Prior or Feedback? What an LLM Uses When Adapting Neural Operators

Large language models (LLMs) are increasingly deployed to solve complex scientific and practical problems via iterative optimization. However, dynamically coordinating diverse search mechanisms as candidate quality, failure modes, and resource budgets evolve remains a critical open challenge. Targeted empirical diagnostics reveal that mechanism effectiveness is highly state-dependent. Motivated by this, we analyze how individual decisions drive final outcomes, decomposing the expected terminal improvement under a shared budget into cumulative decision opportunities minus cumulative selection losses. Guided by this opportunity-loss theoretical foundation, we propose OptiCom, a unified framework that represents LLM-driven optimizers within a shared configuration space: C=(A,Q,O,E,M,S), corresponding to artifact, query, operator, evaluation, memory, and strategy. Operating within this space, a fast LLM-based Optimization Controller dynamically composes immediate mechanisms through structured Action Packages, while a slower Strategy Adapter refines long-term selection preferences, operator weights, and templates based on accumulated trajectory feedback. Comprehensive evaluations across 32 benchmark groups demonstrate the superiority of framework: OptiCom achieves an average Max-score rank of 1.72 among 14 evaluated configurations, securing the top score in 23 groups. Ultimately, these results highlight the broad applicability and high extensibility of OptiCom as a general-purpose paradigm for robust LLM test-time scaling.

Memory is the key component for transforming a stateless LLM into a persistent, evolving agent through experience accumulation, long-horizon planning, and continual self-improvement. Existing memory systems typically take the LLM as the center and design memory operations tailored to a specific backbone. In practice, however, users frequently switch between LLMs, for example using Claude for coding and GPT for writing across tasks, or routing different steps to different backbones within a single task for cost-effective trade-offs. As a result, memory written by one model often needs to be consumed by another. Making upstream memory effectively adapt to and activate downstream LLMs remains a critical yet underexplored problem. To bridge this gap, we shift the perspective from LLM-centric memory design to \emph{memory-centric LLM adaptation}. Specifically, we approach the above upstream-downstream memory adaptation problem from both the write and read sides, and design two profile-conditioned operators that are jointly trained to optimize how memory is stored and presented for better task completion. To ensure the learned operators generalize across a broad set of LLMs, we propose a minimum-gain sampling curriculum that prioritizes the least-served LLMs during training. To better measure the operators' actual contribution rather than the LLM's own capability, we design a performance-gap reward that compares against a naive memory baseline. Experiments on HotpotQA, 2WikiMultihopQA, and MuSiQue demonstrate that our model consistently outperforms baselines and remains robust under unseen-model replacement.

To align a Large Language Model (LLM), most existing methods collect explicit human feedback and train a reward model to predict the human preference based on the response text. These existing methods have two key limitations. First, the users rarely provide explicit feedback for LLM responses, which makes the high-quality preference annotation expensive to collect. Second, the methods do not leverage implicit human feedback, which has proven vital to the economic moats of Internet giants. To quantify the value of implicit feedback, we build a new dataset called IFLLM, which collects 1336 multi-turn questions from the 59 Mechanical Turk workers, their mouse trajectories, and eye gazing points to the LLMs' responses from their webcams. IFLLM shows that the users have very diverse types of gazing behavior and mouse trajectories. Our reward model based on the implicit user feedback boosts the accuracy of the text-based reward model from 55% to 64% and nearly triples the relative response quality improvements after applying the DPO to eight LLMs, demonstrating the value of implicit feedback in the wild. Our data collection website, dataset, and codes can be found at https://github.com/themehulpatwari/llm-implicit-feedback/.