This work proposes a four-field evidence tuple (hypothesis, reliability bucket, rationale, provenance, provenance) and shows that fixing it determines both halves of the framework and applies to a class of rules beyond language models: score-summing triage engines, diagnostic panels scored by counting positives, and additive multi-signal detectors.
Abstract
Systems that ask a language model to reach a conclusion from many sources usually concatenate them into one prompt. This conflates two operations with different requirements. Interpreting a source rewards capacity and context. Combining interpretations rewards fixed arithmetic, comparability across instances, and the option to return nothing. Once separated, the design problem becomes the interface between them. We propose a four-field evidence tuple (hypothesis, reliability bucket, rationale, provenance) and show that fixing it determines both halves. The separation also reveals a failure mode in how such systems combine, which we call count-scale drift. Thresholding a sum of unnormalized weights is exactly posterior thresholding, but at an operating point that slides with the number of sources consulted. The slide grows with reader reliability. When source reliabilities differ, the vote rule and the posterior order instances differently, and no threshold reconciles them. Pooling calibrated log-likelihood ratios addresses both problems. The fix is arithmetic rather than architectural, and applies to a class of rules beyond language models: score-summing triage engines, diagnostic panels scored by counting positives, and additive multi-signal detectors. We then instantiate the principle twice on one longitudinal corpus, once after outcomes resolve and once before. The same partition helps in both, at different granularities: over reading in the first, over learning capacity in the second. There, a small sequence encoder on an easy auxiliary objective plus a tree ensemble carrying the censored survival loss reaches 0.921 AUPRC against 0.805 for a hand-crafted baseline. We separate what transfers from what must be re-estimated per domain, and state five predictions that would falsify the framework, three negative results, and which comparisons remain confounded.
This work shows that pooled refitting recomputes the inverse-Gram geometry used to weight source evidence, which can reverse shared preferences, and derive exact and approximate preservation conditions, and develops a three-stage audit that traces strict pairwise reversals through decision changes to task-defined utility loss.
Yanli Yan, Yuanzheng Li, Yong Zhao et al.· 0 citations
Streaming systems that maintain a pool of expert models must repeatedly decide whether to reuse an existing expert for arriving data, spawn a new one, or defer. We present a decision layer that makes all three outcomes statistically meaningful. Reuse and spawn are posed as one-sided sequential hypotheses on a conditional (mechanism-level) discrepancy, separated by an indifference zone; defer is exactly the state in which neither betting e-process has accumulated sufficient evidence. We prove finite-time anytime validity for the observable surrogate discrepancy of a predictable discriminator sequence, and an unconditional one-sided transfer to the population quantity in which each side's slack is the excess risk of a single discriminator; an empirically observed downward-bias regularity makes the spawn side exactly conservative. Recency without sacrificing the guarantee is obtained by a restarted e-detector: a bank of unwindowed betting supermartingales at geometrically spaced restart times (O(log t) memory), with the error budget spent over restart instances, which preserves lifetime anytime validity; spending over expert-creation order likewise controls multiplicity for unboundedly many experts. On synthetic multi-concept streams, Electricity, Covertype, and the recurrence-heavy INSECTS benchmark, the instance-accounted restarted bank achieves zero false spawns and zero false reuses after switches and matches or exceeds the retired windowed heuristic (INSECTS-reoccurring accuracy 0.675), making the deployed algorithm and the guaranteed algorithm one and the same.
Large language models (LLMs) are increasingly used in settings where textual summaries, numerical observations, and external tool outputs may provide conflicting evidence. We study how LLMs arbitrate between such sources when they support opposing decisions. To do so, we introduce a controlled synthetic benchmark in which latent risk trajectories generate both numerical time series and natural language summaries, allowing us to construct conflicts where exactly one evidence source is aligned with the ground-truth label. This design lets us independently manipulate modality, temporal recency, source reliability, and evidence provenance. Across open-weight instruction-tuned models, we find that arbitration behaviour is systematic rather than random: models exhibit distinct text-versus-number preferences, follow temporal recency more consistently than explicit reliability cues, and can over-rely on external forecasts even when they conflict with direct contextual evidence. These results suggest that current LLMs often rely on heuristic arbitration strategies when integrating heterogeneous evidence, highlighting a failure mode for tool-augmented decision systems.
Mattia Carletti, Edward Phillips, Fredrik K. Gustafsson et al.· 0 citations
LLM judge panels are a standard evaluation tool, but prior work reports highly correlated panel errors: nine judges provide roughly the effective information of two independent ones, and aggregation closes only a small fraction of the gap. A natural remedy--a signal from a different evidence source, e.g., executing a test suite--produced no distinguishable change in the panel's effective-vote count at scale (-0.04, 95\% CI [-0.10, +0.02]). Aggregate dependence and conditional decision utility are different questions. Elementary majority arithmetic fixes the affected set for single-ballot substitution: only decisions with a one-vote margin can change. The empirical question is whether panel error rates rise and useful substitutions concentrate there. They do: the entire accuracy gain concentrates on these pivotal queries, where it is large (+10.4 to +23.3 percentage points across three headline configurations), and is exactly zero elsewhere. We confirm the pattern across three code benchmarks and four panel sizes (a 9-judge extension and 56 dependent subsampling checks, gain +6.5 to +16.1 percentage points). On HumanEval+/MBPP+, a majority-side replacement rule raises overall accuracy from 82.44\% to 85.62\% while invoking the signal on 16.2\% of queries; signal-only remains stronger at 87.60\%. Thus population-level dependence diagnostics and margin-stratified utility are complementary, and the affected-set characterization yields a call-reduction rule for any specified single-ballot substitution policy.
This paper investigates whether there exists a token-budget threshold, below which the overhead of planning and verification hurts performance and above which it helps, and evaluates two systems on FinQA and TAT-QA financial reasoning tasks.
Thomas Nolasque, John Grey, Calista Pham et al.· 0 citations
A crossed random-effects (generalizability-theory) decomposition is specified that partitions the total variance of a response-level brand outcome into these four sources, and embeds the components in a decision-study allocation that returns how many repeats, paraphrases, models, and languages to buy for a target reliability.