arXiv subjects

Priyadarsi Mishra

Publications and source records attributed to Priyadarsi Mishra.

3 recordsLinked to original sources

arXiv2026

Distribution-Aware Programming: Learning Specialized Solvers from Experience

Many optimization problems are solved repeatedly on instances drawn from the same underlying distribution. In this setting, a system can begin with a general-purpose solver and use experience from previous instances to learn a cheaper way to solve future ones. We formalize this as \emph{distribution-aware programming}: samples from an unknown deployment distribution are used to produce executable solver code whose quality and runtime generalize to new instances. A simple analysis shows how sample access interpolates between distribution-oblivious and distribution-informed algorithm design, and when the offline cost of specialization is recovered through lower deployment cost. We instantiate this framework with an LLM agent that proposes structural hypotheses, analyzes training instances, and synthesizes specialized solver code; the LLM is used only before deployment. Across \(21\) structured combinatorial-optimization distributions, the synthesized solvers achieve high quality while often replacing generic search or optimization with smaller distribution-specific computations. Against released PACE competition solvers, our method remains competitive while using substantially less runtime: \(75\)--\(125\times\) less on PACE 2025 Dominating Set, \(80\)--\(96\times\) less on Hitting Set, and more than \(34{,}000\times\) less on the PACE 2024 OCM exact track. More broadly, the results suggest using AI not only to solve optimization problems, but to learn how recurring distributions should be solved.

cs.AI↗

arXiv2026

LLM Priors for ERM over Programs

We study program-learning methods that are efficient in both samples and computation. Classical learning theory suggests that when the target admits a short program description, for example a short piece of ``Python code'', it can be learned from few examples by ERM over the program class. However, this approach relies on enumerating candidate programs, which is typically exponential in the description length; gradient-based training avoids this explicit search but, for some families of short programs, can require exponentially many samples to succeed. We propose \textsc{LLM-PV}, a propose-and-verify recipe that enables ERM-style selection over a discrete program class without exhaustive enumeration: a pretrained LLM induces a proposal distribution over candidate programs, each proposal is executed and scored on a held-out validation set, and the best program is selected, with no gradient updates or validation feedback used to adapt the sampling distribution. Across algorithmic tasks including parity variants, pattern matching, and primality testing, \textsc{LLM-PV} often recovers the exact underlying rule from a small labeled set and generalizes far beyond the training sequence lengths, while SGD-trained transformers, fine-tuning, in-context learning, and classical ML baselines can fit the training data yet fail to generalize reliably. Together, these results suggest that pretrained LLM priors can serve as effective search biases for ERM, narrowing the gap between statistical and computational efficiency.

cs.LG↗

arXiv2025

On the Alignment Between Supervised and Self-Supervised Contrastive Learning

Self-supervised contrastive learning (CL) has achieved remarkable empirical success, often producing representations that rival supervised pre-training on downstream tasks. Recent theory explains this by showing that the CL loss closely approximates a supervised surrogate, Negatives-Only Supervised Contrastive Learning (NSCL) loss, as the number of classes grows. Yet this loss-level similarity leaves an open question: {\em Do CL and NSCL also remain aligned at the representation level throughout training, not just in their objectives?} We address this by analyzing the representation alignment of CL and NSCL models trained under shared randomness (same initialization, batches, and augmentations). First, we show that their induced representations remain similar: specifically, we prove that the similarity matrices of CL and NSCL stay close under realistic conditions. Our bounds provide high-probability guarantees on alignment metrics such as centered kernel alignment (CKA) and representational similarity analysis (RSA), and they clarify how alignment improves with more classes, higher temperatures, and its dependence on batch size. In contrast, we demonstrate that parameter-space coupling is inherently unstable: divergence between CL and NSCL weights can grow exponentially with training time. Finally, we validate these predictions empirically, showing that CL-NSCL alignment strengthens with scale and temperature, and that NSCL tracks CL more closely than other supervised objectives. This positions NSCL as a principled bridge between self-supervised and supervised learning. Our code and project page are available at [\href{https://github.com/DLFundamentals/understanding_ssl_v2}{code}, \href{https://dlfundamentals.github.io/cl-nscl-representation-alignment/}{project page}].

cs.LG↗