CDR-Bench: Evaluating Faithful Execution of Compositional, Order-Sensitive Data Refinement Recipes

While large language models (LLMs) perform well on table tasks, they still make data referencing errors (DREs), i.e., incorrectly citing or omitting table values, despite understanding the table structure. Beyond final-answer accuracy, DREs directly compromise the correctness and reliability of intermediate reasoning steps. Yet prior studies have only offered limited, small-scale analyses. In this work, we present the first systematic evaluation of tabular data referencing errors across different models and tasks. Our results show that DREs occur across all tested models (1.7B to 20B parameters). Furthermore, we demonstrate that incorporating data referencing as a critic significantly improves answer accuracy up to 12.0%, through critic-based filtering and rejection sampling. Finally, we trained a lightweight 4B-parameter critic model that achieves an average F1 score of 78.2% in detecting both in-distribution and out-of-distribution DREs, and effectively assists inference for larger models.

LLM orchestration is often assumed to improve reasoning by allocating additional inference-time computation, yet its gains may not justify its cost. Existing comparisons also frequently overlook differences in optimization effort, making it difficult to isolate the value of orchestration itself. We conduct a controlled evaluation of Self-Refine, Best-of-$N$, and Debate against task-only and chain-of-thought (CoT) single-call baselines across five LLM backbones and three domains: competitive programming, chess puzzles, and mathematics. For comparability, we optimize each method with GEPA under the same optimization budget and evaluate all methods on the same difficulty-stratified benchmark items. Orchestration yields moderate but benchmark-dependent gains: averaged across backbones within each benchmark, the largest improvement is 4.6 percentage points over optimized CoT inference and 4.5 points over task-only inference, while requiring approximately 2 to 4 times the mean total tokens of task-only inference. Human-derived difficulty is associated with lower absolute accuracy in all three benchmarks, but within-benchmark analyses do not indicate that orchestration effects increase with task difficulty. By contrast, exploratory mixed-effects analyses reveal strong interactions between orchestration method and backbone model across all three benchmarks, showing that orchestration effectiveness depends substantially on the underlying model. Our results suggest that orchestration decisions should be model-specific and account for whether moderate accuracy gains justify the additional inference cost. More broadly, evaluations of LLM orchestrations should control optimization effort and report model-specific accuracy--cost trade-offs rather than treating additional inference-time structure as uniformly beneficial.

Detecting LLM reasoning failures at inference time without ground-truth labels has motivated a wide range of confidence baselines, including self-consistency, semantic entropy, and P(True), built on within-question sampling and self-evaluation. Operad theory, the formalism for systems built by iterated substitution, suggests a complementary diagnostic: a model's direct answer to a compositional query should agree with the answer it produces by composing a stated decomposition of the same query. We instantiate this idea as operadic consistency (OC), a per-question signal. Across twelve instruction-tuned LLMs (4B to 671B parameters, open-weights and closed-source) on four multi-hop QA datasets, OC is strongly correlated with accuracy on every dataset (Pearson $r \in [0.86, 0.94]$, all $p \leq 0.0004$), and is the only signal we evaluate with $r \geq 0.85$ uniformly across all four datasets. Chain-of-thought self-consistency (CoT-SC; Wang et al., 2023) matches OC on HotpotQA and DROP ($r = 0.93, 0.87$) but drops to $r \approx 0.45$ on MuSiQue and StrategyQA. At the per-question level, OC contributes information beyond CoT-SC and semantic entropy on every dataset (cluster-robust $p \leq 10^{-16}$ for the OC coefficient), and the conclusion is robust to additionally controlling for constructed decomposition-aware baselines ($p \leq 10^{-13}$). The same signal yields selective-prediction improvements (accuracy at fixed coverage) over a tuned CoT-SC baseline at the equal-cost $K = 3$ budget (AUARC lifts of +0.086 to +0.096 and AUROC lifts of +0.092 to +0.164; 95% CIs exclude zero on every cell). On five frontier thinking models, where the decomposition is extracted from the model's own chain of thought, the same equal-cost comparison gives positive selective-prediction point-estimate lift on all 16 (dataset, budget, metric) cells tested, with 95% CIs excluding zero on 12 of the 16.