Sanjeev Arora

Test-time scaling has emerged as a powerful way to improve LLMs. However, existing methods are best suited to short, bounded outputs that can be directly compared, ranked or refined. Long-horizon coding agents violate this premise: each attempt produces an extended trajectory of actions, observations, errors, and partial progress taken by the agent. In this setting, the main challenge is no longer generating more attempts, but representing prior experience in a form that can be effectively selected from and reused. We propose a test-time scaling framework for agentic coding based on compact representations of rollout trajectories. Our framework converts each rollout into a structured summary that preserves its salient hypotheses, progress, and failure modes while discarding low-signal trace details. These representations enable two complementary forms of scaling. For parallel scaling, we introduce Recursive Tournament Voting (RTV), which recursively narrows a population of rollout summaries through small-group comparisons. For sequential scaling, we adapt Parallel-Distill-Refine (PDR) to condition new rollouts on summaries of prior attempts. Our method consistently improves the performance of frontier coding agents across SWE-Bench Verified and Terminal-Bench v2.0. For example, by using our method Claude 4.5 Opus improves from 70.9% to 77.6% on SWE-Bench Verified (mini-SWE-agent) and 46.9% to 59.1% on Terminal-Bench v2.0 (Terminus 1). Our results suggest that test-time scaling for long-horizon agents is fundamentally a problem of representation, selection, and reuse.

Machine unlearning seeks to selectively remove the "influence" of specific training data on a model’s outputs. The ideal goal is Retrain Equivalence--behavior identical to a model trained from scratch on only the retained data. This goal was formulated for models trained on i.i.d. data batches, but modern pipelines often involve multi-stage training, with each stage having a distinct data distribution and objective. Examples include LLM fine-tuning for alignment, reasoning ability, etc. Our study shows via theory and experiments that this shift to multi-stage training introduces a fundamental barrier for machine unlearning. The theory indicates that the outcome of local unlearning—methods that only use gradients computed on the forget set—is path-dependent. That is, a model's behavior during unlearning is influenced by the order of its training stages during learning, making it impossible for path-oblivious algorithms to universally achieve Retrain Equivalence. We empirically demonstrate the same phenomenon in LLM post-training across Llama and Qwen models (1B–14B) with gradient ascent, NPO, and SimNPO local unlearning algorithms. Models fine-tuned via different orderings of identical training stages diverge in behavior during unlearning, with the degradation in GSM8K accuracy after unlearning varying by over 20% across paths. We also observe that some learning paths consistently produce models that unlearn slowly. During unlearning, whether the probability mass gets squeezed into paraphrasing or alternative concepts is also path-dependent. These results consistently show that Retrain Equivalence is an ill-posed target for local unlearning algorithms, so long as the target models are trained in stages. In situations where access to models' training histories is hard, the current work calls for rethinking the definition and desiderata of machine unlearning.