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Nagarajan Natarajan

Publications and source records attributed to Nagarajan Natarajan.

At least 19 recordsLinked to original sources
arXiv2026

Rethinking LLM Verification: Evidence Structure, Uncertainty, and Selective Refinement

Large language models (LLMs) often rely on shortcuts rather than systematic reasoning, raising safety concerns in medical applications. Allowing models to abstain when uncertain improves reliability but introduces a coverage accuracy tradeoff. We propose a two-stage framework for medical hypothesis verification in multiple-choice settings that manages this tradeoff through targeted ontology grounding, applied only when the model abstains. We show that abstention is not random but reflects genuine uncertainty, with abstained predictions associated with lower confidence. Across two frontier models (GPT-5.5, accessed via the Azure OpenAI API, and DeepSeek-R1), the proposed framework improves question-level accuracy by 9.6 percentage points (82.9% to 92.5%) and hypothesis-level accuracy by 4.2 percentage points (92.0% to 96.2%). Our experiments conducted on MedReason and MedQA show that abstention can be repurposed as a control signal for selective reasoning refinement, achieving knowledge-graph-level performance without explicit knowledge graph construction.

cs.CV↗
arXiv2026

VERDICT: Training-Free Step-Wise Verification of Multimodal Reasoning via Disagreement-Aware Consensus

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Existing approaches either require expensive labelled supervision with inconsistent cross-task performance or aggregate scores from multiple sources by simple aggregations, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We formalise this as a coupled scoring problem among disparate, frozen verifiers, interpretable as a coordination game with a unique closed-form equilibrium where agreement signals valid steps while disagreement reveals instability. Towards this end, we propose a training-free domain-agnostic step-wise verification approach we call VERDICT: VERification via Disagreement-Informed Coupled Thresholding. To our knowledge, VERDICT is the first training-free verifier that makes the structure of cross-modal disagreement explicit and actionable. It computes consensus scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, \method consistently improves over the base model by up to +5.95%, and performs competitively with domain-specific critics that demand extensive supervision, demonstrating that cross-modal agreement provides robust verification signals without task-specific adaptation and Training-Free Verification

cs.AI↗
arXiv2026

Code Researcher: Deep Research Agent for Large Systems Code and Commit History

Large Language Model (LLM)-based coding agents have shown promising results on coding benchmarks, but their effectiveness on systems code remains underexplored. Due to the size and complexities of systems code, making changes to a systems codebase requires researching about many pieces of context, derived from the large codebase and its massive commit history, before making changes. Inspired by the recent progress on deep research agents, we design the first deep research agent for code, called Code Researcher, and apply it to the problem of generating patches to mitigate crashes reported in systems code. Code Researcher performs multi-step reasoning about semantics, patterns, and commit history of code to retrieve all relevant context from the codebase and its commit history. We evaluate Code Researcher on kBenchSyz, a benchmark of Linux kernel crashes, and show that it significantly outperforms strong baselines, achieving a crash-resolution rate (CRR) of 48%, compared to 31.5% by SWE-agent and 31% by Agentless, using OpenAI's GPT-4o model. Scaling up sampling budget to 10 trajectories increases Code Researcher's CRR to 54%. Code Researcher is also robust to model choices, reaching 67% with the newer Gemini 2.5-Flash model. Through another experiment on an open-source multimedia software, we show the generalizability of Code Researcher and also conduct ablations. Our experiments highlight the importance of global context gathering and multi-faceted reasoning for large codebases.

cs.SE↗
arXiv2026

A Nash Equilibrium Framework For Training-Free Multimodal Step Verification

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Learned critics need extensive labeled data and show inconsistent performance across different tasks. Meanwhile, existing training-free methods simply average scores from different sources, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We propose a training-free verification approach that treats step-wise verification as a coordination problem among specialized judges. We formalize these judges' interaction as a Nash equilibrium game where agreement signals valid steps while disagreement reveals instability. Our method computes equilibrium scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, our approach achieves consistent improvements of 2.4% to 5.2% over baseline models and shows competitive performance against learned critics, demonstrating that cross-modal agreement (not just average confidence) provides robust verification signals without task-specific adaptation.

cs.CV↗
arXiv2026

interwhen: A Generalizable Framework for Steering Reasoning Models with Test-time Verification

Reasoning models produce long traces of intermediate decisions and tool calls, making test-time verification important for ensuring correctness. Existing approaches either verify only the final answer, which misses early errors, or rely on branch-and-verify strategies that explore multiple trajectories. We introduce interwhen, a single-trajectory verification framework that steers model behavior by providing feedback on intermediate reasoning traces. It addresses two key challenges. First, given a set of verifiers, obtaining verifiable states from the reasoning trace typically requires prompt engineering or external task decomposition into fixed steps. Instead, we propose a monitoring system that periodically polls the reasoning trace and forks inference of the reasoning model to recover intermediate states. Verifiers are run asynchronously alongside generation, adding negligible overhead on correct executions and intervening only when violations occur. Second, beyond math and code, a central challenge for process verification is the scarcity of verifiers. interwhen addresses this through automatic verifier synthesis from natural-language policy documents. Given a policy, it can generate code-based verifiers, including provably correct verifiers in Lean and z3. Together, these contributions yield a plug-and-play test-time verification system that can improve task completion and policy compliance of any reasoning agent. On reasoning benchmarks where policies encode mathematical or logical constraints, interwhen achieves near-perfect accuracy for reasoning models using a fraction of the tokens of baselines. On agentic benchmarks with policy-based verifier generation, it enables improvements in task quality for SLMs without any finetuning, e.g., task completion rate of Qwen3-30B jumps from 32% to 87% on the telecom domain in tau2-bench. Code at https://github.com/microsoft/interwhen.

cs.LO↗
arXiv2026

FrugalRAG: Less is More in RL Finetuning for Multi-Hop Question Answering

Reinforcement learning (RL) based on the final answer's reward has driven recent progress in small language models (SLMs) on reasoning-heavy tasks such as math and code. However, applying the same techniques to retrieval-augmented generation (RAG) benchmarks like multi-hop QA has yielded limited gains, often trailing supervised or prompting-only baselines. Instead, we argue that a viable path for RL in multi-hop QA is to use test-time scaling judiciously to optimize both final answer accuracy and efficiency in reaching that answer. We propose FrugalRAG, a two-stage finetuning framework that adaptively reduces the number of retrieval steps based on a question's difficulty. First, we train an SLM with supervised finetuning on a full-exploration policy that generates broad sub-queries. Then, we apply RL to adaptively prune search depth based on question difficulty, directly rewarding policies that balance correctness with frugality. Unlike prior approaches requiring 10x more data, our method achieves competitive performance with only approximately 1,000 examples. On HotPotQA and other multi-hop QA benchmarks, FrugalRAG attains state-of-the-art efficiency-accuracy tradeoffs, cutting retrieval cost nearly in half. Moreover, on the challenging BrowseCompPlus benchmark, it generalizes zero-shot and surpasses SLM-based and other baselines. These results demonstrate the use of RL not to increase reasoning steps, but to reduce them, as an effective solution for scalable and efficient RAG.

cs.CL↗
arXiv2025

Characterizing Deep Research: A Benchmark and Formal Definition

Information tasks such as writing surveys or analytical reports require complex search and reasoning, and have recently been grouped under the umbrella of \textit{deep research} -- a term also adopted by recent models targeting these capabilities. Despite growing interest, the scope of the deep research task remains underdefined and its distinction from other reasoning-intensive problems is poorly understood. In this paper, we propose a formal characterization of the deep research (DR) task and introduce a benchmark to evaluate the performance of DR systems. We argue that the core defining feature of deep research is not the production of lengthy report-style outputs, but rather the high fan-out over concepts required during the search process, i.e., broad and reasoning-intensive exploration. To enable objective evaluation, we define DR using an intermediate output representation that encodes key claims uncovered during search-separating the reasoning challenge from surface-level report generation. Based on this formulation, we propose a diverse, challenging benchmark LiveDRBench with 100 challenging tasks over scientific topics (e.g., datasets, materials discovery, prior art search) and public interest events (e.g., flight incidents, movie awards). Across state-of-the-art DR systems, F1 score ranges between 0.02 and 0.72 for any sub-category. OpenAI's model performs the best with an overall F1 score of 0.55. Analysis of reasoning traces reveals the distribution over the number of referenced sources, branching, and backtracking events executed by current DR systems, motivating future directions for improving their search mechanisms and grounding capabilities. The benchmark is available at https://github.com/microsoft/LiveDRBench.

cs.CL↗
arXiv2025

Multi-Preference Optimization: Generalizing DPO via Set-Level Contrasts

Direct Preference Optimization (DPO) has become a popular approach for aligning language models using pairwise preferences. However, in practical post-training pipelines, on-policy generation typically yields multiple candidate responses per prompt, which are scored by a reward model to guide learning. In this setting, we propose $\textbf{Multi-Preference Optimization (MPO)}$, a generalization of DPO that optimizes over entire sets of responses by extending the Bradley-Terry model to groupwise comparisons between chosen and rejected sets. To further enhance learning, MPO employs deviation-based weighting, which emphasizes outlier responses that deviate most from the mean reward, effectively inducing a self-paced curriculum. We theoretically prove that MPO reduces alignment bias at a rate of $\mathcal{O}\left(\frac{1}{\sqrt{n}}\right)$ with respect to the number of responses per query. Empirically, MPO achieves state-of-the-art performance on the UltraFeedback benchmark and yields up to $\sim 17.5\%$ improvement over the state-of-the-art baseline in length-controlled win rate on AlpacaEval2, establishing a new baseline for preference-based alignment

cs.LG↗
arXiv2025

Task Facet Learning: A Structured Approach to Prompt Optimization

Given a task in the form of a basic description and its training examples, prompt optimization is the problem of synthesizing the given information into a text prompt for a large language model. Humans solve this problem by also considering the different facets that define a task (e.g., counter-examples, explanations, analogies) and including them in the prompt. However, it is unclear whether existing algorithmic approaches, based on iteratively editing a given prompt or automatically selecting a few in-context examples, can cover the multiple facets required to solve a complex task. In this work, we view prompt optimization as that of learning multiple facets of a task from a set of training examples. We exploit structure in the prompt optimization problem and break down a prompt into loosely coupled semantic sections. The proposed algorithm, UniPrompt, (1) clusters the input space and uses clustered batches so that each batch likely corresponds to a different facet of the task, and (2) utilizes a feedback mechanism to propose adding, editing or deleting a section, which in turn is aggregated over a batch to capture generalizable facets. Empirical evaluation on multiple datasets and a real-world task shows that prompts generated using \shortname{} obtain higher accuracy than human-tuned prompts and those from state-of-the-art methods. In particular, our algorithm can generate long, complex prompts that existing methods are unable to generate. Code for UniPrompt is available at https://aka.ms/uniprompt.

cs.AI↗
arXiv2025

Robust Learning of Diverse Code Edits

Software engineering activities frequently involve edits to existing code. However, contemporary code language models (LMs) lack the ability to handle diverse types of code-edit requirements. In this work, we attempt to overcome this shortcoming through (1) a novel synthetic data generation pipeline and (2) a robust model adaptation algorithm. Starting with seed code examples and diverse editing criteria, our pipeline generates high-quality samples comprising original and modified code, along with natural language instructions in different styles and verbosity. Today's code LMs come bundled with strong abilities, such as code generation and instruction following, which should not be lost due to fine-tuning. To ensure this, we propose a novel adaptation algorithm, SeleKT, that (a) leverages a dense gradient-based step to identify the weights that are most important for code editing, and (b) does a sparse projection onto the base model to avoid overfitting. Using our approach, we obtain a new series of models NextCoder (adapted from QwenCoder-2.5) that achieves strong results on five code-editing benchmarks, outperforming comparable size models and even several larger ones. We show the generality of our approach on two model families (DeepSeekCoder and QwenCoder), compare against other fine-tuning approaches, and demonstrate robustness by showing retention of code generation and general problem-solving abilities post adaptation. We opensource the models, synthetic dataset, and implementation at https://aka.ms/nextcoder.

cs.SE↗
arXiv2025

Plan*RAG: Efficient Test-Time Planning for Retrieval Augmented Generation

We introduce Plan*RAG, a novel framework that enables structured multi-hop reasoning in retrieval-augmented generation (RAG) through test-time reasoning plan generation. While existing approaches such as ReAct maintain reasoning chains within the language model's context window, we observe that this often leads to plan fragmentation and execution failures. Our key insight is that by isolating the reasoning plan as a directed acyclic graph (DAG) outside the LM's working memory, we can enable (1) systematic exploration of reasoning paths, (2) atomic subqueries enabling precise retrievals and grounding, and (3) efficiency through parallel execution and bounded context window utilization. Moreover, Plan*RAG's modular design allows it to be integrated with existing RAG methods, thus providing a practical solution to improve current RAG systems. On standard multi-hop reasoning benchmarks, Plan*RAG consistently achieves improvements over recently proposed methods such as RQ-RAG and Self-RAG, while maintaining comparable computational costs.

cs.CL↗
arXiv2024

ASTRA: Accurate and Scalable ANNS-based Training of Extreme Classifiers

`Extreme Classification'' (or XC) is the task of annotating data points (queries) with relevant labels (documents), from an extremely large set of $L$ possible labels, arising in search and recommendations. The most successful deep learning paradigm that has emerged over the last decade or so for XC is to embed the queries (and labels) using a deep encoder (e.g. DistilBERT), and use linear classifiers on top of the query embeddings. This architecture is of appeal because it enables millisecond-time inference using approximate nearest neighbor search (ANNS). The key question is how do we design training algorithms that are accurate as well as scale to $O(100M)$ labels on a limited number of GPUs. State-of-the-art XC techniques that demonstrate high accuracies (e.g., DEXML, Renée, DEXA) on standard datasets have per-epoch training time that scales as $O(L)$ or employ expensive negative sampling strategies, which are prohibitive in XC scenarios. In this work, we develop an accurate and scalable XC algorithm ASTRA with two key observations: (a) building ANNS index on the classifier vectors and retrieving hard negatives using the classifiers aligns the negative sampling strategy to the loss function optimized; (b) keeping the ANNS indices current as the classifiers change through the epochs is prohibitively expensive while using stale negatives (refreshed periodically) results in poor accuracy; to remedy this, we propose a negative sampling strategy that uses a mixture of importance sampling and uniform sampling. By extensive evaluation on standard XC as well as proprietary datasets with 120M labels, we demonstrate that ASTRA achieves SOTA precision, while reducing training time by 4x-15x relative to the second best.

cs.LG↗
arXiv2024

NoFunEval: Funny How Code LMs Falter on Requirements Beyond Functional Correctness

Existing evaluation benchmarks of language models of code (code LMs) focus almost exclusively on whether the LMs can generate functionally-correct code. In real-world software engineering, developers think beyond functional correctness. They have requirements on "how" a functionality should be implemented to meet overall system design objectives like efficiency, security, and maintainability. They would also trust the code LMs more if the LMs demonstrate robust understanding of such requirements. We propose a new benchmark NoFunEval to evaluate code LMs on non-functional requirements and simple classification instances for both functional and non-functional requirements. We propose a prompting method, Coding Concepts (CoCo), as a way for a developer to communicate the domain knowledge to the LMs. We conduct an extensive evaluation of 27 code LMs. Our finding is that LMs generally falter when tested on our benchmark, hinting at fundamental blindspots in their training setups. Surprisingly, even the classification accuracy on functional-correctness instances derived from the popular HumanEval benchmark is low, calling in question the depth of their comprehension and the source of their success in generating functionally-correct code in the first place. We release our benchmark and evaluation scripts publicly at https://aka.ms/NoFunEval.

cs.SE↗
arXiv2024

CROSS-JEM: Accurate and Efficient Cross-encoders for Short-text Ranking Tasks

Ranking a set of items based on their relevance to a given query is a core problem in search and recommendation. Transformer-based ranking models are the state-of-the-art approaches for such tasks, but they score each query-item independently, ignoring the joint context of other relevant items. This leads to sub-optimal ranking accuracy and high computational costs. In response, we propose Cross-encoders with Joint Efficient Modeling (CROSS-JEM), a novel ranking approach that enables transformer-based models to jointly score multiple items for a query, maximizing parameter utilization. CROSS-JEM leverages (a) redundancies and token overlaps to jointly score multiple items, that are typically short-text phrases arising in search and recommendations, and (b) a novel training objective that models ranking probabilities. CROSS-JEM achieves state-of-the-art accuracy and over 4x lower ranking latency over standard cross-encoders. Our contributions are threefold: (i) we highlight the gap between the ranking application's need for scoring thousands of items per query and the limited capabilities of current cross-encoders; (ii) we introduce CROSS-JEM for joint efficient scoring of multiple items per query; and (iii) we demonstrate state-of-the-art accuracy on standard public datasets and a proprietary dataset. CROSS-JEM opens up new directions for designing tailored early-attention-based ranking models that incorporate strict production constraints such as item multiplicity and latency.

cs.IR↗
arXiv2024

MASAI: Modular Architecture for Software-engineering AI Agents

A common method to solve complex problems in software engineering, is to divide the problem into multiple sub-problems. Inspired by this, we propose a Modular Architecture for Software-engineering AI (MASAI) agents, where different LLM-powered sub-agents are instantiated with well-defined objectives and strategies tuned to achieve those objectives. Our modular architecture offers several advantages: (1) employing and tuning different problem-solving strategies across sub-agents, (2) enabling sub-agents to gather information from different sources scattered throughout a repository, and (3) avoiding unnecessarily long trajectories which inflate costs and add extraneous context. MASAI enabled us to achieve the highest performance (28.33% resolution rate) on the popular and highly challenging SWE-bench Lite dataset consisting of 300 GitHub issues from 11 Python repositories. We conduct a comprehensive evaluation of MASAI relative to other agentic methods and analyze the effects of our design decisions and their contribution to the success of MASAI.

cs.AI↗
arXiv2024

Provably Robust DPO: Aligning Language Models with Noisy Feedback

Learning from preference-based feedback has recently gained traction as a promising approach to align language models with human interests. While these aligned generative models have demonstrated impressive capabilities across various tasks, their dependence on high-quality human preference data poses a bottleneck in practical applications. Specifically, noisy (incorrect and ambiguous) preference pairs in the dataset might restrict the language models from capturing human intent accurately. While practitioners have recently proposed heuristics to mitigate the effect of noisy preferences, a complete theoretical understanding of their workings remain elusive. In this work, we aim to bridge this gap by by introducing a general framework for policy optimization in the presence of random preference flips. We focus on the direct preference optimization (DPO) algorithm in particular since it assumes that preferences adhere to the Bradley-Terry-Luce (BTL) model, raising concerns about the impact of noisy data on the learned policy. We design a novel loss function, which de-bias the effect of noise on average, making a policy trained by minimizing that loss robust to the noise. Under log-linear parameterization of the policy class and assuming good feature coverage of the SFT policy, we prove that the sub-optimality gap of the proposed robust DPO (rDPO) policy compared to the optimal policy is of the order $O(\frac{1}{1-2ε}\sqrt{\frac{d}{n}})$, where $ε< 1/2$ is flip rate of labels, $d$ is policy parameter dimension and $n$ is size of dataset. Our experiments on IMDb sentiment generation and Anthropic's helpful-harmless dataset show that rDPO is robust to noise in preference labels compared to vanilla DPO and other heuristics proposed by practitioners.

cs.LG↗
arXiv2023

GAR-meets-RAG Paradigm for Zero-Shot Information Retrieval

Given a query and a document corpus, the information retrieval (IR) task is to output a ranked list of relevant documents. Combining large language models (LLMs) with embedding-based retrieval models, recent work shows promising results on the zero-shot retrieval problem, i.e., no access to labeled data from the target domain. Two such popular paradigms are generation-augmented retrieval or GAR (generate additional context for the query and then retrieve), and retrieval-augmented generation or RAG (retrieve relevant documents as context and then generate answers). The success of these paradigms hinges on (i) high-recall retrieval models, which are difficult to obtain in the zero-shot setting, and (ii) high-precision (re-)ranking models which typically need a good initialization. In this work, we propose a novel GAR-meets-RAG recurrence formulation that overcomes the challenges of existing paradigms. Our method iteratively improves retrieval (via GAR) and rewrite (via RAG) stages in the zero-shot setting. A key design principle is that the rewrite-retrieval stages improve the recall of the system and a final re-ranking stage improves the precision. We conduct extensive experiments on zero-shot passage retrieval benchmarks, BEIR and TREC-DL. Our method establishes a new state-of-the-art in the BEIR benchmark, outperforming previous best results in Recall@100 and nDCG@10 metrics on 6 out of 8 datasets, with up to 17% relative gains over the previous best.

cs.CL↗
arXiv2023

Differentially Private Reward Estimation with Preference Feedback

Learning from preference-based feedback has recently gained considerable traction as a promising approach to align generative models with human interests. Instead of relying on numerical rewards, the generative models are trained using reinforcement learning with human feedback (RLHF). These approaches first solicit feedback from human labelers typically in the form of pairwise comparisons between two possible actions, then estimate a reward model using these comparisons, and finally employ a policy based on the estimated reward model. An adversarial attack in any step of the above pipeline might reveal private and sensitive information of human labelers. In this work, we adopt the notion of label differential privacy (DP) and focus on the problem of reward estimation from preference-based feedback while protecting privacy of each individual labelers. Specifically, we consider the parametric Bradley-Terry-Luce (BTL) model for such pairwise comparison feedback involving a latent reward parameter $θ^* \in \mathbb{R}^d$. Within a standard minimax estimation framework, we provide tight upper and lower bounds on the error in estimating $θ^*$ under both local and central models of DP. We show, for a given privacy budget $ε$ and number of samples $n$, that the additional cost to ensure label-DP under local model is $Θ\big(\frac{1}{ e^ε-1}\sqrt{\frac{d}{n}}\big)$, while it is $Θ\big(\frac{\text{poly}(d)}{εn} \big)$ under the weaker central model. We perform simulations on synthetic data that corroborate these theoretical results.

cs.LG↗