Correctness

Large language models can be uncertain yet correct, or confident yet wrong, raising the question of whether their output-level uncertainty and their actual correctness are driven by the same internal mechanisms or by distinct feature populations. We introduce a 2x2 framework that partitions model predictions along correctness and confidence axes, and uses sparse autoencoders to identify features associated with each dimension independently. Applying this to Llama-3.1-8B and Gemma-2-9B, we identify three feature populations that play fundamentally different functional roles. Pure uncertainty features are functionally essential: suppressing them severely degrades accuracy. Pure incorrectness features are functionally inert: despite showing statistically significant activation differences between correct and incorrect predictions, the majority produce near-zero change in accuracy when suppressed. Confounded features that encode both signals are detrimental to output quality, and targeted suppression of them yields a 1.1% accuracy improvement and a 75% entropy reduction, with effects transferring across the ARC-Challenge and RACE benchmarks. The feature categories are also informationally distinct: the activations of just 3 confounded features from a single mid-network layer predict model correctness (AUROC ~0.79), enabling selective abstention that raises accuracy from 62% to 81% at 53% coverage. The results demonstrate that uncertainty and correctness are distinct internal phenomena, with implications for interpretability and targeted inference-time intervention.

Large language models are increasingly deployed as protocols: structured multi-call procedures that spend additional computation to transform a baseline answer into a final one. These protocols are evaluated only by end-to-end accuracy, giving limited insight into when they help, when they hurt, and whether their behavior transfers under distribution shift or composition. We propose a paired-outcome measurement interface for auditing a single protocol step on exact-match tasks. For each instance, the interface records a baseline correctness bit $E_0\in\{0,1\}$ and a post-step correctness bit $E_1\in\{0,1\}$, separating correction ($E_0=0\to E_1=1$) from corruption ($E_0=1\to E_1=0$) through two rates: $c=\Pr(E_1=1\mid E_0=0)$ and $γ=\Pr(E_1=0\mid E_0=1)$. These rates predict accuracy changes and define a reusable empirical interface testable across seeds, mixtures, and pipelines. We identify three failure mechanisms. Under mixture shift, pooled estimates of $(c,γ)$ become biased when calibration and deployment mixtures differ; conditioning on a difficulty proxy restores stability without additional model calls. Under presentation contamination, selection protocols alter the interface through stable presentation artifacts when candidate content is fixed. Under state insufficiency, the correctness bit may not carry enough history for multi-step pipelines to compose predictably; a Markov factorization test identifies when composition is valid and where additional state is needed. When a protocol step passes these diagnostics, it becomes an auditable module: gated by estimated gain, conditioned on a difficulty proxy to correct mixture bias, and composed into multi-step pipelines with predictable accuracy. We demonstrate these ideas on synthetic mathematical tasks and on GSM8K, where the calibrated interface correctly predicts when protocol steps should be activated or suppressed.

Reinforcement learning with verifiable rewards (RLVR) and Rubrics as Rewards (RaR) have driven strong gains in domains with clear correctness signals and even in subjective domains by synthesizing evaluation criteria from ideal reference answers. But many real-world tasks admit multiple valid outputs and lack the single ideal answer that rubric generation depends on. We identify this reference-free setting as a gap in current post-training methods and propose Implicit Error Counting (IEC) to fill it. Instead of checking what a response gets right against a rubric, IEC enumerates what it gets wrong, applying severity-weighted scores across task-relevant axes and converting them into calibrated per-aspect rewards. We show that naïve explicit enumeration is too noisy for stable optimization, and that two design choices: implicit score emission and group calibration are necessary to make error counting a reliable reward. As a case study, we validate IEC on virtual try-on (VTO), a domain that is simultaneously too constrained for holistic scoring and too permissive for rubric-based evaluation: subtle garment errors are unacceptable, yet many output variations are correct. We introduce Cascaded Error Counting (CEC) as an evaluation metric, which tracks human preferences well (60% top-1 vs. 30% others), and curate Mismatch-DressCode (MDressBench), a benchmark with maximal attribute mismatch to stress-test reward designs. On MDressBench, IEC outperforms RaR across all metrics (CEC: 5.31 vs. 5.60 on flat references; 5.20 vs. 5.53 on non-flat). On VITON-HD and DressCode, IEC matches or surpasses six baselines on 6 of 8 perceptual metrics. These results suggest that when ideal answers are unavailable, counting errors provide a stronger signal than constructing rubrics.

Inference optimizations are routinely evaluated by throughput alone, without verifying output correctness. We conduct a forensic analysis of batch speculative decoding and find that several widely-used implementations silently produce corrupted outputs (repetitive tokens, <unk> symbols) while reporting competitive speed; failures invisible to metrics like ROUGE. We trace the root cause to the ragged tensor problem: variable token acceptance desynchronizes position IDs, attention masks, and KV-cache across a batch. We formalize the synchronization invariants (rectangular alignment and position-ID contiguity) that valid batched inference must preserve and show that maintaining them incurs superlinear alignment overhead under contiguous layouts. EQSPEC enforces the invariants without custom kernels; EXSPEC schedules same-length sequences to bypass realignment. On SpecBench across three model families, EXSPEC reaches 3 x throughput at batch size 8 with 95% exact match to standard decoding; residual divergence traces to floating-point non-determinism, not synchronization error. Code:https://github.com/eBay/spec_dec

While software requirements are often expressed in natural language, verifying the correctness of a program against such requirements is a hard and underexplored problem. Large language models (LLMs) are promising candidates for addressing this challenge, however our experience shows that they are ineffective in this task, often failing to detect even straightforward bugs. To address this gap, we introduce HoarePrompt, a novel approach that adapts fundamental ideas from program verification to natural language artifacts. Inspired from the strongest postcondition calculus, HoarePrompt employs a systematic, step-by-step process in which an LLM generates natural language descriptions of reachable program states at various code points. To manage loops, we propose few-shot-driven k-induction, an adaptation of the k-induction method widely used in model checking. Once program states are described, HoarePrompt leverages the LLM to assess whether the program, annotated with these state descriptions, conforms to the natural language requirements. For evaluating the quality of classifiers of program correctness with respect to natural language requirements, we constructed CoCoClaNeL, a challenging dataset of solutions to programming competition problems. Our experiments show that HoarePrompt improves the MCC by 61% compared to directly using Zero-shot-CoT prompts for correctness classification. Furthermore, HoarePrompt outperforms a classifier that assesses correctness via LLM-based test generation by an MCC increase of 106%. The inductive reasoning mechanism contributes a 26% boost to MCC, underscoring its effectiveness in managing loops.

Large language models (LLMs) increasingly generate Markdown that is consumed by renderers, agents, code extractors, and structured downstream pipelines. Yet existing evaluations often conflate content quality with format adherence, leaving Markdown boundary failures under-measured. We introduce LatentMD, a benchmark and evaluation protocol for diagnosing CommonMark-level fence-boundary failures in LLM-generated Markdown. LatentMD separates content correctness from boundary correctness, enabling detection of outputs that are content-correct but boundary-broken. The benchmark contains 4,179 prompts and a CLI for scoring arbitrary model outputs. Across 9 LLMs and roughly 37,600 generations, we find that Markdown boundary failures are widespread: 38.0% of valid main-grid outputs are content-correct but boundary-broken, with substantial boundary breakage under unspecified prompts and in a small human-authored validation set. Ablations show that failures are driven primarily by same-family symmetric-delimiter collisions rather than nesting alone, are only partially mitigated by prompt hints, and generalize to Python triple-quote docstrings while JSON remains robust as an asymmetric-delimiter control. LatentMD provides a reproducible diagnostic target for parser-sensitive LLM evaluation.