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CARD: Diagnosing Belief to Action Routing Failures in Vision Language Models

Souptik Kumar Majumdar, Fabian Kögel, Andreas Bulling

arXiv:2608.20763v1cs.CVcs.AI

TL;DR

VLM research has shown that mental-state representations can be encoded, but not whether they drive predictions on other axes, especially cooperative actions. The paper introduces CARD and Relay Chain to test this routing directly, finding that four open-weight VLM families decode belief representations yet fail to use them for action prediction. The authors characterize this as a structural routing failure, while limiting the claim to the evaluated task and models.

  • Problem

    It is unclear whether VLMs’ internal representations of partners’ mental states actually drive downstream predictions on different axes, which matters when cooperative actions depend on those states.

  • Method

    The paper introduces CARD, which steers a representation on one axis and measures a different axis’ prediction, and evaluates it on the Relay Chain cooperative grid-world benchmark.

  • Results

    Across four open-weight VLM families, belief representations causally influence belief and knowledge predictions but not action prediction, despite 78–94% linear decodability.

  • Takeaways & Limitations

    Current VLMs can encode partners’ beliefs well enough to answer belief questions without usefully using those beliefs when asked what to do.

  • Takeaways & Limitations

    The routing failure is demonstrated only on Relay Chain, a 2D grid-world, and four open-weight VLMs; the authors do not claim generality to larger scales, non-cooperative ToM, or real-world video.

Abstract

from arXiv · show

Linear probes and activation steering have uncovered that vision-language models (VLMs) internally represent mental states such as agents' beliefs, knowledge, and intentions. However, it is unclear whether and how these representations are used by downstream predictions along these axes. To close this gap, we introduce Cross-Axis Routing Diagnostic (CARD), which steers activations along one axis while measuring the response of a different axis's prediction. Applied to open-weight VLMs on Relay Chain -- a new cooperative grid-world benchmark we propose -- we diagnose a critical routing failure: models fail to incorporate belief representations into their next action prediction, effectively leaving valuable information about their partners unused.

1 Introduction

CARD addresses whether VLMs’ internal mental-state representations actually influence predictions on different axes, a question left unresolved by behavioural benchmarks, probing, and same-axis steering. It introduces a cross-axis diagnostic and finds belief representations decoded in VLMs but unused for action prediction.

  • Behavioural benchmarks score belief, knowledge, and intent outputs without connecting internal representations to predictions.
  • Existing probes and activation steering test whether a feature affects the same-axis prediction, not whether it routes into action prediction.
  • CARD steers a representation on one axis and measures a different axis’ prediction, using within-axis cells as positive controls.
  • Relay Chain extends cooperative grid-world evaluation with a distinct cooperative action axis for testing belief-to-action routing.
  • 78–94% linear decodability shows belief representations are present, while experiments find they influence belief and knowledge predictions but not action prediction.

2 Related Work

Prior work evaluates mental-state behaviour or inspects encoded representations, but generally does not establish how representations route across prediction axes. CARD builds on these approaches by connecting probing and intervention across axes in multimodal cooperative settings.

  • Behavioural ToM benchmarks evaluate mental-state questions across belief, knowledge, and intentions, including situated multi-agent interactions.
  • SimpleToM reported a gap between explicit and applied ToM, while ToM-SSI reported behavioural decline from percept to belief to intention.
  • Linear probes test whether features are encoded, and standard activation steering tests whether they shift same-feature answers.
  • GridToM brought probing and activation interventions to multimodal grid-world ToM but lacked a cooperative action axis.
  • Random-label controls are used to verify that recovered belief directions are structured rather than probe-expressivity artefacts.

3 Method

CARD probes whether a linearly decodable representation on one axis causally affects predictions on another by steering selected activation directions and measuring cross-axis accuracy changes. The method combines paired-statement probes, polarity-reversed interventions, controls, and counter-scenario evaluation.

  • CARD: CARD identifies a steering vector for one mental-state axis, measures a different axis’ prediction after intervention, and repeats steering in the opposite direction as a control.
  • Probe extraction: Paired matched and negated statements provide activation examples for per-axis logistic-regression probes.
  • Probe extraction: The top-K=56 layer-head pairs ranked by held-out accuracy form the steering pool, with per-head activation standard deviations scaling interventions.
  • Cross-axis intervention: CARD adds a scaled probe direction at the final-token position, then compares TB–FB accuracy gaps under α=+10 and α=−10.
  • Routing diagnosis: A near-zero off-diagonal gap-shift column paired with a non-trivial row indicates that the target prediction is decoupled from the tested direction.
  • Controls: Projection removal subtracts scaled residual projections, with c=1 canonical and c>1 oversubtracting, while mean-accuracy shifts detect uniform answer changes.
  • Evaluation: The evaluation uses 444 scenarios split evenly into disjoint probe and evaluation sets, with accuracy separated by TB/FB and relevant outcome blocks.

4 Dataset and Task

Relay Chain is a three-agent cooperative grid-world designed to make belief-dependent action distinct from belief prediction. It varies what the protagonist observes while preserving trajectories and adds counter scenarios to expose constant-prior shortcuts.

  • Environment: Relay Chain has two lever operators who open sequential gates and a traveller who must cross both to reach the goal.
  • Environment: The task makes optimal action relative to a partner’s perception because no single agent can solve the cooperative relay alone.
  • Scenario representation: Each scenario is a deterministic trajectory tuple with a protagonist, while the VLM receives 4–8 keyframes sampled at relay phases and midpoints.
  • Belief variants: True-Belief and False-Belief layouts preserve trajectories and identities but differ in whether the cooperative event is visible to the protagonist.
  • Counter scenarios: Counter scenarios reverse the event outcome, making safe defaults wrong where they were correct under success-only evaluation.
  • Axes and labels: The benchmark asks binary belief, intent, and knowledge questions, where intent concerns the next cooperative action.
  • Axes and labels: Knowledge controls for observation because its label flips between TB and FB in counter scenarios while belief and intent labels remain constant.

5 Results

The experiments establish that belief is encoded and used for belief and knowledge predictions, but CARD reveals that the same belief direction does not route into intent prediction. Across four VLMs, intent responses remain effectively constant under steering while controls show substantial cross-axis shifts.

  • Positive control: Belief is linearly decodable and behaviorally used on the belief question, ruling out absence or unreadability as explanations for later intent failures.The probe exceeds chance on every VLM, while belief-question behavior tracks event occurrence but not the protagonist’s field of view.
  • Behavioral dissociation: The same models use distinct information across axes: belief questions track world state, knowledge questions track observation, and intent questions collapse to a per-protagonist prior.The intent prior is constant across cells, whereas knowledge responses distinguish whether the protagonist observed the event.
  • CARD diagnosis: Across 36 VLM–protagonist–probe cells, CARD steering substantially shifts belief and knowledge predictions but leaves intent accuracy near its no-steering baseline.The intent null holds across all 12 VLM–protagonist cells, not only lever-operator a1.
  • CARD diagnosis: On a1, 9 of 12 intent flip-rate entries are exactly 0, while the few nonzero entries are at most 15.3% and direction-balanced; belief and knowledge flip many scenarios.This shows the intent null is tight at the scenario level rather than merely an averaging artifact.
  • Interpretation: The authors interpret the dissociation as a structural routing failure: belief is encoded and readable by belief and knowledge predictions, but not used by action prediction.Projection-removal, prompt-resistance, CLEVR, and distributed-token controls address amplitude, prompting, global-hook, and hook-position alternatives.

6 Discussion

The discussion attributes the cooperative-action failure to the intent prediction not using the linear belief direction, despite relevant information being present and used by other predictions.

  • Routing interpretation: The simplest account is that cooperative-action prediction does not use the linear belief direction.Additive steering and projection removal shift belief and knowledge predictions while leaving intent prediction essentially unchanged.
  • Routing interpretation: The failure is specific to intent routing: the prediction varies by protagonist, and the same residual stream supplies belief information used by belief and knowledge predictions.Thus, the intent output is neither globally stuck nor lacking access to the relevant encoded signal.

7 Conclusion and Future work

The paper introduces CARD to distinguish absent mental-state features from encoded but unused ones, and finds a structural belief-to-action routing failure in Relay Chain. The study is limited to one synthetic 2D task and four open-weight VLMs, leaving broader generality and nonlinear readouts open.

  • CARD distinguishes an absent feature from one that is encoded but unused by action prediction.
  • Across Relay Chain, VLMs encode partners’ beliefs well enough to answer belief questions but do not use them when predicting actions.
  • Nonlinear probes remain an open extension that could test whether action prediction reads a subspace missed by linear probes.
  • The routing failure is demonstrated on one 2D grid-world task and four open-weight VLMs.
  • CARD’s mechanistic arms require activation-stream access, so closed-source VLMs are excluded from those analyses.
  • The study does not claim generality to larger model scales, non-cooperative ToM, or real-world video.

A Dataset construction

Relay Chain constructs paired cooperative grid-world scenarios that preserve trajectories and nonprotagonist state while changing protagonists’ perceptual access. The dataset uses success and counter blocks, deterministic labels, paired statements, and disjoint probe/evaluation partitions.

  • 444 scenario bases yield 888 evaluation cases per axis across three protagonist conditions and True-Belief versus False-Belief layouts.True-Belief places the relevant lever within a 5-cell field of view; False-Belief places it beyond that range.
  • Each scenario is a 16–32-step trajectory represented by 4–8 keyframes anchored to relay-phase boundaries.Midpoints are inserted between boundaries, with the last available step used when a phase is unreached.
  • True-Belief and False-Belief layouts share trajectory and event sequence while differing only in the protagonist’s lever position relative to its gate.Nonprotagonist state slices are verified to agree bit-exactly after pair matching.
  • Counter scenarios omit the cooperative event while preserving perceptual access, then recompute binary answers by deterministic enumeration.The traveller stalls before the gate or a lever-holder fails to release the lever at the cooperative deadline.
  • Belief, intent, and knowledge labels separately encode event visibility, recommended action, and perceptual access to determine whether the event occurred.Knowledge depends on visibility rather than actual event occurrence, so success and counter blocks share labels within each layout.
  • Paired-statement activation differences train logistic-regression probes, with top-K selection and CARD evaluation performed on disjoint scenario partitions.The unified 444-scenario partition is split into 222 probe and 222 evaluation scenarios, with three internal seeds.
  • Steering modifies selected last-token self-attention outputs using α ∈ {−10, 0, +10} and training-set projection scale.The top 56 layer-head cells are steered simultaneously, while the remaining forward pass is unchanged.

B.4 Temporal probe accuracy (Qwen2-VL)

The temporal probe analysis finds that Qwen2-VL represents all three cooperative-ToM axes early in the trajectory, while CARD and prompt analyses show intent predictions remain largely insensitive to belief-related interventions.

  • Temporal probe accuracy: Peak probe accuracy reaches 100% from trajectory fraction t=0.25 onward for belief, intent, and knowledge on Qwen2-VL.Mean accuracy varies by axis but remains stable within approximately 1 percentage point across the temporal sweep.
  • Temporal probe accuracy: The temporal sweep is restricted to Qwen2-VL as a single-VLM ablation because each timestep requires a full probe-extraction pass.
  • CARD results: Across the 36-cell CARD sweep, intent accuracy stays near its no-steering baseline while the same hooks substantially shift belief and knowledge predictions.
  • CARD results: Across 108 intent measurements, steering improves intent accuracy by at most 18.7 pp versus 22.9 pp on the belief control.
  • CARD results: The intent answer is invariant to α in 69/108 measurements, and remaining changes favor the constant-prior default rather than belief-conditional behavior.The reported skew is 27 versus 12, with Wilcoxon p = 0.009.
  • CARD heatmaps: CARD heatmaps encode rows as steered axes, columns as queried axes, and cell values as TB−FB gap shifts between α=+10 and α=−10.Large gap shifts do not necessarily indicate improved accuracy; diagonal cells are expected positive controls.
  • Prompt-resistance sweep: No tested prompt variant breaks the preregistered threshold requiring both TB and FB accuracy to exceed 50% for lever-holders.

C.9 Vendor architecture and rigidity ordering

The VLMs differ in decoder rigidity, but CARD’s intent-column null remains informative because probe directions are partially aligned. Positive controls and random-label tests support interpreting the null as routing-specific rather than a broken steering mechanism.

  • The four VLMs differ in decoder architecture and prompt rigidity, with more rigid decoders showing harder-to-move intent answers.
  • Belief–intent probe-direction cosines range from 0.28 to 0.57 across the four VLMs, showing moderate alignment rather than orthogonality.
  • Because belief and intent directions are partially aligned, the intent-column null indicates that intent prediction does not consume the shared subspace.
  • In the CLEVR positive control, steering can move accuracy by up to +60 pp when the model has headroom.
  • In Relay Chain, 9 of 12 lever-holder intent cells are exactly 0.00 on both gap and accuracy shifts, while the three nonzero cells remain bounded.The largest reported shift is |∆gap|=25.0 pp and |∆acc|=13.9 pp.
  • Figure 6 reports CARD baseline-versus-best-steered accuracy by VLM and protagonist, with intent gains null in every cell.Error bars represent standard deviation across three seeds.
  • Random-label probes remain at 47.4–52.0% while true-label probes reach 91.6–100%, yielding selectivity of at least 43.0 pp.

D.4 Lexical-ablation control

Controlled ablations test whether belief probes exploit lexical or visual confounds, while CARD and auxiliary controls assess cross-axis routing. The controls support genuine belief sensitivity but show that intent predictions remain largely unaffected by belief-direction interventions.

  • Confound controls: Controlled ablation arms remove lexical, visual, and clause-only confounds from belief probe training.Arm A equalizes clauses, Arm B uses oracle views and matched captions, and Arm C injects the ignorance clause without a perspective shift.
  • Positive controls: The CLEVR positive control shows cross-axis steering effects, with at least one cell gaining ≥+14 pp on every VLM with available headroom.Gemma and LLaVA obtain +6 to +60 pp gains, while Qwen and InternVL are already at least 96% on shape and colour.
  • Routing diagnostics: Intent gaps remain constant across belief-direction removal strengths, and Qwen2-VL steering changes intent accuracy by at most 0.3 pp across sources and positions.The projection-removal and steering-position tests therefore provide convergent evidence for an intent-column null.
  • Confound controls: Arm B probe accuracy stays within ±2 pp of canonical extraction, while Arm C remains near chance, ruling out lexical and view shortcuts.These results indicate that the probe relies on the belief-true versus belief-false contrast rather than the isolated clause artefact.
  • Polarity diagnostic: The polarity-flip diagnostic distinguishes oracle-like reasoning from constant-prior behavior using the TB−FB gap under reversed question polarity.Qwen a1 preserves the 100→100 pattern, whereas LLaVA a2 collapses, illustrating the two regimes reported across Table 12.

D.6 Scale ablation: Qwen2.5-VL-32B

The scale ablation applies the same CARD pipeline to Qwen2.5-VL-32B and finds the intent routing failure persists despite near-ceiling probe accuracy. Belief and knowledge predictions still respond to the hooks, separating representation recovery from action routing.

  • Probe recovery: Qwen2.5-VL-32B reaches 98.2% belief, 95.9% intent, and 97.5% knowledge held-out probe accuracy.The results are on par with or above those of the 7–8B backbones.
  • Intent routing: At 32B scale, lever-operator a1 intent accuracy remains 30.6% for TB and 100% for FB across all nine probe–α combinations.The invariant response reproduces the constant-prior signature observed in the smaller models.
  • Cross-axis comparison: Belief and knowledge answers move under the same steering hooks, including belief-Q FB accuracy shifting from 96.7% to 98.7% on a3.This contrast shows that the intervention reaches relevant representations even when intent predictions do not change.
  • Scale robustness: The routing failure does not vanish at 4× parameter scale, although the probe recovers the belief direction at ceiling.The experiment uses identical extraction, top-56 steering, and α ∈ {−10, 0, +10} procedures across three probes.
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