathbf\{W\}\_\{q,d\}^\{\(s\)\}\\operatorname\{LayerNorm\}\_\{a\}^\{\(s\)\}\\\!\\left\(\\mathbf\{p\}\_\{a,\\mathrm\{init\}\}\\right\),ℓn,init\(s\)\\displaystyle\\ell\_\{n,\\mathrm\{init\}\}^\{\(s\)\}=1dsel⟨𝐪init\(s\),𝐤n\(s\)⟩,n∈𝒞s,\\displaystyle=\\frac\{1\}\{\\sqrt\{d\_\{\\mathrm\{sel\}\}\}\}\\langle\\mathbf\{q\}\_\{\\mathrm\{init\}\}^\{\(s\)\},\\mathbf\{k\}\_\{n\}^\{\(s\)\}\\rangle,\\qquad n\\in\\mathcal\{C\}\_\{s\},αn,init\(s\)\\displaystyle\\alpha\_\{n,\\mathrm\{init\}\}^\{\(s\)\}=exp⁡\(ℓn,init\(s\)\)∑m∈𝒞sexp⁡\(ℓm,init\(s\)\),\\displaystyle=\\frac\{\\exp\\\!\\left\(\\ell\_\{n,\\rm init\}^\{\(s\)\}\\right\)\}\{\\sum\_\{m\\in\\mathcal\{C\}\_\{s\}\}\\exp\\\!\\left\(\\ell\_\{m,\\rm init\}^\{\(s\)\}\\right\)\},𝐕~init\(s\)\\displaystyle\\widetilde\{\\mathbf\{V\}\}\_\{\\rm init\}^\{\(s\)\}=∑n∈𝒞sαn,init\(s\)​𝐕n\.\\displaystyle=\\sum\_\{n\\in\\mathcal\{C\}\_\{s\}\}\\alpha\_\{n,\\rm init\}^\{\(s\)\}\\mathbf\{V\}\_\{n\}\.The native static interface preserves each backbone’s architecture\-fixed VLM pathway and is independent of the current action state\. The reported StarVLA\-π\\pistatic\-mixture control learns one set of action\-independent logits𝜷\(s\)\\boldsymbol\{\\beta\}^\{\(s\)\}per site and disables Action\-State Reread\. The action\-independent query control retains the learned site\-specific projections and content\-dependent keys, but replaces the pooled action representation with the fixed nonzero vector𝐜0\\mathbf\{c\}\_\{0\}, as defined in the main paper\.

The StarVLA\-π\\piinitial\-state route uses𝐚init\\mathbf\{a\}\_\{\\mathrm\{init\}\}only to construct the router query\. Each site retains the same six VLM candidates and site\-specific projections; the current action state remains the input to native cross\-attention and its residual stream\. The initial\-state and current\-state routes use the same Action\-State Reread configuration\.

## Appendix FRouting\-Policy Controls

TheΔLong\\Delta\_\{\\mathrm\{Long\}\}column in Table[13](https://arxiv.org/html/2609.06079#A4.T13)uses the original static interface as the reference\. For StarVLA\-π\\pi, the initial\-state route conditions every router on the action state entering the first router site, whereas the current\-state route uses the action state entering the corresponding cross\-attention site\. Both routes use the same six\-state VLM memory bank and Action\-State Reread, thereby isolating the effect of the router query state\.

The reported StarVLA\-π\\pistatic\-mixture row also disables Action\-State Reread\. Therefore, its comparison with the current\-state route combines the effects of routing dependence and action\-state rereading, and is interpreted only as a component comparison\. For StarVLA\-π\\pi, all routed variants in Table 7 of the main paper retain the same action\-state reread module and differ only in the VLM\-layer routing rule\.

Uniform routing assigns equal weight to all six vlm layers\. The shallow, middle, and deep routes use the\{𝐕1,𝐕2\}\\\{\\mathbf\{V\}\_\{1\},\\mathbf\{V\}\_\{2\}\\\},\{𝐕3,𝐕4\}\\\{\\mathbf\{V\}\_\{3\},\\mathbf\{V\}\_\{4\}\\\}, and\{𝐕5,𝐕6\}\\\{\\mathbf\{V\}\_\{5\},\\mathbf\{V\}\_\{6\}\\\}groups defined in the main paper\. The action\-independent query preserves the router parameterization while removing dependence on the current action state\. The current\-state route outperforms this control by 0\.8 points on both Avg4and Long\. Comparisons among routed variants in Table 7 of the main paper isolate the routing rule, whereas comparisons with the original interface additionally include the effect of action\-state rereading\. In Table[13](https://arxiv.org/html/2609.06079#A4.T13), only the initial\-state versus current\-state comparison controls for the same Action\-State Reread configuration\.

![Refer to caption](https://arxiv.org/html/2609.06079v1/figure_6.png)Figure 7:Real\-world manipulation task setups\. \(a\) PnP evaluates precise object localization, grasping, and placement\. \(b\) Wipe board involves contact\-rich tool interaction and spatial coverage\. \(c\) Clean Table requires longer\-horizon tool\-use manipulation in a cluttered workspace\.### Routing Diagnostics

Figure 2 in the main paper tracks aggregate routing behavior across the four LIBERO\([Liu et al\. 2023](https://arxiv.org/html/2609.06079#bib.bib27)\)suites during training\. The routing statistics largely stabilize by the 20K\-step diagnostic checkpoint, which is used for the subsequent analyses in Figures 3–5\. These diagnostics are separate from the benchmark\-specific endpoint checkpoints used for performance evaluation\.

We group the 18 cross\-attention router sites by zero\-based DiT index:

E1\\displaystyle\\mathrm\{E1\}=\{0,2,4\},\\displaystyle=\\\{0,2,4\\\},E2\\displaystyle\\mathrm\{E2\}=\{6,8,10\},\\displaystyle=\\\{6,8,10\\\},M1\\displaystyle\\mathrm\{M1\}=\{12,14,16\},\\displaystyle=\\\{12,14,16\\\},M2\\displaystyle\\mathrm\{M2\}=\{18,20,22\},\\displaystyle=\\\{18,20,22\\\},L1\\displaystyle\\mathrm\{L1\}=\{24,26,28\},\\displaystyle=\\\{24,26,28\\\},L2\\displaystyle\\mathrm\{L2\}=\{30,32,34\}\.\\displaystyle=\\\{30,32,34\\\}\.Each profile is the arithmetic mean of its three router distributions\. For each router bin, we first average routing distributions across layers and suites, then normalize the resulting distribution over vlm layers\. These analyses characterize aggregate routing behavior and support suite\-level interpretations of how VLM\-layer allocation relates to the visual, semantic, and action\-relevant demands of different task suites; they do not attribute individual rollout failures to a specific vlm layer or routing decision\.

## Appendix GAdditional Experimental Results

### Reporting Conventions and Data Sources

Table 14:Parameter and inference\-latency overheads\. All percentages denote increases relative to the corresponding original static interface\.Table 15:WidowX Visual Matching task success rates \(%\), obtained from our reevaluation under the common benchmark protocol\. Pooled SR is computed from pooled success counts before task\-level rates are rounded\. Bold denotes the highest pooled SR\.
Table 16:Google Robot task\-family success rates \(%\) from our common\-protocol reevaluation\. VM/VA denote Visual Matching/Variant Aggregation\. Aggregate VM and VA are unweighted means across the four task families; Overall SR is their mean\. Bold denotes the highest Overall SR\.

#### Evaluation metrics\.

We use success rate \(SR\) as the primary metric for all manipulation benchmarks, where a rollout is counted as successful if the task\-specific completion criterion is satisfied\. ForNsuccN\_\{\\mathrm\{succ\}\}successful rollouts amongNevalN\_\{\\mathrm\{eval\}\}evaluated rollouts, we computeSR=100​Nsucc/Neval\\mathrm\{SR\}=100N\_\{\\mathrm\{succ\}\}/N\_\{\\mathrm\{eval\}\}\. SR is selected because it directly measures whether the learned policy completes the target manipulation objective, which is the standard evaluation criterion for robot control benchmarks\.

For LIBERO, we report the success rate of each task suite and the unweighted macro\-average across the four suites, denoted as Avg4, whereAvg4=14​∑j=14SRj\\mathrm\{Avg\}\_\{4\}=\\frac\{1\}\{4\}\\sum\_\{j=1\}^\{4\}\\mathrm\{SR\}\_\{j\}\. For SimplerEnv, we report the benchmark\-defined Overall success rate together with the WidowX success rate\. For RoboCasa\-GR1, we report the macro\-average success rate over the 24 evaluated tasks, treating each task equally regardless of rollout count\. Higher values indicate better manipulation performance\. Within each backbone, component variants use identical training and evaluation settings\.

Table[14](https://arxiv.org/html/2609.06079#A7.T14)reports parameter and inference\-latency overheads for both backbones\. The additional latency mainly comes from the router computation and the attention operations introduced by the routing and reread modules\. Latency is measured on the same hardware for all variants with batch size one\. We discard the first 50 warm\-up inference runs and report the average latency over the following 100 inference runs\. The parameter\-count and latency overheads depend in part on the retained vlm layers and action\-state locations, which remain fixed for each backbone\.

All entries in Tables[16](https://arxiv.org/html/2609.06079#A7.T16)and[16](https://arxiv.org/html/2609.06079#A7.T16)are obtained through reevaluation of the displayed models\. Within each benchmark, every model is evaluated under the same protocol used for its corresponding aggregate score\.

## Appendix HReal\-World Experimental Details

#### Robot setup\.

We conduct real\-world experiments using a Franka robotic arm equipped with a parallel gripper\. The policy receives RGB observations and robot proprioceptive states as inputs, following the same observation and action interfaces used during training\. RGB observations are captured using SC3000 mounted around the workspace, and all experiments are conducted in a fixed tabletop manipulation environment\. The control frequency is set to 10 Hz, and the workspace configuration remains unchanged across all trials to ensure consistent evaluation\.

#### Task setup\.

We evaluate LayerRoute on three real\-world manipulation tasks: Pick\-and\-Place \(PnP\), Wipe board, and Clean Table \(Figure[7](https://arxiv.org/html/2609.06079#A6.F7)\)\. These tasks cover complementary manipulation requirements, including object grasping and placement, contact\-rich surface interaction, and longer\-horizon tool\-use coordination\. For each task, we collect 50 demonstration trajectories and fine\-tune bothπ0\.5\\pi\_\{0\.5\}andπ0\.5\+L​a​y​e​r​R​o​u​t​e\\pi\_\{0\.5\}\+LayerRoute\{\}for 20K steps under identical training configurations\.

#### Evaluation protocol\.

All models are evaluated using the same real\-world protocol without additional fine\-tuning\. For each task, we perform 50 independent evaluation trials using the trained checkpoint\. Task success is determined according to task\-specific completion criteria: successful object placement for PnP, successful board wiping for Wipe board, and successful table cleaning for Clean Table\. Reported success rates are computed over the 50 trials for each task\. Detailed hardware specifications, task definitions, training and inference configurations, and evaluation criteria are provided in the Supplementary Material\.

## Appendix ILimitations

LayerRoute introduces additional parameter and inference\-latency overheads in both backbones, which may constrain deployment in resource\-limited settings\. We evaluate LayerRoute on only StarVLA\-π\\piandπ0\.5\\pi\_\{0\.5\}; extending the evaluation to broader VLA architectures and reducing overhead remain important directions for future work\. In addition, LayerRoute relies on access to intermediate VLM and action states, which may require architecture\-specific integration for new VLA designs\.