Increasing test-time compute for LLMs shows promise across domains but remains underexplored in code generation, despite extensive study in math. In this paper, we propose S*, the first hybrid test-time scaling framework that substantially improves the coverage and selection accuracy of generated code. S* augments the existing parallel scaling approach with sequential scaling to further increase the performance. It further leverages a novel selection mechanism that adaptively generates distinguishing inputs for pairwise comparison, combined with execution-grounded information to robustly identify correct solutions.We evaluate S* across 12 Large Language Models and Large Reasoning Models and show that: (1) S* consistently improves performance across model families and sizes, enabling a 3B model to outperform GPT-4o-mini; (2) S* enables non-reasoning models to surpass reasoning models—GPT-4o-mini with S* outperforms o1-preview by 3.7% on LiveCodeBench; (3) S* further boosts state-of-the-art reasoning models—DeepSeek-R1-Distill-Qwen-32B with S* achieves 85.7% on LiveCodeBench, approaching o1 (high) at 88.5%. Codes, model generations and intermediate experiments results are available under Codes, model generations and intermediate ex-periments results are available under https://github.com/NovaSky-AI/SkyThought.

Large reasoning models (LRMs) tackle complex problems by following long chain-of-thoughts (Long CoT) that incorporate reflection, backtracking, and self-validation. However, the training techniques and data requirements to elicit Long CoT remain poorly understood. In this work, we find that language models can effectively learn Long CoT reasoning through data-efficient supervised fine-tuning (SFT) and further parameter-efficient low-rank adaptation (LoRA). Crucially, we find that the structure of Long CoT is critical to the learning process in this data-efficient fine-tuning process. Training on content-incorrect examples, e.g. those lead to incorrect answers or corrupted digits, still leads to significant performance gains. In contrast, training on structurally incorrect examples, e.g., with shuffled or deleted reasoning steps, yield smaller improvements or even degrade performance.

Recent work learns contextual representations of source code by reconstructing tokens from their context. For downstream semantic understanding tasks like code clone detection, these representations should ideally capture program functionality. However, we show that the popular reconstruction-based RoBERTa model is sensitive to source code edits, even when the edits preserve semantics. We propose ContraCode: a contrastive pre-training task that learns code functionality, not form. ContraCode pre-trains a neural network to identify functionally similar variants of a program among many non-equivalent distractors. We scalably generate these variants using an automated source-to-source compiler as a form of data augmentation. Contrastive pre-training outperforms RoBERTa on an adversarial code clone detection benchmark by 39% AUROC. Surprisingly, improved adversarial robustness translates to better accuracy over natural code; ContraCode improves summarization and TypeScript type inference accuracy by 2 to 13 percentage points over competitive baselines. All source is available at https://github.com/parasj/contracode.

Question answering models struggle to generalize to novel compositions of training patterns. Current end-to-end models learn a flat input embedding which can lose input syntax context. Prior approaches improve generalization by learning permutation invariant models, but these methods do not scale to more complex train-test splits. We propose Grounded Graph Decoding, a method to improve compositional generalization of language representations by grounding structured predictions with an attention mechanism. Grounding enables the model to retain syntax information from the input that significantly improves generalization to complex inputs. By predicting a structured graph containing conjunctions of query clauses, we learn a group invariant representation without making assumptions on the target domain. Our model performs competitively on the Compositional Freebase Questions (CFQ) dataset, a challenging benchmark for compositional generalization in question answering. Especially, our model effectively solves the MCD1 split with 98% accuracy. All source is available at https://github.com/gaiyu0/cfq.