Anupam Nayak

Anupam Nayak, Baris Askin, Muhammed Ustaomeroglu et al.

Reasoning post-training with reinforcement learning from verifiable rewards (RLVR) is typically studied in centralized settings, yet many realistic applications involve decentralized private data distributed across organizations. Federated training is a natural solution, but scaling RLVR in this regime is challenging: full-model synchronization is expensive, and performing many local steps can cause severe client drift under heterogeneous data. We propose a federated RLVR framework that combines LoRA-based local adaptation with public-data-based off-policy steps to improve both communication efficiency and cross-client coordination. In particular, a small shared public dataset is used to periodically exchange and reuse response-level training signals across organizations, providing a lightweight anchor toward a more globally aligned objective without exposing private data. Our method selectively replaces locally incorrect responses with globally correct ones during public-data steps, thereby keeping training closer to the local policy while still benefiting from cross-client coordination. Across mathematical and medical reasoning benchmarks and models, our method consistently improves over standard baselines. Our results highlight a simple and effective recipe for federated reasoning post-training: combining low-rank communication with limited public-data coordination.

Baris Askin, Shivam Patel, Anupam Nayak et al.

Large language models (LLMs) are increasingly accessed as remotely hosted services by edge and enterprise clients that cannot run frontier models locally. Since models vary widely in capability and price, routing queries to models that balance quality and inference cost is essential. Existing router approaches assume access to centralized query-model evaluation data. However, these data are often fragmented across clients, such as end users and organizations, and are privacy-sensitive, which makes centralizing data infeasible. Additionally, per-client router training is ineffective since local evaluation data is limited and covers only a restricted query distribution and a biased subset of model evaluations. We introduce the first federated framework for LLM routing, enabling clients to learn a shared routing policy from local offline query-model evaluation data. Our framework supports both parametric multilayer perceptron router and nonparametric K-means router under heterogeneous client query distributions and non-uniform model coverage. Across two benchmarks, federated collaboration improves the accuracy-cost frontier over client-local routers, both via increased effective model coverage and better query generalization. Our theoretical results also validate that federated training reduces routing suboptimality.

Anupam Nayak, Kota Srinivas Reddy, Nikhil Karamchandani

We study the well-known coded caching problem in an online learning framework, wherein requests arrive sequentially, and an online policy can update the cache contents based on the history of requests seen thus far. We introduce a caching policy based on the Follow-The-Perturbed-Leader principle and show that for any time horizon T and any request sequence, it achieves a sub-linear regret of \mathcal{O}(\sqrt(T) ) with respect to an oracle that knows the request sequence beforehand. Our study marks the first examination of adversarial regret in the coded caching setup. Furthermore, we also address the issue of switching cost by establishing an upper bound on the expected number of cache updates made by our algorithm under unrestricted switching and also provide an upper bound on the regret under restricted switching when cache updates can only happen in a pre-specified subset of timeslots. Finally, we validate our theoretical insights with numerical results using a real-world dataset

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Baris Askin, Muhammed Ustaomeroglu, Anupam Nayak et al.

Fine-tuning LLMs on narrow harmful datasets can induce Emergent Misalignment (EM), where models exhibit misaligned behavior far beyond the fine-tuning distribution. We argue that emergent misalignment can be better understood as a data-mediated transfer phenomenon: harmful fine-tuning examples do not induce uniform behavioral spillover, but interact with the structural properties of the dataset and the difficulty of the tasks relative to the model. Across our experiments, we find that misalignment appears more readily when fine-tuning and evaluation prompts share similar underlying functional structure, when prompts leave more room for coherent harmful completions, and when the target behavior has been more reliably learned by the model. The training pipeline itself also matters: pretraining composition shapes later misalignment. We further study Subliminal Learning (SL), where misalignment is transmitted by fine-tuning on seemingly benign data generated by a harmful teacher. Moving beyond the standard SFT setting, we for the first time compare this transfer under off-policy and on-policy distillation as well, allowing us to separate the roles of the teacher guidance and the training data distribution in transmitting misalignment. Together, these results argue for a data-centric view: Emergent/subliminal misalignment should not be treated as a simple consequence of isolated harmful fine-tuning examples, but as the result of interactions between fine-tuning data structure, pretraining distributions, and training channels.

Neharika Jali, Anupam Nayak, Gauri Joshi

As LLM reasoning performance plateau, improving inference-time compute efficiency is crucial to mitigate overthinking and long thinking traces even for simple queries. Prior approaches including length regularization, adaptive routing, and difficulty-based budget allocation primarily focus on single-turn settings and fail to address the sequential dependencies inherent in multi-turn reasoning.In this work, we formulate multi-turn reasoning as a sequential compute allocation problem and model it as a multi-objective Markov Decision Process. We propose TAB: Turn-Adaptive Budgets, a budget allocation policy trained via Group Relative Policy Optimization (GRPO) that learns to maximize task accuracy while respecting global per-problem token constraints. Consequently, TAB takes as input the conversation history and learns to adaptively allocate smaller budgets to easier turns and save appropriate number of tokens for the crucial harder reasoning steps. Our experiments on mathematical reasoning benchmarks demonstrate that TAB achieves a superior accuracy-tokens tradeoff saving up to 35% tokens while maintaining accuracy over static and off-the-shelf LLM budget baselines. Further, for systems where a plan of all sub-questions is available apriori, we propose TAB All-SubQ, a budget allocation policy that budgets tokens based on the conversation history and all past and future sub-questions saving up to 40% tokens over baselines.

Arian Raje, Anupam Nayak, Gauri Joshi

Mixture-of-Experts (MoE) model architectures can significantly reduce the number of activated parameters per token, enabling computationally efficient training and inference. However, their large overall parameter counts and model sizes have precluded their widespread usage in resource-constrained settings as all of the parameters must still be loaded into GPU memory. Prior works aim to address this memory bottleneck by offloading certain experts into CPU memory and porting them to GPU memory only when they are activated. In practice, these methods suffer from the significant I/O latency incurred by expert transfer. We present MELINOE, a method that fine-tunes an MoE model to more strongly prefer activating a smaller number of experts per sequence. Caching these preferred experts in GPU memory reduces expert churn and CPU-GPU transfer overhead. MELINOE increases throughput by $1.2-3\times$ over efficient baselines and up to $14.7\times$ over transfer-heavy baselines while retaining or even improving the performance of the model on a downstream task, making it a reliable method for improving MoE inference efficiency.

Anupam Nayak, Tong Yang, Osman Yagan et al.

Reverse Kullback-Leibler (KL) divergence-based regularization with respect to a fixed reference policy is widely used in modern reinforcement learning to preserve the desired traits of the reference policy and sometimes to promote exploration (using uniform reference policy, known as entropy regularization). Beyond serving as a mere anchor, the reference policy can also be interpreted as encoding prior knowledge about good actions in the environment. In the context of alignment, recent game-theoretic approaches have leveraged KL regularization with pretrained language models as reference policies, achieving notable empirical success in self-play methods. Despite these advances, the theoretical benefits of KL regularization in game-theoretic settings remain poorly understood. In this work, we develop and analyze algorithms that provably achieve improved sample efficiency under KL regularization. We study both two-player zero-sum Matrix games and Markov games: for Matrix games, we propose OMG, an algorithm based on best response sampling with optimistic bonuses, and extend this idea to Markov games through the algorithm SOMG, which also uses best response sampling and a novel concept of superoptimistic bonuses. Both algorithms achieve a logarithmic regret in $T$ that scales inversely with the KL regularization strength $β$ in addition to the standard $\widetilde{\mathcal{O}}(\sqrt{T})$ regret independent of $β$ which is attained in both regularized and unregularized settings