Do LLMs exhibit human-like response biases? A case study in survey designLindia Tjuatja, Valerie Chen, Sherry Tongshuang Wu et al. · cmu
As large language models (LLMs) become more capable, there is growing excitement about the possibility of using LLMs as proxies for humans in real-world tasks where subjective labels are desired, such as in surveys and opinion polling. One widely-cited barrier to the adoption of LLMs as proxies for humans in subjective tasks is their sensitivity to prompt wording - but interestingly, humans also display sensitivities to instruction changes in the form of response biases. We investigate the extent to which LLMs reflect human response biases, if at all. We look to survey design, where human response biases caused by changes in the wordings of "prompts" have been extensively explored in social psychology literature. Drawing from these works, we design a dataset and framework to evaluate whether LLMs exhibit human-like response biases in survey questionnaires. Our comprehensive evaluation of nine models shows that popular open and commercial LLMs generally fail to reflect human-like behavior, particularly in models that have undergone RLHF. Furthermore, even if a model shows a significant change in the same direction as humans, we find that they are sensitive to perturbations that do not elicit significant changes in humans. These results highlight the pitfalls of using LLMs as human proxies, and underscore the need for finer-grained characterizations of model behavior. Our code, dataset, and collected samples are available at https://github.com/lindiatjuatja/BiasMonkey
21.4HCJun 5, 2022
Use-Case-Grounded Simulations for Explanation EvaluationValerie Chen, Nari Johnson, Nicholay Topin et al. · cmu
A growing body of research runs human subject evaluations to study whether providing users with explanations of machine learning models can help them with practical real-world use cases. However, running user studies is challenging and costly, and consequently each study typically only evaluates a limited number of different settings, e.g., studies often only evaluate a few arbitrarily selected explanation methods. To address these challenges and aid user study design, we introduce Use-Case-Grounded Simulated Evaluations (SimEvals). SimEvals involve training algorithmic agents that take as input the information content (such as model explanations) that would be presented to each participant in a human subject study, to predict answers to the use case of interest. The algorithmic agent's test set accuracy provides a measure of the predictiveness of the information content for the downstream use case. We run a comprehensive evaluation on three real-world use cases (forward simulation, model debugging, and counterfactual reasoning) to demonstrate that Simevals can effectively identify which explanation methods will help humans for each use case. These results provide evidence that SimEvals can be used to efficiently screen an important set of user study design decisions, e.g. selecting which explanations should be presented to the user, before running a potentially costly user study.
Where Does My Model Underperform? A Human Evaluation of Slice Discovery AlgorithmsNari Johnson, Ángel Alexander Cabrera, Gregory Plumb et al. · cmu
Machine learning (ML) models that achieve high average accuracy can still underperform on semantically coherent subsets ("slices") of data. This behavior can have significant societal consequences for the safety or bias of the model in deployment, but identifying these underperforming slices can be difficult in practice, especially in domains where practitioners lack access to group annotations to define coherent subsets of their data. Motivated by these challenges, ML researchers have developed new slice discovery algorithms that aim to group together coherent and high-error subsets of data. However, there has been little evaluation focused on whether these tools help humans form correct hypotheses about where (for which groups) their model underperforms. We conduct a controlled user study (N = 15) where we show 40 slices output by two state-of-the-art slice discovery algorithms to users, and ask them to form hypotheses about an object detection model. Our results provide positive evidence that these tools provide some benefit over a naive baseline, and also shed light on challenges faced by users during the hypothesis formation step. We conclude by discussing design opportunities for ML and HCI researchers. Our findings point to the importance of centering users when creating and evaluating new tools for slice discovery.
13.6LGMay 13, 2022
Perspectives on Incorporating Expert Feedback into Model UpdatesValerie Chen, Umang Bhatt, Hoda Heidari et al. · cambridge, cmu
Machine learning (ML) practitioners are increasingly tasked with developing models that are aligned with non-technical experts' values and goals. However, there has been insufficient consideration on how practitioners should translate domain expertise into ML updates. In this paper, we consider how to capture interactions between practitioners and experts systematically. We devise a taxonomy to match expert feedback types with practitioner updates. A practitioner may receive feedback from an expert at the observation- or domain-level, and convert this feedback into updates to the dataset, loss function, or parameter space. We review existing work from ML and human-computer interaction to describe this feedback-update taxonomy, and highlight the insufficient consideration given to incorporating feedback from non-technical experts. We end with a set of open questions that naturally arise from our proposed taxonomy and subsequent survey.
15.5LGApr 13, 2023
Learning Personalized Decision Support PoliciesUmang Bhatt, Valerie Chen, Katherine M. Collins et al. · cambridge, cmu
Individual human decision-makers may benefit from different forms of support to improve decision outcomes, but when each form of support will yield better outcomes? In this work, we posit that personalizing access to decision support tools can be an effective mechanism for instantiating the appropriate use of AI assistance. Specifically, we propose the general problem of learning a decision support policy that, for a given input, chooses which form of support to provide to decision-makers for whom we initially have no prior information. We develop $\texttt{Modiste}$, an interactive tool to learn personalized decision support policies. $\texttt{Modiste}$ leverages stochastic contextual bandit techniques to personalize a decision support policy for each decision-maker and supports extensions to the multi-objective setting to account for auxiliary objectives like the cost of support. We find that personalized policies outperform offline policies, and, in the cost-aware setting, reduce the incurred cost with minimal degradation to performance. Our experiments include various realistic forms of support (e.g., expert consensus and predictions from a large language model) on vision and language tasks. Our human subject experiments validate our computational experiments, demonstrating that personalization can yield benefits in practice for real users, who interact with $\texttt{Modiste}$.
9.2HCJul 28, 2023
FeedbackLogs: Recording and Incorporating Stakeholder Feedback into Machine Learning PipelinesMatthew Barker, Emma Kallina, Dhananjay Ashok et al. · cambridge, cmu
Even though machine learning (ML) pipelines affect an increasing array of stakeholders, there is little work on how input from stakeholders is recorded and incorporated. We propose FeedbackLogs, addenda to existing documentation of ML pipelines, to track the input of multiple stakeholders. Each log records important details about the feedback collection process, the feedback itself, and how the feedback is used to update the ML pipeline. In this paper, we introduce and formalise a process for collecting a FeedbackLog. We also provide concrete use cases where FeedbackLogs can be employed as evidence for algorithmic auditing and as a tool to record updates based on stakeholder feedback.
Towards a More Rigorous Science of Blindspot Discovery in Image Classification ModelsGregory Plumb, Nari Johnson, Ángel Alexander Cabrera et al. · cmu
A growing body of work studies Blindspot Discovery Methods ("BDM"s): methods that use an image embedding to find semantically meaningful (i.e., united by a human-understandable concept) subsets of the data where an image classifier performs significantly worse. Motivated by observed gaps in prior work, we introduce a new framework for evaluating BDMs, SpotCheck, that uses synthetic image datasets to train models with known blindspots and a new BDM, PlaneSpot, that uses a 2D image representation. We use SpotCheck to run controlled experiments that identify factors that influence BDM performance (e.g., the number of blindspots in a model, or features used to define the blindspot) and show that PlaneSpot is competitive with and in many cases outperforms existing BDMs. Importantly, we validate these findings by designing additional experiments that use real image data from MS-COCO, a large image benchmark dataset. Our findings suggest several promising directions for future work on BDM design and evaluation. Overall, we hope that the methodology and analyses presented in this work will help facilitate a more rigorous science of blindspot discovery.
Assisting Human Decisions in Document MatchingJoon Sik Kim, Valerie Chen, Danish Pruthi et al. · cmu
Many practical applications, ranging from paper-reviewer assignment in peer review to job-applicant matching for hiring, require human decision makers to identify relevant matches by combining their expertise with predictions from machine learning models. In many such model-assisted document matching tasks, the decision makers have stressed the need for assistive information about the model outputs (or the data) to facilitate their decisions. In this paper, we devise a proxy matching task that allows us to evaluate which kinds of assistive information improve decision makers' performance (in terms of accuracy and time). Through a crowdsourced (N=271 participants) study, we find that providing black-box model explanations reduces users' accuracy on the matching task, contrary to the commonly-held belief that they can be helpful by allowing better understanding of the model. On the other hand, custom methods that are designed to closely attend to some task-specific desiderata are found to be effective in improving user performance. Surprisingly, we also find that the users' perceived utility of assistive information is misaligned with their objective utility (measured through their task performance).
AutoML for Climate Change: A Call to ActionRenbo Tu, Nicholas Roberts, Vishak Prasad et al.
The challenge that climate change poses to humanity has spurred a rapidly developing field of artificial intelligence research focused on climate change applications. The climate change AI (CCAI) community works on a diverse, challenging set of problems which often involve physics-constrained ML or heterogeneous spatiotemporal data. It would be desirable to use automated machine learning (AutoML) techniques to automatically find high-performing architectures and hyperparameters for a given dataset. In this work, we benchmark popular AutoML libraries on three high-leverage CCAI applications: climate modeling, wind power forecasting, and catalyst discovery. We find that out-of-the-box AutoML libraries currently fail to meaningfully surpass the performance of human-designed CCAI models. However, we also identify a few key weaknesses, which stem from the fact that most AutoML techniques are tailored to computer vision and NLP applications. For example, while dozens of search spaces have been designed for image and language data, none have been designed for spatiotemporal data. Addressing these key weaknesses can lead to the discovery of novel architectures that yield substantial performance gains across numerous CCAI applications. Therefore, we present a call to action to the AutoML community, since there are a number of concrete, promising directions for future work in the space of AutoML for CCAI. We release our code and a list of resources at https://github.com/climate-change-automl/climate-change-automl.
Cross-Modal Fine-Tuning: Align then RefineJunhong Shen, Liam Li, Lucio M. Dery et al.
Fine-tuning large-scale pretrained models has led to tremendous progress in well-studied modalities such as vision and NLP. However, similar gains have not been observed in many other modalities due to a lack of relevant pretrained models. In this work, we propose ORCA, a general cross-modal fine-tuning framework that extends the applicability of a single large-scale pretrained model to diverse modalities. ORCA adapts to a target task via an align-then-refine workflow: given the target input, ORCA first learns an embedding network that aligns the embedded feature distribution with the pretraining modality. The pretrained model is then fine-tuned on the embedded data to exploit the knowledge shared across modalities. Through extensive experiments, we show that ORCA obtains state-of-the-art results on 3 benchmarks containing over 60 datasets from 12 modalities, outperforming a wide range of hand-designed, AutoML, general-purpose, and task-specific methods. We highlight the importance of data alignment via a series of ablation studies and demonstrate ORCA's utility in data-limited regimes.
11.1LGJun 24, 2022
On the Importance of Application-Grounded Experimental Design for Evaluating Explainable ML MethodsKasun Amarasinghe, Kit T. Rodolfa, Sérgio Jesus et al. · cmu
Most existing evaluations of explainable machine learning (ML) methods rely on simplifying assumptions or proxies that do not reflect real-world use cases; the handful of more robust evaluations on real-world settings have shortcomings in their design, resulting in limited conclusions of methods' real-world utility. In this work, we seek to bridge this gap by conducting a study that evaluates three popular explainable ML methods in a setting consistent with the intended deployment context. We build on a previous study on e-commerce fraud detection and make crucial modifications to its setup relaxing the simplifying assumptions made in the original work that departed from the deployment context. In doing so, we draw drastically different conclusions from the earlier work and find no evidence for the incremental utility of the tested methods in the task. Our results highlight how seemingly trivial experimental design choices can yield misleading conclusions, with lessons about the necessity of not only evaluating explainable ML methods using tasks, data, users, and metrics grounded in the intended deployment contexts but also developing methods tailored to specific applications. In addition, we believe the design of this experiment can serve as a template for future study designs evaluating explainable ML methods in other real-world contexts.
AANG: Automating Auxiliary LearningLucio M. Dery, Paul Michel, Mikhail Khodak et al.
Auxiliary objectives, supplementary learning signals that are introduced to help aid learning on data-starved or highly complex end-tasks, are commonplace in machine learning. Whilst much work has been done to formulate useful auxiliary objectives, their construction is still an art which proceeds by slow and tedious hand-design. Intuition for how and when these objectives improve end-task performance has also had limited theoretical backing. In this work, we present an approach for automatically generating a suite of auxiliary objectives. We achieve this by deconstructing existing objectives within a novel unified taxonomy, identifying connections between them, and generating new ones based on the uncovered structure. Next, we theoretically formalize widely-held intuitions about how auxiliary learning improves generalization on the end-task. This leads us to a principled and efficient algorithm for searching the space of generated objectives to find those most useful to a specified end-task. With natural language processing (NLP) as our domain of study, we demonstrate that our automated auxiliary learning pipeline leads to strong improvements over competitive baselines across continued training experiments on a pre-trained model on 5 NLP tasks.
Efficient Architecture Search for Diverse TasksJunhong Shen, Mikhail Khodak, Ameet Talwalkar
While neural architecture search (NAS) has enabled automated machine learning (AutoML) for well-researched areas, its application to tasks beyond computer vision is still under-explored. As less-studied domains are precisely those where we expect AutoML to have the greatest impact, in this work we study NAS for efficiently solving diverse problems. Seeking an approach that is fast, simple, and broadly applicable, we fix a standard convolutional network (CNN) topology and propose to search for the right kernel sizes and dilations its operations should take on. This dramatically expands the model's capacity to extract features at multiple resolutions for different types of data while only requiring search over the operation space. To overcome the efficiency challenges of naive weight-sharing in this search space, we introduce DASH, a differentiable NAS algorithm that computes the mixture-of-operations using the Fourier diagonalization of convolution, achieving both a better asymptotic complexity and an up-to-10x search time speedup in practice. We evaluate DASH on ten tasks spanning a variety of application domains such as PDE solving, protein folding, and heart disease detection. DASH outperforms state-of-the-art AutoML methods in aggregate, attaining the best-known automated performance on seven tasks. Meanwhile, on six of the ten tasks, the combined search and retraining time is less than 2x slower than simply training a CNN backbone that is far less accurate.
14.1LGJul 20, 2022
Provably tuning the ElasticNet across instancesMaria-Florina Balcan, Mikhail Khodak, Dravyansh Sharma et al.
An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization parameters of Ridge regression, LASSO, and the ElasticNet across multiple problem instances, a setting that encompasses both cross-validation and multi-task hyperparameter optimization. We obtain a novel structural result for the ElasticNet which characterizes the loss as a function of the tuning parameters as a piecewise-rational function with algebraic boundaries. We use this to bound the structural complexity of the regularized loss functions and show generalization guarantees for tuning the ElasticNet regression coefficients in the statistical setting. We also consider the more challenging online learning setting, where we show vanishing average expected regret relative to the optimal parameter pair. We further extend our results to tuning classification algorithms obtained by thresholding regression fits regularized by Ridge, LASSO, or ElasticNet. Our results are the first general learning-theoretic guarantees for this important class of problems that avoid strong assumptions on the data distribution. Furthermore, our guarantees hold for both validation and popular information criterion objectives.
On Noisy Evaluation in Federated Hyperparameter TuningKevin Kuo, Pratiksha Thaker, Mikhail Khodak et al.
Hyperparameter tuning is critical to the success of federated learning applications. Unfortunately, appropriately selecting hyperparameters is challenging in federated networks. Issues of scale, privacy, and heterogeneity introduce noise in the tuning process and make it difficult to evaluate the performance of various hyperparameters. In this work, we perform the first systematic study on the effect of noisy evaluation in federated hyperparameter tuning. We first identify and rigorously explore key sources of noise, including client subsampling, data and systems heterogeneity, and data privacy. Surprisingly, our results indicate that even small amounts of noise can significantly impact tuning methods-reducing the performance of state-of-the-art approaches to that of naive baselines. To address noisy evaluation in such scenarios, we propose a simple and effective approach that leverages public proxy data to boost the evaluation signal. Our work establishes general challenges, baselines, and best practices for future work in federated hyperparameter tuning.
16.4LGJul 2, 2024
Agreement-Based Cascading for Efficient InferenceSteven Kolawole, Don Dennis, Ameet Talwalkar et al.
Adaptive inference schemes reduce the cost of machine learning inference by assigning smaller models to easier examples, attempting to avoid invocation of larger models when possible. In this work we explore a simple, effective adaptive inference technique we term Agreement-Based Cascading (ABC). ABC builds a cascade of models of increasing size/complexity, and uses agreement between ensembles of models at each level of the cascade as a basis for data-dependent routing. Although ensemble execution introduces additional expense, we show that these costs can be easily offset in practice due to large expected differences in model sizes, parallel inference execution capabilities, and accuracy benefits of ensembling. We examine ABC theoretically and empirically in terms of these parameters, showing that the approach can reliably act as a drop-in replacement for existing models and surpass the best single model it aims to replace in terms of both efficiency and accuracy. Additionally, we explore the performance of ABC relative to existing cascading methods in three common scenarios: (1) edge-to-cloud inference, where ABC reduces communication costs by up to 14x; (2) cloud-based model serving, where it achieves a 3x reduction in rental costs; and (3) inference via model API services, where ABC achieves a 2-25x reduction in average price per token/request relative to state-of-the-art LLM cascades.
1.8LGAug 25, 2022
SONAR: Joint Architecture and System Optimization SearchElias Jääsaari, Michelle Ma, Ameet Talwalkar et al.
There is a growing need to deploy machine learning for different tasks on a wide array of new hardware platforms. Such deployment scenarios require tackling multiple challenges, including identifying a model architecture that can achieve a suitable predictive accuracy (architecture search), and finding an efficient implementation of the model to satisfy underlying hardware-specific systems constraints such as latency (system optimization search). Existing works treat architecture search and system optimization search as separate problems and solve them sequentially. In this paper, we instead propose to solve these problems jointly, and introduce a simple but effective baseline method called SONAR that interleaves these two search problems. SONAR aims to efficiently optimize for predictive accuracy and inference latency by applying early stopping to both search processes. Our experiments on multiple different hardware back-ends show that SONAR identifies nearly optimal architectures 30 times faster than a brute force approach.
19.3SEMar 25
Comparing Developer and LLM Biases in Code EvaluationAditya Mittal, Ryan Shar, Zichu Wu et al. · cmu
As LLMs are increasingly used as judges in code applications, they should be evaluated in realistic interactive settings that capture partial context and ambiguous intent. We present TRACE (Tool for Rubric Analysis in Code Evaluation), a framework that evaluates LLM judges' ability to predict human preferences and automatically extracts rubric items to reveal systematic biases in how humans and models weigh each item. Across three modalities -- chat-based programming, IDE autocompletion, and instructed code editing -- we use TRACE to measure how well LLM judges align with developer preferences. Among 13 different models, the best judges underperform human annotators by 12-23%. TRACE identifies 35 significant sources of misalignment between humans and judges across interaction modalities, the majority of which correspond to existing software engineering code quality criteria. For example, in chat-based coding, judges are biased towards longer code explanations while humans prefer shorter ones. We find significant misalignment on the majority of existing code quality dimensions, showing alignment gaps between LLM judges and human preference in realistic coding applications.
8.8LGOct 3, 2023
Learning to Relax: Setting Solver Parameters Across a Sequence of Linear System InstancesMikhail Khodak, Edmond Chow, Maria-Florina Balcan et al.
Solving a linear system $Ax=b$ is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter $ω$ has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed $ω$ as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best $ω$ for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.
The RealHumanEval: Evaluating Large Language Models' Abilities to Support ProgrammersHussein Mozannar, Valerie Chen, Mohammed Alsobay et al. · cmu, microsoft-research
Evaluation of large language models for code has primarily relied on static benchmarks, including HumanEval (Chen et al., 2021), or more recently using human preferences of LLM responses. As LLMs are increasingly used as programmer assistants, we study whether gains on existing benchmarks or more preferred LLM responses translate to programmer productivity when coding with LLMs, including time spent coding. We introduce RealHumanEval, a web interface to measure the ability of LLMs to assist programmers, through either autocomplete or chat support. We conducted a user study (N=243) using RealHumanEval in which users interacted with seven LLMs of varying base model performance. Despite static benchmarks not incorporating humans-in-the-loop, we find that improvements in benchmark performance lead to increased programmer productivity; however gaps in benchmark versus human performance are not proportional -- a trend that holds across both forms of LLM support. In contrast, we find that programmer preferences do not correlate with their actual performance, motivating the need for better proxy signals. We open-source RealHumanEval to enable human-centric evaluation of new models and the study data to facilitate efforts to improve code models.
ScribeAgent: Towards Specialized Web Agents Using Production-Scale Workflow DataJunhong Shen, Atishay Jain, Zedian Xiao et al.
Large Language Model (LLM) agents are rapidly improving to handle increasingly complex web-based tasks. Most of these agents rely on general-purpose, proprietary models like GPT-4 and focus on designing better prompts to improve their planning abilities. However, general-purpose LLMs are not specifically trained to understand specialized web contexts such as HTML, and they often struggle with long-horizon planning. We explore an alternative approach that fine-tunes open-source LLMs using production-scale workflow data collected from over 250 domains corresponding to 6 billion tokens. This simple yet effective approach shows substantial gains over prompting-based agents on existing benchmarks -- ScribeAgent achieves state-of-the-art direct generation performance on Mind2Web and improves the task success rate by 7.3% over the previous best text-only web agents on WebArena. We further perform detailed ablation studies on various fine-tuning design choices and provide insights into LLM selection, training recipes, context window optimization, and effect of dataset sizes.
Specialized Foundation Models Struggle to Beat Supervised BaselinesZongzhe Xu, Ritvik Gupta, Wenduo Cheng et al.
Following its success for vision and text, the "foundation model" (FM) paradigm -- pretraining large models on massive data, then fine-tuning on target tasks -- has rapidly expanded to domains in the sciences, engineering, healthcare, and beyond. Has this achieved what the original FMs accomplished, i.e. the supplanting of traditional supervised learning in their domains? To answer we look at three modalities -- genomics, satellite imaging, and time series -- with multiple recent FMs and compare them to a standard supervised learning workflow: model development, hyperparameter tuning, and training, all using only data from the target task. Across these three specialized domains, we find that it is consistently possible to train simple supervised models -- no more complicated than a lightly modified wide ResNet or UNet -- that match or even outperform the latest foundation models. Our work demonstrates that the benefits of large-scale pretraining have yet to be realized in many specialized areas, reinforces the need to compare new FMs to strong, well-tuned baselines, and introduces two new, easy-to-use, open-source, and automated workflows for doing so.
This Time is Different: An Observability Perspective on Time Series Foundation ModelsBen Cohen, Emaad Khwaja, Youssef Doubli et al.
We introduce Toto, a time series forecasting foundation model with 151 million parameters. Toto uses a modern decoder-only architecture coupled with architectural innovations designed to account for specific challenges found in multivariate observability time series data. Toto's pre-training corpus is a mixture of observability data, open datasets, and synthetic data, and is 4-10$\times$ larger than those of leading time series foundation models. Additionally, we introduce BOOM, a large-scale benchmark consisting of 350 million observations across 2,807 real-world time series. For both Toto and BOOM, we source observability data exclusively from Datadog's own telemetry and internal observability metrics. Extensive evaluations demonstrate that Toto achieves state-of-the-art performance on both BOOM and on established general purpose time series forecasting benchmarks. Toto's model weights, inference code, and evaluation scripts, as well as BOOM's data and evaluation code, are all available as open source under the Apache 2.0 License available at https://huggingface.co/Datadog/Toto-Open-Base-1.0 and https://github.com/DataDog/toto.
20.5LGMay 22, 2025Code
A Comprehensive Evaluation of Contemporary ML-Based Solvers for Combinatorial OptimizationShengyu Feng, Weiwei Sun, Shanda Li et al.
Machine learning (ML) has demonstrated considerable potential in supporting model design and optimization for combinatorial optimization (CO) problems. However, much of the progress to date has been evaluated on small-scale, synthetic datasets, raising concerns about the practical effectiveness of ML-based solvers in real-world, large-scale CO scenarios. Additionally, many existing CO benchmarks lack sufficient training data, limiting their utility for evaluating data-driven approaches. To address these limitations, we introduce FrontierCO, a comprehensive benchmark that covers eight canonical CO problem types and evaluates 16 representative ML-based solvers--including graph neural networks and large language model (LLM) agents. FrontierCO features challenging instances drawn from industrial applications and frontier CO research, offering both realistic problem difficulty and abundant training data. Our empirical results provide critical insights into the strengths and limitations of current ML methods, helping to guide more robust and practically relevant advances at the intersection of machine learning and combinatorial optimization. Our data is available at https://huggingface.co/datasets/CO-Bench/FrontierCO.
Multitask Learning Can Improve Worst-Group OutcomesAtharva Kulkarni, Lucio Dery, Amrith Setlur et al. · cmu
In order to create machine learning systems that serve a variety of users well, it is vital to not only achieve high average performance but also ensure equitable outcomes across diverse groups. However, most machine learning methods are designed to improve a model's average performance on a chosen end task without consideration for their impact on worst group error. Multitask learning (MTL) is one such widely used technique. In this paper, we seek not only to understand the impact of MTL on worst-group accuracy but also to explore its potential as a tool to address the challenge of group-wise fairness. We primarily consider the standard setting of fine-tuning a pre-trained model, where, following recent work \citep{gururangan2020don, dery2023aang}, we multitask the end task with the pre-training objective constructed from the end task data itself. In settings with few or no group annotations, we find that multitasking often, but not consistently, achieves better worst-group accuracy than Just-Train-Twice (JTT; \citet{pmlr-v139-liu21f}) -- a representative distributionally robust optimization (DRO) method. Leveraging insights from synthetic data experiments, we propose to modify standard MTL by regularizing the joint multitask representation space. We run a large number of fine-tuning experiments across computer vision and natural language processing datasets and find that our regularized MTL approach \emph{consistently} outperforms JTT on both average and worst-group outcomes. Our official code can be found here: \href{https://github.com/atharvajk98/MTL-group-robustness.git}{\url{https://github.com/atharvajk98/MTL-group-robustness}}.
Towards Community-Driven Agents for Machine Learning EngineeringSijie Li, Weiwei Sun, Shanda Li et al.
Large language model-based machine learning (ML) agents have shown great promise in automating ML research. However, existing agents typically operate in isolation on a given research problem, without engaging with the broader research community, where human researchers often gain insights and contribute by sharing knowledge. To bridge this gap, we introduce MLE-Live, a live evaluation framework designed to assess an agent's ability to communicate with and leverage collective knowledge from a simulated Kaggle research community. Building on this framework, we propose CoMind, a novel agent that excels at exchanging insights and developing novel solutions within a community context. CoMind achieves state-of-the-art performance on MLE-Live and outperforms 79.2% human competitors on average across four ongoing Kaggle competitions. Our code is released at https://github.com/comind-ml/CoMind.
Gradient Descent on Neural Networks Typically Occurs at the Edge of StabilityJeremy M. Cohen, Simran Kaur, Yuanzhi Li et al.
We empirically demonstrate that full-batch gradient descent on neural network training objectives typically operates in a regime we call the Edge of Stability. In this regime, the maximum eigenvalue of the training loss Hessian hovers just above the numerical value $2 / \text{(step size)}$, and the training loss behaves non-monotonically over short timescales, yet consistently decreases over long timescales. Since this behavior is inconsistent with several widespread presumptions in the field of optimization, our findings raise questions as to whether these presumptions are relevant to neural network training. We hope that our findings will inspire future efforts aimed at rigorously understanding optimization at the Edge of Stability. Code is available at https://github.com/locuslab/edge-of-stability.
LEAF: A Benchmark for Federated SettingsSebastian Caldas, Sai Meher Karthik Duddu, Peter Wu et al.
Modern federated networks, such as those comprised of wearable devices, mobile phones, or autonomous vehicles, generate massive amounts of data each day. This wealth of data can help to learn models that can improve the user experience on each device. However, the scale and heterogeneity of federated data presents new challenges in research areas such as federated learning, meta-learning, and multi-task learning. As the machine learning community begins to tackle these challenges, we are at a critical time to ensure that developments made in these areas are grounded with realistic benchmarks. To this end, we propose LEAF, a modular benchmarking framework for learning in federated settings. LEAF includes a suite of open-source federated datasets, a rigorous evaluation framework, and a set of reference implementations, all geared towards capturing the obstacles and intricacies of practical federated environments.
34.0LGMay 26, 2015
MLlib: Machine Learning in Apache SparkXiangrui Meng, Joseph Bradley, Burak Yavuz et al.
Apache Spark is a popular open-source platform for large-scale data processing that is well-suited for iterative machine learning tasks. In this paper we present MLlib, Spark's open-source distributed machine learning library. MLlib provides efficient functionality for a wide range of learning settings and includes several underlying statistical, optimization, and linear algebra primitives. Shipped with Spark, MLlib supports several languages and provides a high-level API that leverages Spark's rich ecosystem to simplify the development of end-to-end machine learning pipelines. MLlib has experienced a rapid growth due to its vibrant open-source community of over 140 contributors, and includes extensive documentation to support further growth and to let users quickly get up to speed.
Everybody Prune Now: Structured Pruning of LLMs with only Forward PassesLucio Dery, Steven Kolawole, Jean-François Kagy et al.
Structured pruning is a promising approach to create smaller, faster LLMs. However, existing methods typically rely on backward passes, which can inflate memory requirements and compute costs. In this work we introduce Bonsai, a gradient-free structured pruning method that eliminates the need for backpropagation, significantly reducing memory requirements and compute costs while achieving state-of-the-art pruning performance. Bonsai uses forward-pass-only perturbative pruning to enable efficient compression of large models on a broader range of hardware configurations. Unlike existing structured pruning approaches, Bonsai not only achieves better compression with fewer resources, but also produces models that are twice as fast as those generated by semi-structured pruning. As a concrete demonstration, we use Bonsai to prune an 8B LLaMA-3 model to 50% sparsity on a single A6000 GPU -- a task infeasible with backprop-based methods, which require 2-3x memory. Our results show that removing backprop as a requirement not only enables pruning larger models on constrained hardware but can also lead to state-of-the-art efficiency and performance.
UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal AdaptationJunhong Shen, Tanya Marwah, Ameet Talwalkar
We present Unified PDE Solvers (UPS), a data- and compute-efficient approach to developing unified neural operators for diverse families of spatiotemporal PDEs from various domains, dimensions, and resolutions. UPS embeds different PDEs into a shared representation space and processes them using a FNO-transformer architecture. Rather than training the network from scratch, which is data-demanding and computationally expensive, we warm-start the transformer from pretrained LLMs and perform explicit alignment to reduce the modality gap while improving data and compute efficiency. The cross-modal UPS achieves state-of-the-art results on a wide range of 1D and 2D PDE families from PDEBench, outperforming existing unified models using 4 times less data and 26 times less compute. Meanwhile, it is capable of few-shot transfer to unseen PDE families and coefficients.
28.7LGOct 31, 2024
Understanding Optimization in Deep Learning with Central FlowsJeremy M. Cohen, Alex Damian, Ameet Talwalkar et al.
Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime called the "edge of stability." In this paper, we develop theory that can describe the dynamics of optimization in this regime. Our key insight is that while the *exact* trajectory of an oscillatory optimizer may be challenging to analyze, the *time-averaged* (i.e. smoothed) trajectory is often much more tractable. To analyze an optimizer, we derive a differential equation called a "central flow" that characterizes this time-averaged trajectory. We empirically show that these central flows can predict long-term optimization trajectories for generic neural networks with a high degree of numerical accuracy. By interpreting these central flows, we are able to understand how gradient descent makes progress even as the loss sometimes goes up; how adaptive optimizers "adapt" to the local loss landscape; and how adaptive optimizers implicitly navigate towards regions where they can take larger steps. Our results suggest that central flows can be a valuable theoretical tool for reasoning about optimization in deep learning.
14.4LGJun 5, 2025
Sample Complexity and Representation Ability of Test-time Scaling ParadigmsBaihe Huang, Shanda Li, Tianhao Wu et al.
Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $Θ(1/Δ^2)$ samples to produce the correct answer, while best-of-$n$ only needs $Θ(1/Δ)$, where $Δ< 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods.
6.2CVOct 15, 2025
RECODE: Reasoning Through Code Generation for Visual Question AnsweringJunhong Shen, Mu Cai, Bo Hu et al.
Multimodal Large Language Models (MLLMs) struggle with precise reasoning for structured visuals like charts and diagrams, as pixel-based perception lacks a mechanism for verification. To address this, we propose to leverage derendering -- the process of reverse-engineering visuals into executable code -- as a new modality for verifiable visual reasoning. Specifically, we propose RECODE, an agentic framework that first generates multiple candidate programs to reproduce the input image. It then uses a critic to select the most faithful reconstruction and iteratively refines the code. This process not only transforms an ambiguous perceptual task into a verifiable, symbolic problem, but also enables precise calculations and logical inferences later on. On various visual reasoning benchmarks such as CharXiv, ChartQA, and Geometry3K, RECODE significantly outperforms methods that do not leverage code or only use code for drawing auxiliary lines or cropping. Our work demonstrates that grounding visual perception in executable code provides a new path toward more accurate and verifiable multimodal reasoning.
18.2HCJun 24, 2024
Modulating Language Model Experiences through FrictionsKatherine M. Collins, Valerie Chen, Ilia Sucholutsky et al.
Language models are transforming the ways that their users engage with the world. Despite impressive capabilities, over-consumption of language model outputs risks propagating unchecked errors in the short-term and damaging human capabilities for critical thinking in the long-term. How can we develop scaffolding around language models to curate more appropriate use? We propose selective frictions for language model experiences, inspired by behavioral science interventions, to dampen misuse. Frictions involve small modifications to a user's experience, e.g., the addition of a button impeding model access and reminding a user of their expertise relative to the model. Through a user study with real humans, we observe shifts in user behavior from the imposition of a friction over LLMs in the context of a multi-topic question-answering task as a representative task that people may use LLMs for, e.g., in education and information retrieval. We find that frictions modulate over-reliance by driving down users' click rates while minimally affecting accuracy for those topics. Yet, frictions may have unintended effects. We find marked differences in users' click behaviors even on topics where frictions were not provisioned. Our contributions motivate further study of human-AI behavioral interaction to inform more effective and appropriate LLM use.
16.5LGFeb 18, 2022
Learning Predictions for Algorithms with PredictionsMikhail Khodak, Maria-Florina Balcan, Ameet Talwalkar et al.
A burgeoning paradigm in algorithm design is the field of algorithms with predictions, in which algorithms can take advantage of a possibly-imperfect prediction of some aspect of the problem. While much work has focused on using predictions to improve competitive ratios, running times, or other performance measures, less effort has been devoted to the question of how to obtain the predictions themselves, especially in the critical online setting. We introduce a general design approach for algorithms that learn predictors: (1) identify a functional dependence of the performance measure on the prediction quality and (2) apply techniques from online learning to learn predictors, tune robustness-consistency trade-offs, and bound the sample complexity. We demonstrate the effectiveness of our approach by applying it to bipartite matching, ski-rental, page migration, and job scheduling. In several settings we improve upon multiple existing results while utilizing a much simpler analysis, while in the others we provide the first learning-theoretic guarantees.
8.6GTDec 12, 2021
Bayesian Persuasion for Algorithmic RecourseKeegan Harris, Valerie Chen, Joon Sik Kim et al.
When subjected to automated decision-making, decision subjects may strategically modify their observable features in ways they believe will maximize their chances of receiving a favorable decision. In many practical situations, the underlying assessment rule is deliberately kept secret to avoid gaming and maintain competitive advantage. The resulting opacity forces the decision subjects to rely on incomplete information when making strategic feature modifications. We capture such settings as a game of Bayesian persuasion, in which the decision maker offers a form of recourse to the decision subject by providing them with an action recommendation (or signal) to incentivize them to modify their features in desirable ways. We show that when using persuasion, the decision maker and decision subject are never worse off in expectation, while the decision maker can be significantly better off. While the decision maker's problem of finding the optimal Bayesian incentive-compatible (BIC) signaling policy takes the form of optimization over infinitely-many variables, we show that this optimization can be cast as a linear program over finitely-many regions of the space of possible assessment rules. While this reformulation simplifies the problem dramatically, solving the linear program requires reasoning about exponentially-many variables, even in relatively simple cases. Motivated by this observation, we provide a polynomial-time approximation scheme that recovers a near-optimal signaling policy. Finally, our numerical simulations on semi-synthetic data empirically demonstrate the benefits of using persuasion in the algorithmic recourse setting.
NAS-Bench-360: Benchmarking Neural Architecture Search on Diverse TasksRenbo Tu, Nicholas Roberts, Mikhail Khodak et al.
Most existing neural architecture search (NAS) benchmarks and algorithms prioritize well-studied tasks, e.g. image classification on CIFAR or ImageNet. This makes the performance of NAS approaches in more diverse areas poorly understood. In this paper, we present NAS-Bench-360, a benchmark suite to evaluate methods on domains beyond those traditionally studied in architecture search, and use it to address the following question: do state-of-the-art NAS methods perform well on diverse tasks? To construct the benchmark, we curate ten tasks spanning a diverse array of application domains, dataset sizes, problem dimensionalities, and learning objectives. Each task is carefully chosen to interoperate with modern CNN-based search methods while possibly being far-afield from its original development domain. To speed up and reduce the cost of NAS research, for two of the tasks we release the precomputed performance of 15,625 architectures comprising a standard CNN search space. Experimentally, we show the need for more robust NAS evaluation of the kind NAS-Bench-360 enables by showing that several modern NAS procedures perform inconsistently across the ten tasks, with many catastrophically poor results. We also demonstrate how NAS-Bench-360 and its associated precomputed results will enable future scientific discoveries by testing whether several recent hypotheses promoted in the NAS literature hold on diverse tasks. NAS-Bench-360 is hosted at https://nb360.ml.cmu.edu.
Should We Be Pre-training? An Argument for End-task Aware Training as an AlternativeLucio M. Dery, Paul Michel, Ameet Talwalkar et al.
In most settings of practical concern, machine learning practitioners know in advance what end-task they wish to boost with auxiliary tasks. However, widely used methods for leveraging auxiliary data like pre-training and its continued-pretraining variant are end-task agnostic: they rarely, if ever, exploit knowledge of the target task. We study replacing end-task agnostic continued training of pre-trained language models with end-task aware training of said models. We argue that for sufficiently important end-tasks, the benefits of leveraging auxiliary data in a task-aware fashion can justify forgoing the traditional approach of obtaining generic, end-task agnostic representations as with (continued) pre-training. On three different low-resource NLP tasks from two domains, we demonstrate that multi-tasking the end-task and auxiliary objectives results in significantly better downstream task performance than the widely-used task-agnostic continued pre-training paradigm of Gururangan et al. (2020). We next introduce an online meta-learning algorithm that learns a set of multi-task weights to better balance among our multiple auxiliary objectives, achieving further improvements on end-task performance and data efficiency.
9.9LGAug 19, 2021
Learning-to-learn non-convex piecewise-Lipschitz functionsMaria-Florina Balcan, Mikhail Khodak, Dravyansh Sharma et al.
We analyze the meta-learning of the initialization and step-size of learning algorithms for piecewise-Lipschitz functions, a non-convex setting with applications to both machine learning and algorithms. Starting from recent regret bounds for the exponential forecaster on losses with dispersed discontinuities, we generalize them to be initialization-dependent and then use this result to propose a practical meta-learning procedure that learns both the initialization and the step-size of the algorithm from multiple online learning tasks. Asymptotically, we guarantee that the average regret across tasks scales with a natural notion of task-similarity that measures the amount of overlap between near-optimal regions of different tasks. Finally, we instantiate the method and its guarantee in two important settings: robust meta-learning and multi-task data-driven algorithm design.
A Field Guide to Federated OptimizationJianyu Wang, Zachary Charles, Zheng Xu et al.
Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.
23.0LGJun 8, 2021
Federated Hyperparameter Tuning: Challenges, Baselines, and Connections to Weight-SharingMikhail Khodak, Renbo Tu, Tian Li et al.
Tuning hyperparameters is a crucial but arduous part of the machine learning pipeline. Hyperparameter optimization is even more challenging in federated learning, where models are learned over a distributed network of heterogeneous devices; here, the need to keep data on device and perform local training makes it difficult to efficiently train and evaluate configurations. In this work, we investigate the problem of federated hyperparameter tuning. We first identify key challenges and show how standard approaches may be adapted to form baselines for the federated setting. Then, by making a novel connection to the neural architecture search technique of weight-sharing, we introduce a new method, FedEx, to accelerate federated hyperparameter tuning that is applicable to widely-used federated optimization methods such as FedAvg and recent variants. Theoretically, we show that a FedEx variant correctly tunes the on-device learning rate in the setting of online convex optimization across devices. Empirically, we show that FedEx can outperform natural baselines for federated hyperparameter tuning by several percentage points on the Shakespeare, FEMNIST, and CIFAR-10 benchmarks, obtaining higher accuracy using the same training budget.
21.8LGJun 3, 2021
Finding and Fixing Spurious Patterns with ExplanationsGregory Plumb, Marco Tulio Ribeiro, Ameet Talwalkar
Image classifiers often use spurious patterns, such as "relying on the presence of a person to detect a tennis racket, which do not generalize. In this work, we present an end-to-end pipeline for identifying and mitigating spurious patterns for such models, under the assumption that we have access to pixel-wise object-annotations. We start by identifying patterns such as "the model's prediction for tennis racket changes 63% of the time if we hide the people." Then, if a pattern is spurious, we mitigate it via a novel form of data augmentation. We demonstrate that our method identifies a diverse set of spurious patterns and that it mitigates them by producing a model that is both more accurate on a distribution where the spurious pattern is not helpful and more robust to distribution shift.
Sanity Simulations for Saliency MethodsJoon Sik Kim, Gregory Plumb, Ameet Talwalkar
Saliency methods are a popular class of feature attribution explanation methods that aim to capture a model's predictive reasoning by identifying "important" pixels in an input image. However, the development and adoption of these methods are hindered by the lack of access to ground-truth model reasoning, which prevents accurate evaluation. In this work, we design a synthetic benchmarking framework, SMERF, that allows us to perform ground-truth-based evaluation while controlling the complexity of the model's reasoning. Experimentally, SMERF reveals significant limitations in existing saliency methods and, as a result, represents a useful tool for the development of new saliency methods.
Rethinking Neural Operations for Diverse TasksNicholas Roberts, Mikhail Khodak, Tri Dao et al.
An important goal of AutoML is to automate-away the design of neural networks on new tasks in under-explored domains. Motivated by this goal, we study the problem of enabling users to discover the right neural operations given data from their specific domain. We introduce a search space of operations called XD-Operations that mimic the inductive bias of standard multi-channel convolutions while being much more expressive: we prove that it includes many named operations across multiple application areas. Starting with any standard backbone such as ResNet, we show how to transform it into a search space over XD-operations and how to traverse the space using a simple weight-sharing scheme. On a diverse set of tasks -- solving PDEs, distance prediction for protein folding, and music modeling -- our approach consistently yields models with lower error than baseline networks and often even lower error than expert-designed domain-specific approaches.
18.2LGMar 10, 2021
Interpretable Machine Learning: Moving From Mythos to DiagnosticsValerie Chen, Jeffrey Li, Joon Sik Kim et al.
Despite increasing interest in the field of Interpretable Machine Learning (IML), a significant gap persists between the technical objectives targeted by researchers' methods and the high-level goals of consumers' use cases. In this work, we synthesize foundational work on IML methods and evaluation into an actionable taxonomy. This taxonomy serves as a tool to conceptualize the gap between researchers and consumers, illustrated by the lack of connections between its methods and use cases components. It also provides the foundation from which we describe a three-step workflow to better enable researchers and consumers to work together to discover what types of methods are useful for what use cases. Eventually, by building on the results generated from this workflow, a more complete version of the taxonomy will increasingly allow consumers to find relevant methods for their target use cases and researchers to identify applicable use cases for their proposed methods.
16.0LGJan 30, 2021
On Data Efficiency of Meta-learningMaruan Al-Shedivat, Liam Li, Eric Xing et al.
Meta-learning has enabled learning statistical models that can be quickly adapted to new prediction tasks. Motivated by use-cases in personalized federated learning, we study the often overlooked aspect of the modern meta-learning algorithms -- their data efficiency. To shed more light on which methods are more efficient, we use techniques from algorithmic stability to derive bounds on the transfer risk that have important practical implications, indicating how much supervision is needed and how it must be allocated for each method to attain the desired level of generalization. Further, we introduce a new simple framework for evaluating meta-learning methods under a limit on the available supervision, conduct an empirical study of MAML, Reptile, and Protonets, and demonstrate the differences in the behavior of these methods on few-shot and federated learning benchmarks. Finally, we propose active meta-learning, which incorporates active data selection into learning-to-learn, leading to better performance of all methods in the limited supervision regime.
13.2LGNov 2, 2020
A Learning Theoretic Perspective on Local ExplainabilityJeffrey Li, Vaishnavh Nagarajan, Gregory Plumb et al.
In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the test-time accuracy of a model using a notion of how locally explainable it is. Second, we explore the novel problem of explanation generalization which is an important concern for a growing class of finite sample-based local approximation explanations. Finally, we validate our theoretical results empirically and show that they reflect what can be seen in practice.
Geometry-Aware Gradient Algorithms for Neural Architecture SearchLiam Li, Mikhail Khodak, Maria-Florina Balcan et al.
Recent state-of-the-art methods for neural architecture search (NAS) exploit gradient-based optimization by relaxing the problem into continuous optimization over architectures and shared-weights, a noisy process that remains poorly understood. We argue for the study of single-level empirical risk minimization to understand NAS with weight-sharing, reducing the design of NAS methods to devising optimizers and regularizers that can quickly obtain high-quality solutions to this problem. Invoking the theory of mirror descent, we present a geometry-aware framework that exploits the underlying structure of this optimization to return sparse architectural parameters, leading to simple yet novel algorithms that enjoy fast convergence guarantees and achieve state-of-the-art accuracy on the latest NAS benchmarks in computer vision. Notably, we exceed the best published results for both CIFAR and ImageNet on both the DARTS search space and NAS-Bench201; on the latter we achieve near-oracle-optimal performance on CIFAR-10 and CIFAR-100. Together, our theory and experiments demonstrate a principled way to co-design optimizers and continuous relaxations of discrete NAS search spaces.
FACT: A Diagnostic for Group Fairness Trade-offsJoon Sik Kim, Jiahao Chen, Ameet Talwalkar
Group fairness, a class of fairness notions that measure how different groups of individuals are treated differently according to their protected attributes, has been shown to conflict with one another, often with a necessary cost in loss of model's predictive performance. We propose a general diagnostic that enables systematic characterization of these trade-offs in group fairness. We observe that the majority of group fairness notions can be expressed via the fairness-confusion tensor, which is the confusion matrix split according to the protected attribute values. We frame several optimization problems that directly optimize both accuracy and fairness objectives over the elements of this tensor, which yield a general perspective for understanding multiple trade-offs including group fairness incompatibilities. It also suggests an alternate post-processing method for designing fair classifiers. On synthetic and real datasets, we demonstrate the use cases of our diagnostic, particularly on understanding the trade-off landscape between accuracy and fairness.