Algorithmic Blindness in Large Language Models: A Calibration Study of Performance Prediction

Large language models (LLMs) often achieve strong performance on reasoning benchmarks, but final-answer accuracy alone does not show whether they faithfully execute the procedure specified in a prompt. We introduce a controlled diagnostic benchmark for procedural execution, where models are given a step-wise arithmetic procedure and two numeric inputs, and must return the final computed value. Complexity is varied through procedure length and look-back dependencies over intermediate variables. Average first-answer accuracy drops from 63% on 5-step procedures to 20% on 95-step procedures. Generation-level analysis shows that failures often involve missing answers, premature answers, self-correction after an initial error and under-executed traces. These findings suggest that apparent reasoning ability can mask substantial weaknesses in faithful long-horizon procedural execution.

Large language models (LLMs) now generate substantial production code, often for tasks with multiple valid algorithmic solutions. Incidental prompt cues, meaning contextual words or metadata outside the task specification, can steer which algorithm the model selects, even when all outputs pass the same tests. Prompt sensitivity is well studied as a tool to improve output quality. Here, output policy means algorithm choice under fixed correctness. We define algorithm steering as cue-induced shifts in algorithm-family distributions and run 46,535 controlled experiments across 11 tasks, 19 cue types (18 channels plus a memoization semantic-vs-surface ablation that preserves meaning while changing typography and punctuation), and 15 model configurations. We find large, systematic shifts in algorithm-family distributions (up to 100 pp), largely consistent with cue semantics, including in applied tasks such as rate limiting. Direct algorithm naming is the most reliable mitigation we tested. Accidental context therefore creates an "invisible lottery" over performance, security, and maintainability.

Large language models (LLMs) achieve impressive scores on standard benchmarks yet routinely fail questions that any human would answer correctly in seconds. We introduce BrainBench, a benchmark of 100 brainteaser questions spanning 20 carefully designed categories, each targeting a specific commonsense reasoning failure mode in LLMs. Categories range from implicit physical constraints ("Should I walk or drive my rental car to the return lot?") to semantic scope tricks and default assumption hijacks. We evaluate eight frontier models -- four from the Claude family and four from the GPT family -- using a zero-shot protocol with 10 independent runs per question. The best model, Claude Opus 4.6 with extended thinking, achieves only 80.3% accuracy; the worst, GPT-4o, scores 39.7%. Even top-performing models exhibit a 6-16 percentage-point gap between accuracy and consistency, revealing stochastic reasoning. Cross-lingual evaluation in Chinese shows most models degrade by 2-8 percentage points, confirming that these failures reflect reasoning deficits rather than language-specific artifacts. BrainBench provides a fine-grained diagnostic tool for identifying where and why LLMs substitute surface heuristics for genuine commonsense reasoning.