VERDICT: Training-Free Step-Wise Verification of Multimodal Reasoning via Disagreement-Aware Consensus

Conference: ECCV 2026
Paper: ECCV 2026 Poster 4674
Code: None
Area: Multimodal VLM / LLM Reasoning
Keywords: multimodal reasoning, step-wise verification, multi-agent consensus, training-free verification, coordination game

TL;DR

Addressing error cascade from subtle yet locally plausible hallucinations in multimodal chain-of-thought reasoning, VERDICT introduces a training-free and plug-in step-wise verification framework that casts verification among frozen specialized judges into a coordination game with a closed-form unique Nash equilibrium, leveraging disagreement structure for step filtering and stability ranking to achieve up to a +5.95% accuracy gain across six diverse benchmarks.

Background & Motivation

Multimodal large language models (MLLMs) have demonstrated impressive multi-step reasoning capabilities over images and text. By decomposing complex visual problems into sequences of intermediate reasoning steps, these models can effectively address compositional tasks requiring joint perceptual grounding and deductive inference. However, their generated reasoning chains frequently harbor subtle errors, including unsupported visual assertions, ungrounded spatial assumptions, and logical discontinuities that pass undetected precisely because each intermediate step appears locally fluent and superficially plausible. Crucially, such localized errors propagate through subsequent steps, snowballing into irrecoverable deviations that ultimately derail the final answer.

Existing step-level verification strategies fall into two major paradigms, each constrained by severe limitations. Domain-specific critic models—including process reward models (PRMs) such as VisualPRM, Sherlock, and LLaVA-Critic—evaluate individual reasoning steps using discriminatively trained models. Yet, they require costly labeled step-level supervision gathered via human annotation or exhaustive Monte Carlo rollouts. More critically, they display fragile cross-task generalization: a trained critic that boosts performance on one benchmark often catastrophically impairs accuracy on another due to task-specific inductive bias and capability tension. Meanwhile, training-free aggregation baselines (such as simple score averaging, majority voting, or heuristic variance thresholds) treat all evidence sources symmetrically, completely overlooking the diagnostic value embedded within inter-agent disagreement. For instance, an aggregate mean cannot distinguish unanimous moderate confidence (0.7, 0.7, 0.7) from acute cross-modal conflict (0.9, 0.3, 0.9), even though the latter flags severe latent instability.

In multimodal architectures, inherent capability tensions (such as visual grounding disrupting language fluency, or extended reasoning inducing contextual amnesia) imply that evaluators focusing on orthogonal perspectives can legitimately diverge. When an intermediate reasoning step is genuinely valid, disparate evaluators assessing visual grounding, deductive coherence, and contextual relevance should be able to reconcile their assessments; failure to converge despite mutual awareness indicates that the candidate step is fundamentally brittle. Core idea: formalize step-wise multimodal verification as a coupled scoring coordination game among frozen, modality-specialized judges whose unique closed-form Nash equilibrium captures the structure of cross-modal disagreement, enabling dual-criterion step rejection and stability-conscious continuous ranking without any model training.

Method

Overall Architecture

At each reasoning step \(t\), given an image \(I\), query \(Q\), and the sequence of previously accepted steps \(r_{1:t-1}\), the base MLLM generates \(n\) candidate continuations \(\{r_t^{(1)}, \dots, r_t^{(n)}\}\) via temperature sampling. VERDICT routes each candidate step independently to three frozen, modality-specialized judge agents (Visual, Logical, Contextual). Their raw confidence scores are transformed into coupled consensus scores via a closed-form Nash equilibrium solve of a coordination game. A dual acceptance criterion filters out steps failing either collective endorsement or inter-agent agreement, and the candidate exhibiting the highest consensus confidence is selected to advance the reasoning chain.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Multimodal Context (I, Q, r1:t-1) + Candidate Sampling"] --> B["Orthogonal Specialized Evaluation<br/>Visual / Logical / Contextual Judges"]
    B --> C["Coupled Coordination Game<br/>Closed-Form Nash Equilibrium"]
    C --> D["Dual Acceptance Criterion Filtering<br/>Mean Confidence > τ & Dispersion < ε"]
    D -->|Candidate(s) Accepted| E["Max Consensus Confidence Selection"]
    D -->|All Candidates Rejected| F["Residual Fallback Continuous Ranking<br/>Select via s* - Δ*"]
    E --> G["Append Selected Step rt* to Trajectory"]
    F --> G

Key Designs

1. Orthogonal Specialized Evaluation: Disentangling Multimodal Failure Modes

Conventional unified reward models collapse multimodal signals into a single scalar, obscuring whether an error stems from perceptual hallucination or logical fallacy. VERDICT deploys three frozen MLLM instances prompted with specialized rubrics, operating in complete isolation to output independent scalar confidence scores \(\hat{s}_i \in [0, 1]\): - Visual Agent (V): Checks whether entities, attributes, and spatial relationships asserted in the step are grounded in visible image features, directly penalizing perceptual hallucinations. - Logical Agent (L): Evaluates whether the step logically entails from the established context \(r_{1:t-1}\) and genuinely progresses toward answering the question, targeting deductive gaps. - Contextual Agent (C): Ensures the reasoning step remains strictly aligned with the overarching query, penalizing off-topic speculation and contextual drift. Each agent evaluates without exposure to other agents' assessments, ensuring non-redundant and uncorrelated raw evidence.

2. Coupled Coordination Game: Closed-Form Consensus with Asymmetric Stubbornness

Simple averaging discards the relational topology of who disagrees with whom. VERDICT models the interaction among the \(m\) judges as a coordination game. In reporting an adjusted score \(s_i \in [0, 1]\), each agent \(i\) balances coordination toward the mean of other agents \(\bar{s}_{-i} = \frac{1}{m-1} \sum_{j \neq i} s_j\) against fidelity to its own raw observation \(\hat{s}_i\). The payoff function is defined as: $\(u_i(s_i, s_{-i}) = - (s_i - \bar{s}_{-i})^2 - \lambda_i (s_i - \hat{s}_i)^2\)$ where \(\lambda_i > 0\) represents agent \(i\)'s stubbornness parameter. Higher \(\lambda_i\) indicates greater resistance to peer consensus pressure. Reflecting the inductive bias that visual verification is the least negotiable prerequisite in perception tasks, the parameters are set asymmetrically to \(\lambda_V = 1.5, \lambda_L = 1.0, \lambda_C = 0.8\). Because \(u_i\) is strictly concave (\(\frac{\partial^2 u_i}{\partial s_i^2} = -2(1+\lambda_i) < 0\)), by Rosen's theorem there exists a unique Nash equilibrium governed by the linear system: $\((1 + \lambda_i) s_i^* - \frac{1}{m-1} \sum_{j \neq i} s_j^* = \lambda_i \hat{s}_i, \quad i \in \{1, \dots, m\}\)$ This system admits a direct, non-iterative closed-form solution. The consensus scores strictly preserve the aggregate raw mean (\(\bar{s}^* = \frac{1}{m} \sum_{i=1}^m s_i^* = \frac{1}{m} \sum_{i=1}^m \hat{s}_i\)), ensuring that the game redistributes confidence rather than artificially inflating it. As formalized in Proposition 1, the resulting consensus dispersion cannot be replicated by any separable weighted average, capturing true non-linear cross-modal coupling.

3. Dual Acceptance Criterion and Residual Fallback Ranking

Given the equilibrium scores \(\{s_i^*\}\), VERDICT calculates the mean consensus confidence \(\bar{s}^* = \frac{1}{m} \sum_{i=1}^m s_i^*\) (collective endorsement) and the consensus dispersion \(\Delta^* = \frac{1}{m} \sum_{i=1}^m |s_i^* - \bar{s}^*|\) (residual disagreement). A candidate step is admitted into the accepted set if and only if: $\(\text{accept}(r_t^{(j)}) \iff \bar{s}^{*(j)} > \tau \quad \wedge \quad \Delta^{*(j)} < \epsilon\)$ with fixed thresholds \(\tau = 0.6\) and \(\epsilon = 0.1\). The dispersion threshold \(\epsilon\) weeds out steps where cross-modal evidence remains fundamentally irreconcilable, while \(\tau\) screens out pervasive collective doubt. Among accepted candidates, the step with the highest \(\bar{s}^*\) is selected. In the event that no sampled candidate satisfies both conditions (observed in roughly 15% of steps), the system seamlessly invokes a fallback ranking by \(\bar{s}^* - \Delta^*\), preventing deadlocks while prioritizing the most stable available trajectory.

A Worked Example

Consider two candidate reasoning steps sampled during a 3D spatial reasoning question: - Candidate A (Locally Plausible Visual Hallucination): Evaluator raw scores are \(\hat{\mathbf{s}}_A = (0.9, 0.3, 0.9)\) with raw mean \(0.70\). The visual agent spots a salient object (\(0.9\)), but the logical agent detects a contradiction with preceding steps (\(0.3\)). Under coordination weights \(\lambda_V=1.5, \lambda_L=1.0, \lambda_C=0.8\), the equilibrium yields \(\mathbf{s}^*_A \approx (0.80, 0.55, 0.77)\). While the mean is \(\bar{s}^* \approx 0.71 > \tau = 0.6\), the consensus dispersion is \(\Delta^* \approx 0.11 > \epsilon = 0.1\). The step is rejected due to irreconcilable cross-modal friction. - Candidate B (Consistently Grounded Deductive Step): Evaluator raw scores are \(\hat{\mathbf{s}}_B = (0.7, 0.7, 0.7)\). Here all agents arrive at modest agreement. The equilibrium preserves \(\mathbf{s}^*_B = (0.7, 0.7, 0.7)\), yielding \(\bar{s}^* = 0.70\) and \(\Delta^* = 0.00 < \epsilon\). Candidate B safely passes the dual acceptance filter. Under standard arithmetic averaging, Candidate A (\(0.70\)) might erroneously be preferred over Candidate B (\(0.70\) or slightly lower). VERDICT's coupled dispersion exposes Candidate A's fragility and preserves the faithful reasoning path.

Key Experimental Results

Main Results

VERDICT was evaluated using Qwen2.5-VL-7B-Instruct as the base reasoner across six benchmarks covering 3D spatial reasoning (3DSRBench, CV-Bench-3D), 2D perception and grounding (CV-Bench-2D, AI2D), and multimodal abstraction (BLINK, MMStar). It was benchmarked against leading supervised domain-specific critics and five training-free aggregation baselines.

Method / Strategy	Paradigm	3DSRBench	CV-Bench-3D	CV-Bench-2D	BLINK	MMStar	AI2D	Unweighted Avg.
Base Model	Unverified	56.12	76.39	74.27	48.31	61.25	81.52	66.31
Domain-Specific Critics (Trained)
LLaVA-Critic	Supervised critic	52.71 ±0.83	81.58 ±0.91	67.52 ±0.82	49.22 ±0.77	64.07 ±0.61	81.81 ±0.44	66.15
Critic-V (CVPR 25)	SFT VLM critic	53.25 ±0.73	77.66 ±0.81	75.38 ±0.79	46.17 ±0.86	55.83 ±0.59	80.17 ±0.75	64.74
Sherlock (NeurIPS 25)	Self-correcting critic	48.11 ±0.93	58.13 ±1.10	68.78 ±1.98	49.07 ±0.89	57.26 ±0.96	82.77 ±0.52	60.69
VisionSR1 (ICLR 26)	Self-rewarding model	53.05 ±1.82	54.18 ±1.05	73.10 ±1.91	30.09 ±1.45	57.20 ±2.73	80.25 ±0.97	57.98
DreamPRM (NeurIPS 25)	Reweighted PRM	53.08 ±1.88	63.39 ±0.98	75.58 ±1.61	49.89 ±0.82	61.23 ±0.59	81.21 ±0.49	64.06
Domain-Agnostic Baselines (Training-Free)
Variance	Variance threshold	57.21 ±0.57	78.16 ±0.68	76.43 ±0.53	49.61 ±0.49	63.09 ±0.47	81.41 ±0.34	67.65
Mean	Raw score mean	58.34 ±0.53	79.77 ±0.61	77.57 ±0.51	50.17 ±0.58	64.14 ±0.44	82.18 ±0.36	68.70
Min	Pessimistic lower bound	56.11 ±0.58	77.21 ±0.63	75.17 ±0.59	49.39 ±0.55	62.41 ±0.46	81.09 ±0.42	66.90
Majority	Majority thresholding	57.58 ±0.62	77.37 ±0.73	75.53 ±0.68	48.43 ±0.66	62.10 ±0.52	81.78 ±0.48	67.13
Max	Optimistic upper bound	57.37 ±0.55	78.16 ±0.56	76.46 ±0.63	49.17 ±0.43	63.42 ±0.58	82.12 ±0.54	67.78
VERDICT (Ours)	Closed-form consensus	59.02 ±0.45	82.34 ±0.51	79.22 ±0.53	51.32 ±0.48	65.88 ±0.37	83.14 ±0.32	70.15
Net Gain vs Base		+2.90	+5.95	+4.95	+3.01	+4.63	+1.62	+3.84

Ablation Study

The table below reports the mechanistic decomposition of rejection and selection, the sensitivity of stubbornness parameter assignment, and the disentanglement of judge model scale on 3DSRBench.

Configuration	Mechanism Description	3DSRBench Acc (%)	Delta vs. VERDICT
VERDICT (Full Model)	Dual criterion filtering + max \(\bar{s}^*\) selection	59.02	-
No Rejection	Skip filtering; rank all candidates by \(\bar{s}^* - \Delta^*\)	58.21	-0.81
No Selection	Apply dual filtering; select randomly among accepted	57.18	-1.84
Raw Average	Same dual filtering, using raw mean and raw uncoupled dispersion	56.43	-2.59
Random Baseline	No verification filtering or ranking; uniform selection	56.18	-2.84
Stubbornness Assignment Permutation
Swap L & C (\(\lambda_V=1.5, \lambda_L=0.8, \lambda_C=1.0\))	Visual agent maintains highest stubbornness	58.61	-0.41
Swap V & L (\(\lambda_V=1.0, \lambda_L=1.5, \lambda_C=0.8\))	Logical agent made most stubborn	57.83	-1.19
Swap V & C (\(\lambda_V=0.8, \lambda_L=1.0, \lambda_C=1.5\))	Visual agent given lowest stubbornness	57.26	-1.76
Judge Scale Disentanglement (Base Model = 56.12%)
7B Judges (VERDICT vs Mean)	VERDICT: 59.02% / Mean: 58.34%	59.02	Margin: +0.68
4B Judges (VERDICT vs Mean)	VERDICT: 57.45% / Mean: 56.56%	57.45	Margin: +0.89
2B Judges (VERDICT vs Mean)	VERDICT: 55.68% / Mean: 54.47%	55.68	Margin: +1.21

Key Findings

• Intelligent selection drives higher gains than rejection alone: Eliminating selection (No Selection) induces a significant decline of 1.17 to 2.17 percentage points across tasks, whereas eliminating rejection (No Rejection) leads to a smaller drop of 0.26 to 1.08 points. This indicates that the calibrated consensus ranking metric is the primary performance engine.
• Trained critics exhibit severe cross-domain fragility: Every evaluated supervised critic degraded below the base model on at least two benchmarks. For instance, VisionSR1 collapsed by 22.21 points on CV-Bench-3D and 18.22 points on BLINK, while Sherlock lost 18.26 points on CV-Bench-3D. In contrast, VERDICT achieved strictly positive gains across all six benchmarks.
• Algorithmic resilience under weaker evaluators: When downscaling judges to 2B parameters, naive score averaging drops 1.65 points below the unverified baseline, whereas VERDICT limits degradation to only 0.44 points, expanding its margin over Mean from +0.68 (at 7B) to +1.21 (at 2B). The coupled dispersion filter suppresses noise-induced disagreement inherent in smaller models.

Highlights & Insights

• Turning inter-agent disagreement into a diagnostic asset: Rather than treating disagreement as unstructured variance to be averaged out, VERDICT establishes disagreement patterns as a first-class diagnostic signal that pinpoints localized reasoning instability.
• Closed-form Nash equilibrium eliminates iterative debate overhead: Unlike multi-agent debate frameworks that require costly multi-round communicative dialogue, VERDICT achieves game-theoretic consensus via a single-step linear system solve, providing equilibrium guarantees without runtime latency inflation.
• Broad cross-domain plug-and-play capability: The formulation requires zero base-model modification and generalizes readily beyond MLLMs to reward model ensembles, agent workflow auditing, and code generation verification.

Limitations & Future Work

• Vulnerability to unanimous shared errors: If an invalid step falls into a shared cognitive blind spot where all three frozen agents express confident agreement, the consensus equilibrium will converge onto the flawed premise.
• Upper-bounded by candidate generation quality: If none of the \(n\) sampled continuations contains a factually sound reasoning path, verification filtering can only select the least detrimental candidate via fallback ranking.
• Sequential runtime latency: While token generation overhead is minimal (1-5 output tokens per verification step), unparallelized sequential scoring introduces a 3.80x wall-clock overhead compared to raw generation, highlighting the need for future adaptive verification scheduling.

Related Work & Insights

• vs Multimodal PRMs (VisualPRM, MM-PRM): Supervised PRMs suffer from prohibitive data labeling costs and negative transfer across diverse visual tasks; VERDICT avoids fine-tuning altogether, maintaining strict non-degradation guarantees across all benchmarks.
• vs Training-Free Ensembles (Weaver, Variance Baselines): Conventional aggregators rely on symmetric operations that treat all sources identically; VERDICT incorporates asymmetric coordination dynamics, penalizing unresolved friction from perception-critical agents.

Rating

• Novelty: ⭐⭐⭐⭐⭐ [Pioneers a coordination-game consensus formulation for step-wise verification, turning cross-modal disagreement into an actionable diagnostic signal]
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ [Rigorous evaluation across 6 benchmarks with 10 baselines, paired with mechanistic ablations and judge-scale disentanglement]
• Writing Quality: ⭐⭐⭐⭐⭐ [Clear motivation, mathematically grounded formulation, and insightful analytical discussions]
• Value: ⭐⭐⭐⭐⭐ [A robust, training-free verification framework that provides immediate utility for test-time scaling in multimodal reasoning]