Many recursively self-improving systems improve by editing their codebases based on observed rollout behavior. However, recent methods largely treat self-improvement as offline search: variants are optimized and evaluated on fixed benchmarks. This misaligns with real-world deployment, where tasks arrive sequentially and may have different distributions. We study recursive self-improvement as online learning over non-stationary task streams. In this setting, reliable execution and fallback are particularly difficult with limited evidence: different branches of self-improvement see different tasks, so raw rewards conflate capability with task difficulty, leading to overly conservative or optimistic reversion. We propose Online Anchor-calibrated Self-Improvement System (OASIS) that runs an adaptive reference agent on incoming tasks, converts raw rewards into paired comparisons, and uses confidence-calibrated rules for branch continuation and fallback without evaluating every agent on all tasks. Across SWE-Bench Pro and DeepResearch Bench, OASIS consistently improves over both the initial agent and prior RSI baseline SSA, raising the SWE-Bench Pro solve rate from 51.6% to 56.9% using Qwen3.6-35B-A3B and DeepResearch Bench from 35.18 to 39.31 using Gemini 3 Flash. This enables OASIS to outperform larger open weights and proprietary systems, including Qwen3.5-397B-A17B, Minimax 2.7, Qwen3.6-Plus, and GPT-5.3-Codex, with sustained deep self-improvements rather than shallow cycles.

Detecting pre-training data in Large Language Models (LLMs) is crucial for auditing data privacy and copyright compliance, yet it remains challenging in black-box, zero-shot settings where computational resources and training data are scarce. While existing likelihood-based methods have shown promise, they typically aggregate token-level scores using uniform weights, thereby neglecting the inherent information-theoretic dynamics of autoregressive generation. In this paper, we hypothesize and empirically validate that memorization signals are heavily skewed towards the high-entropy initial tokens, where model uncertainty is highest, and decay as context accumulates. To leverage this linguistic property, we introduce Positional Decay Reweighting (PDR), a training-free and plug-and-play framework. PDR explicitly reweights token-level scores to amplify distinct signals from early positions while suppressing noise from later ones. Extensive experiments show that PDR acts as a robust prior and can usually enhance a wide range of advanced methods across multiple benchmarks.

Imagine you are in a supermarket. You have two bananas in your basket and want to buy four apples. How many fruits do you have in total? This seemingly straightforward question can be challenging for data-driven language models, even if trained at scale. However, we would expect such generic language models to possess some mathematical abilities in addition to typical linguistic competence. Towards this goal, we investigate if a commonly used language model, BERT, possesses such mathematical abilities and, if so, to what degree. For that, we fine-tune BERT on a popular dataset for word math problems, AQuA-RAT, and conduct several tests to understand learned representations better. Since we teach models trained on natural language to do formal mathematics, we hypothesize that such models would benefit from training on semi-formal steps that explain how math results are derived. To better accommodate such training, we also propose new pretext tasks for learning mathematical rules. We call them (Neighbor) Reasoning Order Prediction (ROP or NROP). With this new model, we achieve significantly better outcomes than data-driven baselines and even on-par with more tailored models.