Universal LLM reliability is not a finite-library problem: across all possible tasks, tools, schemas, knowledge sources, and evaluator expectations, new intervention-distinguishable failure modes can appear without bound, so no finite intervention dictionary can guarantee bounded residual error for every such mode. But deployed systems do not operate over the whole universe. They operate inside operationally bounded patches (legal review, medical RAG, code repair, customer-support agents, contract extraction) with recurring tasks, schemas, tools, and evaluator expectations. Within such patches, empirical evidence suggests failures are sparse, repetitive, and concentrated in a small recurring catalogue, so reliability becomes a local catalogue-discovery and intervention-coverage problem rather than an exponential token-length problem. We formalize this transition with two propositions and one corollary. Proposition 1 is the worst-case-mode-wise negative result: no finite intervention dictionary covers every distinguishable failure mode of an unbounded domain. Corollary 1 is the inverse-discovery implication: the logarithmic upper bound on mode discovery cannot accommodate linearly more distinct tail modes without exponentially more observed hard-failure events. Proposition 2 is the positive patch-local result: under log active-mode exposure and head-heavy coverage, a sufficient per-hard-decision intervention budget grows polylogarithmically in sequence length and becomes domain-constant once the patch catalogue saturates. The framework relocates rather than dissolves long-context difficulty: where the number of hard decisions itself grows with task length, reliability remains hard; the contribution is to identify the on-axis intervention rather than to make those regimes easy.
While existing benchmarks demonstrate the near-perfect performance of large language models (LLMs) on various tasks, this apparent saturation often obscures the need for rigorous evaluation of their reliability. In real-world deployment, however, achieving extremely high reliability (e.g., "five-nines" (99.999%) vs. "three-nines" (99.9%)) is fundamentally critical, as this gap results in an order-of-magnitude increase in failures, which is catastrophic in reliability-critical applications. Still, estimating such a rare failure probability with tight confidence bounds requires prohibitively large LLM inference sizes, making standard Monte Carlo evaluation infeasible under limited compute budgets. In this paper, we observe that LLM failures exhibit strong systematic patterns: across broad parameterized input spaces, a small subset of inputs disproportionately accounts for the majority of failures. Leveraging this observation, we propose to learn a sampling distribution concentrated on failure-prone inputs via the cross-entropy method (CEM). We evaluate our framework on three LLMs, Qwen2.5-Math-7B-Instruct, gpt-oss-20b-low, and Gemini 2.5 Flash Lite, across parameterized GSM8K templates and achieve up to 156.22x reduction in required inferences compared to naive uniform sampling. Our estimates reveal that models with indistinguishable accuracy on standard benchmarks can differ substantially in estimated failure rates, underscoring that reliability is a distinct and measurable axis of model quality. Our simple yet practical framework enables the evaluation of extreme reliability in LLMs, a distinct and underexplored dimension of evaluation beyond existing benchmarks, for their growing use in reliability-sensitive applications.
Reliability in large language model (LLM) systems is typically framed as a function of model capability. We challenge this by demonstrating that reliability is significantly influenced by \emph{inference-time control} -- the computational layer governing task framing and context selection. We introduce \emph{CogniConsole}, an architectural instantiation that externalizes this control into a structured interface combining programmatic coordination with bounded prompt-based reasoning. Through \emph{controllability-oriented probes} (N=489) in a multi-step interactive environment, we show that increasing structural scaffolding -- from unstructured to fully scaffolded -- \textbf{systematically reduces output variance and failure rates under a fixed model architecture}. Our results indicate that many observed failure modes, such as context drift and inconsistent constraint adherence, arise from under-specified control rather than insufficient capability. This work provides an empirical basis for treating inference-time control as a first-class abstraction, opening new directions for designing and evaluating LLM systems beyond scaling alone.
When a multi-module LLM agent fails, the module most responsible for the failure is not necessarily the best place to intervene. We demonstrate this Diagnostic Paradox empirically: causal analysis consistently identifies the routing module -- which selects which tool to call next -- as the primary bottleneck across three independent agent families. Yet injecting prompt-level correction examples into this module consistently degrades performance, sometimes severely. Patching an upstream query-rewriting module instead reliably improves outcomes. The effect holds with statistical significance on two agent families and directional consistency on a third; alternative repair strategies at the routing module (instruction rewriting, model upgrade) are neutral, confirming that the harm is specific to correction-injection patching. We explain this asymmetry through the Linguistic Contract hypothesis: each downstream module implicitly adapts to its upstream's characteristic error distribution, so correcting the bottleneck breaks this implicit alignment in a way that upstream corrections do not. We operationalize this via a per-agent co-adaptation measure, derived from diagnosis alone, and show it is consistently associated with patching harm across agent families: higher co-adaptation co-occurs with harm, lower with safety. This trend holds across all three agent families, providing preliminary support for the hypothesis beyond a single-agent observation.