RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold

Training on model-generated synthetic data is a promising approach for finetuning LLMs, but it remains unclear when it helps or hurts. In this paper, we investigate this question for math reasoning via an empirical study, followed by building a conceptual understanding of our observations. First, we find that while the typical approach of finetuning a model on synthetic correct or positive problem-solution pairs generated by capable models offers modest performance gains, sampling more correct solutions from the finetuned learner itself followed by subsequent fine-tuning on this self-generated data $\textbf{doubles}$ the efficiency of the same synthetic problems. At the same time, training on model-generated positives can amplify various spurious correlations, resulting in flat or even inverse scaling trends as the amount of data increases. Surprisingly, we find that several of these issues can be addressed if we also utilize negative responses, i.e., model-generated responses that are deemed incorrect by a final answer verifier. Crucially, these negatives must be constructed such that the training can appropriately recover the utility or advantage of each intermediate step in the negative response. With this per-step scheme, we are able to attain consistent gains over only positive data, attaining performance similar to amplifying the amount of synthetic data by $\mathbf{8 \times}$. We show that training on per-step negatives can help to unlearn spurious correlations in the positive data, and is equivalent to advantage-weighted reinforcement learning (RL), implying that it inherits robustness benefits of RL over imitating positive data alone.

Leveraging Public Representations for Private Transfer Learning

Motivated by the recent empirical success of incorporating public data into differentially private learning, we theoretically investigate how a shared representation learned from public data can improve private learning. We explore two common scenarios of transfer learning for linear regression, both of which assume the public and private tasks (regression vectors) share a low-rank subspace in a high-dimensional space. In the first single-task transfer scenario, the goal is to learn a single model shared across all users, each corresponding to a row in a dataset. We provide matching upper and lower bounds showing that our algorithm achieves the optimal excess risk within a natural class of algorithms that search for the linear model within the given subspace estimate. In the second scenario of multitask model personalization, we show that with sufficient public data, users can avoid private coordination, as purely local learning within the given subspace achieves the same utility. Taken together, our results help to characterize the benefits of public data across common regimes of private transfer learning.

Complementary Benefits of Contrastive Learning and Self-Training Under Distribution Shift

Self-training and contrastive learning have emerged as leading techniques for incorporating unlabeled data, both under distribution shift (unsupervised domain adaptation) and when it is absent (semi-supervised learning). However, despite the popularity and compatibility of these techniques, their efficacy in combination remains unexplored. In this paper, we undertake a systematic empirical investigation of this combination, finding that (i) in domain adaptation settings, self-training and contrastive learning offer significant complementary gains; and (ii) in semi-supervised learning settings, surprisingly, the benefits are not synergistic. Across eight distribution shift datasets (e.g., BREEDs, WILDS), we demonstrate that the combined method obtains 3--8% higher accuracy than either approach independently. We then theoretically analyze these techniques in a simplified model of distribution shift, demonstrating scenarios under which the features produced by contrastive learning can yield a good initialization for self-training to further amplify gains and achieve optimal performance, even when either method alone would fail.

Multitask Learning Can Improve Worst-Group Outcomes

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 common setting of fine-tuning a pre-trained model, where, following recent work (Gururangan et al., 2020; Dery et al., 2023), 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 always, achieves better worst-group accuracy than Just-Train-Twice (JTT; Liu et al. (2021)) -- 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 and find that our regularized MTL approach consistently outperforms JTT on both worst and average group outcomes. Our official code can be found here: https://github.com/atharvajk98/MTL-group-robustness.

Deep Neural Networks Tend To Extrapolate Predictably

Conventional wisdom suggests that neural network predictions tend to be unpredictable and overconfident when faced with out-of-distribution (OOD) inputs. Our work reassesses this assumption for neural networks with high-dimensional inputs. Rather than extrapolating in arbitrary ways, we observe that neural network predictions often tend towards a constant value as input data becomes increasingly OOD. Moreover, we find that this value often closely approximates the optimal constant solution (OCS), i.e., the prediction that minimizes the average loss over the training data without observing the input. We present results showing this phenomenon across 8 datasets with different distributional shifts (including CIFAR10-C and ImageNet-R, S), different loss functions (cross entropy, MSE, and Gaussian NLL), and different architectures (CNNs and transformers). Furthermore, we present an explanation for this behavior, which we first validate empirically and then study theoretically in a simplified setting involving deep homogeneous networks with ReLU activations. Finally, we show how one can leverage our insights in practice to enable risk-sensitive decision-making in the presence of OOD inputs.

Contextual Reliability: When Different Features Matter in Different Contexts

Deep neural networks often fail catastrophically by relying on spurious correlations. Most prior work assumes a clear dichotomy into spurious and reliable features; however, this is often unrealistic. For example, most of the time we do not want an autonomous car to simply copy the speed of surrounding cars -- we don't want our car to run a red light if a neighboring car does so. However, we cannot simply enforce invariance to next-lane speed, since it could provide valuable information about an unobservable pedestrian at a crosswalk. Thus, universally ignoring features that are sometimes (but not always) reliable can lead to non-robust performance. We formalize a new setting called contextual reliability which accounts for the fact that the "right" features to use may vary depending on the context. We propose and analyze a two-stage framework called Explicit Non-spurious feature Prediction (ENP) which first identifies the relevant features to use for a given context, then trains a model to rely exclusively on these features. Our work theoretically and empirically demonstrates the advantages of ENP over existing methods and provides new benchmarks for contextual reliability.

Confidence-Based Model Selection: When to Take Shortcuts for Subpopulation Shifts

Effective machine learning models learn both robust features that directly determine the outcome of interest (e.g., an object with wheels is more likely to be a car), and shortcut features (e.g., an object on a road is more likely to be a car). The latter can be a source of error under distributional shift, when the correlations change at test-time. The prevailing sentiment in the robustness literature is to avoid such correlative shortcut features and learn robust predictors. However, while robust predictors perform better on worst-case distributional shifts, they often sacrifice accuracy on majority subpopulations. In this paper, we argue that shortcut features should not be entirely discarded. Instead, if we can identify the subpopulation to which an input belongs, we can adaptively choose among models with different strengths to achieve high performance on both majority and minority subpopulations. We propose COnfidence-baSed MOdel Selection (CosMoS), where we observe that model confidence can effectively guide model selection. Notably, CosMoS does not require any target labels or group annotations, either of which may be difficult to obtain or unavailable. We evaluate CosMoS on four datasets with spurious correlations, each with multiple test sets with varying levels of data distribution shift. We find that CosMoS achieves 2-5% lower average regret across all subpopulations, compared to using only robust predictors or other model aggregation methods.

Project and Probe: Sample-Efficient Domain Adaptation by Interpolating Orthogonal Features

Conventional approaches to robustness try to learn a model based on causal features. However, identifying maximally robust or causal features may be difficult in some scenarios, and in others, non-causal "shortcut" features may actually be more predictive. We propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features with a small target dataset. Our approach, Project and Probe (Pro$^2$), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro$^2$ then learns a linear classifier on top of these projected features using a small target dataset. We theoretically show that Pro$^2$ learns a projection matrix that is optimal for classification in an information-theoretic sense, resulting in better generalization due to a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro$^2$ improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

Bitrate-Constrained DRO: Beyond Worst Case Robustness To Unknown Group Shifts

Training machine learning models robust to distribution shifts is critical for real-world applications. Some robust training algorithms (e.g., Group DRO) specialize to group shifts and require group information on all training points. Other methods (e.g., CVaR DRO) that do not need group annotations can be overly conservative, since they naively upweight high loss points which may form a contrived set that does not correspond to any meaningful group in the real world (e.g., when the high loss points are randomly mislabeled training points). In this work, we address limitations in prior approaches by assuming a more nuanced form of group shift: conditioned on the label, we assume that the true group function (indicator over group) is simple. For example, we may expect that group shifts occur along low bitrate features (e.g., image background, lighting). Thus, we aim to learn a model that maintains high accuracy on simple group functions realized by these low bitrate features, that need not spend valuable model capacity achieving high accuracy on contrived groups of examples. Based on this, we consider the two-player game formulation of DRO where the adversary's capacity is bitrate-constrained. Our resulting practical algorithm, Bitrate-Constrained DRO (BR-DRO), does not require group information on training samples yet matches the performance of Group DRO on datasets that have training group annotations and that of CVaR DRO on long-tailed distributions. Our theoretical analysis reveals that in some settings BR-DRO objective can provably yield statistically efficient and less conservative solutions than unconstrained CVaR DRO.

Adversarial Unlearning: Reducing Confidence Along Adversarial Directions

Supervised learning methods trained with maximum likelihood objectives often overfit on training data. Most regularizers that prevent overfitting look to increase confidence on additional examples (e.g., data augmentation, adversarial training), or reduce it on training data (e.g., label smoothing). In this work we propose a complementary regularization strategy that reduces confidence on self-generated examples. The method, which we call RCAD (Reducing Confidence along Adversarial Directions), aims to reduce confidence on out-of-distribution examples lying along directions adversarially chosen to increase training loss. In contrast to adversarial training, RCAD does not try to robustify the model to output the original label, but rather regularizes it to have reduced confidence on points generated using much larger perturbations than in conventional adversarial training. RCAD can be easily integrated into training pipelines with a few lines of code. Despite its simplicity, we find on many classification benchmarks that RCAD can be added to existing techniques (e.g., label smoothing, MixUp training) to increase test accuracy by 1-3% in absolute value, with more significant gains in the low data regime. We also provide a theoretical analysis that helps to explain these benefits in simplified settings, showing that RCAD can provably help the model unlearn spurious features in the training data.