Nagarajan Natarajan

Daman Arora, Anush Kini, Sayak Ray Chowdhury et al. · cmu

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.

Vishak K Bhat, Prateek Chanda, Ashmit Khandelwal et al.

We present a test-time verification framework, interwhen, that ensures that the output of a reasoning model is valid wrt. a given set of verifiers. Verified reasoning is an important goal in high-stakes scenarios such as deploying agents in the physical world or in domains such as law and finance. However, current techniques either rely on the generate-test paradigm that verifies only after the final answer is produced, or verify partial output through a step-extraction paradigm where the task execution is externally broken down into structured steps. The former is inefficient while the latter artificially restricts a model's problem solving strategies. Instead, we propose to verify a model's reasoning trace as-is, taking full advantage of a model's reasoning capabilities while verifying and steering the model's output only when needed. The key idea is meta-prompting, identifying the verifiable properties that any partial solution should satisfy and then prompting the model to follow a custom format in its trace such that partial outputs can be easily parsed and checked. We consider both self-verification and external verification and find that interwhen provides a useful abstraction to provide feedback and steer reasoning models in each case. Using self-verification, interwhen obtains state-of-the-art results on early stopping reasoning models, without any loss in accuracy. Using external verifiers, interwhen obtains 10 p.p. improvement in accuracy over test-time scaling methods, while ensuring 100% soundness and being 4x more efficient. The code for interwhen is available at https://github.com/microsoft/interwhen

Nalin Wadhwa, Jui Pradhan, Atharv Sonwane et al.

As software projects progress, quality of code assumes paramount importance as it affects reliability, maintainability and security of software. For this reason, static analysis tools are used in developer workflows to flag code quality issues. However, developers need to spend extra efforts to revise their code to improve code quality based on the tool findings. In this work, we investigate the use of (instruction-following) large language models (LLMs) to assist developers in revising code to resolve code quality issues. We present a tool, CORE (short for COde REvisions), architected using a pair of LLMs organized as a duo comprised of a proposer and a ranker. Providers of static analysis tools recommend ways to mitigate the tool warnings and developers follow them to revise their code. The \emph{proposer LLM} of CORE takes the same set of recommendations and applies them to generate candidate code revisions. The candidates which pass the static quality checks are retained. However, the LLM may introduce subtle, unintended functionality changes which may go un-detected by the static analysis. The \emph{ranker LLM} evaluates the changes made by the proposer using a rubric that closely follows the acceptance criteria that a developer would enforce. CORE uses the scores assigned by the ranker LLM to rank the candidate revisions before presenting them to the developer. CORE could revise 59.2% Python files (across 52 quality checks) so that they pass scrutiny by both a tool and a human reviewer. The ranker LLM is able to reduce false positives by 25.8% in these cases. CORE produced revisions that passed the static analysis tool in 76.8% Java files (across 10 quality checks) comparable to 78.3% of a specialized program repair tool, with significantly much less engineering efforts.

Sonu Mehta, Jayashree Mohan, Nagarajan Natarajan et al.

`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.

Sayak Ray Chowdhury, Xingyu Zhou, Nagarajan Natarajan

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.

Rohit Sinha, Kunal Tilaganji, Tanuja Ganu et al.

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.

Abhinav Java, Ashmit Khandelwal, Sukruta Midigeshi et al.

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.

Ramneet Singh, Sathvik Joel, Abhav Mehrotra et al.

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 is a daunting task, even for humans. It 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 for mitigating crashes reported in systems code. Code Researcher performs multi-step reasoning about semantics, patterns, and commit history of code to gather sufficient context. The context is stored in a structured memory which is used for synthesizing a patch. 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 of 58%, compared to 37.5% by SWE-agent. On an average, Code Researcher explores 10 files in each trajectory whereas SWE-agent explores only 1.33 files, highlighting Code Researcher's ability to deeply explore the codebase. Through another experiment on an open-source multimedia software, we show the generalizability of Code Researcher. Our experiments highlight the importance of global context gathering and multi-faceted reasoning for large codebases.

Tushar Aggarwal, Swayam Singh, Abhijeet Awasthi et al.

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.

Sayak Ray Chowdhury, Anush Kini, Nagarajan Natarajan

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.

Manav Singhal, Tushar Aggarwal, Abhijeet Awasthi et al.

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.

Taneesh Gupta, Rahul Madhavan, Xuchao Zhang et al.

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

Prakhar Verma, Sukruta Prakash Midigeshi, Gaurav Sinha et al.

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.

Abhinav Java, Srivathsan Koundinyan, Nagarajan Natarajan et al.

We consider the problem of answering complex questions, given access to a large unstructured document corpus. The de facto approach to solving the problem is to leverage language models that (iteratively) retrieve and reason through the retrieved documents, until the model has sufficient information to generate an answer. Attempts at improving this approach focus on retrieval-augmented generation (RAG) metrics such as accuracy and recall and can be categorized into two types: (a) fine-tuning on large question answering (QA) datasets augmented with chain-of-thought traces, and (b) leveraging RL-based fine-tuning techniques that rely on question-document relevance signals. However, efficiency in the number of retrieval searches is an equally important metric, which has received less attention. In this work, we show that: (1) Large-scale fine-tuning is not needed to improve RAG metrics, contrary to popular claims in recent literature. Specifically, a standard ReAct pipeline with improved prompts can outperform state-of-the-art methods on benchmarks such as HotPotQA. (2) Supervised and RL-based fine-tuning can help RAG from the perspective of frugality, i.e., the latency due to number of searches at inference time. For example, we show that we can achieve competitive RAG metrics at nearly half the cost (in terms of number of searches) on popular RAG benchmarks, using the same base model, and at a small training cost (1000 examples).

Daman Arora, Atharv Sonwane, Nalin Wadhwa et al.

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.

Gurusha Juneja, Gautam Jajoo, Nagarajan Natarajan et al.

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.

Divyam Anshumaan, Sriram Balasubramanian, Shubham Tiwari et al.

Simulating physical network paths (e.g., Internet) is a cornerstone research problem in the emerging sub-field of AI-for-networking. We seek a model that generates end-to-end packet delay values in response to the time-varying load offered by a sender, which is typically a function of the previously output delays. The problem setting is unique, and renders the state-of-the-art text and time-series generative models inapplicable or ineffective. We formulate an ML problem at the intersection of dynamical systems, sequential decision making, and time-series modeling. We propose a novel grey-box approach to network simulation that embeds the semantics of physical network path in a new RNN-style model called RBU, providing the interpretability of standard network simulator tools, the power of neural models, the efficiency of SGD-based techniques for learning, and yielding promising results on synthetic and real-world network traces.

Naman Jain, Skanda Vaidyanath, Arun Iyer et al.

Large pre-trained language models such as GPT-3, Codex, and Google's language model are now capable of generating code from natural language specifications of programmer intent. We view these developments with a mixture of optimism and caution. On the optimistic side, such large language models have the potential to improve productivity by providing an automated AI pair programmer for every programmer in the world. On the cautionary side, since these large language models do not understand program semantics, they offer no guarantees about quality of the suggested code. In this paper, we present an approach to augment these large language models with post-processing steps based on program analysis and synthesis techniques, that understand the syntax and semantics of programs. Further, we show that such techniques can make use of user feedback and improve with usage. We present our experiences from building and evaluating such a tool jigsaw, targeted at synthesizing code for using Python Pandas API using multi-modal inputs. Our experience suggests that as these large language models evolve for synthesizing code from intent, jigsaw has an important role to play in improving the accuracy of the systems.

Ajaykrishna Karthikeyan, Naman Jain, Nagarajan Natarajan et al.

Decision trees provide a rich family of highly non-linear but efficient models, due to which they continue to be the go-to family of predictive models by practitioners across domains. But learning trees is challenging due to their discrete decision boundaries. The state-of-the-art (SOTA) techniques resort to (a) learning \textit{soft} trees thereby losing logarithmic inference time; or (b) using methods tailored to specific supervised learning settings, requiring access to labeled examples and loss function. In this work, by leveraging techniques like overparameterization and straight-through estimators, we propose a unified method that enables accurate end-to-end gradient based tree training and can be deployed in a variety of settings like offline supervised learning and online learning with bandit feedback. Using extensive validation on standard benchmarks, we demonstrate that our method provides best of both worlds, i.e., it is competitive to, and in some cases more accurate than methods designed \textit{specifically} for the supervised settings; and in bandit settings, where most existing tree learning techniques are not applicable, our models are still accurate and significantly outperform the applicable SOTA methods.

Aadirupa Saha, Nagarajan Natarajan, Praneeth Netrapalli et al.

We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions $\f_t$ admit a "pseudo-1d" structure, i.e. $\f_t(\w) = \loss_t(\pred_t(\w))$ where the output of $\pred_t$ is one-dimensional. At each round, the learner observes context $\x_t$, plays prediction $\pred_t(\w_t; \x_t)$ (e.g. $\pred_t(\cdot)=\langle \x_t, \cdot\rangle$) for some $\w_t \in \mathbb{R}^d$ and observes loss $\loss_t(\pred_t(\w_t))$ where $\loss_t$ is a convex Lipschitz-continuous function. The goal is to minimize the standard regret metric. This pseudo-1d bandit convex optimization problem (\SBCO) arises frequently in domains such as online decision-making or parameter-tuning in large systems. For this problem, we first show a lower bound of $\min(\sqrt{dT}, T^{3/4})$ for the regret of any algorithm, where $T$ is the number of rounds. We propose a new algorithm \sbcalg that combines randomized online gradient descent with a kernelized exponential weights method to exploit the pseudo-1d structure effectively, guaranteeing the {\em optimal} regret bound mentioned above, up to additional logarithmic factors. In contrast, applying state-of-the-art online convex optimization methods leads to $\tilde{O}\left(\min\left(d^{9.5}\sqrt{T},\sqrt{d}T^{3/4}\right)\right)$ regret, that is significantly suboptimal in $d$.

Nagarajan Natarajan, Ajaykrishna Karthikeyan, Prateek Jain et al.

We formalize and study ``programming by rewards'' (PBR), a new approach for specifying and synthesizing subroutines for optimizing some quantitative metric such as performance, resource utilization, or correctness over a benchmark. A PBR specification consists of (1) input features $x$, and (2) a reward function $r$, modeled as a black-box component (which we can only run), that assigns a reward for each execution. The goal of the synthesizer is to synthesize a "decision function" $f$ which transforms the features to a decision value for the black-box component so as to maximize the expected reward $E[r \circ f (x)]$ for executing decisions $f(x)$ for various values of $x$. We consider a space of decision functions in a DSL of loop-free if-then-else programs, which can branch on linear functions of the input features in a tree-structure and compute a linear function of the inputs in the leaves of the tree. We find that this DSL captures decision functions that are manually written in practice by programmers. Our technical contribution is the use of continuous-optimization techniques to perform synthesis of such decision functions as if-then-else programs. We also show that the framework is theoretically-founded ---in cases when the rewards satisfy nice properties, the synthesized code is optimal in a precise sense. We have leveraged PBR to synthesize non-trivial decision functions related to search and ranking heuristics in the PROSE codebase (an industrial strength program synthesis framework) and achieve competitive results to manually written procedures over multiple man years of tuning. We present empirical evaluation against other baseline techniques over real-world case studies (including PROSE) as well on simple synthetic benchmarks.

Sahil Bhatia, Saswat Padhi, Nagarajan Natarajan et al.

Automated synthesis of inductive invariants is an important problem in software verification. Once all the invariants have been specified, software verification reduces to checking of verification conditions. Although static analyses to infer invariants have been studied for over forty years, recent years have seen a flurry of data-driven invariant inference techniques which guess invariants from examples instead of analyzing program text. However, these techniques have been demonstrated to scale only to programs with a small number of variables. In this paper, we study these scalability issues and address them in our tool oasis that improves the scale of data-driven invariant inference and outperforms state-of-the-art systems on benchmarks from the invariant inference track of the Syntax Guided Synthesis competition.

Rahul Wadbude, Vivek Gupta, Piyush Rai et al.

We present a novel and scalable label embedding framework for large-scale multi-label learning a.k.a ExMLDS (Extreme Multi-Label Learning using Distributional Semantics). Our approach draws inspiration from ideas rooted in distributional semantics, specifically the Skip Gram Negative Sampling (SGNS) approach, widely used to learn word embeddings for natural language processing tasks. Learning such embeddings can be reduced to a certain matrix factorization. Our approach is novel in that it highlights interesting connections between label embedding methods used for multi-label learning and paragraph/document embedding methods commonly used for learning representations of text data. The framework can also be easily extended to incorporate auxiliary information such as label-label correlations; this is crucial especially when there are a lot of missing labels in the training data. We demonstrate the effectiveness of our approach through an extensive set of experiments on a variety of benchmark datasets, and show that the proposed learning methods perform favorably compared to several baselines and state-of-the-art methods for large-scale multi-label learning. To facilitate end-to-end learning, we develop a joint learning algorithm that can learn the embeddings as well as a regression model that predicts these embeddings given input features, via efficient gradient-based methods.

Prateek Jain, Nagarajan Natarajan

We consider the problem of recommending relevant labels (items) for a given data point (user). In particular, we are interested in the practically important setting where the evaluation is with respect to non-decomposable (over labels) performance metrics like the $F_1$ measure, and the training data has missing labels. To this end, we propose a generic framework that given a performance metric $Ψ$, can devise a regularized objective function and a threshold such that all the values in the predicted score vector above and only above the threshold are selected to be positive. We show that the regret or generalization error in the given metric $Ψ$ is bounded ultimately by estimation error of certain underlying parameters. In particular, we derive regret bounds under three popular settings: a) collaborative filtering, b) multilabel classification, and c) PU (positive-unlabeled) learning. For each of the above problems, we can obtain precise non-asymptotic regret bound which is small even when a large fraction of labels is missing. Our empirical results on synthetic and benchmark datasets demonstrate that by explicitly modeling for missing labels and optimizing the desired performance metric, our algorithm indeed achieves significantly better performance (like $F_1$ score) when compared to methods that do not model missing label information carefully.

Aditya Krishna Menon, Brendan van Rooyen, Nagarajan Natarajan

Suppose we have a sample of instances paired with binary labels corrupted by arbitrary instance- and label-dependent noise. With sufficiently many such samples, can we optimally classify and rank instances with respect to the noise-free distribution? We provide a theoretical analysis of this question, with three main contributions. First, we prove that for instance-dependent noise, any algorithm that is consistent for classification on the noisy distribution is also consistent on the clean distribution. Second, we prove that for a broad class of instance- and label-dependent noise, a similar consistency result holds for the area under the ROC curve. Third, for the latter noise model, when the noise-free class-probability function belongs to the generalised linear model family, we show that the Isotron can efficiently and provably learn from the corrupted sample.

Nagarajan Natarajan, Oluwasanmi Koyejo, Pradeep Ravikumar et al.

We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decision-theoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result is that the expected out-of-sample utility for many performance metrics is provably optimized by a classifier which is equivalent to a signed thresholding of the conditional probability of the positive class. Our analysis bridges a gap in the literature on binary classification, revealed in light of recent results for non-decomposable metrics in population utility maximization style classification. Our results identify checkable properties of a performance metric which are sufficient to guarantee a probability ranking principle. We propose consistent estimators for optimal expected out-of-sample classification. As a consequence of the probability ranking principle, computational requirements can be reduced from exponential to cubic complexity in the general case, and further reduced to quadratic complexity in special cases. We provide empirical results on simulated and benchmark datasets evaluating the performance of the proposed algorithms for decision-theoretic classification and comparing them to baseline and state-of-the-art methods in population utility maximization for non-decomposable metrics.

Cho-Jui Hsieh, Nagarajan Natarajan, Inderjit S. Dhillon

In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only "likes" or "friendships" are observed. The problem of learning from only positive and unlabeled examples, called PU (positive-unlabeled) learning, has been studied in the context of binary classification. We consider the PU matrix completion problem, where an underlying real-valued matrix M is first quantized to generate one-bit observations and then a subset of positive entries is revealed. Under the assumption that M has bounded nuclear norm, we provide recovery guarantees for two different observation models: 1) M parameterizes a distribution that generates a binary matrix, 2) M is thresholded to obtain a binary matrix. For the first case, we propose a "shifted matrix completion" method that recovers M using only a subset of indices corresponding to ones, while for the second case, we propose a "biased matrix completion" method that recovers the (thresholded) binary matrix. Both methods yield strong error bounds --- if M is n by n, the Frobenius error is bounded as O(1/((1-rho)n), where 1-rho denotes the fraction of ones observed. This implies a sample complexity of O(n\log n) ones to achieve a small error, when M is dense and n is large. We extend our methods and guarantees to the inductive matrix completion problem, where rows and columns of M have associated features. We provide efficient and scalable optimization procedures for both the methods and demonstrate the effectiveness of the proposed methods for link prediction (on real-world networks consisting of over 2 million nodes and 90 million links) and semi-supervised clustering tasks.

Kai-Yang Chiang, Cho-Jui Hsieh, Nagarajan Natarajan et al.

The study of social networks is a burgeoning research area. However, most existing work deals with networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive ("like", "trust") or negative ("dislike", "distrust"). The theory of social balance shows that signed networks tend to conform to some local patterns that, in turn, induce certain global characteristics. In this paper, we exploit both local as well as global aspects of social balance theory for two fundamental problems in the analysis of signed networks: sign prediction and clustering. Motivated by local patterns of social balance, we first propose two families of sign prediction methods: measures of social imbalance (MOIs), and supervised learning using high order cycles (HOCs). These methods predict signs of edges based on triangles and \ell-cycles for relatively small values of \ell. Interestingly, by examining measures of social imbalance, we show that the classic Katz measure, which is used widely in unsigned link prediction, actually has a balance theoretic interpretation when applied to signed networks. Furthermore, motivated by the global structure of balanced networks, we propose an effective low rank modeling approach for both sign prediction and clustering. For the low rank modeling approach, we provide theoretical performance guarantees via convex relaxations, scale it up to large problem sizes using a matrix factorization based algorithm, and provide extensive experimental validation including comparisons with local approaches. Our experimental results indicate that, by adopting a more global viewpoint of balance structure, we get significant performance and computational gains in prediction and clustering tasks on signed networks. Our work therefore highlights the usefulness of the global aspect of balance theory for the analysis of signed networks.