Role-Conditioned Sub-Token Routing for Efficient Vision-Language-Action Policies

# Role-Conditioned Sub-Token Routing for Efficient Vision-Language-Action Policies
Source: [https://arxiv.org/html/2608.18410](https://arxiv.org/html/2608.18410)
Wei JiangAffiliation:Futurewei TechnologiesAffiliation:San Jose, CA 95131, USAEmail:[\{wjiang@futurewei\.com](mailto:)Wei WangAffiliation:Futurewei TechnologiesAffiliation:San Jose, CA 95131, USAEmail:[rickweiwang@futurewei\.com](mailto:)

###### Abstract

Vision\-Language\-Action \(VLA\) models process long multimodal token sequences, making inference expensive in both memory and computation\. Existing efficiency methods mainly reduce visual tokens, but aggressive token pruning becomes fragile because removing a token discards its entire representation\. Sub\-token compression provides a complementary alternative by retaining more tokens while reducing their value width\. However, directly applying sub\-token compression to VLA policies is less effective because information important for perception, language understanding, and control is distributed differently across the multimodal representation\.

We introduce Role\-Conditioned Sub\-Token Routing \(RoleSub\), which learns how to compress the value representations of retained tokens\. After visual token reduction, RoleSub partitions each retained value representation into groups in an orthogonal space and uses a lightweight router to determine which groups should be preserved\. The routing decision is conditioned on the token representation, a learned latent role representation, and language context\. The same mechanism can also be applied to language values, allowing visual and language representations to be compressed without removing additional tokens\.

We evaluate RoleSub on OpenVLA\-OFT\-7B across the four LIBERO suites\. At matched visual\-KV budgets, RoleSub outperforms a trained token\-only control in 33 of 36 settings, with the largest gains under aggressive compression\. Combining visual and language compression reduces total KV to 9\.2–11\.3% of the original while retaining strong control performance on most tasks\. These results show that reducing the representation within retained tokens provides an effective complement to token pruning for aggressive VLA compression\.

## 1Introduction

Vision\-Language\-Action \(VLA\) models have emerged as a promising approach to general\-purpose robot control by transferring the perception and reasoning capabilities of large vision\-language models \(VLMs\) to action prediction\. Models such as OpenVLA[5](https://arxiv.org/html/2608.18410#bib.bib1)and OpenVLA\-OFT[4](https://arxiv.org/html/2608.18410#bib.bib2)jointly process visual observations, natural\-language instructions, and robot states to generate manipulation actions, achieving strong performance across a broad range of tasks\. This capability, however, comes with the computational cost of a large multimodal transformer\. At every control step, the policy processes a long prefix dominated by visual tokens, together with language, proprioceptive, and action\-related states\. Reducing the cost of this multimodal context is therefore important for practical VLA systems\.

Existing VLA acceleration methods mainly operate at the token level\. VLA\-ADP[9](https://arxiv.org/html/2608.18410#bib.bib4)and VLA\-Pruner[8](https://arxiv.org/html/2608.18410#bib.bib5), for example, identify visual tokens that are less relevant to the current task and remove them from subsequent computation\. Similar strategies have been extensively studied for VLMs, including FastV[1](https://arxiv.org/html/2608.18410#bib.bib6), VisionZip[12](https://arxiv.org/html/2608.18410#bib.bib7), SparseVLM[14](https://arxiv.org/html/2608.18410#bib.bib8), and FitPrune[13](https://arxiv.org/html/2608.18410#bib.bib9)\. These methods exploit the considerable redundancy among visual tokens and are effective at moderate keep ratios\. Their compression unit is an entire token\. Once a token is removed, all information carried by that token is lost\.

This granularity becomes increasingly restrictive as the budget decreases\. A visual token that appears only moderately important may still contain information needed for object localization, geometric relations, or subsequent manipulation\. Removing the token eliminates all of these signals simultaneously\. The problem is amplified in closed\-loop control: an incorrect action changes the physical state and therefore changes the observations presented to the policy at later steps\. Compression errors that may cause only a local prediction error in a VLM can therefore propagate through an entire VLA trajectory\.

Sub\-token routing provides a complementary way to reduce transformer KV states[3](https://arxiv.org/html/2608.18410#bib.bib15)\. Rather than further reducing the number of retained tokens, it compresses the value representation within each retained token by partitioning the value vector into groups and selecting only a subset of them\. Query and key representations remain unchanged\. Token\-level reduction and sub\-token routing therefore act along two different dimensions: one controls how many token states remain, while the other controls how much value information is retained for each state\. In LLMs and VLMs, combining these two dimensions yields better accuracy–KV trade\-offs than relying on token removal alone, particularly at aggressive compression levels[3](https://arxiv.org/html/2608.18410#bib.bib15)\.

Directly transferring the sub\-token routing to VLA policies, however, leads to a very different result\. In an initial experiment, uniformS=4S\\\!=\\\!4,K=1K\\\!=\\\!1sub\-token routing applied after visual\-token pruning achieves only 43\.8% success on LIBERO\-Spatial\. It indicates that aggressive VLA compression is not determined only by how much information is retained, but also by how that capacity is distributed within the multimodal representation\.

This difference is natural for a VLA policy\. Visual, language, proprioceptive, and action\-related states participate differently in action generation, and even tokens of the same modality may contribute different information depending on the task and control stage\. At the same time, these functions are not expected to occupy known or explicitly separable coordinates of the transformer representation\. It is difficult to predetermine in advance which dimensions correspond to semantics, geometry, temporal context, or control\. A fixed decomposition can easily remove dimensions that become important after interaction with the rest of the network\. What is needed instead is a representation in which the routing structure itself can be learned from the control objective\.

This paper presentsRole\-Conditioned Sub\-Token Routing \(RoleSub\), which extends sub\-token compression with a learned latent decomposition for VLA policies\. For each retained token, the value representation is first transformed into a fixed orthogonal space and partitioned into groups\. A lightweight role estimator produces a soft latent representation that participates in determining which groups are retained\. Importantly, these latent components are not assumed to correspond to predefined or semantically identifiable roles\. Their organization is learned jointly with the policy, allowing the model to discover routing structure that is useful for action prediction\. Group selection also depends on the token representation and the language context, while separate budgets are assigned to different token types\. The orthogonal transformation provides a lossless change of basis, so the representation is altered only through group selection\. This gives the router a structured space in which to learn how limited value capacity should be allocated\.

On OpenVLA\-OFT\-7B across the four LIBERO suites[7](https://arxiv.org/html/2608.18410#bib.bib3), standard training\-free token pruning largely collapses at the aggressive budgets considered in this work\. Since RoleSub is trained jointly with the compressed policy, comparing only against training\-free pruning would not separate the benefit of sub\-token routing from the benefit of adaptation\. We therefore construct a matched\-budget token\-only control using the same training procedure as RoleSub, but without sub\-token routing\. RoleSub outperforms this stronger control in 33 of 36 visual\-KV configurations, with the largest gains appearing under aggressive compression and on long\-horizon tasks\.

The experiments also reveal a strong asymmetry between token\-level and sub\-token compression of language: removing language tokens rapidly degrades control performance, whereas retaining all language tokens and compressing their value representations to one of sixteen groups produces no measurable loss when applied independently\. This suggests that token retention and value\-width retention play different roles in VLA policies\.

Combining visual and language routing reduces the complete multimodal\-prefix KV to 9\.2–11\.3% of its original size while retaining strong performance on most LIBERO suites\. Long\-horizon control remains more sensitive to aggressive language compression, indicating that the appropriate value budget depends on both token type and task demands\.

The main contributions of this work are:

- •We introduce RoleSub, which combines an orthogonal value\-space decomposition, a learned latent role representation, and token\-type\-dependent budgets to adapt sub\-token routing to VLA control\. The latent decomposition is learned jointly from the control objective and does not require predefined or explicitly separable semantic roles\.
- •Under matched visual\-KV budgets, RoleSub outperforms a trained token\-only control in 33 of 36 LIBERO settings, with the largest gains appearing under aggressive compression and on long\-horizon tasks\.
- •We show that token retention and value\-width retention behave differently in VLA policies\. In particular, language tokens are highly sensitive to token removal, while their value representations can be compressed by up to16×16\\timeswithout measurable loss when compressed independently\. Combining visual and language routing further reduces the full multimodal\-prefix KV to 9\.2–11\.3%\.

## 2Related Work

#### Vision\-language\-action models\.

Vision\-Language\-Action models extend pretrained vision\-language representations to robot control by conditioning action prediction on visual observations, language instructions, and robot states\. OpenVLA[5](https://arxiv.org/html/2608.18410#bib.bib1)is a 7B\-parameter open VLA built on a Llama\-2 language model with fused DINOv2 and SigLIP visual features and trained on large\-scale robot demonstrations\. OpenVLA\-OFT[4](https://arxiv.org/html/2608.18410#bib.bib2)improves task adaptation and inference through parallel action decoding, action chunking, continuous action prediction, andℓ1\\ell\_\{1\}regression\. OpenVLA\-OFT serves as the main policy in this work because it provides a strong LIBERO baseline while retaining the transformer structure needed to study multimodal KV compression\.

#### Visual token reduction for VLMs and VLAs\.

A common approach to reducing multimodal transformer cost is to shorten the visual\-token sequence\. In VLMs, FastV[1](https://arxiv.org/html/2608.18410#bib.bib6)prunes visual tokens according to attention patterns observed in early layers, while VisionZip[12](https://arxiv.org/html/2608.18410#bib.bib7)selects informative visual tokens and removes redundant ones\. SparseVLM[14](https://arxiv.org/html/2608.18410#bib.bib8)and FitPrune[13](https://arxiv.org/html/2608.18410#bib.bib9)similarly exploit text relevance or attention structure to reduce visual\-token redundancy\. More recent methods adapt token reduction to VLA policies\. VLA\-ADP[9](https://arxiv.org/html/2608.18410#bib.bib4)combines text\-guided token importance with action\-aware pruning, while VLA\-Pruner[8](https://arxiv.org/html/2608.18410#bib.bib5)incorporates both semantic relevance and action\-related information into visual\-token selection\. These methods operate primarily at token granularity: efficiency is obtained by deciding which visual tokens should remain\. RoleSub instead operates after token selection and reduces the value representation within retained tokens, providing a complementary compression axis when further token removal becomes costly\.

#### KV\-cache and sub\-token compression\.

KV\-cache compression has been studied extensively for long\-context language models\. H2O[15](https://arxiv.org/html/2608.18410#bib.bib11)retains recent and heavy\-hitter tokens, StreamingLLM[11](https://arxiv.org/html/2608.18410#bib.bib12)combines attention sinks with a sliding context, and Quest[10](https://arxiv.org/html/2608.18410#bib.bib10)performs query\-aware selection of relevant cached states\. Other methods reduce the stored representation itself\. MiniCache[6](https://arxiv.org/html/2608.18410#bib.bib13), for example, exploits similarity between KV states across neighboring layers\. Together, these approaches show that useful KV information is distributed nonuniformly across tokens, queries, and model components\.

Sub\-token routing[3](https://arxiv.org/html/2608.18410#bib.bib15)introduces a complementary form of compression by reducing the value width within retained tokens\. Rather than removing additional tokens, it partitions each retained value vector into groups and selects only a subset while leaving the query and key paths unchanged\. Experiments on LLMs and VLMs show that this mechanism can complement token\-level reduction, particularly at small KV budgets\. The VLA setting considered here introduces a different challenge: directly applying uniform sub\-token routing can severely degrade closed\-loop control\. RoleSub addresses this setting by introducing an orthogonal routing space, a learned latent role representation, and token\-type\-dependent value budgets, without assuming that the learned latent components correspond to predefined semantic roles\.

#### Parameter\-efficient adaptation\.

Parameter\-efficient fine\-tuning provides a practical way to adapt large pretrained models without updating the full backbone\. LoRA[2](https://arxiv.org/html/2608.18410#bib.bib14)represents weight updates through low\-rank factors and has been widely used for efficient adaptation of large transformers\. RoleSub trains the routing components together with low\-rank adaptation while keeping the pretrained backbone frozen\. The same adaptation procedure is also used for the matched token\-only control, allowing the effect of sub\-token routing to be separated from the benefit of adapting the policy to compression\.

## 3Method

RoleSub combines token\-level reduction with learned sub\-token routing for multimodal VLA representations\. Token\-level reduction controls which token states remain in the sequence, while sub\-token routing controls how much value information is retained within each surviving state\. These two operations act along different dimensions and can be configured independently for different token types\. For each token selected for sub\-token routing, RoleSub transforms its value representation into an orthogonal routing space and selects a subset of value groups according to the token representation, a learned latent role representation, and the language context\.

Consider a transformer\-based VLA policy withLLattention layers\. At each control step, the policy receives visual observations, a language instruction, proprioceptive state, and action\-related context\. We write the multimodal sequence as

X=\[Xvis,Xlang,Xprop,Xact\]\.X=\\left\[X^\{\\mathrm\{vis\}\},X^\{\\mathrm\{lang\}\},X^\{\\mathrm\{prop\}\},X^\{\\mathrm\{act\}\}\\right\]\.Let𝐡i\(ℓ\)∈ℝd\\mathbf\{h\}\_\{i\}^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{d\}denote the hidden state of tokeniiat layerℓ\\ell, with query, key, and value representations

𝐪i\(ℓ\)=Wq\(ℓ\)​𝐡i\(ℓ\),𝐤i\(ℓ\)=Wk\(ℓ\)​𝐡i\(ℓ\),𝐯i\(ℓ\)=Wv\(ℓ\)​𝐡i\(ℓ\)\.\\mathbf\{q\}\_\{i\}^\{\(\\ell\)\}=W\_\{q\}^\{\(\\ell\)\}\\mathbf\{h\}\_\{i\}^\{\(\\ell\)\},\\qquad\\mathbf\{k\}\_\{i\}^\{\(\\ell\)\}=W\_\{k\}^\{\(\\ell\)\}\\mathbf\{h\}\_\{i\}^\{\(\\ell\)\},\\qquad\\mathbf\{v\}\_\{i\}^\{\(\\ell\)\}=W\_\{v\}^\{\(\\ell\)\}\\mathbf\{h\}\_\{i\}^\{\(\\ell\)\}\.Following sub\-token routing[3](https://arxiv.org/html/2608.18410#bib.bib15), RoleSub keeps the query and key representations unchanged and applies sub\-token compression to the value path\. That is, token\-level reduction changes the number of token states presented to subsequent layers, and value routing changes the amount of value information retained within those states\.

### 3\.1Token\-Level Reduction

Letm∈\{vis,lang,prop,act\}m\\in\\\{\\mathrm\{vis\},\\mathrm\{lang\},\\mathrm\{prop\},\\mathrm\{act\}\\\}denote a token type, and letℐm\\mathcal\{I\}\_\{m\}denote the set of tokens of that type\. For a token type on which token\-level reduction is applied, a selection function assigns each token an importance score

ui=ψm​\(𝐡i,X\),i∈ℐm\.u\_\{i\}=\\psi\_\{m\}\\left\(\\mathbf\{h\}\_\{i\},X\\right\),\\qquad i\\in\\mathcal\{I\}\_\{m\}\.
Given a token\-retention ratiormr\_\{m\}, the selector retains the⌈rm​\|ℐm\|⌉\\left\\lceil r\_\{m\}\|\\mathcal\{I\}\_\{m\}\|\\right\\rceilhighest\-scoring tokens, forming the retained setℐmkeep\\mathcal\{I\}\_\{m\}^\{\\mathrm\{keep\}\}, where⌈⋅⌉\\left\\lceil\\cdot\\right\\rceildenotes the ceiling function\. When token\-level reduction is not applied to typemm,rm=1r\_\{m\}=1and all tokens inℐm\\mathcal\{I\}\_\{m\}are retrained\. RoleSub does not require a particular token\-selection rule and can therefore be combined with different token\-level reduction methods\.

Token retention and sub\-token routing are controlled independently\. For example, A token type may retain all of its tokens while still compressing their value representations\. This allows RoleSub to reduce token count and value width as two distinct compression dimensions\.

### 3\.2Orthogonal Value\-Space Decomposition

For each retained token selected for sub\-token routing, RoleSub first maps its value representation into an orthogonal routing space\. Let𝐯i\(ℓ\)∈ℝdv\\mathbf\{v\}\_\{i\}^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{d\_\{v\}\}denote the value vector of tokeniiat layerℓ\\ell, wheredvd\_\{v\}is the dimensionality𝐯i\(ℓ\)\\mathbf\{v\}\_\{i\}^\{\(\\ell\)\}\. For each layer, we use a fixed orthonormal matrix

R\(ℓ\)∈ℝdv×dv,R\(ℓ\)⊤​R\(ℓ\)=I,R^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{d\_\{v\}\\times d\_\{v\}\},\\qquad R^\{\(\\ell\)\\top\}R^\{\(\\ell\)\}=I,whereIIis thedv×dvd\_\{v\}\\times d\_\{v\}identity matrix\. The value vector is transformed as

𝐳i\(ℓ\)=R\(ℓ\)⊤​𝐯i\(ℓ\),\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}=R^\{\(\\ell\)\\top\}\\mathbf\{v\}\_\{i\}^\{\(\\ell\)\},where𝐳i\(ℓ\)∈ℝdv\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{d\_\{v\}\}is the value representation in the orthogonal routing space\. We divide𝐳i\(ℓ\)\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}intoSSnon\-overlapping groups,

𝐳i\(ℓ\)=\[𝐳i,1\(ℓ\)∣𝐳i,2\(ℓ\)​∣⋯∣​𝐳i,S\(ℓ\)\]\.\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}=\\left\[\\mathbf\{z\}\_\{i,1\}^\{\(\\ell\)\}\\mid\\mathbf\{z\}\_\{i,2\}^\{\(\\ell\)\}\\mid\\cdots\\mid\\mathbf\{z\}\_\{i,S\}^\{\(\\ell\)\}\\right\]\.Assuming equal\-sized groups, each𝐳i,s\(ℓ\)∈ℝds\\mathbf\{z\}\_\{i,s\}^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{d\_\{s\}\}has dimensionds=dv/Sd\_\{s\}=d\_\{v\}/S\.

For tokenii, the router retainsKiK\_\{i\}of theSSgroups\. Let𝐦i\(ℓ\)=\[mi,1\(ℓ\),…,mi,S\(ℓ\)\]∈\{0,1\}S\\mathbf\{m\}\_\{i\}^\{\(\\ell\)\}=\\left\[m\_\{i,1\}^\{\(\\ell\)\},\\ldots,m\_\{i,S\}^\{\(\\ell\)\}\\right\]\\in\\\{0,1\\\}^\{S\}denote the group\-selection mask, wheremi,s\(ℓ\)=1m\_\{i,s\}^\{\(\\ell\)\}=1indicates that groupssis retained andmi,s\(ℓ\)=0m\_\{i,s\}^\{\(\\ell\)\}=0indicates that it is removed\. The mask satisfies

∑s=1Smi,s\(ℓ\)=Ki\.\\sum\\nolimits\_\{s=1\}^\{S\}m\_\{i,s\}^\{\(\\ell\)\}=K\_\{i\}\.
We expand this group\-level mask to the full value dimension as

Mi\(ℓ\)=diag⁡\(mi,1\(ℓ\)​Ids,…,mi,S\(ℓ\)​Ids\)∈ℝdv×dv,M\_\{i\}^\{\(\\ell\)\}=\\operatorname\{diag\}\\left\(m\_\{i,1\}^\{\(\\ell\)\}I\_\{d\_\{s\}\},\\ldots,m\_\{i,S\}^\{\(\\ell\)\}I\_\{d\_\{s\}\}\\right\)\\in\\mathbb\{R\}^\{d\_\{v\}\\times d\_\{v\}\},whereIdsI\_\{d\_\{s\}\}is theds×dsd\_\{s\}\\times d\_\{s\}identity matrix\. The masked representation is then

𝐳~i\(ℓ\)=Mi\(ℓ\)​𝐳i\(ℓ\)\.\\widetilde\{\\mathbf\{z\}\}\_\{i\}^\{\(\\ell\)\}=M\_\{i\}^\{\(\\ell\)\}\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}\.Finally, the routed representation is transformed back to the original value space:

𝐯~i\(ℓ\)=R\(ℓ\)​𝐳~i\(ℓ\)=R\(ℓ\)​Mi\(ℓ\)​R\(ℓ\)⊤​𝐯i\(ℓ\)\.\\widetilde\{\\mathbf\{v\}\}\_\{i\}^\{\(\\ell\)\}=R^\{\(\\ell\)\}\\widetilde\{\\mathbf\{z\}\}\_\{i\}^\{\(\\ell\)\}=R^\{\(\\ell\)\}M\_\{i\}^\{\(\\ell\)\}R^\{\(\\ell\)\\top\}\\mathbf\{v\}\_\{i\}^\{\(\\ell\)\}\.The orthogonal transformation itself is lossless\. If all groups are retained, thenmi,s\(ℓ\)=1m\_\{i,s\}^\{\(\\ell\)\}=1for everyss, soMi\(ℓ\)=IM\_\{i\}^\{\(\\ell\)\}=Iand𝐯~i\(ℓ\)=R\(ℓ\)​R\(ℓ\)⊤​𝐯i\(ℓ\)=𝐯i\(ℓ\)\.\\ \\widetilde\{\\mathbf\{v\}\}\_\{i\}^\{\(\\ell\)\}=R^\{\(\\ell\)\}R^\{\(\\ell\)\\top\}\\mathbf\{v\}\_\{i\}^\{\(\\ell\)\}=\\mathbf\{v\}\_\{i\}^\{\(\\ell\)\}\.Thus, information is removed only through group selection\. The groups are not assigned predefined semantic meanings\. They provide a structured space in which the routing mechanism learns which parts of the value representation to retain\.

### 3\.3Learned Latent Role Representation

To provide an additional learned signal for value\-group selection, RoleSub associates each token with a low\-dimensional latent role representation\. For tokeniiat layerℓ\\ell, RoleSub computes a vector𝐚i\(ℓ\)\\mathbf\{a\}\_\{i\}^\{\(\\ell\)\}through a lightweight role estimator as

𝐚i\(ℓ\)=softmax⁡\(frole\(ℓ\)​\(𝐡i\(ℓ\)\)\)∈ℝC,\\mathbf\{a\}\_\{i\}^\{\(\\ell\)\}=\\operatorname\{softmax\}\\left\(f\_\{\\mathrm\{role\}\}^\{\(\\ell\)\}\\left\(\\mathbf\{h\}\_\{i\}^\{\(\\ell\)\}\\right\)\\right\)\\in\\mathbb\{R\}^\{C\},\(1\)whereCCis the number of latent role components andfrole\(ℓ\)f\_\{\\mathrm\{role\}\}^\{\(\\ell\)\}is the role\-estimation network at layerℓ\\ell\. The vector𝐚i\(ℓ\)\\mathbf\{a\}\_\{i\}^\{\(\\ell\)\}is a soft representation, so a token may participate in multiple latent components\. These components are not assigned predefined semantic meanings\. Instead, their organization is learned jointly with the policy through their contribution to value\-group routing and action prediction\.

### 3\.4Role\-Conditioned Value Routing

For each routed token, RoleSub assigns a routing score to each of theSSvalue groups using three sources of information: the token’s current hidden state, its latent role representation, and the language context\.

First, a token\-state scoring head maps the hidden state of tokeniito group\-level routing scores:

𝜸i,token\(ℓ\)=fv\(ℓ\)​\(𝐡i\(ℓ\)\)∈ℝS,\\bm\{\\gamma\}\_\{i,\\mathrm\{token\}\}^\{\(\\ell\)\}=f\_\{v\}^\{\(\\ell\)\}\\left\(\\mathbf\{h\}\_\{i\}^\{\(\\ell\)\}\\right\)\\in\\mathbb\{R\}^\{S\},wherefv\(ℓ\)f\_\{v\}^\{\(\\ell\)\}is a learned scoring function\. Thess\-th elementγi,token,s\(ℓ\)\\gamma\_\{i,\\mathrm\{token\},s\}^\{\(\\ell\)\}measures the preference for retaining value groupssbased on the current hidden state of tokenii\.

The latent role representation provides a second routing signal:

𝜸i,role\(ℓ\)=Wrole\(ℓ\)​𝐚i\(ℓ\)∈ℝS,\\bm\{\\gamma\}\_\{i,\\mathrm\{role\}\}^\{\(\\ell\)\}=W\_\{\\mathrm\{role\}\}^\{\(\\ell\)\}\\mathbf\{a\}\_\{i\}^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{S\},whereWrole\(ℓ\)∈ℝS×CW\_\{\\mathrm\{role\}\}^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{S\\times C\}is a learned projection from theCClatent role components to theSSvalue\-group scores\. The routing decision also incorporates the current language instruction\. Letℐlangkeep\\mathcal\{I\}\_\{\\mathrm\{lang\}\}^\{\\mathrm\{keep\}\}denote the retained language tokens\. Their hidden states are summarized as

𝐡¯lang\(ℓ\)=Pool⁡\(\{𝐡j\(ℓ\):j∈ℐlangkeep\}\),\\overline\{\\mathbf\{h\}\}\_\{\\mathrm\{lang\}\}^\{\(\\ell\)\}=\\operatorname\{Pool\}\\left\(\\left\\\{\\mathbf\{h\}\_\{j\}^\{\(\\ell\)\}:j\\in\\mathcal\{I\}\_\{\\mathrm\{lang\}\}^\{\\mathrm\{keep\}\}\\right\\\}\\right\),wherePool⁡\(⋅\)\\operatorname\{Pool\}\(\\cdot\)aggregates the language\-token hidden states into a single representation\. A learned language scoring function then produces

𝜸lang\(ℓ\)=flang\(ℓ\)​\(𝐡¯lang\(ℓ\)\)∈ℝS\.\\bm\{\\gamma\}\_\{\\mathrm\{lang\}\}^\{\(\\ell\)\}=f\_\{\\mathrm\{lang\}\}^\{\(\\ell\)\}\\left\(\\overline\{\\mathbf\{h\}\}\_\{\\mathrm\{lang\}\}^\{\(\\ell\)\}\\right\)\\in\\mathbb\{R\}^\{S\}\.The three routing signals are combined to produce the routing score

𝜸i\(ℓ\)=𝜸i,token\(ℓ\)\+αrole​𝜸i,role\(ℓ\)\+αlang​𝜸lang\(ℓ\),\\bm\{\\gamma\}\_\{i\}^\{\(\\ell\)\}=\\bm\{\\gamma\}\_\{i,\\mathrm\{token\}\}^\{\(\\ell\)\}\+\\alpha\_\{\\mathrm\{role\}\}\\bm\{\\gamma\}\_\{i,\\mathrm\{role\}\}^\{\(\\ell\)\}\+\\alpha\_\{\\mathrm\{lang\}\}\\bm\{\\gamma\}\_\{\\mathrm\{lang\}\}^\{\(\\ell\)\},\(2\)whereαrole\\alpha\_\{\\mathrm\{role\}\}andαlang\\alpha\_\{\\mathrm\{lang\}\}control the contributions of the latent\-role and language\-context terms\.

If tokeniiis assigned a budgetKiK\_\{i\}, the router retains theKiK\_\{i\}groups with the highest routing scores\. Because the Top\-KiK\_\{i\}selection is discrete, a straight\-through estimator is used during backpropagation\. The same routing mechanism is applied to different token types, while their value\-group budgets can be controlled separately\.

### 3\.5Token\-Type\-Dependent Value Budgets

The routing scores in Equation[2](https://arxiv.org/html/2608.18410#S3.E2)determine which value groups are useful for a token\. RoleSub additionally allows the number of retained groups to vary across tokens\. This is useful because retained tokens need not require the same amount of value information\. Some tokens may carry information that is more important to the current control decision\.

For each token typem∈\{vis,lang,prop,act\},m\\in\\\{\\mathrm\{vis\},\\mathrm\{lang\},\\mathrm\{prop\},\\mathrm\{act\}\\\},letKmK\_\{m\}denote the target average number of retained value groups out of the totalSSgroups\. The corresponding total group budget for the retained tokens of typemmin the retained setℐmkeep\\mathcal\{I\}\_\{m\}^\{\\mathrm\{keep\}\}is

Bm=Km​\|ℐmkeep\|\.B\_\{m\}=K\_\{m\}\\left\|\\mathcal\{I\}\_\{m\}^\{\\mathrm\{keep\}\}\\right\|\.Rather than assigning exactlyKmK\_\{m\}groups to every token, RoleSub uses the latent role representation𝐚i\(ℓ\)\\mathbf\{a\}\_\{i\}^\{\(\\ell\)\}as a token\-level priority signal for distributingBmB\_\{m\}\. We denote this role\-driven soft allocation by

\{Ki\(ℓ\):i∈ℐmkeep\}=ℬ\(ℓ\)​\(\{𝐚i\(ℓ\):i∈ℐmkeep\},Bm\),\\left\\\{K\_\{i\}^\{\(\\ell\)\}:i\\in\\mathcal\{I\}\_\{m\}^\{\\mathrm\{keep\}\}\\right\\\}=\\mathcal\{B\}^\{\(\\ell\)\}\\left\(\\left\\\{\\mathbf\{a\}\_\{i\}^\{\(\\ell\)\}:i\\in\\mathcal\{I\}\_\{m\}^\{\\mathrm\{keep\}\}\\right\\\},B\_\{m\}\\right\),whereℬ\(ℓ\)\\mathcal\{B\}^\{\(\\ell\)\}is the budget allocator at layerℓ\\ell\. The allocator compares the role\-derived priorities of tokens within the same token type and assigns more value\-group capacity to higher\-priority tokens and less to lower\-priority tokens, subject to

0≤Ki\(ℓ\)≤S,∑i∈ℐmkeepKi\(ℓ\)=Bm\.0\\leq K\_\{i\}^\{\(\\ell\)\}\\leq S,\\qquad\\sum\\nolimits\_\{i\\in\\mathcal\{I\}\_\{m\}^\{\\mathrm\{keep\}\}\}K\_\{i\}^\{\(\\ell\)\}=B\_\{m\}\.That is, the average allocation remainsKmK\_\{m\}even though individual tokens can have different budgets\. WhenKm=SK\_\{m\}=S, all tokens of typemmretain their complete value representations and no within\-type allocation is necessary\. ForKm<SK\_\{m\}<S, the allocator redistributes the available value capacity among tokens while maintainingKmK\_\{m\}for that token type\.

### 3\.6Training

We keep the pretrained VLA backbone frozen and jointly train LoRA adapters[2](https://arxiv.org/html/2608.18410#bib.bib14), the routing functions, and the latent role estimators using the action\-prediction objective\.

LetTaT\_\{a\}denote the number of actions in an action chunk,𝐲t\\mathbf\{y\}\_\{t\}the ground\-truth action at positiontt, and𝐲^t\\widehat\{\\mathbf\{y\}\}\_\{t\}the corresponding prediction\. The training loss is

ℒact=1Ta​∑t=1Ta‖𝐲^t−𝐲t‖1\.\\mathcal\{L\}\_\{\\mathrm\{act\}\}=\\frac\{1\}\{T\_\{a\}\}\\sum\\nolimits\_\{t=1\}^\{T\_\{a\}\}\\left\\\|\\widehat\{\\mathbf\{y\}\}\_\{t\}\-\\mathbf\{y\}\_\{t\}\\right\\\|\_\{1\}\.\(3\)The components of the latent role representation𝐚i\(ℓ\)\\mathbf\{a\}\_\{i\}^\{\(\\ell\)\}are learned jointly with the routing mechanism through their effect on the selected value groups and, ultimately, on the action\-prediction loss\.

## 4Experiments

### 4\.1Experimental Setup

#### Model\.

We use OpenVLA\-OFT\-7B[4](https://arxiv.org/html/2608.18410#bib.bib2), which is built on OpenVLA[5](https://arxiv.org/html/2608.18410#bib.bib1)\. The underlying OpenVLA architecture combines a Llama\-2\-7B language model with fused SigLIP and DINOv2 visual features\. OpenVLA\-OFT uses parallel action decoding, continuous action prediction, action chunking, proprioceptive input, and two camera views\. In our configuration, each control step predicts an eight\-action chunk\. The multimodal prefix contains 512 visual tokens from two camera views, together with language, proprioceptive, and action\-context tokens\. The number of language tokens depends on the instruction\.

#### Token\-level reduction\.

For visual\-token reduction, we use the QK\-based selection mechanism of the VLA\-ADP implementation[9](https://arxiv.org/html/2608.18410#bib.bib4)\. Token importance is computed at the embedding layer\. The retained visual\-token budget is divided evenly between the two camera views\. We evaluate visual retention ratios

rvis∈\{0\.015625,0\.03125,0\.0625\},r\_\{\\mathrm\{vis\}\}\\in\\\{0\.015625,\\,0\.03125,\\,0\.0625\\\},corresponding to 8, 16, and 32 retained visual tokens out of the original 512\.

#### RoleSub configuration\.

The value dimension isdv=4096d\_\{v\}=4096\. For each transformer layer, we use a fixed orthonormal matrixR\(ℓ\)R^\{\(\\ell\)\}initialized from a random Stiefel matrix and kept frozen throughout training\. The transformed value representation is divided intoS=16S=16groups, 256 dimensions each\.

The latent role estimator producesC=6C=6latent components\. The routing score combines the token\-state, latent\-role, and language\-context terms defined in Sec\.[3\.4](https://arxiv.org/html/2608.18410#S3.SS4)\. We set

αrole=αlang=0\.1\.\\alpha\_\{\\mathrm\{role\}\}=\\alpha\_\{\\mathrm\{lang\}\}=0\.1\.For the main visual\-compression experiments, we evaluate

Kvis∈\{1,2,4\},K\_\{\\mathrm\{vis\}\}\\in\\\{1,2,4\\\},\(4\)while language, proprioceptive, and action\-context values remain uncompressed\. We separately varyKlangK\_\{\\mathrm\{lang\}\}in the language\-only and combined experiments\.

#### Training data\.

We train on the no\-op\-filtered LIBERO RLDS data[7](https://arxiv.org/html/2608.18410#bib.bib3)\. The Spatial, Object, Goal, and LIBERO\-10 suites contain 432, 454, 428, and 379 training episodes, respectively\. Image augmentation is enabled during training\.

#### Optimization\.

We keep the pretrained VLA backbone frozen and jointly train LoRA adapters[2](https://arxiv.org/html/2608.18410#bib.bib14), the routing functions, and the latent role estimators\. LoRA is applied to all linear layers with rank 32, scaling 16, and zero dropout\. Training uses AdamW with a learning rate of2×10−42\\times 10^\{\-4\}and an effective batch size of 8\.

The LoRA adapters contain approximately 110\.8M trainable parameters out of 7\.65B total model parameters\. The routing heads add approximately 4\.20M parameters, and the latent role estimator adds approximately 0\.55M parameters\. The orthogonal matrices are frozen and therefore introduce no trainable parameters\.

#### Evaluation\.

We evaluate closed\-loop task success on the four LIBERO suites[7](https://arxiv.org/html/2608.18410#bib.bib3)\. Each suite contains 10 tasks\. Each evaluated checkpoint is run for 50 trials per task\. The simulator configuration and evaluation seed are fixed across compared methods\.

### 4\.2Baselines

#### Uncompressed VLA\.

The dense reference is the official OpenVLA\-OFT checkpoint for each LIBERO suite[4](https://arxiv.org/html/2608.18410#bib.bib2), evaluated using the same configuration as the compressed models\.

#### Training\-free token\-only pruning\.

We apply visual\-token pruning directly to the finetuned VLA without additional training\. This baseline tests whether the aggressive KV budgets considered in this work can be reached simply by removing more visual tokens\.

#### Matched\-budget trained token\-only pruning\.

Because RoleSub is trained jointly with the compressed policy, comparison against training\-free pruning alone would confound the effect of routing with the effect of adaptation\. We therefore construct a trained token\-only pruning using the same LoRA training procedure as RoleSub but without sub\-token routing\.

For a RoleSub configuration with visual\-token retention ratiorvisr\_\{\\mathrm\{vis\}\}and mean value\-group budgetKvisK\_\{\\mathrm\{vis\}\}, each retained visual token uses the full key representation andKvis/SK\_\{\\mathrm\{vis\}\}/Sof the value representation\. The matched token\-only pruning therefore retains

rmatched=rvis​\(S\+Kvis\)/2​Sr\_\{\\mathrm\{matched\}\}=r\_\{\\mathrm\{vis\}\}\\left\(S\+K\_\{\\mathrm\{vis\}\}\\right\)/\{2S\}of the original visual tokens while keeping their complete key and value representations\. This control isolates whether retaining more token locations with compressed values provides an advantage over retaining fewer tokens with complete values at the same visual\-KV budget\.

#### Plain sub\-token routing\.

We also construct a trained sub\-token routing control that retains the same token and value budgets as RoleSub but removes the VLA\-specific routing structure\. It operates directly in the native value basis by settingR=IR=I, removes the latent\-role contribution from the routing score, and assigns the sameKvisK\_\{\\mathrm\{vis\}\}groups to every retained visual token\. This comparison isolates the contribution of the orthogonal routing space, latent role conditioning, and adaptive within\-type budget allocation from the general benefit of reducing values within retained tokens\.

### 4\.3Visual Compression at Matched KV Budget

We first evaluate sub\-token routing on visual representations\. Language, proprioceptive, and action\-context values remain uncompressed\. We vary the number of retained visual tokens and the value\-group budgetKvis∈\{1,2,4\}K\_\{\\mathrm\{vis\}\}\\in\\\{1,2,4\\\}\. For each configuration, the trained token\-only pruning uses the same LoRA training procedure and is matched to the same visual\-KV budget\. Table[1](https://arxiv.org/html/2608.18410#S4.T1)reports the results\.

Table 1:Visual compression at matched KV budgets\. RoleSub retains 8, 16, or 32 of the original 512 visual tokens and varies the mean retained value\-group budgetKvisK\_\{\\mathrm\{vis\}\}\. The trained token\-only pruning retains complete values but uses fewer visual tokens to match the same visual\-KV budget\.Before comparing the two trained methods, we test whether the same aggressive budgets can be reached by applying token pruning directly to the finetuned VLA without additional training\. At the twelve operating points matched to theKvis=1K\_\{\\mathrm\{vis\}\}=1configurations, training\-free token pruning produces zero success in 10 of 12 cases\. The only nonzero results are 29\.0 on Goal and 9\.2 on Spatial at the largest visual budget\. Thus, simply increasing the amount of token pruning is not viable in the compression rate considered here\. We therefore use the trained token\-only model as the primary matched\-budget baseline to compare, so that both methods are adapted under compression\.

From the Table[1](https://arxiv.org/html/2608.18410#S4.T1), RoleSub outperforms the trained token\-only pruning in 33 of 36 matched\-budget settings\. The largest gains appear on LIBERO\-10 and under the smallest visual\-token budgets\. On LIBERO\-10, RoleSub improves over the matched token\-only pruning by as much as 10\.5 percentage points, while the largest Goal improvement is 8\.7 points\.

The three exceptions occur at the 8\-token setting on the near\-saturated Object or Spatial suites, where the differences are only 0\.1–1\.1 points\. At the 32\-token settings, RoleSub is close to the dense policy across Goal, Object, and Spatial while using only 3\.32–3\.91% of the original visual KV\. LIBERO\-10 remains more sensitive to compression, but RoleSub consistently outperforms the matched token\-only pruning across all nine visual configurations\.

### 4\.4Effect of Role\-Conditioned Routing

We next compare RoleSub with plain sub\-token routing atKvis=1K\_\{\\mathrm\{vis\}\}=1\. The plain router uses the same visual\-token pruning and value\-group reduction budgets, but operates in the native value basis \(R=IR=I\) and removes the latent\-role conditioning\. As shown in Table[2](https://arxiv.org/html/2608.18410#S4.T2), RoleSub has more advantages under the more restrictive visual budgets\. With only 8 retained visual tokens, RoleSub improves LIBERO\-10 from 59\.8% to 74\.2%, a gain of 14\.4 percentage points, and improves Goal from 89\.4% to 95\.2%\. At larger visual budgets, the gap narrows as both methods retain more information\. Object and Spatial are less discriminative because both methods already operate close to the success ceiling\.

Table 2:Comparison with plain sub\-token routing atKvis=1K\_\{\\mathrm\{vis\}\}=1\.These results show that plain within\-token value compression is not sufficient to explain the gains of RoleSub\. The additional routing structure becomes most useful when the representation budget is highly constrained, where the policy is more sensitive to how the limited value capacity is distributed\.

### 4\.5Language Token and Value Compression

The above experiments suggest that removing a complete visual token can be much more destructive than reducing the value capacity of a retained token\. We observe an even stronger effect for language\. Directly pruning language tokens causes a sharp loss in performance, motivating us to ask whether the language representation can instead be compressed along the value dimension while preserving the complete instruction sequence\.

We first evaluate language\-token pruning on the Goal suite\. The retained tokens keep their complete key and value representations\. While mild pruning can be tolerated, but performance degrades rapidly once a larger fraction of the instruction tokens is removed\. For example, when 53% of token are retained, the success rate drop to about only 40%\. These results indicate that the policy depends strongly on preserving the language\-token sequence\.

We therefore test a different compression axis\. Instead of removing language tokens, we retain every language token and reduce only its value width usingKlang∈\{8,4,2,1\}K\_\{\\mathrm\{lang\}\}\\in\\\{8,4,2,1\\\}\. Visual, proprioceptive, and action\-context representations remain uncompressed\. Since keys remain full, the language\-KV fraction for a value\-group budgetKlangK\_\{\\mathrm\{lang\}\}is

ρlang=\(1\+Klang/S\)/2\.\\rho\_\{\\mathrm\{lang\}\}=\\left\(1\+K\_\{\\mathrm\{lang\}\}/S\\right\)/\{2\}\.\(5\)As shown in Table[3](https://arxiv.org/html/2608.18410#S4.T3), in contrast to token pruning, language value compression is essentially lossless across the entire sweep\. Even atKlang=1K\_\{\\mathrm\{lang\}\}=1, where each language token retains only one of 16 value groups, performance remains at the dense\-policy level on all four suites\. These results indicate that language\-token positions are critical to the VLA policy, whereas much of the value width associated with those tokens is redundant\.

Table 3:Language\-only value routing withS=16S=16value groups\.
### 4\.6Combined Visual and Language Compression

We next combine visual and language compression in the same model\. Following the visual experiments, we retain 8, 16, or 32 of the 512 visual tokens and apply sub\-token routing to the retained visual tokens withKvis=1K\_\{\\mathrm\{vis\}\}=1\. All language tokens are retained, while their value representations are compressed withKlang=1K\_\{\\mathrm\{lang\}\}=1\. Proprioceptive and action\-context representations remain uncompressed\. The resulting total KV fractions are 9\.2%, 9\.9%, and 11\.3%, respectively\.

Table 4:Combined visual and language compression withKvis=Klang=1K\_\{\\mathrm\{vis\}\}=K\_\{\\mathrm\{lang\}\}=1\. “Visual\-only” uses the same visual\-token retention andKvis=1K\_\{\\mathrm\{vis\}\}=1, but keeps the language values uncompressed\.As shown in Table[4](https://arxiv.org/html/2608.18410#S4.T4), Object and Spatial tasks remain very close to their visual\-only results after language compression is added, with differences between−1\.4\-1\.4and\+0\.7\+0\.7percentage points\. Goal also remains relatively stable, with losses of 0\.8–2\.9 points\. That is, visual and language compression can be reasonably combined on these tasks to reduce the total KV to about 9–11%\.

LIBERO\-10 is quite sensitive to combining the two forms of compression\. AddingKlang=1K\_\{\\mathrm\{lang\}\}=1language\-value compression reduces success by 10\.0–11\.2 points relative to the corresponding visual\-only settings\. This differs from the language\-only experiment in Table[3](https://arxiv.org/html/2608.18410#S4.T3), whereKlang=1K\_\{\\mathrm\{lang\}\}=1causes no measurable loss when the visual representation is not compressed\. The result shows that the effect of language compression depends on how much visual information is also retained\. We examine this interaction further by varying the language value budget in the next subsection\.

### 4\.7Language Budget on LIBERO\-10

We vary the language value budget while keeping the visual routing configuration fixed atKvis=1K\_\{\\mathrm\{vis\}\}=1\. We evaluateKlang∈\{1,8,16\}K\_\{\\mathrm\{lang\}\}\\in\\\{1,8,16\\\}for each of the 8\-, 16\-, and 32\-token visual settings\. Here,Klang=16K\_\{\\mathrm\{lang\}\}=16retains the full language value representation\.

Table 5:LIBERO\-10 success rate with different language value budgets\.Kvis=1K\_\{\\mathrm\{vis\}\}=1in all settings\.As shown in Table[5](https://arxiv.org/html/2608.18410#S4.T5), increasing the language value budget improves LIBERO\-10 performance at all three visual\-token settings\. Moving fromKlang=1K\_\{\\mathrm\{lang\}\}=1toKlang=8K\_\{\\mathrm\{lang\}\}=8improves success by 4\.2, 7\.0, and 7\.2 percentage points for 8, 16, and 32 visual tokens, respectively\. With 32 visual tokens,Klang=8K\_\{\\mathrm\{lang\}\}=8reaches 84\.8%, compared with 87\.6% when the full language values are retained\.

The results also show an interaction between the visual and language budgets\. When only eight visual tokens are retained, increasing the language budget from 8 to 16 groups gives a much larger improvement, from 68\.4% to 83\.6%\. In contrast, with 32 visual tokens, eight language groups already recover most of the performance obtained with full language values\. This suggests that the visual and language representations are not used independently by the policy\. When information from one modality is strongly reduced, the policy appears to rely more heavily on the other\. The observed coupling between the two representations is not explicitly modeled in RoleSub and could be explored in future work, for example through joint cross\-modal budget allocation or routing\.

## 5Limitations

RoleSub learns a latent role representation for routing, but the learned components are not guaranteed to correspond to distinct or interpretable semantic roles\. The current experiments evaluate their usefulness for compression rather than their semantic meaning\.

The visual and language experiments also reveal an interaction between the two modalities\. In particular, aggressive language compression is nearly lossless when applied alone but becomes more costly on LIBERO\-10 when the visual representation is also heavily compressed\. RoleSub currently assigns visual and language budgets separately rather than explicitly optimizing their joint allocation\. Modeling this cross\-modal dependence is an important direction for future work\.

Finally, this work evaluates reduction in retained KV rather than end\-to\-end inference latency\. Realizing the corresponding runtime benefit requires efficient implementations of sub\-token routing and sparse value computation\.

## 6Conclusion

We presented RoleSub, a sub\-token routing method for compressing the KV representations of VLA policies\. Rather than relying only on token removal, RoleSub retains more token locations while reducing the value representation within each retained token\. A learned latent role representation, an orthogonal value\-space decomposition, and token\-type\-dependent budgets guide how the available value capacity is allocated\.

On OpenVLA\-OFT\-7B across the four LIBERO suites, RoleSub consistently outperforms trained token\-only pruning at matched visual\-KV budgets, especially under aggressive compression\. The experiments also show a clear difference between token and value compression: language tokens are difficult to remove, while their value representations can be compressed much more aggressively\.

By combining visual and language compression, RoleSub reduces the total KV to 9\.2–11\.3% of the original while preserving strong performance on most tasks\. The results further indicate that visual and language compression are coupled, particularly for long\-horizon control\. Overall, RoleSub shows that compressing representations within retained tokens provides an effective complement to token\-level reduction for efficient VLA policies\.

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