Luke Huan

Ferhat Erata, Hao Zhou, Luke Huan

We introduce fidelity probes: natural-language questions generated from a reference artifact with code-derived ground-truth answers, answered from a candidate specification. The fraction of agreeing probes, which we call the fidelity, decomposes into contradiction and coverage-gap rates that drive targeted spec edits to convergence. On a 15-program, roughly 12k-line COBOL benchmark (AWS CardDemo), we raise frozen-test specification fidelity from 0.63 to 0.94 over eight iterations, with the plateau location predicted by a two-state Markov fixed point $F^\dagger$ from just four iterations of rate data. Probes come from an LLM reading the code or from a static-analysis pipeline over its control-flow, data-flow, and system-dependence graphs, with a tunable mixture. A probe-resampling protocol with a frozen held-out set gives a Hoeffding-bounded overfitting discriminant; our measured train/test gap stays more than an order of magnitude below this envelope. Three graph-grounded mixtures lift fidelity by +16 to +30 points; cross-distribution evaluation shows the LLM and symbolic channels are empirically complementary. A cross-family generator sweep on five independent LLM lineages (Anthropic, DeepSeek, Google, Alibaba, OpenAI) confirms the convergence behaviour is not tied to any single model family: three of five non-Claude generators produce trajectories consistent with the Markov fixed-point prediction, and the frozen-test protocol actively falsifies the two generators whose probe distributions drift across iterations. The method applies to any pair of artifacts that are supposed to describe the same behaviour.

Tao Yu, Gaurav Gupta, Karthick Gopalswamy et al.

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision ($16$-bit floating points) and can be naturally extended to work with even lower precision such as $8$-bit. Experimental results show that pre-training using Collage removes the requirement of using $32$-bit floating-point copies of the model and attains similar/better training performance compared to $(16, 32)$-bit mixed-precision strategy, with up to $3.7\times$ speedup and $\sim 15\%$ to $23\%$ less memory usage in practice.