Consensus

A natural way to cut reasoning-model inference cost is to repeatedly probe a single partial trajectory for its current answer and stop once probes agree -- self-consensus. We ask whether any such rule is both safe and token-saving, and whether one can be selected once and reused. A preregistered sweep of 3,520 consensus rules, replayed on frozen trajectories from two models and three benchmarks, clears none of three acceptance gates fixed in advance; the frontier reproduces on a held-out split and on two unseen models -- while a boundary-confidence control (DEER) swept through the same pipeline clears all three. The reason lies in the signal: agreement establishes that the current answer persists under a fixed probing procedure, not that the reasoning has terminated -- a consensus-termination gap. Stopping on it commits non-terminal answers. At a rule still saving 32% of the tokens, one stop in nine fires on an answer the trajectory itself later abandons, and most of those stops cut off a correction it would otherwise have made. Widening the agreement window does not remove them: the share levels off near 7%, and by then the saving has fallen to 8%. Probe re-wording and a hand-labelled error taxonomy show the agreed answer is often a placeholder the model had not settled on. Used on its own as the stop signal, agreement fails not because it is insufficiently strict, but because it repeatedly measures the wrong object.

Many learning systems return a single point estimate even when admissible outputs form disconnected or non-convex sets. Under squared loss, an ambiguous conditional distribution can therefore have a Bayes-optimal conditional mean that is invalid. We formalize this failure as conditional mean collapse and introduce Settling, an equilibrium-based inference operator that separates proposal generation, consistency evaluation, and test-time equilibrium selection. The operator treats a mean-seeking proposal as an initialization and refines it toward a locally stable configuration; conditional on initialization, refinement is deterministic. We establish exact-gradient descent, local convergence, and an inexact-gradient robustness condition relevant to learned consistency critics. In a reproducible 100-context geometric diagnostic, the mean-seeking baseline succeeds in 0/100 contexts, stochastic denoising in 100/100, and Settling in 99/100 while producing substantially lower trajectory roughness. A 1,200-run sensitivity study yields 97-100% success across obstacle-jitter ranges up to 0.20 and 94-100% across one-time initialization perturbations from 0.05 to 0.50. Cross-domain panels remain mechanism illustrations; learned high-dimensional validation remains an open empirical test.

Existing methods for test-time reinforcement learning (TTRL) derive rewards from answer-level self-voting on unlabeled test-time tasks with canonical answers, but this breaks down for code generation because programs cannot be compared by surface form and therefore do not directly provide a usable training signal. To make TTRL applicable to code generation, we propose probe-driven TTRL, which constructs output-free probe inputs from the problem statement, executes candidate programs on these probes, and defines a Probe Consensus Reward (PCR) from the resulting behavioral agreement. PCR provides a behavioral training signal for open-vocabulary programs, but it is not a fully reliable verifier and remains susceptible to reward hacking through spurious consensus. We therefore introduce Entropy-Regularized Rank-Masked Policy Optimization (ERPO), which converts low PCR into conservative negative updates through rank masking and controls policy drift with an entropy ceiling. On coding benchmarks, ERPO substantially improves pass@1 and pass@k in both in-domain adaptation and zero-shot transfer.

Multi-step LLM reasoning lacks a machine-recheckable ledger: discarded reasoning paths leave no auditable record. We propose the Deposon scattering layer, which binds each node of an LLM-generated concept-decomposition graph to a two-parameter Deposon state; paths undergo three-channel scattering -- transmission, reflection, irreversible dissipation -- obeying T+R+A=1 for arbitrary parameters, with a maximum per-path energy-audit deviation of 2.2E-16 (machine epsilon). We report all three evidence tiers honestly. On synthetic trap benchmarks the path-filtering gain is closed (pre-registered): unified reaches 100% versus a decoy-capture baseline at 7%/10%. On real benchmarks the layer is indistinguishable from a trivial six-keyword rule filter (GSM8K 0.87 >= 0.85, McNemar p=0.5; StrategyQA 0.899 = 0.899); no difference is detected here, so we sharpen the claim to "the differential value lies solely in machine verifiability." Fusion yields a second negative result: convex combinations with a semantic prior never improve (physics 0.484 -> 0.452), and the apparent lambda=2 gain is an anti-field artifact; any fusion gain must be nonlinear. Modeling the reverse dynamics as a potential game on the graph, we evidence an auditable scalar's monotonicity and near-gradientness and quantify the empirical coordination ratio (ECR). The three formalized dynamical-equivalence propositions (P1a/P1b/T-P1c) are falsified under the pre-registered kill protocol, and the potential-game claim is downgraded to approximate (cyclic-graph median residual 0.669): only consistency-level evidence survives at the dynamical level. Code: github.com/zeroandcat/Deposon.

Multi-agent federations need governance that answers three questions under adversarial conditions: who participated (identity), did they conform (enforcement), and who decides (authority). A separate question is whether the verification machinery that polices a federation's outputs can also steer a generate-and-test loop toward better answers. Part I. PRIMA introduced prime-power agent identity and a consensus token whose factorization indexes participation, but assumed honest agents. We present PRIMUS, which couples prime-power identity with BLS aggregate signatures (PIAC), derives a safe-kill threshold that reduces false-positive agent termination from 80% to 0.00% under 10% channel noise, gives the closed-form economic boundary where singleton governance outperforms Byzantine quorum ($γ^* \approx 9f$, verified flat across n = 50 to 10,000), and specifies VRF succession with lease and fencing that makes safety unconditional under partial synchrony. Five problems are identified as provably unfixable within the model and stated as scope boundaries. Part II. A verifier is not a solver. We ask whether PRIMA's binary artifact-fidelity verdict can be converted into a graded fitness signal, and measure the conversion on binary covering codes. Calibration against injected fault burden is strong ($ρ$ = 0.676 deterministic, 0.819 full); against real LLM-generated candidates the same scores fall to 0.158 and 0.406, roughly a quarter of the calibration value (the same-designer confound, measured). As a pre-filter it beats a random-score control convincingly and a binary gate narrowly. Under 400 iterations of explicit optimization it was not gamed, but only because the objective saturated after one honest answer. A cross-family judge preserves the burden-ordering signal while destroying individual judgments. No covering-code record resulted. Measured program cost: USD 164.78.

Weakly supervised 3D occupancy prediction reduces the reliance on costly 3D annotations by learning from 2D pseudo-labels generated by vision foundation models. However, existing methods typically use these imperfect pseudo-labels directly as supervision, making occupancy learning vulnerable to erroneous geometric and semantic targets. We observe that agreement across repeated observations provides an inexpensive and reliable cue for assessing pseudo-label reliability. Based on this observation, we propose \textbf{LetOccVote}, a weakly supervised Gaussian-based occupancy framework that leverages cross-frame voting to improve both geometric and semantic supervision. For geometry, Depth Vote exploits cross-frame geometric agreement to refine supported pseudo depth and reject contradictory estimates before volumetric lifting and depth supervision. For semantics, Semantic Vote aggregates pseudo-semantic observations in a shared 3D space to identify reliable and contested evidence, strengthening reliable semantic supervision while filtering unreliable pseudo-label segments. The entire framework is trained solely with 2D pseudo-label supervision without requiring 3D occupancy annotations. On Occ3D-nuScenes, LetOccVote achieves 53.27 IoU and 20.39 mIoU, establishing state-of-the-art performance among methods with 2D pseudo-label supervision.

Bayesian Network (BN) fusion combines multiple input networks into a single structure, balancing dependency preservation with computational tractability. While unrestricted fusion retains all dependencies, it often results in overly complex networks with high treewidth, which affects inference scalability. Limited fusion mitigates this by pruning edges to control treewidth but risks overfitting to input-specific noise and omitting dependencies from the original BNs. This paper introduces a consensus framework that prioritizes shared structures among input networks while enforcing treewidth constraints, ensuring a good consensus. We propose genetic algorithms with advanced initialization, specialized operators, and a tailored fitness function. Additionally, we adapt existing methods to this problem and implement greedy baselines for benchmarking and further optimization. Experiments on synthetic and real-world BNs show the superiority of the proposed genetic algorithms over the adapted methods and greedy baselines.

Multi-agent systems have shown strong performance in domains with reliable verifiers such as coding, where multi-parallel candidate generation selected by a verifier is effective. However, such pipelines would not generalize to open-ended, long-horizon research tasks without a verifier. While majority voting or self-consistency is often used to reach consensus as a proxy verifier, parallel agents repeatedly explore the same evidence, while access to peers' partial findings cause search to converge on an early candidate before alternatives are tested. We present ArcticSwarm, a multi-agent research architecture that separates evidence gathering from evidence integration. Subagents publish findings to a shared bulletin board, while gated isolation lets selected search tasks maintain their own prior, preventing early consensus. Structured review at three commitment boundaries enforce only confident candidates to be propagated. As a result, ArcticSwarm reaches 82.6% on the full BrowseComp-Plus set with the open-weight Qwen 3.5-27B model, compared with 78.8% without gated isolation and 74.5% additionally with structured review disabled, outperforming aligned baseline MiroFlow runs (70.6%). Extending to live-web BrowseComp, ArcticSwarm reaches 73.6% with GPT-5, which is well above the reported provider system (54.9%) and MiroFlow (63.4%). Overall, the results show that restricting peer reads during evidence gathering and strengthening commitment boundaries before a hypothesis is shared can broaden search and improve long-horizon multi-agent deep research.

Information sharing can improve a pooled estimate while eliminating independent rescue actions. This paper separates those effects in exact finite discovery models. A centralized action-budget profile shows that equal one-person accuracy can coexist with different portfolio values. Under a registered incremental-sharing protocol, a sharing step improves discovery exactly when pooled residual error contracts faster than an independent rescue attempt. Exact bounded registries exhibit compression, aggregation, neutral curves, and a bounded zero mixed class. In a two-agent Bayesian game with a hidden mixture of common and independent signal sources, the registered selected equilibrium yields a strict positive sharing interval at signal accuracy 3/5, while alternative equilibria show that the result is selection-dependent rather than universal. The models are synthetic and finite; no human or organizational data are used.

The Rashomon effect is a machine learning phenomenon where equally accurate models produce different predictions for the same inputs (predictive multiplicity). Existing work primarily focuses on multiplicity within individual models, but in more complex decision systems, the impact of the Rashomon effect is less well understood. In this work, we study multiplicity from the perspective of auditing incorrect ensemble predictions, where the decision to divert an instance for human review is based on a consistency criterion that combines the ensemble margin with a measure of local prediction variability for each constituent model. With mild assumptions about stability and smoothness, we show that the consistency scores of finite ensembles converge to the corresponding consistency score of the expected model from the Rashomon set as the ensemble size and the number of samples used to measure local prediction variability increase. To demonstrate the efficacy of the proposed criterion, we evaluate the framework with respect to transformer models applied to natural language understanding tasks and parameter-efficient fine-tuning of large language models used for tabular data classification tasks. Our experiments show that ensembling models from the Rashomon set substantially reduces the risk of incorrect predictions going unchecked compared with auditing a single model, while incurring only a moderate increase in the number of diversions. Moreover, the auditing behavior of the full Rashomon set can be closely approximated by finite ensembles of relatively modest size, with the risk approaching zero for some datasets. We further demonstrate that the proposed measure exhibits stronger agreement with established predictive multiplicity metrics than existing consistency measures, providing a more reliable way to capture multiplicity in the Rashomon set.

Multi-Agent Debate (MAD) has been widely adopted to improve LLM-based evaluation by prompting multiple agents to negotiate and reach a consensus. However, for subjective rubric-based scoring, inter-agent agreement does not guarantee alignment with human judgments. In this paper, we compare a single-judge baseline against a consensus-based MAD protocol on subjective evaluation tasks and design three ablations to isolate the impact of role prompting, multi-round interaction, and explicit score sharing. Evaluations across six LLMs show that the single-judge baseline achieves the strongest human alignment on average across six judge models, whereas MAD shows degradation in human alignment on both tasks. Our ablations demonstrate that this performance drop stems primarily from asymmetric role prompting rather than the interaction itself. Specifically, assigning a strict judge role introduces a systematic downward bias that the consensus process fails to correct. The central finding is that this bias reflects strict-stance dominance beyond averaging: the consensus score falls well beyond the arithmetic midpoint of the standalone strict and lenient conditions, rather than averaging them out. Removing role asymmetry (Symmetric MAD) largely recovers baseline performance, while masking peer scores widens inter-agent disagreement on average and worsens average human alignment. These findings demonstrate that multi-agent consensus can enforce artificial agreement at the expense of true human alignment, revealing a structural limitation in consensus-style, role-specialized MAD protocols for subjective scoring.

Music recommendation relies primarily on two signals: user-item interactions, which fail in the cold-start regime, and intrinsic musical content, available for any recording. We argue that a third, largely untapped signal is both richer and more principled: critical adjacency, the pairwise relation established when an expert critic explicitly links two artists in long-form prose. It encodes deliberate judgments about which artists belong together. Prior work established its internal validity, showing it recovers coherent, interpretable communities and can match collaborative filtering in user-satisfaction simulations, with no user data. What has been missing is external validation: whether this critic-sourced relation is grounded in the music itself versus sociological context. We test it against acoustic content, reframing the question as one of construct validity. Representing artists as empirical distributions over 80 low-level Essentia acoustic descriptors and modeling pairwise proximity via marginal optimal-transport (Wasserstein) distances, we evaluate how far critical adjacency is sonically recoverable under a cold-start, artist-disjoint split. Our ensemble recovers these edges at out-of-sample AUC of 0.767 (95% CI 0.761-0.775). Recoverability rises monotonically with critical consensus, reaching 0.865 on multi-source attested edges. Stratified evaluations align with sociological models of genre: tightly bounded, scene-based genres show higher recoverability than broad industry umbrella terms. Critical discourse is thus a rich source of information for recommendation, decomposing into a reproducible "sonic core" and a "sociological remainder" driven by narrative positioning, subcultural context, and canonical placement. The work offers both a scalable cold-start discovery mechanism and a sociologically grounded approach to MIR and MRS research.

Agreement among repeated samples of a language model is routinely read as evidence about answer reliability, yet wrong answers can agree just as strongly as right ones. This paper asks what information wrong-consensus agreement actually contains, and answers with a quantitative decomposition. A pluralistic agreement index Gamma, normalized by the reference scale d=(1-p)/(C-1), is split into a mechanical component (agreement delivered by a per-case answer preference alone) and a preference-unexplained residual. The mechanical reference is leak-free: each case's preference and accuracy are estimated from its other runs only. On public GPT-4.1 per-run data, coverage phi (the mechanical/empirical ratio) shows a benchmark-associated direction: 0.81-0.93 on multiple-choice GPQA-Diamond against 0.59-0.78 on open-domain AIME, where a residual of 1.54-2.80 Gamma units survives, more than absorbed by a calibrated run-level preference-heterogeneity reference. A controlled replication under one fixed protocol (four runs per question, K=32 votes) on five open-weights checkpoints (Qwen3.5-9B/122B, Qwen3.8-27B, Gemma4-26B/31B) finds near-complete mechanical coverage in all ten cells (phi approximately 1, with a small overshoot consistent with a quantified finite-donor plug-in bias), robust to a two-run design; the largest cell (qwen3.5-122b, p=0.222) sits inside the GPT-4.1 AIME accuracy range and still saturates (phi=1.041). A cross-system contrast at comparable aggregate accuracy contrasts near-complete mechanical agreement in the open-weights models against a larger preference-unexplained residual in the frontier family. This contrast is confounded with sampling protocol by design. Agreement is graded evidence, not certification. No new voting method is proposed; code and evidence are committed.

Agent harnesses combine retrieval, routing, state, provenance, and verification, but locally successful components may disagree on shared state. We model this failure with a finite \emph{capability sheaf}: stalks encode typed behavior signatures, restriction maps retain shared fields, and accepted runs are useful global sections. An exact finite constraint-satisfaction problem (CSP) defines acceptance, while a linearized relative cohomology class provides a diagnostic and search feature. A controlled experiment over 20 task clusters introduces hidden interior mediators whose raw states are nuisance variables. Quotienting their coboundaries reduces the candidate budget from 2,000 to 1,000 per cluster; aligning the hidden state removes the gap. Exact CSP matches the quotient, so the result demonstrates invariance to stale representatives, not superiority over exact reasoning. We then test the method on a discovery split from the SWE-bench Multilingual pool of PatchFuseBench: 160 issues from 20 repositories, 875 real candidate patches, 2,579 source-aware edit atoms, and 153 newly executed patches. A first pool-level construction is constant because $[b-Dx]=[b]$ in $\operatorname{coker}D$ and therefore cannot rank configurations. A candidate-indexed repair is nontrivial on 848/875 candidates and varies within 120/160 issues. It resolves 118 issues versus 116 for a matched noncohomological selector, but the difference is not supported across repositories (exact sign-flip $p=0.75$). A leave-one-repository-out abstention gate reaches 127/160, tying the strong anchor and exceeding its matched gate by one issue ($p=1.0$). The discovery gate therefore fails and the confirmatory split remains sealed. The study supports the controlled invariance mechanism and an identifiability correction, but not a real-world cohomological advantage.

Improving reasoning LLMs requires the ability to judge the quality of long reasoning traces for effective reasoning data curation, strong training signals during reinforcement learning, and an in-depth understanding of reasoning behaviors during model performance evaluation. Additionally, surfacing reasoning mistakes that the model makes would enable improving the model's performance at runtime through providing feedback. Due to the difficulty of this complex task on long reasoning traces, single-model judges (even frontier models) do not do well at identifying reasoning defects. Additionally, leveraging frontier models during online training of reasoning LLMs is generally prohibited due to guardrails in terms of use. In this work, we introduce Reasoning Jury, a system that replaces the single judge with a jury of LLMs and a moderated consensus mechanism, to improve the fidelity of judgments for identifying reasoning defects. In reasoning jury, defects of a reasoning trace and their severity are surfaced through a deliberation where a moderator conducts a discussion amongst the jury where the jurors critique each other's judgments and get to modify their initial votes. The moderator derives a consensus through deliberation amongst jurors or consolidation of judgements. We show that Reasoning Jury with a jury of open-weight models (e.g., gpt-oss-120b) is able to significantly outperform frontier models (opus-4.6, sonnet-4.6, and gemini-3.1-pro) at correctly identifying reasoning defects. Besides accuracy performance improvements, the aggregated cost of the jury (initial verdicts, deliberations, consolidation, etc.) is a fraction (8 to 15%) of the cost of running frontier models in LLM-as-a-judge setup. We also show how these judgements can be leveraged to understand failure modes of reasoning LLMs on benchmarks, which allows much deeper understanding of a model's performance.

Self-consistency (SC) via majority vote is a widely used way to spend inference-time compute: sample N chains of thought, return the plurality answer. On the full GPQA Diamond benchmark (198 graduate-level science questions), majority voting reduces per-problem accuracy on a majority of problems for two instruction-tuned models from different families: 56.6% of problems for Qwen2.5-7B and 65.7% for Llama-3-8B, with Qwen the primary demonstration and Llama corroborating the direction from a near-chance baseline. The effect was pre-registered on a 151-problem confirmatory split after being observed on 47 exploratory problems, and all four confirmatory hypotheses passed. A grid oracle that routes each problem to the best N across {1, 2, 4, 8, 16, 32, 64} marks a theoretical upper bound 14 accuracy points above N = 1 for Qwen and 17 for Llama, an oracle bound requiring ground truth rather than a deployable method. No verifier-free gate reaches it: neither a plurality-agreement gate nor a token-entropy gate moves accuracy more than 0.002 from fixed-budget voting at N = 64. The mechanism is direct: confidence does not track correctness on these problems. In the highest-agreement bin the plurality answer is correct about half the time for Qwen, and for Llama that bin is less accurate than its lowest-agreement bin. We pre-register and confirm these findings on small instruction-tuned models; we do not test reasoning-native models, which we flag as the central open question.

Reinforcement learning with verifiable rewards has been especially effective in mathematics and coding, where answers can be checked automatically. Many open-ended medical questions lack comparably cheap outcome verifiers: responses may be partly correct, incomplete, or contain clinically consequential errors. Rubrics written or validated by physicians offer strong clinical grounding, but involving experts in every instance is costly. Model-generated rubrics make this supervision scalable. We introduce ConRub-Med to preserve useful distinctions as rubric feedback moves from construction to policy optimization. For each prompt, three heterogeneous language models propose atomic criteria independently; a separate model reviews them, retaining only criteria with semantic support from all three generators. Three-State scoring distinguishes correct coverage, missing information, and incorrect claims. Errors receive negative rather than zero credit. When every response in a complete Group Relative Policy Optimization (GRPO) group receives the same final reward, a pairwise judge provides sequence advantages only if both candidate orders agree, without changing the scalar rewards. Groups without ties use vanilla GRPO. In a blinded study matched by question, two medical experts rate panels from the full pipeline as more clinically relevant than panels produced by one generator. Across the evaluated open models, ConRub-Med ranks first on six of nine benchmarks and achieves the highest medical and generalization averages. Using the resulting rubric dataset of 5,166 prompts, it scores $38.98 \pm 1.04$ (mean $\pm$ SD) on HealthBench-Hard, compared with InfiMed-ORBIT's 33.60 with 8,000 samples and 37.30 with 28,000.

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Existing approaches either require expensive labelled supervision with inconsistent cross-task performance or aggregate scores from multiple sources by simple aggregations, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We formalise this as a coupled scoring problem among disparate, frozen verifiers, interpretable as a coordination game with a unique closed-form equilibrium where agreement signals valid steps while disagreement reveals instability. Towards this end, we propose a training-free domain-agnostic step-wise verification approach we call VERDICT: VERification via Disagreement-Informed Coupled Thresholding. To our knowledge, VERDICT is the first training-free verifier that makes the structure of cross-modal disagreement explicit and actionable. It computes consensus scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, \method consistently improves over the base model by up to +5.95%, and performs competitively with domain-specific critics that demand extensive supervision, demonstrating that cross-modal agreement provides robust verification signals without task-specific adaptation and Training-Free Verification

Test-time scaling often uses an external verifier, such as compilers and test cases in coding or trained value functions in robotics applications, to obtain high-quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because we do not have access to such high-quality verifiers in many real-world applications. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and tasks. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning, as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

Large language models can write parametric CAD programs from a natural-language description (text-to-CAD generation), but a single sample is often wrong. Increasing test-time compute by sampling multiple candidates only helps if a good candidate can be identified, yet no ground-truth model is available at generation time. Existing systems often require a separate verifier, such as a vision-language judge, to select among candidates. We investigate whether the candidate pool itself provides enough signal for effective selection and a verifier-free alternative. We introduce 3D CAD consensus selection, hereafter consensus selection: sample $N$ parametric CAD programs, compile them to 3D models, and return the candidate that agrees most with the rest of the pool. The method is training-free and compatible with existing CAD agents. We investigate geometric and topological notions of agreement, each of which improves its corresponding evaluation metric. On the exact candidate pools of a state-of-the-art CAD generation method, geometric consensus improves all three geometric metrics over the method's verifier, while topological consensus matches it on topology. Across every tested LLM and prompt variant, geometric consensus also improves geometric accuracy over random selection from the same pool, reducing Chamfer distance by $1-10\%$.

Cooperative capabilities in language models are dual-use. The same social reasoning that supports civic deliberation can also enable strategic omission, false consensus, and manipulative framing. We argue that Cooperative AI evaluations should separate what models can do under benign instructions from what they tend to do under realistic civic pressure. We introduce DiffCoop-Civic, a 10-scenario pilot evaluation suite spanning preference understanding, evidence and persuasion, commitment design, asymmetric information, and dissent preservation. Across seven models from four model families, subtle omission pressure produces a near-uniform shift: manipulative enablement rises by 1.17 points and dissent preservation falls by 1.67 points on a 5-point scale. Overt false-consensus pressure behaves differently: it triggers refusal or redirection in some aligned API models, but direct compliance in several open-weight models. A lightweight Pareto-Trace prompting intervention improves pressure robustness without simply relying on hard refusal. An anonymous reproducibility package is available at https://anonymous.4open.science/r/diffcoop-civil-771C.

Text-based person anomaly search requires retrieving real-world pedestrian images from detailed natural-language descriptions using models trained primarily on synthetic data. This Sim2Real setting is particularly challenging because visually similar candidates may differ only in subtle actions, object interactions, or appearance attributes, while applying multimodal large language models to the entire gallery is computationally expensive. We propose an anchor-constrained coarse-to-fine retrieval framework that combines global semantic matching with fine-grained verification. First, each query is represented by its original caption, a structured concatenation, and several semantic facets. Heterogeneous vision-language retrievers are then integrated through robust per-query score calibration and soft claim-aware fusion. Full and concatenated captions serve as anchors to preserve candidate recall, whereas appearance, action, and object facets provide bounded corrective evidence. The resulting candidate pool is further refined by a discriminative Qwen3 reranker and two complementary semantic verification modules based on anomaly-aware cloze completion and multi-agent evidence reasoning. Finally, an uncertainty-gated consensus module adaptively reweights the three experts on ambiguous queries. Experiments on the PAB benchmark show that the proposed soft claim-aware retrieval achieves 86.44% mAP@10, substantially outperforming individual retrieval backbones. The complete framework further improves performance to 95.41% mAP@10, 94.44% R@1, and 99.09% R@5. These results demonstrate that preserving strong global retrieval while restricting expensive semantic reasoning to a small candidate pool is effective for fine-grained Sim2Real person anomaly search. Our code will be available on Github.

On unlabeled test data, reinforcement learning lacks a ground-truth reward; test-time RL methods derive one from the model's own roll-outs, rewarding those that match the majority vote over $N$ sampled answers. That vote discards a correct answer whenever it is a minority and scores every majority-matching roll-out identically. We replace it with \emph{CoRE} (Consensus Rewards via Equilibrium): the $N$ roll-outs form a graph whose edges combine answer agreement, reasoning similarity, and generation confidence, and replicator dynamics extract its dominant set, yielding a refined pseudo-label, a graded per-roll-out reward, and a per-question cohesiveness gate. CoRE strictly generalizes voting: majority voting is recovered as a special case; a block-value analysis gives a sharp threshold for when consensus recovers a correct minority against a larger wrong plurality; and confidence calibration provably lowers that threshold multiplicatively. Across seven backbones and five benchmarks (42 model--benchmark cells, three seeds each), \emph{CoRE} improves the untrained base by $+21.7$ points on average versus $+20.4$ for majority-vote TTRL, wins wherever agreement is contestable with margins over the vote of up to $+7.5$ points, and reaches the voting baseline's plateau accuracy in $54$--$70$% fewer steps. Consensus, not counting: treating the roll-out group as a graph rather than a ballot box turns a brittle vote into a calibrated, graded, self-supervised reward at no extra roll-out cost.

Cross-view geo-localization is challenging due to drastic viewpoint changes and large appearance discrepancies between street-level and satellite imagery. Although existing methods often use geometric warping to expose co-visible cues, such transformations rely on restrictive spatial assumptions and inevitably introduce severe visual distortions under view-dependent visibility, yielding noisy supervision and fragile correspondences. To overcome this, we propose a novel joint-view consensus-guided learning framework that entirely bypasses explicit geometric warping. Instead of forcing rigid spatial alignment, we dynamically mine and adaptively strengthen a semantic consensus directly within the feature space. Specifically, an auxiliary joint-view pathway during training enables direct cross-view interaction, allowing each view to selectively aggregate corroborative evidence into a unified consensus representation. To resolve feature heterogeneity among the single- and joint-view streams, we introduce global pattern probes acting as a semantic dictionary to project divergent modalities into a strictly aligned metric space. Guided by a consensus-mediated contrastive objective, single-view embeddings are explicitly pulled toward the joint-view anchor during training, distilling this consensus-mining capability into the single-view encoders for robust retrieval at inference. Extensive experiments demonstrate that our method achieves state-of-the-art performance across four standard benchmarks, underscoring the importance of discovering cross-view semantic consensus for reliable geo-localization.

Decentralized intelligence systems with heterogeneous devices and limited coordination increasingly rely on decentralized federated learning (DFL). However, DFL suffers from convergence inefficiency under data heterogeneity due to the use of a uniform learning rate (LR) that ignores layer-specific optimization needs. Foundational layers are responsible for maintaining network consensus, while specialized layers adapt to local data characteristics, leading to conflicting gradients and degraded performance under non-IID conditions. To address this fundamental tension, this work introduces FedA2L, a method that dynamically adjusts layer-wise LRs based on model divergence signals. By leveraging local update intensity and network consensus constraints, FedA2L seamlessly integrates into existing DFL protocols without additional communication or coordination. Extensive evaluations across DFL algorithms, various model architectures, and datasets demonstrate that FedA2L achieves up to 4.94 times faster convergence than vanilla DFL and reduces communication rounds by up to 59% compared to scheduler-based baselines. Furthermore, FedA2L exhibits resilience to severe data heterogeneity, larger network sizes, and sparse topologies, reducing communication overhead and establishing it as a versatile optimization tool for resource-constrained or large-scale distributed learning in edge and IoT deployments. The code is released at https://github.com/nclabteam/FedA2L.

On-policy self-distillation improves language-model reasoning by querying a teacher on states actually visited by the student. Recent methods create a powerful information asymmetry by exposing the teacher to privileged context, yet they fundamentally rely on external supervision---such as gold solutions or verifiers---to construct this advantage. We introduce CoDA (Consensus and Disagreement Alignment), a fully unsupervised framework that creates reliable privileged information entirely from the latent uncertainty structure of a model's own unlabeled rollouts. CoDA extracts two complementary signals. In the positive branch, answer-level consensus identifies a stable reasoning mode, which conditions a frozen self-teacher to provide dense distributional guidance on fresh student trajectories. However, because agreement does not guarantee correctness, positive-only distillation risks amplifying correlated errors into a false consensus. To break this harmful feedback loop, CoDA incorporates a negative branch that exploits disagreement: minority trajectories are treated as unstable alternatives and gently penalized via a reference-anchored, KTO-style calibration objective. This unpaired binary feedback provides robust regularization without requiring the strong assumption that the consensus is the absolute ground truth. Empirical evaluations on competition-level mathematical benchmarks demonstrate that CoDA significantly improves reasoning, outperforming self-generated baselines and effectively stabilizing training against erroneous consensus.

Multimodal LLM judge panels can cross-reference peers, but a quoted peer judgment may itself be untrusted. We expose source-blind anchoring as a text-level attack surface in vision-language model (VLM) panels. Quoting independent visual judgments creates large anchoring gaps (19--26 percentage points) under both self and peer framing. A matched-content, label-only control changes the broken rate by only $-0.17$pp (95% CI $[-0.68,0.35]$), showing that the self/peer label itself does not explain the effect. Under our tested construction, deliberately generated, concise wrong quotes overturn originally-correct verdicts 1.5--2.7$\times$ more often than naturally occurring wrong peer statements, with bootstrap 95% CIs excluding parity across two datasets and seven VLM judges. Because the two statement populations differ in selection and form, this ratio measures differential damage under the tested attack rather than a provenance-only causal effect. We then introduce panel-consensus verification, which cross-checks a quote against independently collected blind votes. It blocks 84.9% of fabricated attacks, cuts their net harm by 97.5%, and preserves the positive but statistically inconclusive point estimate for genuine peer information under leave-one-out re-verification. These results identify a low-cost attack surface and a concrete defense for safer multimodal collaborative evaluation.

Average-reward reinforcement-learning regret is known up to logarithmic factors, but the numerical content of published guarantees is difficult to compare because probability mode, structural parameter, logarithmic normalization, prior information, and planning assumptions differ. We introduce a constant-aware comparison protocol and derive an explicit finite lower certificate for communicating MDPs. The construction is a binary tree of two-state blocks; its proof uses exact trajectory-level Bernoulli KL divergence and keeps action budget, diameter, occupancy, navigation cost, and terminal bias explicit. A common closed-form envelope improves the published coefficient $0.015$ across a finite frontier: $0.0200$ in a moderate regime and up to $0.0291$ under stronger action, diameter, and horizon conditions, a $94\%$ increase. The limiting coefficient is $\frac1{32}\sqrt{(A-3)/A}$. For upper bounds, we give an auditable composition rule for a span-constrained optimistic learner, but do not claim a coefficient while adaptive directional-variance and planning certificates remain open. We also formalize valid expectation conversion and constant comparability. Controlled diagnostics test diameter dependence, bonus-by-width interactions, span misspecification, and the finite lower certificate on its exact family.

A model's agreement across perturbed inputs is used both as a label-free reliability signal and as a self-training target, on the premise that agreement tracks correctness. That coupling is rarely measured directly: natural-image perturbations preserve meaning only by assumption, and no exact answer key localizes errors. Scientific figures remove both obstacles, a figure is drawn from data by a program, so redrawing it yields images that are semantically equivalent by construction and share a programmatically exact answer. We build RENDEQ, a generator of such render-equivalence sets, and measure the coupling on three open-weight VLMs, checking every finding across three independent instantiations. Re-rendering beats resampling on both accuracy and reliability. Agreement beats an evidence-carrying baseline, mean token log-probability, on two of three models and ties on the third, reversing an intermediate, buggy replication traced to a rendering-pipeline failure. The dispersion behind this is concentrated in one style factor, the plotting library, more than double the next-largest factor and an order of magnitude above the noise floor. Fine-tuning on the model's own cross-render consensus inverts: accuracy falls in every one of five replication runs, the opposite sign to published results on natural images. Agreement certifies correctness only above a threshold set by how diffuse a model's errors are, and an objective that rewards agreement destroys exactly that diffuseness.

Test-time reinforcement learning (TTRL) improves the reasoning capabilities of large language models without labeled data by updating the policy with pseudo-labels constructed through majority voting. While effective, the reward signal assigned from majority voting is highly sensitive to consensus strength, defined as the frequency of the most common answer within a rollout group. In TTRL, consensus strength plays a dual role: it reflects both the reliability of the pseudo-label and the distribution of advantages. Low consensus can amplify updates from unreliable pseudo-labels through disproportionately large advantages, whereas high consensus reduces reward contrast and ultimately yields vanishing gradients. In this paper, we introduce Hi-TTRL, a test-time reinforcement learning framework that utilizes hints during sampling to regulate rollout consensus strength. Hi-TTRL first estimates consensus strength from a partial rollout group. When the consensus strength falls outside a target interval, it invokes a Markov chain Monte Carlo (MCMC) hint sampler. The sampler targets the power-transformed prefix distribution and uses finite-step approximate sampling to generate rollout prefixes as hints. By tuning the power exponent, Hi-TTRL generates hints with a sharpened or flattened power target, steering rollout consensus strength toward the target interval. Experiments on multiple datasets and backbones show that Hi-TTRL consistently improves over standard TTRL, with ablations and consensus-steering analyses validating the effectiveness of adaptive hint-guided consensus regulation.

Biomedical literature is increasingly mined for knowledge beyond the questions it was written to answer. Because the target concepts are not known in advance, annotators prefer open-ended labels, whose agreement is hard to quantify. We study soft inter-rater reliability for annotators providing unstructured texts for biomedical annotation tasks. Synthetic experiments show that soft reliability can be quantified using a variety of semantic equivalence measures, and that the choice of measure affects failure modes of the estimation. Embeddings are scalable, but limited when differentiating similar but distinct concepts. Large language models are promising, but limited by scalability for estimating agreement by chance. Finally, we suggest measures based on natural language inference as a sensible compromise.

LLM-based multi-agent systems promise effective collaborative reasoning, but communication may amplify local errors into collective risks, and while existing evaluations emphasize final outcomes, they leave the reliability and propagation dynamics of distributed information aggregation unclear, so we introduce ForesightSafety-TIDE, a controlled evaluation framework that strictly pairs all-honest collaboration with controlled deception by a key evidence holder and analyzes the aggregation process through multi-stage voting, testimony adoption, and evidence-root lineage propagation, and using 120 five-agent object-movement environments where partial observations jointly determine a unique endpoint, we evaluate 3 homogeneous LLM-based multi-agent systems, and across these paired conditions, aggregate truth recovery falls from 72.50% to 14.17%, with significant declines for every system, while process tracing and exit ablations show that a single false testimony is adopted more readily than truthful testimony, propagates to higher orders, and persists through honest agents after the deceiver exits, and observers without first-hand evidence suppress incorrect consensus but do not improve truth recovery, so together, these findings reveal both the fragility of distributed fact recovery and its underlying mechanism: false evidence gains collective influence through its adoption and continued propagation by other agents after entering communication.

Multi-agent LLM debates achieve strong performance on decision-making tasks as well as problem-solving benchmarks, yet their safety and fairness risks remain poorly understood. Notably, interaction can amplify the biases of single LLMs, raising concerns for real-world deployment. We identify the emergence of collective (often biased) norms in multi-agent LLM debates and show that noise (e.g., LLM sampling temperature) is a key driver. To explain this, we propose an analytical framework drawing on physics-inspired theoretical models of social dynamics. We predict a phase transition to collective bias when conformity surpasses a critical threshold given the LLMs' initial bias and debate noise. We test the theoretical predictions through controlled experiments and observe a finite-size crossover consistent with an underlying phase transition. We further find that agent heterogeneity suppresses emergence by smoothing (rounding) this transition. Finally, we show that these insights generalize to realistic decision-making tasks, including investment decisions and LLM-as-a-judge evaluation.

Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored. We study a minimal LLM Naming Game in which the listener's decision is a single-token LLM call at decoding temperature $T$, replacing the inventory check of the deterministic Naming Game. Each interaction decomposes into an in-inventory and an out-inventory channel with conditional rates $π(T)\!\equiv\!P(\text{YES}\mid w\in P_j)$ and $φ(T)\!\equiv\!P(\text{YES}\mid w\notin P_j)$, whose balance controls an ordering-disordering drift. A mean-field theory of the two-rate dynamics yields an analytical ordering condition that generalizes the consensus threshold of the stochastic Naming Game to a critical line in the $(π,φ)$ plane. Across three open-weight architectures, consensus is always reached, but through three distinct listener regimes: permissive (repaint-noise dominated), near-deterministic, and conservative (missed-collapse dominated). The effective finite-size exponent $β(T)$ in $t_{\rm conv}\!\sim\!N^β$ shifts with temperature, and the temperature-sensitivity $α$ in $t_c\!\sim\!e^{αT}$ ranges from ${\approx}\,0.67$ to ${\approx}\,0$ across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.

Symbolic alpha factor discovery can score a completed expression, but it provides no direct label for the structural decisions that produced it. Generative flow networks (GFlowNets) preserve a diverse, reward-proportional distribution over complete expressions, yet their trajectory-level objective does not compare unchosen sibling actions at an intermediate state. We introduce AlphaG-OPD, a structural on-policy distillation framework that turns terminal factor evaluations into local action guidance. Its design separates three decisions. Component I determines where to teach by exposing grammar-valid siblings at partial abstract-syntax-tree (AST) states visited by the current forward policy. Component II determines what is reliable enough to teach: it evaluates three supported siblings under four shared suffixes and admits a KL-bounded target only when their matched comparisons exhibit sufficient winner agreement and a positive empirical lower confidence bound (LCB). Component III determines how strongly and for how long to teach by consolidating accepted targets through bounded replay, score-indexed expiry, and forward-gradient balancing, without additional factor evaluations. Terminal reward, Trajectory Balance, the backward policy, grammar, and factor-pool rules remain unchanged. An equal-physical-score four-arm ablation tests paired teaching, reliability gating, and consolidation. Across China's CSI300, CSI500, and CSI1000 and the U.S. S&P 500, the complete method delivers strong cross-market performance over multiple random seeds.

Traditional distributed consensus protocols classify nodes as either honest-but-faulty or actively malicious (Byzantine). However, in organizational structures, departmental agents rarely fit this binary. Instead, they exhibit bounded rationality and self-interested preferences while operating under asymmetric information. This paper presents the Organizational Consensus Algorithm (OCA), a mechanism design framework tailored for internal negotiation and decision coordination. OCA models inter-departmental conflict as an incomplete information dynamic game, integrating internal token staking, an exception-triggered challenge mechanism, and confidence-weighted consensus rules. Rather than enforcing instantaneous total ordering, OCA leverages a retrospective penalty system driven by delayed verifiable outcomes to deter structural bias and reduce exhaustive coordination overhead. A Python simulation prototype was developed to evaluate OCA. Across independent trials with varying organizational scales, OCA reports lower coordination overhead, higher informative reporting rates, and bounded welfare loss in noisy environments. Crucially, these results remain conditional on the stated simulation model and do not by themselves establish a general truthful equilibrium.

Machine learning is transforming molecular sciences by accelerating property prediction, simulation, and the discovery of new molecules and materials. Acquiring labeled data in these domains is often costly and time-consuming, whereas large collections of unlabeled molecular data are readily available. Standard semi-supervised learning methods often rely on label-preserving augmentations, which are challenging to design in the molecular domain, where minor changes can drastically alter properties. In this work, we show that semi-supervised methods that rely on an ensemble consensus can boost predictive accuracy across a diverse range of molecular datasets, task types, and graph neural network architectures. We find that training with an ensemble consensus objective increases robustness in models and exhibits an effect similar to knowledge distillation; an individual member of an ensemble trained this way outperforms a full ensemble trained in a traditional supervised fashion in almost all cases. In addition, this type of semi-supervised training reduces calibration error.

Large Language Models (LLMs) explore problems through chain-of-thought, but this exploration is buried in unstructured prose. On high-stakes tasks, users cannot tell which steps are well-supported, which alternatives were seriously considered, or how the final conclusion compares to those the model discarded. We propose a framework that ensembles the reasoning structure, not just the answers, of multiple LLMs by weighted merging of Directed Acyclic Graphs (DAGs) extracted from reasoning chains. We weight each step by how many traces independently attest to it, to return "Consensus Reasoning". Across six benchmarks spanning statutory interpretation, graduate-level science, narrative multi-hop reasoning, and first-order logic, our ensemble outperforms a matched-budget majority-vote baseline, with a maximum accuracy gain of 3.1% on MuSR-MM (narrative multi-hop reasoning). On a single model, the framework matches or exceeds self-consistency at the same trace budget while additionally exposing an inspectable consensus reasoning graph. Ensemble weights correlate with LLM-judge rankings of reasoning quality at Spearman $ρ= 0.30$-$0.51$, and consensus subgraphs are preferred over alternatives leading to the majority-vote answer in 54.4-65.4% of head-to-head comparisons across five of six datasets. We observe that our framework can also be used to analyze diverse reasoning perspectives for a problem.

Every major wave of platform software follows the same arc: an initial period of experimentation with competing frameworks and ad-hoc implementations, followed by the articulation of a small set of stable abstractions with well-defined semantics, and finally consolidation around those abstractions into a platform that applications can portably target. POSIX did this for classical operating systems; Kubernetes did it for the cloud. Agentic AI systems - autonomous, LLM-driven agents that plan, use tools, maintain memory, and collaborate - are currently in the experimentation phase of the third such wave. dozens of frameworks and protocols have emerged, but no community consensus exists on what the core abstractions are or what guarantees they carry. Without that consensus, agentic applications cannot be written portably, platforms cannot compose reliably, and the field cannot advance beyond prototype deployments. We argue that the path forward is to follow the prior-wave methodology: derive new agentic abstractions by extending classical OS and cloud OS primitives to stochastic, natural-language-mediated execution, specify their semantics precisely, and consolidate around them - just as POSIX and Kubernetes consolidated their respective waves.

Long COVID (LC) poses a challenge for clinical decision support because relevant evidence is distributed across sources with different update cycles, evidentiary roles, and levels of clinical maturity. We present a clinician-facing chatbot that organizes four sources within a retrieval-augmented workflow: expert-curated consensus guidance, current PubMed literature, registered interventional trials, and evidence from living systematic reviews. Consensus guidance is always included to frame responses, while the remaining sources are retrieved in parallel when selected by the user. In an exploratory automated evaluation on 50 clinician-facing questions, our chatbot showed comparable mean ratings to OpenEvidence, with numerically higher scores and lower score variability in an LLM-judged comparison.

Rotary position embeddings (RoPE) modify attention scores through position-dependent rotations, but their effect on normalized token dynamics is not captured by the vanilla spherical self-attention model. We study the continuous-time dynamics obtained when queries and keys are rotated while values remain on the unit sphere. The resulting attention kernel is reversible and admits a sharp uniform softmax floor, yet the natural RoPE interaction energy has derivatives of both signs within one fixed nontrivial system. Every consensus state remains an equilibrium, and its transverse linearization is a reversible Markov operator whose kernel depends on the consensus point through its energy across RoPE planes. On a resonant single-frequency ring we derive an exact Bessel-aliasing spectrum, including non-coprime frequencies and the correct fixed-ring large-$β$ asymptotics. Globally, closed hemispheres are invariant, while pairwise non-obtuse configurations and strict open semicircles contract with explicit half-angle and single-point tail bounds. These regional estimates instantiate a kernel-generic positivity principle with the sharp RoPE softmax floor. RoPE also selects an explicit score-flattening twisted branch; the generic resonant family is non-hyperbolic and linearly unstable, whereas an odd antipodal family becomes a hyperbolic saddle after quotienting global rotation. In multiple dimensions, the local consensus gap can depend non-monotonically on the allocation of energy across frequency planes, so no universal ordering by frequency is valid. Independent matrix, finite-difference, and nonlinear-flow computations cross-check the theorem boundaries and the reported constants.

Centralised reward signals dominate modern AI learning systems, but they impose a single external definition of correct or valuable knowledge. We present a decentralised, consensus-based multi-agent learning framework in which expertise emerges through peer validation rather than prescribed reward. Agents update beliefs via weighted social consensus, while trust is allocated according to competence inferred from peer consistency instead of ground truth. Subject-matter expert (SME) status is assigned dynamically as a top-percentile competence rank rather than a fixed label. We evaluate the framework across 84 simulation runs spanning 30 to 10,000 agents, multiple graph topologies, sparse large-scale networks, scalar and vector belief representations, dimensionality sweeps (D=1-500), multi-seed robustness tests, and parameter sensitivity analyses. Phase 1 shows that SME rotation is robust, persistent, topology-invariant, and scale-invariant: 90-100% of agents attain SME status, with most expertise turnover occurring after belief convergence and increasing with network size. Phases 2 and 3 show that vector beliefs introduce heterogeneous convergence with cascade dynamics and reveal five distinct dynamical regimes as belief dimensionality increases. At high dimensionality (D=150-200), the network reaches stable partial consensus while expertise becomes increasingly concentrated in a single agent. ETA sensitivity analysis demonstrates that this concentration is driven by belief dimensionality rather than stochastic noise. We interpret this behaviour as an emergent property of decentralised learning: in complex high-dimensional consensus spaces, the agent most consistently aligned with the collective belief naturally emerges as the recognised expert.

Retrieval-Augmented Generation (RAG) lets a large language model answer questions using documents retrieved from an external knowledge base at query time. This makes RAG useful for private data, fast-changing information, and reducing hallucination, but it also means the model's answer is only as trustworthy as whatever the retriever hands it. If the knowledge base accepts writes from more than one party, an attacker needs only a handful of adversarial documents to steer the model toward a chosen wrong answer. PoisonedRAG demonstrated this: as few as five crafted documents flip an undefended system's answer roughly 90% of the time, and three natural single-stage defenses (perplexity filtering, query paraphrasing, knowledge-base expansion) leave attack success at 30% or higher. We built TriShieldRAG to close that gap. Rather than relying on one checkpoint, we place three independent, formally specified rings across the pipeline: an Ingest Guard that screens documents for lexical and statistical poisoning signatures; a Retrieval Scorer that re-ranks the retrieved set by a provenance and consistency-weighted trust score; and a Cross-LLM Consensus stage that polls three architecturally diverse language models (Claude, Mistral Small, Llama 3.2) and allows one bounded re-retrieval on disagreement. We derive the conditions under which Rings 2 and 3 are expected to work: a minority-poison assumption and an explicit provenance-tag assumption. Our reported configuration is consistent with this analysis, though we have not yet run the controlled poison-fraction sweep needed to confirm it independently. Evaluated against the non-adaptive attacker from the original PoisonedRAG, over a 5,000-document Wikipedia knowledge base with 10 target questions, the full pipeline reduces attack success rate from roughly 91% to roughly 13% while preserving accuracy on benign queries.

Recent work shows that fine-tuning language models on even a small amount of poisoned data can install targeted misbehavior, and ostensibly benign data can transmit hidden preferences that generalize broadly. Standard defenses, such as data filtering, mixing in harmless data, and regularization, attenuate these effects but do not eliminate them. We instead pursue robustness through redundancy: collecting multiple datasets from different sources and only learning what is common between them. Thus, if only a subset of sources are malicious, the misbehavior will be blocked. In order to implement this defense strategy, we fine-tune a separate reference model on each source's dataset and aggregate their next-token distributions at decoding time. We introduce two consensus decoders: a token-wise minimum, which caps each token at the lowest probability any source assigns, and a base-relative variant, which reverts to the base probability on any token the sources move in opposing directions. We further relax exact agreement to tolerate partial support across sources and different surface expressions of the same intention. Across controlled poisoning tasks, subliminal learning, and emergent misalignment, consensus decoding suppresses source-specific misbehavior while preserving shared desirable behavior, including cases where union training and weight averaging retain the unwanted behavior.

Communication allows large language model agents to pool evidence, but it also creates paths along which an erroneous claim can spread. We formulate a correction-aware network model that tracks susceptible, exposed, infectious, and corrected agents and derive its early-invasion condition for heterogeneous communication networks. We then couple this propagation model to an analytic majority-vote benchmark in which a clean-task reliability target imposes a minimum connectivity requirement. Under fixed exposure per communication edge, reliability and error control impose opposing graph constraints. We characterize when their intersection is empty and when it contains an intermediate connectivity range, and identify regular graphs that attain the smallest invasion factor within the reliable graph class when such graphs exist. Under a fixed sender budget, the homogeneous first-order threshold is independent of network density, showing that the communication-budget convention determines whether added edges increase early propagation risk. Finite-network simulations on 21,000 trajectories illustrate these directional predictions. A controlled grok-4.3 experiment then evaluates three six-node topologies on 36 new closed-world tasks, with a balanced 12-task subset continued to full cascades. Mean first-generation offspring increased from 0.667 to 1.333 and 1.667 as degree increased from 2 to 4 and 5, while the adoption fraction among exposed neighbours remained 0.333. Mean non-seed erroneous adoption in the full-cascade subset was 0.200, 0.333, and 0.333. Together, these results provide a tractable basis for selecting connectivity under explicit reliability and propagation constraints.

We investigate a decentralized reinforcement learning problem involving multiple agents that interact with the same Markov Decision Process (MDP). The agents can exchange information over a network to collectively learn the optimal state-action value function. For this setting, we introduce a novel epoch-based distributed $Q$-learning algorithm called VRDQ, where within each epoch, agents locally estimate the Bellman optimality operator and diffuse information using a consensus-based protocol. For both static and time-varying networks, we establish high-probability finite-time convergence rates for VRDQ that enjoy linear speedups from collaboration. Crucially, we prove that such speedups in sample-complexity require only $\tilde{O}(1)$ communication, substantially improving upon the communication costs in prior work.

The integration of iterative LLMs within multi-agent diagnostic frameworks requires a rigorous quantitative reevaluation of underlying communication topologies. Frequently used architectural paradigms depend on scale-free or small-world networks, assuming optimal communication efficiency. Our study mathematically dismantles that assumption for semantic data. By mapping multi-agent communication uncertainty trajectories onto a 768-dimensional Bio_ClinicalBERT embedding space via an analytical isotropic variance proxy using Barab'asi--Albert (BA) and Watts--Strogatz (WS) networks, we prove that structural bottlenecks compromise diagnostic safety. Our phase transition matrices illustrate that localized dense cliques confine hallucinated data, preventing global consensus and forcing the system toward a permanent entropy saturation threshold of $H_{\infty} \approx 5.947$. As a result, we measure a severe terminal cosine similarity degradation of 53.29%, completely overwriting the original ground-truth. Moreover, the terminal semantic drift reveals a catastrophic variance amplification of 51.81% ($ρ= 1.5181$) in highly clustered architectures, proving total system unpredictability when compared to Erdős--R'enyi configurations ($ρ= 1.0766$). Instead of reducing errors, hub-centric systems autonomously compound localized hallucinations. By introducing dynamic spectral monitoring operating at an $\mathcal{O}(N^3)$ time complexity and imposing a strict lower bound on algebraic connectivity ($λ_{2_{min}}$) via the continuous eigen-decomposition of the graph Laplacian, we present a mathematically rigorous technique to ensure global state diffusion. Securing the reliability of autonomous medical diagnostics necessitates treating topological stability as a non-negotiable quantitative imperative.

The operation of blockchain is governed by consensus algorithms (CA). Several consensus mechanisms require significant computational power, while others necessitate high amounts of stakes to select the participant to validate and verify the transactions in the block, leading to centralisation of power and participant exclusion. This paper proposes a novel methodology to address these issues in reputation-based consensus algorithms by studying the reputation behaviour of the validator using intuitionistic fuzzy sets (IFSs) and uninorm aggregation operations (UAOs). Our approach uses IFSs to express the "reputation" because the reputation values in a consensus algorithm eventually imply uncertainty, and IFSs facilitate the representation of a lack of precise knowledge about reputation. Moreover, this methodology utilises uninorm aggregation operations to monitor reputation over time and reinforces the importance of negative and positive reputation. Consequently, this solution allows validators to rectify past failures in subsequent verification processes and foster an equitable consensus algorithm design. The proposed framework maintains linear computational complexity and does not introduce additional communication overhead beyond the underlying consensus protocol. Supported by experimental results, our methodology demonstrates improved performance and evaluation, promising advancements in blockchain network fairness and inclusivity.

Tsetlin Machine (TM) is a rule-based machine-learning algorithm comprising collectives of two-action Tsetlin Automata (TAs) that cooperatively form conjunctive logical clauses from Boolean inputs through stochastic feedback. Although few recent studies have examined TM Federated Learning, the broader area of distributed and decentralized TM learning has not received much attention in the existing literature and warrants further exploration. In this work, we propose a paradigm for decentralized collaborative learning under a vertical feature-partitioning setting among an ensemble of Tsetlin Machines using consensus-based inference. Within this decentralized paradigm, each agent maintains its own private TM model, and there is no exchange of raw data among agents. Inference combines individual agents model predictions into a global consensus. The paradigm accommodates heterogeneous TM-based agents with differing data acquisition means, local data distributions, or computational resources, thereby facilitating the integration and fusion of information in settings such as multi-modal sensing environments. Experiments conducted using two-dimensional grid and connected graph network topologies demonstrate that the classification accuracies achieved are comparable to those of centralized models.

In recent years, multi-view learning has attracted increasing attention, as it integrates the complementary information of heterogeneous views. Most existing multi-view classification methods rely on accurate annotations to guarantee performance. However, noisy labels are ubiquitous in practice due to imperfect annotation, and the refinement signals that existing methods derive from models trained on such noisy supervision can gradually lose their reliability. To deal with this problem, we propose a novel Global Anchor-based Label Auditing method (GALA) for multi-view classification to resist the negative impact of noisy labels. Specifically, we construct a global anchor for each class in every view, which aggregates the samples of the whole class and thus offers a stable reference insensitive to individual predictions. Then, each view measures how close an instance is to the anchor of its observed label relative to the nearest competing anchor, and the per-view evaluations are fused with the classifier confidence into a cross-view audit score. Based on the audit scores, suspicious samples are assigned small weights, and an adaptive correction strategy rewrites a label only when the anchor-based candidate agrees with the classifier prediction. Finally, the corrected labels in turn refine the anchors and supervise noise-robust representation learning. Extensive experiments on six datasets demonstrate that GALA outperforms eight state-of-the-art methods, especially under high noise rates.

Organizations often pool dispersed information into one ranking and then allow many agents to act on that shared view. In a discovery problem, this can improve beliefs while reducing coverage. We develop an exactly solvable benchmark with sixteen boxes, one target, eight searchers, and noisy private clues. Pooling raises the accuracy of the best single recommendation from 0.20 to 0.3835, but repeating that recommendation lowers group discovery from 0.8322 under decentralized clue-following to 0.3835. A coordinated eight-action portfolio using the same pooled reports reaches 0.8594, and seven coordinated actions recover the decentralized benchmark. The paradox is a protocol failure, not an information failure: a one-answer rule compresses a portfolio of available actions into one repeated choice. We then replace the planner with self-interested searchers who split a prize. The equal-split game is a potential game. Its anonymous symmetric equilibrium obeys a water-filling rule. In the canonical instance it achieves 0.5991: strictly above consensus, but below both private search and the planner. The exact mixed price of anarchy is 2 - 1/N. A sole-rescue reward, which pays only an agent who covers the target alone, makes every pure Nash equilibrium first-best. Finally, a latent common-cue model shows how correlated reports collapse effective discovery channels. The centralized planner gain rises strictly with copying, and in the canonical environment the symmetric market overtakes decentralized report-following at copying probability c = 0.788462. In a proportional large-market limit the five-protocol ordering survives exactly: consensus discovery vanishes while blind, market, private, and portfolio search converge to 0.500, 0.547, 0.847, and 0.874. The contribution is a compact benchmark that separates information, allocation, incentives, and dependence into exact, reusable quantities.

Test-time collaboration, including self-consistency, best-of-N selection, critic models, and verifier pipelines, is often credited with broadly improving LLM reasoning, yet its gains are uneven and sometimes negative. We ask when training-free collaboration should be expected to help. For a fixed candidate pool, we decompose a selector or verifier's net gain into measurable factors: recoverable mass, verification-signal coverage, conditional selection quality, and harm to already-correct outputs. This reframes collaboration as a candidate-selection problem rather than as an intrinsic property of a multi-agent topology. Across LiveCodeBench, MATH Level-5 hard subjects, and GPQA-Diamond, gains are bounded first by the oracle gap and then by signal fidelity, which we measure directly as candidate-level agreement between verifier verdicts and official labels. On LiveCodeBench, a public-test verifier (MCC 0.825) gains +8.14 percentage points (pp) over a first-sample baseline; a generated-test verifier (MCC 0.248) improves by +2.70pp and is not statistically distinguishable from an LLM selector, but operates at near-zero harm versus the selector's 4.69% harm rate. On MATH, a symbolic answer-equivalence selector beats self-consistency by +4.67pp, while LLM selectors are negative. On GPQA-Diamond, recoverable mass is only 3.03% and 87.54% of candidate pools are answer-identical; a weaker model's pools shrink both further, suggesting that oracle gap is a joint property of task, model, and sampling configuration. Our framework yields a practical pre-deployment diagnostic: estimate the oracle gap, then measure coverage, signal fidelity, and harm before investing in collaboration.

Traditional benchmarks for LLMs primarily rely on static datasets and objective scoring metrics, which often fail to capture differences in response quality when multiple answers are acceptable. In such settings, correctness alone is insufficient to distinguish between responses that vary in clarity, completeness, and usefulness. This paper introduces a consensus-based evaluation framework that measures relative preference among model-generated responses rather than absolute correctness. Instead of evaluating outputs against a fixed ground truth, we assess how a panel of diverse LLMs ranks anonymized candidate responses to the same prompt. This approach treats aggregate inter-model agreement as a proxy for perceived response quality under blind conditions. We conduct a controlled study using five state-of-the-art LLMs across multiple domains, including programming, general knowledge, safety, logical reasoning, and mathematics. Each model generates responses and independently ranks peer outputs through a structured voting process. Scores are aggregated into a Relative Intelligence Index (RII), representing how frequently a model's responses are preferred by other models. Our findings reveal consistent preference patterns across domains, with certain models more frequently ranked highly by their peers. However, we emphasize that these results reflect inter-model preference alignment rather than objective correctness or human judgment. This framework provides a scalable, model-driven method for comparative evaluation, offering an alternative perspective on response quality in scenarios where multiple valid answers exist. While not directly aligned with human evaluation, prior work suggests that aggregated model preferences can partially correlate with human judgments, motivating this as a proxy signal.

LoRA adapters provide an efficient way to specialize a pretrained model for many downstream tasks, but deploying one adapter per task requires adapter storage and task selection at inference time. Model merging addresses this issue by combining independently trained adapters into one multi-task adapter. Recent SVD-based LoRA merging methods mainly focus on constructing shared or task specific directions, while the coefficients assigned to the final directions are often directly from the original task SVD. On a fixed merged basis, inherited coefficients preserve component order with high rank correlation, yet their magnitudes differ substantially from the coefficients induced by the task updates. To address this mismatch, we propose CT-Merging, a LoRA-aware merging algorithm that estimates consensus directions from average task subspace projectors and assigns task-level RMS coefficient scales in the final update. CT-Merging uses repeated support across task SVD subspaces to construct the common basis, while reducing reliance on rank wise SVD magnitudes after direction construction. On the DC-Merge CLIP adapter benchmark, CT-Merging achieves superior average normalized accuracy compared to state-of-the-art merging methods and further improves over DC-Merge by 2.56 points on ViT-B/32 and 1.51 points on ViT-L/14 KnoTS-trained checkpoints.

State machine replication (SMR) and Byzantine fault-tolerant (BFT) consensus guarantee agreement despite a bounded number of arbitrary, colluding faulty participants. However, these guarantees rely on participants outside this set correctly executing the protocol's transition semantics. Agentic validators expose a weaker boundary: an authenticated, responsive, non-equivocating, and protocol-compliant reasoning participant may still endorse a semantically invalid transition due to reasoning errors. We call this failure mode an epistemic fault, and the collective phenomenon the Honest Quorum Problem (where "honest" means protocol-compliant, not semantically correct). Such a quorum can satisfy ordinary checks while forming a certificate for an invalid transition. Thus, agreement alone does not guarantee semantic validity or execution safety. Furthermore, because agentic validators often share model weights, training distributions, prompts, or toolchains, they are highly susceptible to correlated epistemic faults. We define Epistemic Byzantine Fault Tolerance (EBFT), a fault-tolerance model for agentic infrastructure and post-deterministic distributed systems. EBFT augments the conventional Byzantine fault bound with two separate, confidence-indexed quantities: $e_δ$ bounds coherent invalid endorsements outside the Byzantine set, and $u_ε$ bounds unusable validator support that degrades liveness. These quantities characterize semantic safety risk and liveness degradation independently. We derive quorum-threshold conditions for semantic validity, consensus agreement, liveness, and feasible threshold selection, and outline a calibration methodology for estimating these budgets. We show that adding nominally distinct agents improves fault tolerance only when it measurably reduces the upper-tail concentration of invalid endorsements or unusable support.

The Internet taught us that the value of a network depends on \emph{how} its nodes connect: broadcast stars scale as $V\!\propto\!N$ (Sarnoff), fully-connected meshes as $N^2$ (Metcalfe), and group-forming networks as $2^{N}$ (Reed). We ask the analogous question for networks of AI agents. We model the net value of connection as a function of coordination-group size, derive from it the properties an optimal collaboration protocol must have, and introduce ANet Patu-1 -- a self-organizing consensus protocol in which the network continuously re-forms its own coalitions, adaptively riding the upper envelope of all three regimes at $O(1)$ parallel consensus rounds. To measure value without opinion-grading, we score an emergent protocol by formally specifying it and deriving its complexity, the way distributed algorithms are analyzed. Two results follow. (i)~Emergence -- a crowd of the \emph{cheapest} model, when heterogeneous, starts weak but its collective value compounds with $N$ and \emph{overtakes} a crowd of a far \emph{stronger} model that is homogeneous: a crossover that marks a scaling law for collaboration rather than for scale. (ii)~Reflexivity -- a heterogeneous network, given only its own problem and no design hints, converges on ANet Patu-1 itself, reconstructing the high-dimensional law that governs its own connective value.

The simultaneous arrival of multiple mobile robots at a target point is crucial for cooperation tasks such as cooperative encirclement, disaster relief, and environmental monitoring. Although the simultaneous arrival problem itself is already complex, the problem becomes more challenging when there are constraints on the robot trajectory curvatures and the speeds are required to be constant (possibly different for different robots), and the control law for robots needs to be distributed. These constraints are typical for a multi-robot system consisting of, e.g., fixed-wing UAVs. To address this challenge, this paper proposes a distributed switching control method based on the maximum consensus protocol. By exploiting the geometric properties of Dubins paths along with optimization principles, a virtual time variable is introduced, and a hybrid control law that combines optimal control with saturated proportional control is designed. Under the proposed control law, each robot is driven to approach the maximum virtual time among its neighbors, thereby achieving simultaneous arrival under some mild conditions. Furthermore, we prove that in certain cases the proposed method attains a theoretically optimal arrival time. The approach is scalable and real-time, with low communication overhead. Its effectiveness and robustness are validated through extensive simulations and experiments.

Sampling multiple solutions and returning the majority answer is among the most reliable ways to improve the reasoning accuracy of large language models without labels, and a growing family of methods converts this consensus signal into training supervision. However, existing approaches use consensus only in restricted forms: as a filter that selects solutions for fine-tuning, as a preference between answers, or as a scalar reward for reinforcement learning, discarding most of the information that the agreeing solutions contain. We present CANON (Consensus-ANchored self-distillatiON), a label-free training method that turns consensus into dense, token-level supervision. For each unlabeled prompt, CANON samples multiple solutions, extracts the majority answer, and conditions a frozen snapshot of the model on a solution that reaches it; this consensus-anchored teacher then supervises the model on its own rollouts at every token. Experiments on mathematical and scientific reasoning benchmarks show that CANON improves pass@1 by up to 12 points, outperforming label-free reinforcement learning by 6 points at a seventh of its compute and approaching a teacher conditioned on gold solutions; trained on pooled unlabeled data, it transfers to held-out benchmarks, matching training methods that use gold labels. Analysis suggests that the improvements are not pure distribution sharpening: after training, the model solves problems it previously never solved in 32 attempts, and its majority vote itself becomes more accurate.

In operational 1:N face identification, a crucial question arises for each probe: is this person enrolled in the gallery or not? The stakes are high and asymmetric. Rejecting a mate-present (MP) probe loses a valid lead; accepting a mate-absent (MA) probe makes every returned candidate a false identification, at worst a wrongful arrest. Most approaches threshold match scores, but scores shift substantially with image quality and gallery size and composition, making thresholds fixed before deployment brittle under realistic conditions. Our prior work introduced 1-consistency, the only method based on rank consensus across multiple independently trained matchers: a probe is labeled MP if all matchers return the same rank-1 identity. This work stress-tests 1-consistency across 36 (gallery, probe quality) scenarios spanning four quality levels and two structural axes: images per identity and total enrolled identities. We benchmark against two score-thresholding methods that bracket what any deployed threshold could achieve. Fixed Score-Thresholding (FST), calibrated once on baseline conditions, collapses asymmetrically as quality degrades: MP recall falls below 2% while MA recall holds near 100%. Oracle Score-Thresholding (OST), re-tuned per scenario, is the best any threshold could theoretically do, yet for degraded probes 1-consistency matches it with zero tuning. The two differ mainly in error type (OST favors MP recall, 1-consistency favors MA recall), but on one axis 1-consistency does not merely match the oracle: when it labels a probe MP, it returns the correct mate 97-100% of the time versus OST's 66-84% under severe degradation. In short, 1-consistency delivers oracle-level accuracy without the impossible requirement: it sets no threshold, so it needs no advance knowledge of the conditions a probe will arrive in, which is what makes it usable.

Deep research agents are increasingly used to produce long-form financial reports, yet large-scale evaluation remains bottlenecked by the need for human experts to define and execute high-quality rubrics. We address this problem by proposing a scalable pipeline for generating high-quality rubrics without human experts in the final loop. We build a financial deep research benchmark from 104 real-world user queries and automatically synthesize 14,450 query-specific candidate rubrics from model-generated reports. To justify removing human experts from rubric execution, we compare rubric judgments from three human experts with those from a three-LLM judge panel on a sampled subset, and show that LLM-based evaluation is sufficiently consistent with human evaluation to replace it for large-scale rubric screening, including 98.67% label-level agreement on jointly unanimous items. We then derive consensus-derived gold rubrics through two filters: a strict consistency filter, which keeps a rubric only if the three LLM judges unanimously agree on every report under the same query, and a distinguishability filter, which keeps a rubric only if it assigns at least one majority-yes and at least one majority-no label across the evaluated systems. This process retains 3,687 consistency-passed rubrics, of which 2,600 remain distinguishable and form the final set of consensus-derived gold rubrics. Using this final rubric set, we obtain clearly differentiated rankings across 10 deep research systems, with item-level pass rates ranging from 58.58% to 22.23%. More broadly, because the pipeline removes human-expert execution from rubric generation and evaluation, it is naturally scalable for benchmark evaluation, automatic system comparison, and future studies of evaluation-driven system improvement.