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Dec 12

Improved Active Multi-Task Representation Learning via Lasso

To leverage the copious amount of data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, most existing works design a source task selection strategy from a purely empirical perspective. Recently, chen2022active gave the first active multi-task representation learning (A-MTRL) algorithm which adaptively samples from source tasks and can provably reduce the total sample complexity using the L2-regularized-target-source-relevance parameter nu^2. But their work is theoretically suboptimal in terms of total source sample complexity and is less practical in some real-world scenarios where sparse training source task selection is desired. In this paper, we address both issues. Specifically, we show the strict dominance of the L1-regularized-relevance-based (nu^1-based) strategy by giving a lower bound for the nu^2-based strategy. When nu^1 is unknown, we propose a practical algorithm that uses the LASSO program to estimate nu^1. Our algorithm successfully recovers the optimal result in the known case. In addition to our sample complexity results, we also characterize the potential of our nu^1-based strategy in sample-cost-sensitive settings. Finally, we provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method.

  • 4 authors
·
Jun 4, 2023

SMOTE: Synthetic Minority Over-sampling Technique

An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of "normal" examples with only a small percentage of "abnormal" or "interesting" examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.

  • 4 authors
·
Jun 9, 2011

e1: Learning Adaptive Control of Reasoning Effort

Increasing the thinking budget of AI models can significantly improve accuracy, but not all questions warrant the same amount of reasoning. Users may prefer to allocate different amounts of reasoning effort depending on how they value output quality versus latency and cost. To leverage this tradeoff effectively, users need fine-grained control over the amount of thinking used for a particular query, but few approaches enable such control. Existing methods require users to specify the absolute number of desired tokens, but this requires knowing the difficulty of the problem beforehand to appropriately set the token budget for a query. To address these issues, we propose Adaptive Effort Control, a self-adaptive reinforcement learning method that trains models to use a user-specified fraction of tokens relative to the current average chain-of-thought length for each query. This approach eliminates dataset- and phase-specific tuning while producing better cost-accuracy tradeoff curves compared to standard methods. Users can dynamically adjust the cost-accuracy trade-off through a continuous effort parameter specified at inference time. We observe that the model automatically learns to allocate resources proportionally to the task difficulty and, across model scales ranging from 1.5B to 32B parameters, our approach enables a 2-3x reduction in chain-of-thought length while maintaining or improving performance relative to the base model used for RL training.

  • 5 authors
·
Oct 30

Efficient estimation of multiple expectations with the same sample by adaptive importance sampling and control variates

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

  • 3 authors
·
Nov 30, 2022

Adaptive Sampling Strategies to Construct Equitable Training Datasets

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models.

  • 7 authors
·
Jan 31, 2022

Sharper Bounds for ell_p Sensitivity Sampling

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

  • 2 authors
·
Jun 1, 2023

Learning to Actively Learn: A Robust Approach

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

  • 3 authors
·
Oct 29, 2020

EconProver: Towards More Economical Test-Time Scaling for Automated Theorem Proving

Large Language Models (LLMs) have recently advanced the field of Automated Theorem Proving (ATP), attaining substantial performance gains through widely adopted test-time scaling strategies, notably reflective Chain-of-Thought (CoT) reasoning and increased sampling passes. However, they both introduce significant computational overhead for inference. Moreover, existing cost analyses typically regulate only the number of sampling passes, while neglecting the substantial disparities in sampling costs introduced by different scaling strategies. In this paper, we systematically compare the efficiency of different test-time scaling strategies for ATP models and demonstrate the inefficiency of the current state-of-the-art (SOTA) open-source approaches. We then investigate approaches to significantly reduce token usage and sample passes while maintaining the original performance. Specifically, we propose two complementary methods that can be integrated into a unified EconRL pipeline for amplified benefits: (1) a dynamic Chain-of-Thought (CoT) switching mechanism designed to mitigate unnecessary token consumption, and (2) Diverse parallel-scaled reinforcement learning (RL) with trainable prefixes to enhance pass rates under constrained sampling passes. Experiments on miniF2F and ProofNet demonstrate that our EconProver achieves comparable performance to baseline methods with only 12% of the computational cost. This work provides actionable insights for deploying lightweight ATP models without sacrificing performance.

  • 8 authors
·
Sep 15 2

TTSnap: Test-Time Scaling of Diffusion Models via Noise-Aware Pruning

A prominent approach to test-time scaling for text-to-image diffusion models formulates the problem as a search over multiple noise seeds, selecting the one that maximizes a certain image-reward function. The effectiveness of this strategy heavily depends on the number and diversity of noise seeds explored. However, verifying each candidate is computationally expensive, because each must be fully denoised before a reward can be computed. This severely limits the number of samples that can be explored under a fixed budget. We propose test-time scaling with noise-aware pruning (TTSnap), a framework that prunes low-quality candidates without fully denoising them. The key challenge is that reward models are learned in the clean image domain, and the ranking of rewards predicted for intermediate estimates are often inconsistent with those predicted for clean images. To overcome this, we train noise-aware reward models via self-distillation to align the reward for intermediate estimates with that of the final clean images. To stabilize learning across different noise levels, we adopt a curriculum training strategy that progressively shifts the data domain from clean images to noise images. In addition, we introduce a new metric that measures reward alignment and computational budget utilization. Experiments demonstrate that our approach improves performance by over 16\% compared with existing methods, enabling more efficient and effective test-time scaling. It also provides orthogonal gains when combined with post-training techniques and local test-time optimization. Code: https://github.com/TerrysLearning/TTSnap/.

  • 9 authors
·
Nov 27

Awareness in Practice: Tensions in Access to Sensitive Attribute Data for Antidiscrimination

Organizations cannot address demographic disparities that they cannot see. Recent research on machine learning and fairness has emphasized that awareness of sensitive attributes, such as race and sex, is critical to the development of interventions. However, on the ground, the existence of these data cannot be taken for granted. This paper uses the domains of employment, credit, and healthcare in the United States to surface conditions that have shaped the availability of sensitive attribute data. For each domain, we describe how and when private companies collect or infer sensitive attribute data for antidiscrimination purposes. An inconsistent story emerges: Some companies are required by law to collect sensitive attribute data, while others are prohibited from doing so. Still others, in the absence of legal mandates, have determined that collection and imputation of these data are appropriate to address disparities. This story has important implications for fairness research and its future applications. If companies that mediate access to life opportunities are unable or hesitant to collect or infer sensitive attribute data, then proposed techniques to detect and mitigate bias in machine learning models might never be implemented outside the lab. We conclude that today's legal requirements and corporate practices, while highly inconsistent across domains, offer lessons for how to approach the collection and inference of sensitive data in appropriate circumstances. We urge stakeholders, including machine learning practitioners, to actively help chart a path forward that takes both policy goals and technical needs into account.

  • 3 authors
·
Dec 12, 2019

Enhancing Sample Utilization through Sample Adaptive Augmentation in Semi-Supervised Learning

In semi-supervised learning, unlabeled samples can be utilized through augmentation and consistency regularization. However, we observed certain samples, even undergoing strong augmentation, are still correctly classified with high confidence, resulting in a loss close to zero. It indicates that these samples have been already learned well and do not provide any additional optimization benefits to the model. We refer to these samples as ``naive samples". Unfortunately, existing SSL models overlook the characteristics of naive samples, and they just apply the same learning strategy to all samples. To further optimize the SSL model, we emphasize the importance of giving attention to naive samples and augmenting them in a more diverse manner. Sample adaptive augmentation (SAA) is proposed for this stated purpose and consists of two modules: 1) sample selection module; 2) sample augmentation module. Specifically, the sample selection module picks out {naive samples} based on historical training information at each epoch, then the naive samples will be augmented in a more diverse manner in the sample augmentation module. Thanks to the extreme ease of implementation of the above modules, SAA is advantageous for being simple and lightweight. We add SAA on top of FixMatch and FlexMatch respectively, and experiments demonstrate SAA can significantly improve the models. For example, SAA helped improve the accuracy of FixMatch from 92.50% to 94.76% and that of FlexMatch from 95.01% to 95.31% on CIFAR-10 with 40 labels.

  • 6 authors
·
Sep 7, 2023

Add-One-In: Incremental Sample Selection for Large Language Models via a Choice-Based Greedy Paradigm

Selecting high-quality and diverse training samples from extensive datasets plays a crucial role in reducing training overhead and enhancing the performance of Large Language Models (LLMs). However, existing studies fall short in assessing the overall value of selected data, focusing primarily on individual quality, and struggle to strike an effective balance between ensuring diversity and minimizing data point traversals. Therefore, this paper introduces a novel choice-based sample selection framework that shifts the focus from evaluating individual sample quality to comparing the contribution value of different samples when incorporated into the subset. Thanks to the advanced language understanding capabilities of LLMs, we utilize LLMs to evaluate the value of each option during the selection process. Furthermore, we design a greedy sampling process where samples are incrementally added to the subset, thereby improving efficiency by eliminating the need for exhaustive traversal of the entire dataset with the limited budget. Extensive experiments demonstrate that selected data from our method not only surpass the performance of the full dataset but also achieves competitive results with state-of-the-art (SOTA) studies, while requiring fewer selections. Moreover, we validate our approach on a larger medical dataset, highlighting its practical applicability in real-world applications.

  • 8 authors
·
Mar 4

Bayesian Estimation of Differential Privacy

Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they afford in practice. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget varepsilon spent on training a model. Existing approaches derive confidence intervals for varepsilon from confidence intervals for the false positive and false negative rates of membership inference attacks. Unfortunately, obtaining narrow high-confidence intervals for epsilon using this method requires an impractically large sample size and training as many models as samples. We propose a novel Bayesian method that greatly reduces sample size, and adapt and validate a heuristic to draw more than one sample per trained model. Our Bayesian method exploits the hypothesis testing interpretation of differential privacy to obtain a posterior for varepsilon (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. For the same sample size and confidence, we derive confidence intervals for varepsilon around 40% narrower than prior work. The heuristic, which we adapt from label-only DP, can be used to further reduce the number of trained models needed to get enough samples by up to 2 orders of magnitude.

  • 9 authors
·
Jun 10, 2022

Sampler Design for Implicit Feedback Data by Noisy-label Robust Learning

Implicit feedback data is extensively explored in recommendation as it is easy to collect and generally applicable. However, predicting users' preference on implicit feedback data is a challenging task since we can only observe positive (voted) samples and unvoted samples. It is difficult to distinguish between the negative samples and unlabeled positive samples from the unvoted ones. Existing works, such as Bayesian Personalized Ranking (BPR), sample unvoted items as negative samples uniformly, therefore suffer from a critical noisy-label issue. To address this gap, we design an adaptive sampler based on noisy-label robust learning for implicit feedback data. To formulate the issue, we first introduce Bayesian Point-wise Optimization (BPO) to learn a model, e.g., Matrix Factorization (MF), by maximum likelihood estimation. We predict users' preferences with the model and learn it by maximizing likelihood of observed data labels, i.e., a user prefers her positive samples and has no interests in her unvoted samples. However, in reality, a user may have interests in some of her unvoted samples, which are indeed positive samples mislabeled as negative ones. We then consider the risk of these noisy labels, and propose a Noisy-label Robust BPO (NBPO). NBPO also maximizes the observation likelihood while connects users' preference and observed labels by the likelihood of label flipping based on the Bayes' theorem. In NBPO, a user prefers her true positive samples and shows no interests in her true negative samples, hence the optimization quality is dramatically improved. Extensive experiments on two public real-world datasets show the significant improvement of our proposed optimization methods.

  • 2 authors
·
Jun 28, 2020

Does your data spark joy? Performance gains from domain upsampling at the end of training

Pretraining datasets for large language models (LLMs) have grown to trillions of tokens composed of large amounts of CommonCrawl (CC) web scrape along with smaller, domain-specific datasets. It is expensive to understand the impact of these domain-specific datasets on model capabilities as training at large FLOP scales is required to reveal significant changes to difficult and emergent benchmarks. Given the increasing cost of experimenting with pretraining data, how does one determine the optimal balance between the diversity in general web scrapes and the information density of domain specific data? In this work, we show how to leverage the smaller domain specific datasets by upsampling them relative to CC at the end of training to drive performance improvements on difficult benchmarks. This simple technique allows us to improve up to 6.90 pp on MMLU, 8.26 pp on GSM8K, and 6.17 pp on HumanEval relative to the base data mix for a 7B model trained for 1 trillion (T) tokens, thus rivaling Llama-2 (7B)x2014a model trained for twice as long. We experiment with ablating the duration of domain upsampling from 5% to 30% of training and find that 10% to 20% percent is optimal for navigating the tradeoff between general language modeling capabilities and targeted benchmarks. We also use domain upsampling to characterize at scale the utility of individual datasets for improving various benchmarks by removing them during this final phase of training. This tool opens up the ability to experiment with the impact of different pretraining datasets at scale, but at an order of magnitude lower cost compared to full pretraining runs.

  • 5 authors
·
Jun 5, 2024

Efficient Differentially Private Fine-Tuning of LLMs via Reinforcement Learning

The tension between data privacy and model utility has become the defining bottleneck for the practical deployment of large language models (LLMs) trained on sensitive corpora including healthcare. Differentially private stochastic gradient descent (DP-SGD) guarantees formal privacy, yet it does so at a pronounced cost: gradients are forcibly clipped and perturbed with noise, degrading sample efficiency and final accuracy. Numerous variants have been proposed to soften this trade-off, but they all share a handicap: their control knobs are hard-coded, global, and oblivious to the evolving optimization landscape. Consequently, practitioners are forced either to over-spend privacy budget in pursuit of utility, or to accept mediocre models in order to stay within privacy constraints. We present RLDP, the first framework to cast DP optimization itself as a closed-loop control problem amenable to modern deep reinforcement learning (RL). RLDP continuously senses rich statistics of the learning dynamics and acts by selecting fine-grained per parameter gradient-clipping thresholds as well as the magnitude of injected Gaussian noise. A soft actor-critic (SAC) hyper-policy is trained online during language model fine-tuning; it learns, from scratch, how to allocate the privacy budget where it matters and when it matters. Across more than 1,600 ablation experiments on GPT2-small, Llama-1B, Llama-3B, and Mistral-7B, RLDP delivers perplexity reductions of 1.3-30.5% (mean 5.4%) and an average 5.6% downstream utility gain. RLDP reaches each baseline's final utility after only 13-43% of the gradient-update budget (mean speed-up 71%), all while honoring the same (epsilon, delta)-DP contract and exhibiting equal or lower susceptibility to membership-inference and canary-extraction attacks.

  • 5 authors
·
Jul 30 2

Inference Scaling scriptsizeFLaws: The Limits of LLM Resampling with Imperfect Verifiers

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

  • 3 authors
·
Nov 26, 2024

VADE: Variance-Aware Dynamic Sampling via Online Sample-Level Difficulty Estimation for Multimodal RL

Group-based policy optimization methods like GRPO and GSPO have become standard for training multimodal models, leveraging group-wise rollouts and relative advantage estimation. However, they suffer from a critical gradient vanishing problem when all responses within a group receive identical rewards, causing advantage estimates to collapse and training signals to diminish. Existing attempts to mitigate this issue fall into two paradigms: filtering-based and sampling-based methods. Filtering-based methods first generate rollouts broadly and then retroactively filter out uninformative groups, leading to substantial computational overhead. Sampling-based methods proactively select effective samples before rollout but rely on static criteria or prior dataset knowledge, lacking real-time adaptability. To address these issues, we propose VADE, a Variance-Aware Dynamic sampling framework via online sample-level difficulty Estimation. Our framework integrates three key components: online sample-level difficulty estimation using Beta distributions, a Thompson sampler that maximizes information gain through the estimated correctness probability, and a two-scale prior decay mechanism that maintains robust estimation under policy evolution. This three components design enables VADE to dynamically select the most informative samples, thereby amplifying training signals while eliminating extra rollout costs. Extensive experiments on multimodal reasoning benchmarks show that VADE consistently outperforms strong baselines in both performance and sample efficiency, while achieving a dramatic reduction in computational overhead. More importantly, our framework can serves as a plug-and-play component to be seamlessly integrated into existing group-based RL algorithms. Code and models are available at https://VADE-RL.github.io.

  • 8 authors
·
Nov 24

Do uHear? Validation of uHear App for Preliminary Screening of Hearing Ability in Soundscape Studies

Studies involving soundscape perception often exclude participants with hearing loss to prevent impaired perception from affecting experimental results. Participants are typically screened with pure tone audiometry, the "gold standard" for identifying and quantifying hearing loss at specific frequencies, and excluded if a study-dependent threshold is not met. However, procuring professional audiometric equipment for soundscape studies may be cost-ineffective, and manually performing audiometric tests is labour-intensive. Moreover, testing requirements for soundscape studies may not require sensitivities and specificities as high as that in a medical diagnosis setting. Hence, in this study, we investigate the effectiveness of the uHear app, an iOS application, as an affordable and automatic alternative to a conventional audiometer in screening participants for hearing loss for the purpose of soundscape studies or listening tests in general. Based on audiometric comparisons with the audiometer of 163 participants, the uHear app was found to have high precision (98.04%) when using the World Health Organization (WHO) grading scheme for assessing normal hearing. Precision is further improved (98.69%) when all frequencies assessed with the uHear app is considered in the grading, which lends further support to this cost-effective, automated alternative to screen for normal hearing.

  • 6 authors
·
Jul 16, 2022

Understanding the Effect of Noise in LLM Training Data with Algorithmic Chains of Thought

During both pretraining and fine-tuning, Large Language Models (LLMs) are trained on trillions of tokens of text of widely varying quality. Both phases of training typically involve heuristically filtering out ``low-quality'' or noisy training samples, yet little is known quantitatively about how the type or intensity of noise affects downstream performance. In this work, we study how noise in chain of thought (CoT) impacts task performance in the highly-controlled setting of algorithmically solvable tasks. First, we develop the Traced Integer (TInt) framework to generate highly customizable noised execution traces for any arithmetic function on lists of integers. We then define two types of noise: static noise, a local form of noise which is applied after the CoT trace is computed, and dynamic noise, a global form of noise which propagates errors in the trace as it is computed. We then evaluate the test performance of pretrained models both prompted and fine-tuned on noised datasets with varying levels of dataset contamination and intensity. We find fine-tuned models are extremely robust to high levels of static noise but struggle significantly more with lower levels of dynamic noise. In contrast, few-shot prompted models appear more sensitive to even static noise. We conclude with a discussion of how our findings impact noise filtering best-practices, in particular emphasizing the importance of removing samples containing destructive dynamic noise with global errors.

  • 2 authors
·
Feb 6, 2024

Small Edits, Big Consequences: Telling Good from Bad Robustness in Large Language Models

Large language models (LLMs) now write code in settings where misreading a single word can break safety or cost money, yet we still expect them to overlook stray typos. To probe where useful robustness ends and harmful insensitivity begins, we compile 50 LeetCode problems and craft three minimal prompt perturbations that should vary in importance: (i) progressive underspecification deleting 10 % of words per step; (ii) lexical flip swapping a pivotal quantifier ("max" to "min"); and (iii) jargon inflation replacing a common noun with an obscure technical synonym. Six frontier models, including three "reasoning-tuned" versions, solve each mutated prompt, and their Python outputs are checked against the original test suites to reveal whether they reused the baseline solution or adapted. Among 11 853 generations we observe a sharp double asymmetry. Models remain correct in 85 % of cases even after 90 % of the prompt is missing, showing over-robustness to underspecification, yet only 54 % react to a single quantifier flip that reverses the task, with reasoning-tuned variants even less sensitive than their bases. Jargon edits lie in between, passing through 56 %. Current LLMs thus blur the line between harmless noise and meaning - changing edits, often treating both as ignorable. Masking salient anchors such as function names can force re - evaluation. We advocate evaluation and training protocols that reward differential sensitivity: stay steady under benign noise but adapt - or refuse - when semantics truly change.

  • 2 authors
·
Jul 14

Balancing Label Quantity and Quality for Scalable Elicitation

Scalable oversight studies methods of training and evaluating AI systems in domains where human judgment is unreliable or expensive, such as scientific research and software engineering in complex codebases. Most work in this area has focused on methods of improving the quality of labels. Recent work by Burns et al. (2023) considers the complementary problem of training models with low-quality labels, finding that large pretrained models often have an inductive bias towards producing correct answers. In practice, however, neither label quantity nor quality is fixed: practitioners face a quantity-quality tradeoff. In this paper, we explore the microeconomics of the quantity-quality tradeoff on binary NLP classification tasks used in Burns et al. (2023). While sample-efficient learning has been studied extensively, little public research has focused on scalable elicitation: eliciting capabilities from pretrained models subject to labeling cost constraints. We find that this setting has novel dynamics caused by the tradeoff between label quantity and quality, as well as the model's existing latent capabilities. We observe three regimes of eliciting classification knowledge from pretrained models using supervised finetuning: quantity-dominant, quality-dominant, and a mixed regime involving the use of low- and high-quality data together to attain higher accuracy at a lower cost than using either alone. We explore sample-efficient elicitation methods that make use of two datasets of differing qualities, and establish a Pareto frontier of scalable elicitation methods that optimally trade off labeling cost and classifier performance. We find that the accuracy of supervised fine-tuning can be improved by up to 5 percentage points at a fixed labeling budget by adding a few-shot prompt to make use of the model's existing knowledge of the task.

  • 2 authors
·
Oct 17, 2024

REX: Revisiting Budgeted Training with an Improved Schedule

Deep learning practitioners often operate on a computational and monetary budget. Thus, it is critical to design optimization algorithms that perform well under any budget. The linear learning rate schedule is considered the best budget-aware schedule, as it outperforms most other schedules in the low budget regime. On the other hand, learning rate schedules -- such as the 30-60-90 step schedule -- are known to achieve high performance when the model can be trained for many epochs. Yet, it is often not known a priori whether one's budget will be large or small; thus, the optimal choice of learning rate schedule is made on a case-by-case basis. In this paper, we frame the learning rate schedule selection problem as a combination of i) selecting a profile (i.e., the continuous function that models the learning rate schedule), and ii) choosing a sampling rate (i.e., how frequently the learning rate is updated/sampled from this profile). We propose a novel profile and sampling rate combination called the Reflected Exponential (REX) schedule, which we evaluate across seven different experimental settings with both SGD and Adam optimizers. REX outperforms the linear schedule in the low budget regime, while matching or exceeding the performance of several state-of-the-art learning rate schedules (linear, step, exponential, cosine, step decay on plateau, and OneCycle) in both high and low budget regimes. Furthermore, REX requires no added computation, storage, or hyperparameters.

  • 3 authors
·
Jul 9, 2021

POSIX: A Prompt Sensitivity Index For Large Language Models

Despite their remarkable capabilities, Large Language Models (LLMs) are found to be surprisingly sensitive to minor variations in prompts, often generating significantly divergent outputs in response to minor variations in the prompts, such as spelling errors, alteration of wording or the prompt template. However, while assessing the quality of an LLM, the focus often tends to be solely on its performance on downstream tasks, while very little to no attention is paid to prompt sensitivity. To fill this gap, we propose POSIX - a novel PrOmpt Sensitivity IndeX as a reliable measure of prompt sensitivity, thereby offering a more comprehensive evaluation of LLM performance. The key idea behind POSIX is to capture the relative change in loglikelihood of a given response upon replacing the corresponding prompt with a different intent-preserving prompt. We provide thorough empirical evidence demonstrating the efficacy of POSIX in capturing prompt sensitivity and subsequently use it to measure and thereby compare prompt sensitivity of various open-source LLMs. We find that merely increasing the parameter count or instruction tuning does not necessarily reduce prompt sensitivity whereas adding some few-shot exemplars, even just one, almost always leads to significant decrease in prompt sensitivity. We also find that alterations to prompt template lead to the highest sensitivity in the case of MCQ type tasks, whereas paraphrasing results in the highest sensitivity in open-ended generation tasks. The code for reproducing our results is open-sourced at https://github.com/kowndinya-renduchintala/POSIX.

  • 4 authors
·
Oct 3, 2024

SPRIGHT: A Fast and Robust Framework for Sparse Walsh-Hadamard Transform

We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some N-length input vector in the presence of noise, where the N-point Walsh spectrum is K-sparse with K = {O}(N^{delta}) scaling sub-linearly in the input dimension N for some 0<delta<1. Over the past decade, there has been a resurgence in research related to the computation of Discrete Fourier Transform (DFT) for some length-N input signal that has a K-sparse Fourier spectrum. In particular, through a sparse-graph code design, our earlier work on the Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm computes the K-sparse DFT in time {O}(Klog K) by taking {O}(K) noiseless samples. Inspired by the coding-theoretic design framework, Scheibler et al. proposed the Sparse Fast Hadamard Transform (SparseFHT) algorithm that elegantly computes the K-sparse WHT in the absence of noise using {O}(Klog N) samples in time {O}(Klog^2 N). However, the SparseFHT algorithm explicitly exploits the noiseless nature of the problem, and is not equipped to deal with scenarios where the observations are corrupted by noise. Therefore, a question of critical interest is whether this coding-theoretic framework can be made robust to noise. Further, if the answer is yes, what is the extra price that needs to be paid for being robust to noise? In this paper, we show, quite interestingly, that there is {\it no extra price} that needs to be paid for being robust to noise other than a constant factor. In other words, we can maintain the same sample complexity {O}(Klog N) and the computational complexity {O}(Klog^2 N) as those of the noiseless case, using our SParse Robust Iterative Graph-based Hadamard Transform (SPRIGHT) algorithm.

  • 4 authors
·
Aug 25, 2015

Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques

Offline optimization has recently emerged as an increasingly popular approach to mitigate the prohibitively expensive cost of online experimentation. The key idea is to learn a surrogate of the black-box function that underlines the target experiment using a static (offline) dataset of its previous input-output queries. Such an approach is, however, fraught with an out-of-distribution issue where the learned surrogate becomes inaccurate outside the offline data regimes. To mitigate this, existing offline optimizers have proposed numerous conditioning techniques to prevent the learned surrogate from being too erratic. Nonetheless, such conditioning strategies are often specific to particular surrogate or search models, which might not generalize to a different model choice. This motivates us to develop a model-agnostic approach instead, which incorporates a notion of model sharpness into the training loss of the surrogate as a regularizer. Our approach is supported by a new theoretical analysis demonstrating that reducing surrogate sharpness on the offline dataset provably reduces its generalized sharpness on unseen data. Our analysis extends existing theories from bounding generalized prediction loss (on unseen data) with loss sharpness to bounding the worst-case generalized surrogate sharpness with its empirical estimate on training data, providing a new perspective on sharpness regularization. Our extensive experimentation on a diverse range of optimization tasks also shows that reducing surrogate sharpness often leads to significant improvement, marking (up to) a noticeable 9.6% performance boost. Our code is publicly available at https://github.com/cuong-dm/IGNITE

  • 4 authors
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Mar 6

Upsample or Upweight? Balanced Training on Heavily Imbalanced Datasets

Data availability across domains often follows a long-tail distribution: a few domains have abundant data, while most face dat . a scarcity. This imbalance poses challenges in training language models uniformly across all domains. In our study, we focus on multilingual settings, where data sizes vary significantly between high- and low-resource languages. Common strategies to address this include upsampling low-resource languages (Temperature Sampling) or upweighting their loss (Scalarization). Although often considered equivalent, this assumption has not been proven, which motivates our study. Through both theoretical and empirical analysis, we identify the conditions under which these approaches are equivalent and when they diverge. Specifically, we demonstrate that these two methods are equivalent under full gradient descent, but this equivalence breaks down with stochastic gradient descent. Empirically, we observe that Temperature Sampling converges more quickly but is prone to overfitting. We argue that this faster convergence is likely due to the lower variance in gradient estimations, as shown theoretically. Based on these insights, we propose Cooldown, a strategy that reduces sampling temperature during training, accelerating convergence without overfitting to low-resource languages. Our method is competitive with existing data re-weighting and offers computational efficiency.

  • 5 authors
·
Oct 6, 2024

Balancing the Budget: Understanding Trade-offs Between Supervised and Preference-Based Finetuning

Post-training of Large Language Models often involves a pipeline of Supervised Finetuning (SFT) followed by Preference Finetuning (PFT) using methods like Direct Preference Optimization. Both stages require annotated data that are very different in structure and costs. We study how to optimally allocate a fixed training data budget between the two stages, through extensive experiments spanning four diverse tasks, multiple model sizes and various data annotation costs. Our findings reveal that just SFT on the base model dominates performance in low-data regimes (<1,000 annotated examples). With larger data-budgets, we observe that a combination of SFT and PFT, often with increasing portions allocated towards preference data yields optimal performance. However, completely eliminating SFT and running PFT directly on the base model yields suboptimal performance, described as the cold start problem on tasks like mathematics. We observe that this is due to the distribution shift arising from using DPO directly on the base model to elicit step-by-step reasoning. This limitation can be effectively addressed by allocating even a small portion (<10%) of the budget to SFT first, resulting in performance improvements of 15-20% on analytical benchmarks like GSM8k. These results provide actionable insights for researchers and practitioners optimizing model development under budget constraints, where high-quality data curation often represents a significant portion of the total costs of model development.

  • 3 authors
·
Feb 16

m1: Unleash the Potential of Test-Time Scaling for Medical Reasoning with Large Language Models

Test-time scaling has emerged as a powerful technique for enhancing the reasoning capabilities of large language models. However, its effectiveness in medical reasoning remains uncertain, as the medical domain fundamentally differs from mathematical tasks in terms of knowledge representation and decision-making processes. In this paper, we provide the first comprehensive investigation of test-time scaling for medical reasoning and present m1, a simple yet effective approach that increases a model's medical reasoning capability at inference. Our evaluation across diverse medical tasks demonstrates that test-time scaling consistently enhances medical reasoning, enabling lightweight fine-tuned models under 10B parameters to establish new state-of-the-art performance, while our 32B model rivals previous 70B-scale medical LLMs. However, we identify an optimal reasoning token budget of approximately 4K, beyond which performance may degrade due to overthinking. Budget forcing, which extends test-time computation through iterative prompts, helps models double-check answers but does not necessarily improve the overall medical QA performance and, in some cases, even introduces errors into previously correct responses. Our case-by-case analysis identifies insufficient medical knowledge as a key bottleneck that prevents further performance gains through test-time scaling. We find that increasing data scale, improving data quality, and expanding model capacity consistently enhance medical knowledge grounding, enabling continued performance improvements, particularly on challenging medical benchmarks where smaller models reach saturation. These findings underscore fundamental differences between medical and mathematical reasoning in LLMs, highlighting that enriched medical knowledge, other than increased reasoning depth alone, is essential for realizing the benefits of test-time scaling.

  • 5 authors
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Apr 1 2