arXiv subjects

Anupam Nayak

Publications and source records attributed to Anupam Nayak.

11 recordsLinked to original sources

arXiv2026

On-Policy Attention Linearization

Hybrid transformer architectures that replace most softmax attention layers with linear attention offer transformer-level quality at a fraction of the memory cost. Rather than pretraining such models, a growing body of work distills them from already trained full-attention transformers. However, these distilled models often collapse on long-context retrieval and reasoning tasks, particularly when operating in thinking mode, where the efficiency gains of hybrid architectures matter most. Since linear attention layers must compress context into a fixed-size state, their errors compound over long sequences. As off-policy distillation never teaches the student model to recover from this drift, tasks that necessitate longer sequence lengths become especially challenging. We introduce On-Policy Attention Linearization (OPAL) in which the hybrid attention student samples its own long-context trajectories and receives dense supervision from the frozen full-attention teacher. Applying OPAL to Qwen3-4B and MiMo-7B-RL-0530, we recover $87$--$94\%$ of full-attention performance on commonsense reasoning, $100\%$ on needle-in-a-haystack (NIAH) retrieval, and $83$--$93\%$ on mathematical reasoning with only 3B training tokens. We achieve these results without supervised fine-tuning (SFT) or reinforcement learning with verifiable rewards (RLVR). Compared with the strongest prior linearization method, which recovers $68\%$ of its teacher's retrieval performance and $21.6\%$ absolute average mathematical reasoning accuracy, OPAL fully recovers retrieval and achieves $67.6$--$72.2\%$ on math reasoning.

cs.LG↗

arXiv2026

Not All Turns Are Equally Hard: Adaptive Thinking Budgets For Efficient Multi-Turn Reasoning in Agents

As LLM reasoning performance plateaus, 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 diverse agentic benchmarks demonstrate that TAB achieves a superior accuracy-cost tradeoff saving up to 35% tokens and reducing latency up to 30% while maintaining accuracy over static and off-the-shelf LLM budget baselines. Further, for systems where a plan of all turns is available apriori, we propose TAB All-SubQ, a budget allocation policy that budgets tokens based on the conversation history and entire plan saving up to 40% tokens over baselines.

cs.LG↗

arXiv2026

Global PIQA: Evaluating Commonsense Reasoning Across 100+ Languages and Cultures

To date, there exist almost no culturally-specific evaluation benchmarks for large language models (LLMs) that cover a large number of languages and cultures. In this paper, we present Global PIQA, a participatory commonsense reasoning benchmark for over 100 languages, constructed by hand by over 350 researchers from over 65 countries around the world. The 141 language varieties in Global PIQA cover five continents, 19 language families, and 24 writing systems. In the non-parallel split of Global PIQA, over 50% of examples reference local foods, customs, traditions, or other culturally-specific elements. In the parallel split, we translate more "culturally agnostic" commonsense reasoning questions into 131 language varieties, for direct cross-lingual comparisons. In both splits, all examples have been verified by native speakers of the languages. We find that state-of-the-art LLMs perform well on Global PIQA in aggregate, but they exhibit weaker performance in lower-resource languages (e.g. up to a 68% accuracy gap between languages in the parallel split). Global PIQA highlights that in many languages and cultures, everyday knowledge remains an area for improvement in LLMs, alongside more widely-discussed capabilities such as complex reasoning and expert knowledge. Beyond its uses for LLM evaluation, Global PIQA provides a glimpse into the wide diversity of cultures in which human language is embedded.

cs.CL↗

arXiv2026

Emergent and Subliminal Misalignment Through the Lens of Data-Mediated Transfer

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.

cs.LG↗

arXiv2026

PubSwap: Public-Data Off-Policy Coordination for Federated RLVR

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.

cs.LG↗

arXiv2026

Achieving Logarithmic Regret in KL-Regularized Zero-Sum Markov Games

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 traditional $\widetilde{\mathcal{O}}(\sqrt{T})$ regret without the $β^{-1}$ dependence.

cs.LG↗

arXiv2026

MELINOE: Fine-Tuning Enables Memory-Efficient Inference for Mixture-of-Experts Models

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.

cs.LG↗

arXiv2026

Federate the Router: Learning Language Model Routers with Sparse and Decentralized Evaluations

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.

cs.LG↗

arXiv2024

On the Regret of Coded Caching with Adversarial Requests

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

cs.IT↗

arXiv2023

On the Regret of Online Coded Caching

We consider the widely studied problem of coded caching under non-uniform requests where users independently request files according to some underlying popularity distribution in each slot. This work is a first step towards analyzing this framework through the lens of online learning. We consider the case where the underlying request distribution is apriori unknown and propose an online policy as well as study its regret with respect to an oracle which knows the underlying distribution and employs a well-known order-optimal placement and coded delivery strategy. We also bound the switching cost of this strategy and also discuss a lower bound on the regret of any online scheme in a restricted but natural class of policies.

cs.IT↗

arXiv2023

A Decentralized Policy for Minimization of Age of Incorrect Information in Slotted ALOHA Systems

The Age of Incorrect Information (AoII) is a metric that can combine the freshness of the information available to a gateway in an Internet of Things (IoT) network with the accuracy of that information. As such, minimizing the AoII can allow the operators of IoT systems to have a more precise and up-to-date picture of the environment in which the sensors are deployed. However, most IoT systems do not allow for centralized scheduling or explicit coordination, as sensors need to be extremely simple and consume as little power as possible. Finding a decentralized policy to minimize the AoII can be extremely challenging in this setting. This paper presents a heuristic to optimize AoII for a slotted ALOHA system, starting from a threshold-based policy and using dual methods to converge to a better solution. This method can significantly outperform state-independent policies, finding an efficient balance between frequent updates and a low number of packet collisions.

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