Systems that generate GPU kernels with language models report high correctness rates. Those rates come from a single loose test: run the kernel on a few random inputs at one fixed shape and accept it if the output is close to a reference. A kernel can pass that test and still be silently wrong. It can return an ordinary number where the true answer is a NaN or an infinity, differ from run to run, break when the shape changes, or accumulate in fp16 where the reference keeps an fp32 total. We build the instrument that checks correctness properly: a contract-grade verifier of twelve adversarial gates, each a property a correct kernel must satisfy, several of them tolerance-free, so no choice of threshold can explain a failure away. Aimed outward, the verifier audits 2,638 machine-generated kernels that a public system's own harness had already accepted as correct. It finds 39.5% broken beyond any tolerance argument and 62.1% carrying at least one violation. The field's standard test accepts 1,487 kernels the verifier rejects, against only 14 the other way. We defend the finding four independent ways: a 7/7 positive control, a threshold-calibration sweep, 98.5% agreement with the reference benchmark's own correctness code, and a stratified hand-audit. Aimed inward, the verifier judges a kernel of our own: the first native Blackwell tcgen05 training backward for the gated-linear-recurrence (GDN) family, including the reverse-state stage the field still runs on a fallback. We establish its correctness independently, against a double-precision oracle, and train five family members through it. The correctness signal behind reported progress in kernel generation is far weaker than the numbers suggest, and a set of tolerance-free contracts would close most of the gap.
Liexin Cheng, Xue Cheng, Shuaiqiang Liu +1q-fin.CP cs.AI
Automated code generation is becoming an important tool in quantitative finance, where large language models can generate option pricing implementations directly from mathematical model specifications. Validating such implementations, however, requires considerably more than conventional software testing: numerical pricing methods must remain mathematically consistent, numerically stable, and reliable across a wide range of model parameters. We introduce RIDGE, an autonomous validation framework in which generated pricing implementations are subjected to structured no-arbitrage tests, stress tests, benchmark comparisons, and consistency checks. Validation evidence is interpreted diagnostically, while the resulting knowledge is accumulated in a repository and reused across models and successive validation iterations. This enables systematic refinement of both the pricing implementation and the validation methodology. The framework is applied to five stochastic volatility models. Across these studies, all detected implementation defects are removed and, in two cases, the validation process itself leads to new semi-analytic pricing methodologies. The supplementary material is available in the GitHub repository: https://github.com/ShQiangLiu/ridge.
Fred Mesnard, Thierry Marianne, Étienne Payet +1cs.LO cs.AI
Ninety-Nine Prolog Problems (P-99) is a famous set of Prolog exercises. We solved the first thirty three just by prompting an LLM (Large Language Model). We used Claude from Anthropic. By solved we mean: generate the Prolog code and a test file, run the tests and check whether they pass, then formally prove types, groundness, termination, uniqueness, existence and also sometimes functional correctness with LPTP (Logic Program Theorem Prover). Hence our approach is an experiment in vibe-coding/vericoding of P-99. It is a vibe-coding experiment because we started from informal specifications written in English and let Claude generate the Prolog code. It also fits within vericoding because the LLM proved reliability guarantees on the generated Prolog code. Claude wrote 58 logic procedures, 508 tests, 257 lemmas for a total of 11800 proof lines. We manually checked each file generated by the LLM. We checked the Prolog code, ran the tests, examined the logical statements generated by Claude and proof-checked Claude's proofs with LPTP. This paper describes this experiment and provides the main details so that it can be reproduced by the interested reader.
Large language models now translate natural-language descriptions of decision problems into solver-ready optimization models, and they fail silently. A generated model often runs and still encodes the wrong problem, while standard evaluation compares optimal values against labeled answers that deployment does not provide. How to certify such a model without any reference is the question this paper addresses. We develop falsification-based verification. Every numeric quantity in a problem description plays a role that the text itself states, such as a capacity, a requirement, or a unit cost, and any correct model must respond to changes in these quantities as the stated roles dictate. From duality and sensitivity analysis we derive a battery of solver-based tests that are individually sound, so a violation certifies a faulty model and the false-positive rate is zero by design. We characterize the errors that no test of this kind can see, give conditions under which each canonical error class is detected with certainty, and prove that perturbation testers with tuned thresholds cannot be simultaneously sound and nontrivial. Across 326 ground-truth models, a synthetic family, and four public benchmarks with two generators, the battery flags 0.0% of faithful models while a threshold tester flags 54.9%; it detects 56.1% of core formulation errors, 70.0% under certified preconditions, and 40.4% of the errors that value-based scoring provably cannot see, and it reproduces the predicted detectability pattern including its blind spots. Every flag carries a machine-checkable certificate that localizes the defect, and a full audit costs about 25 millisecond-scale solver calls per model. Classical sensitivity analysis and duality thus offer a rigorous, label-free audit that complements existing evaluation of AI-generated optimization models.
With the rapid development of Large Language Models (LLMs), text watermarking has emerged as a crucial technique for identifying machine-generated content. However, directly applying existing logits-based watermarking methods to code generation remains challenging, since the low-entropy nature of code exacerbates the trade-off between code quality and watermark detectability. In this paper, we propose a novel code watermarking approach called Grammar-Driven Watermark (GDW) for LLMs. GDW preserves syntactic validity through a grammar-guided three-level masking mechanism and injects watermark signals via structural role-aware modulation, assigning a stronger bias to content-bearing tokens while applying a more conservative bias to syntax-critical tokens. Aligning with the generation process, we further design a role-aware weighted detection statistic to improve detectability. Experiments across multiple programming languages, models, and decoding strategies show that GDW establishes a stronger quality-detectability trade-off frontier than existing methods, while maintaining robustness against variable-renaming attacks.
LLM-generated code often compiles, passes tests, and appears correct, yet breaks once deployed. The root cause is frequently structural rather than logical. A generated endpoint references configuration keys never declared in the project, an import targets a package that does not exist in any registry, or a new route omits the authentication guard applied to every sibling endpoint. Each patch is locally valid but globally incoherent, and standard CI toolchains rarely surface these failures. As LLM-powered coding tools see widespread adoption, this blind spot poses a growing risk to software quality. We call this the \textbf{patchwork problem}. This paper formalizes structural coherence as consistency invariants over graph representations of repository artifacts, including import, call, dependency, configuration, schema, resource, control-flow, and routing graphs, and introduces an eight-category failure taxonomy distinguishing defects specific to LLM generation from those merely amplified by it. We present a hybrid verification framework that delegates to mature static analysis tools where they already excel and deploys purpose-built detectors for cross-cutting invariants underserved by existing toolchains, targeting provable constraint violations rather than heuristic pattern matching. Empirical evaluation across two frontier models under four prompting strategies reveals that the vast majority of structural failures evade type checking, testing, and SAST entirely, and that failure patterns diverge qualitatively between models in ways that challenge model-agnostic mitigation strategies. External validation on real-world AI-generated repositories confirms that these failures are not artifacts of controlled experimentation but are prevalent wherever LLMs write code with minimal human oversight.
Correctness and readability are key measures of code quality, respectively ensuring functional fidelity and ease of comprehension. While most existing research focuses on improving the correctness of large language models~(LLMs) generated codes, readability remains under-addressed. Enhancing readability through targeted control is challenging due to its subjective nature. In this article, we employ representation engineering~(RepE) as the targeted control method given its characteristics of low data dependency and low computational cost. Prior work on RepE has primarily focused on the targeted control for a single task, but improving the code readability requires the control across multiple tasks. Accordingly we proposes the multitask RepE framework and theoretically discuss the impact of the multitask steering method on the tradeoff between the code readability and correctness. We further provide comprehensive experiments in support. All the relevant implementations are open-source and available upon request.