Ruicheng Xian

Ruicheng Xian, Honglei Zhuang, Zhen Qin et al. · deepmind

Domain adaptation aims to transfer the knowledge learned on (data-rich) source domains to (low-resource) target domains, and a popular method is invariant representation learning, which matches and aligns the data distributions on the feature space. Although this method is studied extensively and applied on classification and regression problems, its adoption on ranking problems is sporadic, and the few existing implementations lack theoretical justifications. This paper revisits invariant representation learning for ranking. Upon reviewing prior work, we found that they implement what we call item-level alignment, which aligns the distributions of the items being ranked from all lists in aggregate but ignores their list structure. However, the list structure should be leveraged, because it is intrinsic to ranking problems where the data and the metrics are defined and computed on lists, not the items by themselves. To close this discrepancy, we propose list-level alignment -- learning domain-invariant representations at the higher level of lists. The benefits are twofold: it leads to the first domain adaptation generalization bound for ranking, in turn providing theoretical support for the proposed method, and it achieves better empirical transfer performance for unsupervised domain adaptation on ranking tasks, including passage reranking.

Yuzheng Hu, Ruicheng Xian, Qilong Wu et al.

Linear scalarization, i.e., combining all loss functions by a weighted sum, has been the default choice in the literature of multi-task learning (MTL) since its inception. In recent years, there is a surge of interest in developing Specialized Multi-Task Optimizers (SMTOs) that treat MTL as a multi-objective optimization problem. However, it remains open whether there is a fundamental advantage of SMTOs over scalarization. In fact, heated debates exist in the community comparing these two types of algorithms, mostly from an empirical perspective. To approach the above question, in this paper, we revisit scalarization from a theoretical perspective. We focus on linear MTL models and study whether scalarization is capable of fully exploring the Pareto front. Our findings reveal that, in contrast to recent works that claimed empirical advantages of scalarization, scalarization is inherently incapable of full exploration, especially for those Pareto optimal solutions that strike the balanced trade-offs between multiple tasks. More concretely, when the model is under-parametrized, we reveal a multi-surface structure of the feasible region and identify necessary and sufficient conditions for full exploration. This leads to the conclusion that scalarization is in general incapable of tracing out the Pareto front. Our theoretical results partially answer the open questions in Xin et al. (2021), and provide a more intuitive explanation on why scalarization fails beyond non-convexity. We additionally perform experiments on a real-world dataset using both scalarization and state-of-the-art SMTOs. The experimental results not only corroborate our theoretical findings, but also unveil the potential of SMTOs in finding balanced solutions, which cannot be achieved by scalarization.

Ruicheng Xian, Lang Yin, Han Zhao

To mitigate the bias exhibited by machine learning models, fairness criteria can be integrated into the training process to ensure fair treatment across all demographics, but it often comes at the expense of model performance. Understanding such tradeoffs, therefore, underlies the design of fair algorithms. To this end, this paper provides a complete characterization of the inherent tradeoff of demographic parity on classification problems, under the most general multi-group, multi-class, and noisy setting. Specifically, we show that the minimum error rate achievable by randomized and attribute-aware fair classifiers is given by the optimal value of a Wasserstein-barycenter problem. On the practical side, our findings lead to a simple post-processing algorithm that derives fair classifiers from score functions, which yields the optimal fair classifier when the score is Bayes optimal. We provide suboptimality analysis and sample complexity for our algorithm, and demonstrate its effectiveness on benchmark datasets.

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Ruicheng Xian, Han Zhao

We present a post-processing algorithm for fair classification that covers group fairness criteria including statistical parity, equal opportunity, and equalized odds under a single framework, and is applicable to multiclass problems in both attribute-aware and attribute-blind settings. Our algorithm, called "LinearPost", achieves fairness post-hoc by linearly transforming the predictions of the (unfair) base predictor with a "fairness risk" according to a weighted combination of the (predicted) group memberships. It yields the Bayes optimal fair classifier if the base predictors being post-processed are Bayes optimal, otherwise, the resulting classifier may not be optimal, but fairness is guaranteed as long as the group membership predictor is multicalibrated. The parameters of the post-processing can be efficiently computed and estimated from solving an empirical linear program. Empirical evaluations demonstrate the advantage of our algorithm in the high fairness regime compared to existing post-processing and in-processing fair classification algorithms.

Ruicheng Xian, Qiaobo Li, Gautam Kamath et al.

This paper describes a differentially private post-processing algorithm for learning fair regressors satisfying statistical parity, addressing privacy concerns of machine learning models trained on sensitive data, as well as fairness concerns of their potential to propagate historical biases. Our algorithm can be applied to post-process any given regressor to improve fairness by remapping its outputs. It consists of three steps: first, the output distributions are estimated privately via histogram density estimation and the Laplace mechanism, then their Wasserstein barycenter is computed, and the optimal transports to the barycenter are used for post-processing to satisfy fairness. We analyze the sample complexity of our algorithm and provide fairness guarantee, revealing a trade-off between the statistical bias and variance induced from the choice of the number of bins in the histogram, in which using less bins always favors fairness at the expense of error.

Yuzheng Hu, Fan Wu, Ruicheng Xian et al.

We propose the notion of empirical privacy variance and study it in the context of differentially private fine-tuning of language models. Specifically, we show that models calibrated to the same $(\varepsilon, δ)$-DP guarantee using DP-SGD with different hyperparameter configurations can exhibit significant variations in empirical privacy, which we quantify through the lens of memorization. We investigate the generality of this phenomenon across multiple dimensions and discuss why it is surprising and relevant. Through regression analysis, we examine how individual and composite hyperparameters influence empirical privacy. The results reveal a no-free-lunch trade-off: existing practices of hyperparameter tuning in DP-SGD, which focus on optimizing utility under a fixed privacy budget, often come at the expense of empirical privacy. To address this, we propose refined heuristics for hyperparameter selection that explicitly account for empirical privacy, showing that they are both precise and practically useful. Finally, we take preliminary steps to understand empirical privacy variance. We propose two hypotheses, identify limitations in existing techniques like privacy auditing, and outline open questions for future research.

Ruicheng Xian, Yuxuan Wan, Han Zhao

Instruction fine-tuned large language models (LLMs) enable a simple zero-shot or few-shot prompting paradigm, also known as in-context learning, for building prediction models. This convenience, combined with continued advances in LLM capability, has the potential to drive their adoption across a broad range of domains, including high-stakes applications where group fairness -- preventing disparate impacts across demographic groups -- is essential. The majority of existing approaches to enforcing group fairness on LLM-based classifiers rely on traditional fair algorithms applied via model fine-tuning or head-tuning on final-layer embeddings, but they are no longer applicable to closed-weight LLMs under the in-context learning setting, which include some of the most capable commercial models today, such as GPT-4, Gemini, and Claude. In this paper, we propose a framework for deriving fair classifiers from closed-weight LLMs via prompting: the LLM is treated as a feature extractor, and features are elicited from its probabilistic predictions (e.g., token log probabilities) using prompts strategically designed for the specified fairness criterion to obtain sufficient statistics for fair classification; a fair algorithm is then applied to these features to train a lightweight fair classifier in a post-hoc manner. Experiments on five datasets, including three tabular ones, demonstrate strong accuracy-fairness tradeoffs for the classifiers derived by our framework from both open-weight and closed-weight LLMs; in particular, our framework is data-efficient and outperforms fair classifiers trained on LLM embeddings (i.e., head-tuning) or from scratch on raw tabular features.

Ziwei Ji, Matus Telgarsky, Ruicheng Xian

This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has two main contributions: a generic scheme to approximate functions with the NTK by sampling from transport mappings between the initial weights and their desired values, and the construction of transport mappings via Fourier transforms. Regarding the first contribution, the proof scheme provides another perspective on how the NTK regime arises from rescaling: redundancy in the weights due to resampling allows individual weights to be scaled down. Regarding the second contribution, the most notable transport mapping asserts that roughly $1 / δ^{10d}$ nodes are sufficient to approximate continuous functions, where $δ$ depends on the continuity properties of the target function. By contrast, nearly the same proof yields a bound of $1 / δ^{2d}$ for shallow ReLU networks; this gap suggests a tantalizing direction for future work, separating shallow ReLU networks and their linearization.

Bolton Bailey, Ziwei Ji, Matus Telgarsky et al.

This paper investigates the approximation power of three types of random neural networks: (a) infinite width networks, with weights following an arbitrary distribution; (b) finite width networks obtained by subsampling the preceding infinite width networks; (c) finite width networks obtained by starting with standard Gaussian initialization, and then adding a vanishingly small correction to the weights. The primary result is a fully quantified bound on the rate of approximation of general general continuous functions: in all three cases, a function $f$ can be approximated with complexity $\|f\|_1 (d/δ)^{\mathcal{O}(d)}$, where $δ$ depends on continuity properties of $f$ and the complexity measure depends on the weight magnitudes and/or cardinalities. Along the way, a variety of ancillary results are developed: an exact construction of Gaussian densities with infinite width networks, an elementary stand-alone proof scheme for approximation via convolutions of radial basis functions, subsampling rates for infinite width networks, and depth separation for corrected networks.