Machine learning models are often required to perform well across several pre-defined settings, such as a set of user groups. Worst-case performance is a common metric to capture this requirement, and is the objective of group distributionally robust optimization (group DRO). Unfortunately, these methods struggle when the loss is non-convex in the parameters, or the model class is non-parametric. Here, we make a classical move to address this: we reparameterize group DRO from parameter space to function space, which results in a number of advantages. First, we show that group DRO over the space of bounded functions admits a minimax theorem. Second, for cross-entropy and mean squared error, we show that the minimax optimal mixture distribution is the solution of a simple convex optimization problem. Thus, provided one is working with a model class of universal function approximators, group DRO can be solved by a convex optimization problem followed by a classical risk minimization problem. We call our method MixMax. In our experiments, we found that MixMax matched or outperformed the standard group DRO baselines, and in particular, MixMax improved the performance of XGBoost over the only baseline, data balancing, for variations of the ACSIncome and CelebA annotations datasets.

Modern machine learning models are expensive to train, and there is a growing concern about the challenge of retroactively removing specific training data. Achieving exact unlearning in deep learning pipelines—producing models as if certain data had never been included in training—remains an open problem. In this paper, we revisit exact unlearning in deep learning and show that for large language models (LLMs) we can efficiently exactly unlearn “fine-tuning data" (the data used to adapt a pre-trained model). This follows from two observations. First, we can use in-context learning to adapt the LLM to the fine-tuning dataset instead of SGD based algorithms. Second, we show that accurate in-context learning can be done with quantized k-means, which allows for effectively constant time unlearning operations. Our evaluation shows that this unlearning recipe has similar performance to fine-tuning alternatives, but vastly reduces the unlearning costs. Our study also highlights the need for new measures of unlearning cost when adapting the learning algorithm to have faster unlearn operations.

We present a principled, per-instance approach to quantifying the difficulty of unlearning via fine-tuning. We begin by sharpening an analysis of noisy gradient descent for unlearning (Chien et al., 2024), obtaining a better utility–unlearning trade-off by replacing worst-case privacy loss bounds with per-instance privacy losses (Thudi et al., 2024), each of which bounds the (R ´enyi) divergence to retraining without an individual datapoint. To demonstrate the practical applicability of our theory, we present empirical results showing that our theoretical predictions are born out both for Stochastic Gradient Langevin Dynamics (SGLD) as well as for standard fine-tuning without explicit noise. We further demonstrate that per-instance privacy losses correlate well with several existing data difficulty metrics, while also identifying harder groups of data points, and introduce novel evaluation methods based on loss barriers. All together, our findings provide a foundation for more efficient and adaptive unlearning strategies tailored to the unique properties of individual data points.

Modern machine learning pipelines are increasingly combining and mixing data from diverse and disparate sources, e.g., pre-training large language models. Yet, finding the optimal data mixture is a challenging and open problem. We formalize this data mixing problem as a bi-level objective: the best mixture is the one that would lead to the best model for a downstream objective. Unfortunately, this objective is generally intractable. In this paper, we make the observation that the bi-level data mixing objective becomes convex as our model class becomes larger. We develop and study a gradient-based approach for optimizing this convex objective, which we call MixMin, and test it on language modeling and chemistry tasks. MixMin was the only method that uniformly improved the data mixture in all our experiments. With MixMin, we improved the data mixture using less than 0.2% additional compute for a pythia-$410M$ model trained on $8.2B$ tokens, resulting between 1-5% relative improvement to negative log likelihood on PIQA, ARC Easy, SciQ, and OpenWebMath. Crucially, we found that MixMin mixtures for smaller models improved training of larger models, suggesting that MixMin mixtures may be scale-invariant. When mixing bioassay data to train an XGBoost model, we saw improvements to average precision scores of $0.03-0.15$.

Spectral sparsification for directed Eulerian graphs is a key component in the design of fast algorithms for solving directed Laplacian linear systems. Directed Laplacian linear system solvers are crucial algorithmic primitives to fast computation of fundamental problems on random walks, such as computing stationary distribution, hitting and commute time, and personalized PageRank vectors. While spectral sparsification is well understood for undirected graphs and it is known that for every graph $G,$ $(1+\varepsilon)$-sparsifiers with $O(n\varepsilon^{-2})$ edges exist [Batson-Spielman-Srivastava, STOC '09] (which is optimal), the best known constructions of Eulerian sparsifiers require $Ω(n\varepsilon^{-2}\log^4 n)$ edges and are based on short-cycle decompositions [Chu et al., FOCS '18]. In this paper, we give improved constructions of Eulerian sparsifiers, specifically: 1. We show that for every directed Eulerian graph $\vec{G},$ there exist an Eulerian sparsifier with $O(n\varepsilon^{-2} \log^2 n \log^2\log n + n\varepsilon^{-4/3}\log^{8/3} n)$ edges. This result is based on combining short-cycle decompositions [Chu-Gao-Peng-Sachdeva-Sawlani-Wang, FOCS '18, SICOMP] and [Parter-Yogev, ICALP '19], with recent progress on the matrix Spencer conjecture [Bansal-Meka-Jiang, STOC '23]. 2. We give an improved analysis of the constructions based on short-cycle decompositions, giving an $m^{1+δ}$-time algorithm for any constant $δ> 0$ for constructing Eulerian sparsifiers with $O(n\varepsilon^{-2}\log^3 n)$ edges.

Proof-of-Learning (PoL) proposes that a model owner logs training checkpoints to establish a proof of having expended the computation necessary for training. The authors of PoL forego cryptographic approaches and trade rigorous security guarantees for scalability to deep learning. They empirically argued the benefit of this approach by showing how spoofing—computing a proof for a stolen model—is as expensive as obtaining the proof honestly by training the model. However, recent work has provided a counter-example and thus has invalidated this observation.In this work we demonstrate, first, that while it is true that current PoL verification is not robust to adversaries, recent work has largely underestimated this lack of robustness. This is because existing spoofing strategies are either unreproducible or target weakened instantiations of PoL—meaning they are easily thwarted by changing hyperparameters of the verification. Instead, we introduce the first spoofing strategies that can be reproduced across different configurations of the PoL verification and can be done for a fraction of the cost of previous spoofing strategies. This is possible because we identify key vulnerabilities of PoL and systematically analyze the underlying assumptions needed for robust verification of a proof. On the theoretical side, we show how realizing these assumptions reduces to open problems in learning theory. We conclude that one cannot develop a provably robust PoL verification mechanism without further understanding of optimization in deep learning.

Training reliable deep learning models which avoid making overconfident but incorrect predictions is a longstanding challenge. This challenge is further exacerbated when learning has to be differentially private: protection provided to sensitive data comes at the price of injecting additional randomness into the learning process. In this work, we conduct a thorough empirical investigation of selective classifiers---that can abstain under uncertainty---under a differential privacy constraint. We find that some popular selective prediction approaches are ineffective in a differentially private setting because they increase the risk of privacy leakage. At the same time, we identify that a recent approach that only uses checkpoints produced by an off-the-shelf private learning algorithm stands out as particularly suitable under DP. Further, we show that differential privacy does not just harm utility but also degrades selective classification performance. To analyze this effect across privacy levels, we propose a novel evaluation mechanism which isolates selective prediction performance across model utility levels at full coverage. Our experimental results show that recovering the performance level attainable by non-private models is possible but comes at a considerable coverage cost as the privacy budget decreases.

Machine unlearning is the process through which a deployed machine learning model is made to forget about some of its training data points. While naively retraining the model from scratch is an option, it is almost always associated with large computational overheads for deep learning models. Thus, several approaches to approximately unlearn have been proposed along with corresponding metrics that formalize what it means for a model to forget about a data point. In this work, we first taxonomize approaches and metrics of approximate unlearning. As a result, we identify verification error, i.e., the$\ell_{2}$difference between the weights of an approximately unlearned and a naively retrained model, as an approximate unlearning metric that should be optimized for as it subsumes a large class of other metrics. We theoretically analyze the canonical training algorithm, stochastic gradient descent (SGD), to surface the variables which are relevant to reducing the verification error of approximate unlearning for SGD. From this analysis, we first derive an easy-to-compute proxy for verification error (termed unlearning error). The analysis also informs the design of a new training objective penalty that limits the overall change in weights during SGD and as a result facilitates approximate unlearning with lower verification error. We validate our theoretical work through an empirical evaluation on learning with CIFAR-10, CIFAR-100, and IMDB sentiment analysis.

Training machine learning (ML) models typically involves expensive iterative optimization. Once the model’s final parameters are released, there is currently no mechanism for the entity which trained the model to prove that these parameters were indeed the result of this optimization procedure. Such a mechanism would support security of ML applications in several ways. For instance, it would simplify ownership resolution when multiple parties contest ownership of a specific model. It would also facilitate the distributed training across untrusted workers where Byzantine workers might otherwise mount a denial-ofservice by returning incorrect model updates.In this paper, we remediate this problem by introducing the concept of proof-of-learning in ML. Inspired by research on both proof-of-work and verified computations, we observe how a seminal training algorithm, stochastic gradient descent, accumulates secret information due to its stochasticity. This produces a natural construction for a proof-of-learning which demonstrates that a party has expended the compute require to obtain a set of model parameters correctly. In particular, our analyses and experiments show that an adversary seeking to illegitimately manufacture a proof-of-learning needs to perform at least as much work than is needed for gradient descent itself.We also instantiate a concrete proof-of-learning mechanism in both of the scenarios described above. In model ownership resolution, it protects the intellectual property of models released publicly. In distributed training, it preserves availability of the training procedure. Our empirical evaluation validates that our proof-of-learning mechanism is robust to variance induced by the hardware (e.g., ML accelerators) and software stacks.