Amrith Setlur

Amrith Setlur, Benjamin Eysenbach, Virginia Smith et al. · cmu

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.

Annie S. Chen, Yoonho Lee, Amrith Setlur et al. · cmu

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. 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. Theoretically, we find that Pro$^2$ results in more sample-efficient generalization by inducing 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.

Amrith Setlur, Don Dennis, Benjamin Eysenbach et al. · cmu

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.

Annie S. Chen, Yoonho Lee, Amrith Setlur et al. · cmu

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.

Gaurav Ghosal, Amrith Setlur, Daniel S. Brown et al. · cmu

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.

Matthew Y. R. Yang, Hao Bai, Ian Wu et al.

Outcome-reward reinforcement learning (RL) has proven effective at improving the reasoning capabilities of large language models (LLMs). However, standard RL assigns credit only at the level of the final answer, penalizing entire reasoning traces when the outcome is incorrect and uniformly reinforcing all steps when it is correct. As a result, correct intermediate steps may be discouraged in failed traces, while spurious steps may be reinforced in successful ones. We refer to this failure mode as the problem of credit assignment. While a natural remedy is to train a process reward model, accurately optimizing such models to identify corrective reasoning steps remains challenging. We introduce Intervention Training (InT), a training paradigm in which the model performs fine-grained credit assignment on its own reasoning traces by proposing short, targeted corrections that steer trajectories toward higher reward. Using reference solutions commonly available in mathematical reasoning datasets and exploiting the fact that verifying a model-generated solution is easier than generating a correct one from scratch, the model identifies the first error in its reasoning and proposes a single-step intervention to redirect the trajectory toward the correct solution. We then apply supervised fine-tuning (SFT) to the on-policy rollout up to the point of error concatenated with the intervention, localizing error to the specific step that caused failure. We show that the resulting model serves as a far better initialization for RL training. After running InT and subsequent fine-tuning with RL, we improve accuracy by nearly 14% over a 4B-parameter base model on IMO-AnswerBench, outperforming larger open-source models such as gpt-oss-20b.

Zhoujun Cheng, Yutao Xie, Yuxiao Qu et al. · cmu

While scaling laws guide compute allocation for LLM pre-training, analogous prescriptions for reinforcement learning (RL) post-training of large language models (LLMs) remain poorly understood. We study the compute-optimal allocation of sampling compute for on-policy RL methods in LLMs, framing scaling as a compute-constrained optimization over three resources: parallel rollouts per problem, number of problems per batch, and number of update steps. We find that the compute-optimal number of parallel rollouts per problem increases predictably with compute budget and then saturates. This trend holds across both easy and hard problems, though driven by different mechanisms: solution sharpening on easy problems and coverage expansion on hard problems. We further show that increasing the number of parallel rollouts mitigates interference across problems, while the number of problems per batch primarily affects training stability and can be chosen within a broad range. Validated across base models and data distributions, our results recast RL scaling laws as prescriptive allocation rules and provide practical guidance for compute-efficient LLM RL post-training.

Katie Kang, Amrith Setlur, Claire Tomlin et al. · cmu

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.

Yuxiao Qu, Amrith Setlur, Virginia Smith et al.

Reinforcement learning (RL) has improved the reasoning abilities of large language models (LLMs), yet state-of-the-art methods still fail to learn on many training problems. On hard problems, on-policy RL rarely explores even a single correct rollout, yielding zero reward and no learning signal for driving improvement. We find that natural solutions to remedy this exploration problem from classical RL, such as entropy bonuses, more permissive clipping of the importance ratio, or direct optimization of pass@k objectives, do not resolve this issue and often destabilize optimization without improving solvability. A natural alternative is to leverage transfer from easier problems. However, we show that mixing easy and hard problems during RL training is counterproductive due to ray interference, where optimization focuses on already-solvable problems in a way that actively inhibits progress on harder ones. To address this challenge, we introduce Privileged On-Policy Exploration (POPE), an approach that leverages human- or other oracle solutions as privileged information to guide exploration on hard problems, unlike methods that use oracle solutions as training targets (e.g., off-policy RL methods or warmstarting from SFT). POPE augments hard problems with prefixes of oracle solutions, enabling RL to obtain non-zero rewards during guided rollouts. Crucially, the resulting behaviors transfer back to the original, unguided problems through a synergy between instruction-following and reasoning. Empirically, POPE expands the set of solvable problems and substantially improves performance on challenging reasoning benchmarks.

Amrith Setlur, Zijian Wang, Andrew Cohen et al.

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

Junhong Shen, Hao Bai, Lunjun Zhang et al. · cmu

The current paradigm of test-time scaling relies on generating long reasoning traces ("thinking" more) before producing a response. In agent problems that require interaction, this can be done by generating thinking traces before acting in the world. However, this process does not allow agents to acquire new information from the environment or adapt their behavior over time. In this work, we propose to scale test-time interaction, an untapped dimension of test-time scaling that increases the agent's interaction horizon to enable running rich behaviors such as exploration, backtracking, and dynamic re-planning within a single rollout. To demonstrate the promise of this scaling dimension, we study the domain of web agents. We first show that even prompting-based interaction scaling without any training can improve task success on web benchmarks non-trivially. Building on this, we introduce TTI (Test-Time Interaction), a curriculum-based online reinforcement learning (RL) approach that trains agents by adaptively adjusting their rollout lengths. Using a Gemma 3 12B model, TTI produces state-of-the-art open-source, open-data web agents on WebVoyager and WebArena benchmarks. We further show that TTI enables agents to balance exploration and exploitation adaptively. Our results establish interaction scaling as a powerful, complementary axis to scaling per-step compute, offering new avenues for training adaptive agents.

Ian Wu, Yuxiao Qu, Amrith Setlur et al.

Large Language Models (LLMs) that can continually improve beyond their training budgets are able to solve increasingly difficult problems by adapting at test time, a property we refer to as extrapolation. However, standard reinforcement learning (RL) operates over fixed problem distributions and training budgets, which limits extrapolation amidst distribution shift at test time. To address this, we introduce RC, an iterative decoding algorithm that replaces standard autoregressive decoding during both training and inference. RC exploits an asymmetry between the response generation and summarization capabilities of LLMs to construct reasoning chains that consistently improve across iterations. Models trained to use RC can extrapolate and continually improve over reasoning horizons more than an order of magnitude longer than those seen during training. Empirically, training a 4B model with RC using a 16k-token training budget improves performance on HMMT 2025 from 40% to nearly 70% with 0.5m tokens at test time, outperforming both comparably sized models and many larger reasoning LLMs. Finally, we also show that models trained with RC can more effectively leverage existing scaffolds to further scale test-time performance, due to the improved summary-conditioned generation abilities learned through training.

Atharva 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}}.

Yuxiao Qu, Matthew Y. R. Yang, Amrith Setlur et al. · cmu

Training models to effectively use test-time compute is crucial for improving the reasoning performance of LLMs. Current methods mostly do so via fine-tuning on search traces or running RL with 0/1 outcome reward, but do these approaches efficiently utilize test-time compute? Would these approaches continue to scale as the budget improves? In this paper, we try to answer these questions. We formalize the problem of optimizing test-time compute as a meta-reinforcement learning (RL) problem, which provides a principled perspective on spending test-time compute. This perspective enables us to view the long output stream from the LLM as consisting of several episodes run at test time and leads us to use a notion of cumulative regret over output tokens as a way to measure the efficacy of test-time compute. Akin to how RL algorithms can best tradeoff exploration and exploitation over training, minimizing cumulative regret would also provide the best balance between exploration and exploitation in the token stream. While we show that state-of-the-art models do not minimize regret, one can do so by maximizing a dense reward bonus in conjunction with the outcome 0/1 reward RL. This bonus is the ''progress'' made by each subsequent block in the output stream, quantified by the change in the likelihood of eventual success. Using these insights, we develop Meta Reinforcement Fine-Tuning, or MRT, a new class of fine-tuning methods for optimizing test-time compute. MRT leads to a 2-3x relative gain in performance and roughly a 1.5x gain in token efficiency for math reasoning compared to outcome-reward RL.

Amrith Setlur, Nived Rajaraman, Sergey Levine et al. · cmu

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdős, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Amrith Setlur, Matthew Y. R. Yang, Charlie Snell et al. · cmu

Test-time scaling offers a promising path to improve LLM reasoning by utilizing more compute at inference time; however, the true promise of this paradigm lies in extrapolation (i.e., improvement in performance on hard problems as LLMs keep "thinking" for longer, beyond the maximum token budget they were trained on). Surprisingly, we find that most existing reasoning models do not extrapolate well. We show that one way to enable extrapolation is by training the LLM to perform in-context exploration: training the LLM to effectively spend its test time budget by chaining operations (such as generation, verification, refinement, etc.), or testing multiple hypotheses before it commits to an answer. To enable in-context exploration, we identify three key ingredients as part of our recipe e3: (1) chaining skills that the base LLM has asymmetric competence in, e.g., chaining verification (easy) with generation (hard), as a way to implement in-context search; (2) leveraging "negative" gradients from incorrect traces to amplify exploration during RL, resulting in longer search traces that chains additional asymmetries; and (3) coupling task difficulty with training token budget during training via a specifically-designed curriculum to structure in-context exploration. Our recipe e3 produces the best known 1.7B model according to AIME'25 and HMMT'25 scores, and extrapolates to 2x the training token budget. Our e3-1.7B model not only attains high pass@1 scores, but also improves pass@k over the base model.

Katie Kang, Amrith Setlur, Dibya Ghosh et al. · berkeley, cmu

Despite the remarkable capabilities of modern large language models (LLMs), the mechanisms behind their problem-solving abilities remain elusive. In this work, we aim to better understand how the learning dynamics of LLM finetuning shapes downstream generalization. Our analysis focuses on reasoning tasks, whose problem structure allows us to distinguish between memorization (the exact replication of reasoning steps from the training data) and performance (the correctness of the final solution). We find that a model's generalization behavior can be effectively characterized by a training metric we call pre-memorization train accuracy: the accuracy of model samples on training queries before they begin to copy the exact reasoning steps from the training set. On the dataset level, this metric is able to reliably predict test accuracy, achieving $R^2$ of around or exceeding 0.9 across various models (Llama3 8, Gemma2 9B), datasets (GSM8k, MATH), and training configurations. On a per-example level, this metric is also indicative of whether individual model predictions are robust to perturbations in the training query. By connecting a model's learning behavior to its generalization, pre-memorization train accuracy can guide targeted improvements to training strategies. We focus on data curation as an example, and show that prioritizing examples with low pre-memorization accuracy leads to 1.5-2x improvements in data efficiency compared to i.i.d. data scaling, and outperforms other standard data curation techniques.

Kevin Kuo, Amrith Setlur, Kartik Srinivas et al. · cmu

Approximate unlearning has gained popularity as an approach to efficiently update an LLM so that it behaves (roughly) as if it was not trained on a subset of data to begin with. However, existing methods are brittle in practice and can easily be attacked to reveal supposedly unlearned information. To alleviate issues with approximate unlearning, we instead propose SIFT-Masks (SIgn-Fixed Tuning-Masks), an exact unlearning method based on model merging. SIFT-Masks addresses two key limitations of standard model merging: (1) merging a large number of tasks can severely harm utility; and (2) methods that boost utility by sharing extra information across tasks make exact unlearning prohibitively expensive. SIFT-Masks solves these issues by (1) applying local masks to recover task-specific performance; and (2) constraining finetuning to align with a global sign vector as a lightweight approach to determine masks independently before merging. Across four settings where we merge up to 500 models, SIFT-Masks improves accuracy by 5-80% over naive merging and uses up to 250x less compute for exact unlearning compared to other merging baselines.

Saurabh Garg, Amrith Setlur, Zachary Chase Lipton et al. · cmu

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.

LM-Provers, Yuxiao Qu, Amrith Setlur et al.

Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large "internal" models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon. This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math? In this paper, we answer this question by building QED-Nano, a 4B model post-trained for Olympiad-level proofs. Our training recipe has three stages: (1) supervised fine-tuning to imbue good proof-writing styles by distilling from DeepSeek-Math-V2, (2) reinforcement learning (RL) with rubric-based rewards, and (3) expanding RL with a reasoning cache, which decomposes long proofs into iterative summarize-and-refine cycles and enables stronger test-time reasoning. QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B, and approaches the performance of proprietary models like Gemini 3 Pro, at a fraction of the inference cost. To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

Pratiksha Thaker, Amrith Setlur, Zhiwei Steven Wu et al. · cmu

Public pretraining is a promising approach to improve differentially private model training. However, recent work has noted that many positive research results studying this paradigm only consider in-distribution tasks, and may not apply to settings where there is distribution shift between the pretraining and finetuning data -- a scenario that is likely when finetuning private tasks due to the sensitive nature of the data. In this work, we show empirically across three tasks that even in settings with large distribution shift, where both zero-shot performance from public data and training from scratch with private data give unusably weak results, public features can in fact improve private training accuracy by up to 67\% over private training from scratch. We provide a theoretical explanation for this phenomenon, showing that if the public and private data share a low-dimensional representation, public representations can improve the sample complexity of private training even if it is impossible to learn the private task from the public data alone. Altogether, our results provide evidence that public data can indeed make private training practical in realistic settings of extreme distribution shift.

Yuxiao Qu, Anikait Singh, Yoonho Lee et al. · cmu, stanford

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives, intermediate results, or shared procedures, and building upon them. While RL post-training on long chains of thought ultimately aims to uncover this kind of algorithmic behavior, most reasoning traces learned by large models fail to consistently capture or reuse procedures, instead drifting into verbose and degenerate exploration. To address more effective reasoning, we introduce reasoning abstractions: concise natural language descriptions of procedural and factual knowledge that guide the model toward learning successful reasoning. We train models to be capable of proposing multiple abstractions given a problem, followed by RL that incentivizes building a solution while using the information provided by these abstractions. This results in a two-player RL training paradigm, abbreviated as RLAD, that jointly trains an abstraction generator and a solution generator. This setup effectively enables structured exploration, decouples learning signals of abstraction proposal and solution generation, and improves generalization to harder problems. We also show that allocating more test-time compute to generating abstractions is more beneficial for performance than generating more solutions at large test budgets, illustrating the role of abstractions in guiding meaningful exploration.

Amrith Setlur, Pratiksha Thaker, Jonathan Ullman · cmu

The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their parts. However, there are settings such as mean estimation where we have strong lower bounds, showing that when the two data sources have the same distribution, there is no complementary value to combining the two data sources. In this work we extend the known lower bounds for public-private learning to setting where the two data sources exhibit significant distribution shift. Our results apply to both Gaussian mean estimation where the two distributions have different means, and to Gaussian linear regression where the two distributions exhibit parameter shift. We find that when the shift is small (relative to the desired accuracy), either public or private data must be sufficiently abundant to estimate the private parameter. Conversely, when the shift is large, public data provides no benefit.

Amrith Setlur, Saurabh Garg, Xinyang Geng et al.

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.

Amrith Setlur, Oscar Li, Virginia Smith

We categorize meta-learning evaluation into two settings: $\textit{in-distribution}$ [ID], in which the train and test tasks are sampled $\textit{iid}$ from the same underlying task distribution, and $\textit{out-of-distribution}$ [OOD], in which they are not. While most meta-learning theory and some FSL applications follow the ID setting, we identify that most existing few-shot classification benchmarks instead reflect OOD evaluation, as they use disjoint sets of train (base) and test (novel) classes for task generation. This discrepancy is problematic because -- as we show on numerous benchmarks -- meta-learning methods that perform better on existing OOD datasets may perform significantly worse in the ID setting. In addition, in the OOD setting, even though current FSL benchmarks seem befitting, our study highlights concerns in 1) reliably performing model selection for a given meta-learning method, and 2) consistently comparing the performance of different methods. To address these concerns, we provide suggestions on how to construct FSL benchmarks to allow for ID evaluation as well as more reliable OOD evaluation. Our work aims to inform the meta-learning community about the importance and distinction of ID vs. OOD evaluation, as well as the subtleties of OOD evaluation with current benchmarks.

Amrith Setlur, Oscar Li, Virginia Smith

Meta-learning is a popular framework for learning with limited data in which an algorithm is produced by training over multiple few-shot learning tasks. For classification problems, these tasks are typically constructed by sampling a small number of support and query examples from a subset of the classes. While conventional wisdom is that task diversity should improve the performance of meta-learning, in this work we find evidence to the contrary: we propose a modification to traditional meta-learning approaches in which we keep the support sets fixed across tasks, thus reducing task diversity. Surprisingly, we find that not only does this modification not result in adverse effects, it almost always improves the performance for a variety of datasets and meta-learning methods. We also provide several initial analyses to understand this phenomenon. Our work serves to: (i) more closely investigate the effect of support set construction for the problem of meta-learning, and (ii) suggest a simple, general, and competitive baseline for few-shot learning.

Divyansh Kaushik, Amrith Setlur, Eduard Hovy et al.

In attempts to produce ML models less reliant on spurious patterns in NLP datasets, researchers have recently proposed curating counterfactually augmented data (CAD) via a human-in-the-loop process in which given some documents and their (initial) labels, humans must revise the text to make a counterfactual label applicable. Importantly, edits that are not necessary to flip the applicable label are prohibited. Models trained on the augmented data appear, empirically, to rely less on semantically irrelevant words and to generalize better out of domain. While this work draws loosely on causal thinking, the underlying causal model (even at an abstract level) and the principles underlying the observed out-of-domain improvements remain unclear. In this paper, we introduce a toy analog based on linear Gaussian models, observing interesting relationships between causal models, measurement noise, out-of-domain generalization, and reliance on spurious signals. Our analysis provides some insights that help to explain the efficacy of CAD. Moreover, we develop the hypothesis that while adding noise to causal features should degrade both in-domain and out-of-domain performance, adding noise to non-causal features should lead to relative improvements in out-of-domain performance. This idea inspires a speculative test for determining whether a feature attribution technique has identified the causal spans. If adding noise (e.g., by random word flips) to the highlighted spans degrades both in-domain and out-of-domain performance on a battery of challenge datasets, but adding noise to the complement gives improvements out-of-domain, it suggests we have identified causal spans. We present a large-scale empirical study comparing spans edited to create CAD to those selected by attention and saliency maps. Across numerous domains and models, we find that the hypothesized phenomenon is pronounced for CAD.

Hai Pham, Amrith Setlur, Saket Dingliwal et al.

Despite the advent of deep learning in computer vision, the general handwriting recognition problem is far from solved. Most existing approaches focus on handwriting datasets that have clearly written text and carefully segmented labels. In this paper, we instead focus on learning handwritten characters from maintenance logs, a constrained setting where data is very limited and noisy. We break the problem into two consecutive stages of word segmentation and word recognition respectively and utilize data augmentation techniques to train both stages. Extensive comparisons with popular baselines for scene-text detection and word recognition show that our system achieves a lower error rate and is more suited to handle noisy and difficult documents

Amrith Setlur, Barnabas Poczos, Alan W Black

This paper extends recent work on nonlinear Independent Component Analysis (ICA) by introducing a theoretical framework for nonlinear Independent Subspace Analysis (ISA) in the presence of auxiliary variables. Observed high dimensional acoustic features like log Mel spectrograms can be considered as surface level manifestations of nonlinear transformations over individual multivariate sources of information like speaker characteristics, phonological content etc. Under assumptions of energy based models we use the theory of nonlinear ISA to propose an algorithm that learns unsupervised speech representations whose subspaces are independent and potentially highly correlated with the original non-stationary multivariate sources. We show how nonlinear ICA with auxiliary variables can be extended to a generic identifiable model for subspaces as well while also providing sufficient conditions for the identifiability of these high dimensional subspaces. Our proposed methodology is generic and can be integrated with standard unsupervised approaches to learn speech representations with subspaces that can theoretically capture independent higher order speech signals. We evaluate the gains of our algorithm when integrated with the Autoregressive Predictive Decoding (APC) model by showing empirical results on the speaker verification and phoneme recognition tasks.

Amrith Setlur, Saket Dingliwal, Barnabas Poczos

Meta-learning has proven to be successful for few-shot learning across the regression, classification, and reinforcement learning paradigms. Recent approaches have adopted Bayesian interpretations to improve gradient-based meta-learners by quantifying the uncertainty of the post-adaptation estimates. Most of these works almost completely ignore the latent relationship between the covariate distribution $(p(x))$ of a task and the corresponding conditional distribution $p(y|x)$. In this paper, we identify the need to explicitly model the meta-distribution over the task covariates in a hierarchical Bayesian framework. We begin by introducing a graphical model that leverages the samples from the marginal $p(x)$ to better infer the posterior over the optimal parameters of the conditional distribution $(p(y|x))$ for each task. Based on this model we propose a computationally feasible meta-learning algorithm by introducing meaningful relaxations in our final objective. We demonstrate the gains of our algorithm over initialization based meta-learning baselines on popular classification benchmarks. Finally, to understand the potential benefit of modeling task covariates we further evaluate our method on a synthetic regression dataset.

Aman Madaan, Amrith Setlur, Tanmay Parekh et al.

This paper introduces a new task of politeness transfer which involves converting non-polite sentences to polite sentences while preserving the meaning. We also provide a dataset of more than 1.39 instances automatically labeled for politeness to encourage benchmark evaluations on this new task. We design a tag and generate pipeline that identifies stylistic attributes and subsequently generates a sentence in the target style while preserving most of the source content. For politeness as well as five other transfer tasks, our model outperforms the state-of-the-art methods on automatic metrics for content preservation, with a comparable or better performance on style transfer accuracy. Additionally, our model surpasses existing methods on human evaluations for grammaticality, meaning preservation and transfer accuracy across all the six style transfer tasks. The data and code is located at https://github.com/tag-and-generate.

Amrith Setlur, Barnabás Póczós

Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving approximate inference over the latent variables by minimizing a tight upper bound on the approximation gap. Given a discrete latent variable $Z$, the proposed approximation reduces inference complexity from $O(|Z|^c)$ to $O(|Z|)$. We use convex conjugates to determine this upper bound in a closed form and show that its addition to the optimization objective results in improved results for models assuming proportional hazards as in Survival Analysis.