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Authors:Barproda Halder, Faisal Hamman, Pasan Dissanayake, Qiuyi Zhang, Ilia Sucholutsky, Sanghamitra Dutta

Abstract:Spurious patterns refer to a mathematical association between two or more variables in a dataset that are not causally related. However, this notion of spuriousness, which is usually introduced due to sampling biases in the dataset, has classically lacked a formal definition. To address this gap, this work presents the first information-theoretic formalization of spuriousness in a dataset (given a split of spurious and core features) using a mathematical framework called Partial Information Decomposition (PID). Specifically, we disentangle the joint information content that the spurious and core features share about another target variable (e.g., the prediction label) into distinct components, namely unique, redundant, and synergistic information. We propose the use of unique information, with roots in Blackwell Sufficiency, as a novel metric to formally quantify dataset spuriousness and derive its desirable properties. We empirically demonstrate how higher unique information in the spurious features in a dataset could lead a model into choosing the spurious features over the core features for inference, often having low worst-group-accuracy. We also propose a novel autoencoder-based estimator for computing unique information that is able to handle high-dimensional image data. Finally, we also show how this unique information in the spurious feature is reduced across several dataset-based spurious-pattern-mitigation techniques such as data reweighting and varying levels of background mixing, demonstrating a novel tradeoff between unique information (spuriousness) and worst-group-accuracy.

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Authors:Angelica Chen, Sadhika Malladi, Lily H. Zhang, Xinyi Chen, Qiuyi Zhang, Rajesh Ranganath, Kyunghyun Cho

Abstract:Preference learning algorithms (e.g., RLHF and DPO) are frequently used to steer LLMs to produce generations that are more preferred by humans, but our understanding of their inner workings is still limited. In this work, we study the conventional wisdom that preference learning trains models to assign higher likelihoods to more preferred outputs than less preferred outputs, measured via $\textit{ranking accuracy}$. Surprisingly, we find that most state-of-the-art preference-tuned models achieve a ranking accuracy of less than 60% on common preference datasets. We furthermore derive the $\textit{idealized ranking accuracy}$ that a preference-tuned LLM would achieve if it optimized the DPO or RLHF objective perfectly. We demonstrate that existing models exhibit a significant $\textit{alignment gap}$ -- $\textit{i.e.}$, a gap between the observed and idealized ranking accuracies. We attribute this discrepancy to the DPO objective, which is empirically and theoretically ill-suited to fix even mild ranking errors in the reference model, and derive a simple and efficient formula for quantifying the difficulty of learning a given preference datapoint. Finally, we demonstrate that ranking accuracy strongly correlates with the empirically popular win rate metric when the model is close to the reference model used in the objective, shedding further light on the differences between on-policy (e.g., RLHF) and off-policy (e.g., DPO) preference learning algorithms.

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Abstract:Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under the strict notion of strongly adaptive regret, which measures the maximum regret over any contiguous interval $I$. Due to its worst-case nature, there is an almost-linear $\Omega(|I|^{1-\epsilon})$ regret lower bound, when only one query per round is allowed [Daniely el al, ICML 2015]. Surprisingly, with just two queries per round, we give Strongly Adaptive Bandit Learner (StABL) that achieves $\tilde{O}(\sqrt{n|I|})$ adaptive regret for multi-armed bandits with $n$ arms. The bound is tight and cannot be improved in general. Our algorithm leverages a multiplicative update scheme of varying stepsizes and a carefully chosen observation distribution to control the variance. Furthermore, we extend our results and provide optimal algorithms in the bandit convex optimization setting. Finally, we empirically demonstrate the superior performance of our algorithms under volatile environments and for downstream tasks, such as algorithm selection for hyperparameter optimization.

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Abstract:Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation after removing low-sensitivity datapoints via subsampling. However, fast algorithms for approximating $\ell_p$ sensitivities, which we show is equivalent to approximate $\ell_p$ regression, are known for only the $\ell_2$ setting, in which they are termed leverage scores. In this work, we provide efficient algorithms for approximating $\ell_p$ sensitivities and related summary statistics of a given matrix. In particular, for a given $n \times d$ matrix, we compute $\alpha$-approximation to its $\ell_1$ sensitivities at the cost of $O(n/\alpha)$ sensitivity computations. For estimating the total $\ell_p$ sensitivity (i.e. the sum of $\ell_p$ sensitivities), we provide an algorithm based on importance sampling of $\ell_p$ Lewis weights, which computes a constant factor approximation to the total sensitivity at the cost of roughly $O(\sqrt{d})$ sensitivity computations. Furthermore, we estimate the maximum $\ell_1$ sensitivity, up to a $\sqrt{d}$ factor, using $O(d)$ sensitivity computations. We generalize all these results to $\ell_p$ norms for $p > 1$. Lastly, we experimentally show that for a wide class of matrices in real-world datasets, the total sensitivity can be quickly approximated and is significantly smaller than the theoretical prediction, demonstrating that real-world datasets have low intrinsic effective dimensionality.

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Authors:Ilia Sucholutsky, Lukas Muttenthaler, Adrian Weller, Andi Peng, Andreea Bobu, Been Kim, Bradley C. Love, Erin Grant, Iris Groen, Jascha Achterberg(+20 more)

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Abstract:Biological and artificial information processing systems form representations that they can use to categorize, reason, plan, navigate, and make decisions. How can we measure the extent to which the representations formed by these diverse systems agree? Do similarities in representations then translate into similar behavior? How can a system's representations be modified to better match those of another system? These questions pertaining to the study of representational alignment are at the heart of some of the most active research areas in cognitive science, neuroscience, and machine learning. For example, cognitive scientists measure the representational alignment of multiple individuals to identify shared cognitive priors, neuroscientists align fMRI responses from multiple individuals into a shared representational space for group-level analyses, and ML researchers distill knowledge from teacher models into student models by increasing their alignment. Unfortunately, there is limited knowledge transfer between research communities interested in representational alignment, so progress in one field often ends up being rediscovered independently in another. Thus, greater cross-field communication would be advantageous. To improve communication between these fields, we propose a unifying framework that can serve as a common language between researchers studying representational alignment. We survey the literature from all three fields and demonstrate how prior work fits into this framework. Finally, we lay out open problems in representational alignment where progress can benefit all three of these fields. We hope that our work can catalyze cross-disciplinary collaboration and accelerate progress for all communities studying and developing information processing systems. We note that this is a working paper and encourage readers to reach out with their suggestions for future revisions.

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Authors:Lukas Muttenthaler, Robert A. Vandermeulen, Qiuyi Zhang, Thomas Unterthiner, Klaus-Robert Müller

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Abstract:Model overconfidence and poor calibration are common in machine learning and difficult to account for when applying standard empirical risk minimization. In this work, we propose a novel method to alleviate these problems that we call odd-$k$-out learning (OKO), which minimizes the cross-entropy error for sets rather than for single examples. This naturally allows the model to capture correlations across data examples and achieves both better accuracy and calibration, especially in limited training data and class-imbalanced regimes. Perhaps surprisingly, OKO often yields better calibration even when training with hard labels and dropping any additional calibration parameter tuning, such as temperature scaling. We provide theoretical justification, establishing that OKO naturally yields better calibration, and provide extensive experimental analyses that corroborate our theoretical findings. We emphasize that OKO is a general framework that can be easily adapted to many settings and the trained model can be applied to single examples at inference time, without introducing significant run-time overhead or architecture changes.

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Authors:Qiuyi Zhang

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Abstract:Scalarization is a general technique that can be deployed in any multiobjective setting to reduce multiple objectives into one, such as recently in RLHF for training reward models that align human preferences. Yet some have dismissed this classical approach because linear scalarizations are known to miss concave regions of the Pareto frontier. To that end, we aim to find simple non-linear scalarizations that can explore a diverse set of $k$ objectives on the Pareto frontier, as measured by the dominated hypervolume. We show that hypervolume scalarizations with uniformly random weights are surprisingly optimal for provably minimizing the hypervolume regret, achieving an optimal sublinear regret bound of $O(T^{-1/k})$, with matching lower bounds that preclude any algorithm from doing better asymptotically. As a theoretical case study, we consider the multiobjective stochastic linear bandits problem and demonstrate that by exploiting the sublinear regret bounds of the hypervolume scalarizations, we can derive a novel non-Euclidean analysis that produces improved hypervolume regret bounds of $\tilde{O}( d T^{-1/2} + T^{-1/k})$. We support our theory with strong empirical performance of using simple hypervolume scalarizations that consistently outperforms both the linear and Chebyshev scalarizations, as well as standard multiobjective algorithms in bayesian optimization, such as EHVI.

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Abstract:We consider the problem of minimizing the number of matrix-vector queries needed for accurate trace estimation in the dynamic setting where our underlying matrix is changing slowly, such as during an optimization process. Specifically, for any $m$ matrices $A_1,...,A_m$ with consecutive differences bounded in Schatten-$1$ norm by $\alpha$, we provide a novel binary tree summation procedure that simultaneously estimates all $m$ traces up to $\epsilon$ error with $\delta$ failure probability with an optimal query complexity of $\widetilde{O}\left(m \alpha\sqrt{\log(1/\delta)}/\epsilon + m\log(1/\delta)\right)$, improving the dependence on both $\alpha$ and $\delta$ from Dharangutte and Musco (NeurIPS, 2021). Our procedure works without additional norm bounds on $A_i$ and can be generalized to a bound for the $p$-th Schatten norm for $p \in [1,2]$, giving a complexity of $\widetilde{O}\left(m \alpha\left(\sqrt{\log(1/\delta)}/\epsilon\right)^p +m \log(1/\delta)\right)$. By using novel reductions to communication complexity and information-theoretic analyses of Gaussian matrices, we provide matching lower bounds for static and dynamic trace estimation in all relevant parameters, including the failure probability. Our lower bounds (1) give the first tight bounds for Hutchinson's estimator in the matrix-vector product model with Frobenius norm error even in the static setting, and (2) are the first unconditional lower bounds for dynamic trace estimation, resolving open questions of prior work.

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Authors:Yutian Chen, Xingyou Song, Chansoo Lee, Zi Wang, Qiuyi Zhang, David Dohan, Kazuya Kawakami, Greg Kochanski, Arnaud Doucet, Marc'aurelio Ranzato(+2 more)

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Abstract:Meta-learning hyperparameter optimization (HPO) algorithms from prior experiments is a promising approach to improve optimization efficiency over objective functions from a similar distribution. However, existing methods are restricted to learning from experiments sharing the same set of hyperparameters. In this paper, we introduce the OptFormer, the first text-based Transformer HPO framework that provides a universal end-to-end interface for jointly learning policy and function prediction when trained on vast tuning data from the wild. Our extensive experiments demonstrate that the OptFormer can imitate at least 7 different HPO algorithms, which can be further improved via its function uncertainty estimates. Compared to a Gaussian Process, the OptFormer also learns a robust prior distribution for hyperparameter response functions, and can thereby provide more accurate and better calibrated predictions. This work paves the path to future extensions for training a Transformer-based model as a general HPO optimizer.

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Authors:Atish Agarwala, Abhimanyu Das, Brendan Juba, Rina Panigrahy, Vatsal Sharan, Xin Wang, Qiuyi Zhang

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Abstract:Can deep learning solve multiple tasks simultaneously, even when they are unrelated and very different? We investigate how the representations of the underlying tasks affect the ability of a single neural network to learn them jointly. We present theoretical and empirical findings that a single neural network is capable of simultaneously learning multiple tasks from a combined data set, for a variety of methods for representing tasks -- for example, when the distinct tasks are encoded by well-separated clusters or decision trees over certain task-code attributes. More concretely, we present a novel analysis that shows that families of simple programming-like constructs for the codes encoding the tasks are learnable by two-layer neural networks with standard training. We study more generally how the complexity of learning such combined tasks grows with the complexity of the task codes; we find that combining many tasks may incur a sample complexity penalty, even though the individual tasks are easy to learn. We provide empirical support for the usefulness of the learning bounds by training networks on clusters, decision trees, and SQL-style aggregation.

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