A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. With the goal of using PRMs to improve a *base* policy via test-time search and reinforcement learning (RL), we ask: ``How should we design process rewards?'' Our key insight is that, to be effective, the process reward for a step should measure *progress*: a change in the likelihood of producing a correct response in the future, before and after taking the step, as measured under a *prover* policy distinct from the base policy. Such progress values can {distinguish} good and bad steps generated by the base policy, even though the base policy itself cannot. Theoretically, we show that even weaker provers can improve the base policy, as long as they distinguish steps without being too misaligned with the base policy. Our results show that process rewards defined as progress under such provers improve the efficiency of exploration during test-time search and online RL. We empirically validate our claims by training **process advantage verifiers (PAVs)** to measure progress under such provers and show that compared to ORM, they are >8% more accurate, and 1.5-5x more compute-efficient. Equipped with these insights, our PAVs enable **one of the first results** showing a 6x gain in sample efficiency for a policy trained using online RL with PRMs vs. ORMs.

Modern large language models (LLMs) excel at fitting finetuning data, but often struggle on unseen examples. In order to teach models genuine reasoning abilities rather than superficial pattern matching, our work aims 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 performance on test prompts 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 almost perfectly predict test accuracy, achieving $R^2$ of $\geq 0.9$ across various models (Llama3 8B, 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 dynamics to test performance, pre-memorization train accuracy can inform training decisions, such as the makeup of the training data. Our experiments on data curation 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 other data scaling techniques.

Training models to efficiently use test-time compute is crucial for improving the reasoning performance of LLMs. While current methods mostly do so via fine-tuning on search traces or running RL against the 0/1 outcome reward, 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 from the lens of exploration and exploitation. It also motivates the use of cumulative regret to measure the efficacy of test-time compute by viewing a long output stream as consisting of several episodes from the model. While current state-of-the-art models do not optimize regret, we show that regret can be minimized by running final 0/1 reward RL regularized by a dense reward bonus, given by the "information gain" from each subsequent block in the output stream. We prescribe an approach for quantifying information gain, which measures the utility of an intermediate segment of tokens towards improving accuracy of the final answer. We instantiate this idea to develop MRT, a new class of finetuning methods for optimizing test-time compute. Fine-tuning with MRT leads to substantial improvements in both performance and token efficiency on the AIME dataset.

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: (i) distilling successful search or thinking traces; and (ii), using verification (e.g., 0/1 outcome rewards, 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], implying a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF widening as test-time budget grows. We corroborate our theory empirically on didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Test-time scaling in agentic tasks often relies on generating long reasoning traces ("think" more) before acting, but this does not allow agents to acquire new information from the environment or adapt behavior over time. In this work, we propose scaling test-time interaction, an untapped dimension for test-time scaling that increases the agent's interaction horizon to enable rich behaviors such as exploration, backtracking, and dynamic re-planning within a single rollout. To demonstrate the promise of this scaling dimension, we situate our study in the domain of web agents. We first show that even prompting-based interaction scaling can improve task success on web benchmarks non-trivially. Building on this, we introduce TTI, a curriculum-based online reinforcement learning (RL) approach that trains agents by adaptively adjusting their interaction lengths during rollout. Using a Gemma 3 12B model, TTI sets a new state-of-the-art among open-source agents trained on public data on WebVoyager and WebArena. Case studies further reveal that TTI enables agents to balance exploration and exploitation adaptively. Our results establish interaction scaling as a powerful, complementary axis to scaling per-action compute, offering new avenues for training robust and adaptive agents.

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.

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.

Machine learning models fail catastrophically under distribution shift, but a surprisingly effective way to empirically improve robustness to some types of shift (*e.g.*, Imagenet-A/C) is to use stronger open-vocabulary classifiers derived from foundation models. In this work, we first note that for shifts governed by spurious correlations (features spuriously correlated with the label on the training data, but not on test), the zero-shot and few-shot performance of foundation models is no better than ERM models, and remains unchanged when pretrained data/model size is scaled. Secondly, even in these situations, foundation models are quite accurate at predicting the value of the spurious feature. In a simplified setup, we theoretically analyze both these findings. Specifically, we show that during contrastive pretraining, the simplicity bias of foundation models tends to result in the learning of features that mostly rely on the spurious attribute, compared to more robust features. We leverage these observations to propose Prompting for Robustness (PfR) which first uses foundation models to zero-shot predict the spurious attribute on labeled examples, and then learns a classifier with balanced performance across different groups of labels and spurious attribute. Across 5 vision and language tasks, we show that PfR's performance nearly equals that of an oracle algorithm (group DRO) that leverages human labeled spurious attributes.

Motivated by the problem of next word prediction on user devices we introduce and study the problem of personalized frequency histogram estimation in a federated setting. In this problem, over some domain, each user observes a number of samples from a distribution which is specific to that user. The goal is to compute for all users a personalized estimate of the user's distribution with error measured in KL divergence. We focus on addressing two central challenges: statistical heterogeneity and protection of user privacy. Our approach to the problem relies on discovering and exploiting similar subpopulations of users which are often present and latent in real-world data, while minimizing user privacy leakage at the same time. We first present a non-private clustering-based algorithm for the problem, and give a provably joint differentially private version of it with a private data-dependent initialization scheme. Next, we propose a simple data model which is based on a mixture of Dirichlet distributions, to formally motivate our non-private algorithm and demonstrate some properties of its components. Finally, we provide an extensive empirical evaluation of our private and non-private algorithms under varying levels of statistical and size heterogeneity on the Reddit, StackOverflow, and Amazon Reviews datasets. Our results demonstrate significant improvements over standard and clustering-based baselines, and in particular, they show that it is possible to improve over direct personalization of a single global model.

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 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.

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 \emph{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.

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.

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 surprisingly unexplored. In this paper, we first undertake a systematic empirical investigation of this combination, finding (i) that in domain adaptation settings, self-training and contrastive learning offer significant complementary gains; and (ii) that 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. Finally, we 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.

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.

Neural models for end-to-end text-to-speech (TTS) synthe-sis are increasingly outperforming traditional approaches in statistical parametric speech synthesis. Speech generation in these neural models predominantly relies on using free-form text as the input modality. However, the earlier statistical parametric models were built on encoded phonetic and syn-tactic features. In this work, we explore the possibility of explicitly feeding deterministic linguistic structure to a neural TTS system in the form of Heterogeneous Relational Graphs (HRGs), an expressive formalism capable of representing pho-netic and syntactic information. Specifically, we use Graph Convolutional Networks to learn structurally informed contin-uous representations of the HRGs, which can be seamlessly passed to the encoders of popular neural TTS models like TransformerTTS or Tacotron. Furthermore, our simple HRG based text-to-speech synthesis leverages the syntactic bias in HRGs as demonstrated by improvements in automated met-rics and human evaluation on i) the single speaker dataset LJSpeech; ii) the multi-speaker dataset Arctic; and iii) out-of-domain test sets from the Blizzard challenge.11The code, trained models, and our dataset of HRGs will be released at https://github.com/ars22/GraphNeuralTTS/.

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.

Aman Madaan, Amrith Setlur, Tanmay Parekh, Barnabas Poczos, Graham Neubig, Yiming Yang, Ruslan Salakhutdinov, Alan W Black, Shrimai Prabhumoye. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 2020.

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.

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.

E-commerce companies like Amazon, Alibaba and Flip-kart have an extensive catalogue comprising of billions of products. Matching customer search queries to plausible products is challenging due to the size and diversity of the catalogue. These challenges are compounded in apparel due to the semantic complexity and a large variation of fashion styles, product attributes and colours. Providing aids that can help the customer visualise the styles and colours matching their "search queries" will provide customers with necessary intuition about what can be done next. This helps the customer buy a product with the styles, embellishments and colours of their liking. In this work, we propose a Generative Adversarial Network (GAN) for generating images from text streams like customer search queries. Our GAN learns to incrementally generate possible images complementing the fine-grained style, colour of the apparel in the query. We incorporate a novel colour modelling approach enabling the GAN to render a wide spectrum of colours accurately. We compile a dataset from an e-commerce website to train our model. The proposed approach outperforms the baselines on qualitative and quantitative evaluations.