Reasoning large language models achieve impressive test-time scaling by thinking for longer, but this performance gain comes at significant compute cost.Directly limiting test-time budget hurts overall performance, but not all problems are equally difficult.We propose thought calibration to decide dynamically when thinking can be terminated.To calibrate our decision rule, we view a language model's growing body of thoughts as a nested sequence of reasoning trees, where the goal is to identify the point at which novel reasoning plateaus.We realize this framework through lightweight probes that operate on top of the language model's hidden representations, which are informative of both the reasoning structure and overall consistency of response.Based on three reasoning language models and four datasets, thought calibration preserves model performance with up to a 60% reduction in thinking tokens on in-distribution data, and up to 20% in out-of-distribution data. 1

Contextual sequential decision-making is fundamental to machine learning, with applications in bandits, sequential hypothesis testing, and online risk control. These tasks often rely on statistical measures like expectation, variance, and quantiles. In this paper, we propose a universal algorithmic framework that learns the full underlying distribution, enabling a unified approach to all contextual online decision-making problems. The challenge lies in the uncountably infinite-dimensional regression, where existing contextual bandit algorithms all yield infinite regret. We innovatively propose an efficient infinite-dimensional functional regression oracle for contextual cumulative distribution functions (CDFs) and model every datum as a combination of context-dependent CDF basis functions. Our analysis reveals that the decay rate of the eigenvalue sequence of the design integral operator governs the regression error rate, and consequently, the utility regret rate. Specifically, when the eigenvalue sequence exhibits a polynomial decay of order $\frac{1}{\gamma}\ge 1$, the utility regret is bounded by $\tilde{O}( T^{\frac{3\gamma+2}{2(\gamma+2)}})$. The case that $\gamma=0$ can recover the existing optimal rate in contextual bandits literature with finite-dimensional regression and so as exponential decay. We also provide a numerical method to compute the eigenvalue sequence of integral operators, enabling the practical implementation of our framework.

Estimating associations between spatial covariates and responses — rather than merely predicting responses — is central to environmental science, epidemiology, and economics. For instance, public health officials might be interested in whether air pollution has a strictly positive association with a health outcome, and the magnitude of any effect. Standard machine learning methods often provide accurate predictions but offer limited insight into covariate-response relationships. And we show that existing methods for constructing confidence (or credible) intervals for associations can fail to provide nominal coverage in the face of model misspecification and nonrandom locations — despite both being essentially always present in spatial problems. We introduce a method that constructs valid frequentist confidence intervals for associations in spatial settings. Our method requires minimal assumptions beyond a form of spatial smoothness and a homoskedastic Gaussian error assumption. In particular, we do not require model correctness or covariate overlap between training and target locations. Our approach is the first to guarantee nominal coverage in this setting and outperforms existing techniques in both real and simulated experiments. Our confidence intervals are valid in finite samples when the noise of the Gaussian error is known, and we provide an asymptotically consistent estimation procedure for this noise variance when it is unknown.

Diffusion models can be improved with additional guidance towards more effective representations of input. Indeed, prior empirical work has already shown that aligning internal representations of the diffusion model with those of pre-trained models improves generation quality. In this paper, we present a systematic framework for incorporating representation guidance into diffusion models. We provide alternative decompositions of denoising models along with their associated training criteria, where the decompositions determine when and how the auxiliary representations are incorporated. Guided by our theoretical insights, we introduce two new strategies for enhancing representation alignment in diffusion models. First, we pair examples with target representations either derived from themselves or arisen from different synthetic modalities, and subsequently learn a joint model over the multimodal pairs. Second, we design an optimal training curriculum that balances representation learning and data generation. Our experiments across image, protein sequence, and molecule generation tasks demonstrate superior performance as well as accelerated training. In particular, on the class-conditional ImageNet $256\times 256$ benchmark, our guidance results in $23.3$ times faster training than the original SiT-XL as well as four times speedup over the state-of-the-art method REPA.

In this paper we introduce Hierarchical Diffusion Language Models (HDLM) -- a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are surjectively mapped to high-level tokens with coarse-grained meanings. In the forward process, each token is independently perturbed to its higher-level ancestor with more abstract semantics according to the scheduler, while in the reverse process the model progressively predicts the next, more detailed semantics. Taken together, HDLM provides a general time-varying next semantic scale prediction process for language modeling. We derive closed-form expressions for the diffusion Evidence Lower Bound (ELBO), and show that HDLM can be implemented in a flexible manner while including the existing MDLM as a special case. We also propose practical training techniques based on the insights. Extensive text generation experiments validate the effectiveness of HDLM, which demonstrates consistently lower validation and generative perplexity than baselines.

Motivated by the emergence of decentralized machine learning (ML) ecosystems, we study the delegation of data collection. Taking the field of contract theory as our starting point, we design optimal and near-optimal contracts that deal with two fundamental information asymmetries that arise in decentralized ML: uncertainty in the assessment of model quality and uncertainty regarding the optimal performance of any model. We show that a principal can cope with such asymmetry via simple linear contracts that achieve $1-1/\epsilon$ fraction of the optimal utility. To address the lack of a priori knowledge regarding the optimal performance, we give a convex program that can adaptively and efficiently compute the optimal contract. We also analyze the optimal utility and linear contracts for the more complex setting of multiple interactions.

From the social sciences to machine learning, it is well documented that metrics do not always align with social welfare. In healthcare, Dranove et al. (2003) showed that publishing surgery mortality metrics actually harmed sicker patients by increasing provider selection behavior. Using a principal-agent model, we analyze the incentive misalignments that arise from such average treated outcome metrics, and show that the incentives driving treatment decisions would align with maximizing total patient welfare if the metrics (i) accounted for counterfactual untreated outcomes and (ii) considered total welfare instead of averaging over treated patients. Operationalizing this, we show how counterfactual metrics can be modified to behave reasonably in patient-facing ranking systems. Extending to realistic settings when providers observe more about patients than the regulatory agencies do, we bound the decay in performance by the degree of information asymmetry between principal and agent. In doing so, our model connects principal-agent information asymmetry with unobserved heterogeneity in causal inference.

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an $\mathcal{O}(1/n)$ factor. We also introduce extensions of the idea to distribution shift, quantile risk control, multiple and adversarial risk control, and expectations of U-statistics. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm to bound the false negative rate, graph distance, and token-level F1-score.

We introduce a method for online conformal prediction with decaying step sizes. Like previous methods, ours possesses a retrospective guarantee of coverage for arbitrary sequences. However, unlike previous methods, we can simultaneously estimate a population quantile when it exists. Our theory and experiments indicate substantially improved practical properties: in particular, when the distribution is stable, the coverage is close to the desired level for every time point, not just on average over the observed sequence.

We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct uncertainty sets that correctly cover the unobserved noiseless ground truth labels. We further extend our theory and formulate the requirements for correctly controlling a general loss function, such as the false negative proportion, with noisy labels. Our theory and experiments suggest that conformal prediction and risk-controlling techniques with noisy labels attain conservative risk over the clean ground truth labels whenever the noise is dispersive and increases variability. In other adversarial cases, we can also correct for noise of bounded size in the conformal prediction algorithm in order to ensure achieving the correct risk of the ground truth labels without score or data regularity.

Standard conformal prediction methods provide a marginal coverage guarantee, which means that for a random test point, the conformal prediction set contains the true label with a user-specified probability. In many classification problems, we would like to obtain a stronger guarantee--that for test points of a specific class, the prediction set contains the true label with the same user-chosen probability. For the latter goal, existing conformal prediction methods do not work well when there is a limited amount of labeled data per class, as is often the case in real applications where the number of classes is large. We propose a method called clustered conformal prediction that clusters together classes having "similar" conformal scores and performs conformal prediction at the cluster level. Based on empirical evaluation across four image data sets with many (up to 1000) classes, we find that clustered conformal typically outperforms existing methods in terms of class-conditional coverage and set size metrics.

Contract theory studies the interactions between a principal and an agent when the two parties transact in the presence of private information [Bolton and Dewatripont, 2004, Faure-Grimaud et al., 2001, Salanié, 2005]. The principal would like to achieve her desired outcomes by hiring agents to work for her. The agent wishes to make money by working for the principal. They develop agreements in the form of a contract, which specifies how much the principal would pay under the different possible outcomes of the agent's work.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model’s mistakes and hallucinations. To address this, we develop uncertainty quantification techniques with rigorous statistical guarantees for image-to-image regression problems. In particular, we show how to derive uncertainty intervals around each pixel that are guaranteed to contain the true value with a user-specified confidence probability. Our methods work in conjunction with any base machine learning model, such as a neural network, and endow it with formal mathematical guarantees{—}regardless of the true unknown data distribution or choice of model. Furthermore, they are simple to implement and computationally inexpensive. We evaluate our procedure on three image-to-image regression tasks: quantitative phase microscopy, accelerated magnetic resonance imaging, and super-resolution transmission electron microscopy of a Drosophila melanogaster brain.

Meaningful uncertainty quantification in computer vision requires reasoning about semantic information---say, the hair color of the person in a photo or the location of a car on the street. To this end, recent breakthroughs in generative modeling allow us to represent semantic information in disentangled latent spaces, but providing uncertainties on the semantic latent variables has remained challenging. In this work, we provide principled uncertainty intervals that are guaranteed to contain the true semantic factors for any underlying generative model. The method does the following: (1) it uses quantile regression to output a heuristic uncertainty interval for each element in the latent space (2) calibrates these uncertainties such that they contain the true value of the latent for a new, unseen input. The endpoints of these calibrated intervals can then be propagated through the generator to produce interpretable uncertainty visualizations for each semantic factor. This technique reliably communicates semantically meaningful, principled, and instance-adaptive uncertainty in inverse problems like image super-resolution and image completion. Project page: https://swamiviv.github.io/semanticuncertaintyintervals/

Uncertainty quantification is essential for the reliable deployment of machine learning models to high-stakes application domains. Uncertainty quantification is all the more challenging when training distribution and test distribution are different, even if the distribution shifts are mild. Despite the ubiquity of distribution shifts in real-world applications, existing uncertainty quantification approaches mainly study the in-distribution setting where the train and test distributions are the same. In this paper, we develop a systematic calibration model to handle distribution shifts by leveraging data from multiple domains. Our proposed method---multi-domain temperature scaling---uses the heterogeneity in the domains to improve calibration robustness under distribution shift. Through experiments on three benchmark data sets, we find our proposed method outperforms existing methods as measured on both in-distribution and out-of-distribution test sets.

We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property called conditional coverage. A typical approach to this task is to estimate the conditional quantiles with quantile regression---it is well-known that this leads to correct coverage in the large-sample limit, although it may not be accurate in finite samples. We find in experiments that traditional quantile regression can have poor conditional coverage. To remedy this, we modify the loss function to promote independence between the size of the intervals and the indicator of a miscoverage event. For the true conditional quantiles, these two quantities are independent (orthogonal), so the modified loss function continues to be valid. Moreover, we empirically show that the modified loss function leads to improved conditional coverage, as evaluated by several metrics. We also introduce two new metrics that check conditional coverage by looking at the strength of the dependence between the interval size and the indicator of miscoverage.

An increasingly common setting in machine learning involves multiple parties, each with their own data, who want to jointly make predictions on future test points. Agents wish to benefit from the collective expertise of the full set of agents to make better predictions than they would individually, but may not be willing to release labeled data or model parameters. In this work, we explore a decentralized mechanism to make collective predictions at test time, that is inspired by the literature in social science on human consensus-making. Building on a query model to facilitate information exchange among agents, our approach leverages each agent’s pre-trained model without relying on external validation, model retraining, or data pooling. A theoretical analysis shows that our approach recovers inverse mean-squared-error (MSE) weighting in the large-sample limit which is known to be the optimal way to combine independent, unbiased estimators. Empirically, we demonstrate that our scheme effectively combines models with differing quality across the input space: the proposed consensus prediction achieves significant gains over classical model averaging, and even outperforms weighted averaging schemes that have access to additional validation data. Finally, we propose a decentralized Jackknife procedure as a tool to evaluate the sensitivity of the collective predictions with respect to a single agent's opinion.

While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that controls the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Last, we discuss extensions to uncertainty quantification for ranking, metric learning, and distributionally robust learning.

We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this criterion. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. To rigorously evaluate fitted models, we develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature. Both the model fitting and hypothesis testing leverage a resampled version of the sensitive attribute obeying equalized odds, by construction. We demonstrate the applicability and validity of the proposed framework both in regression and multi-class classification problems, reporting improved performance over state-of-the-art methods. Lastly, we show how to incorporate techniques for equitable uncertainty quantification---unbiased for each group under study---to communicate the results of the data analysis in exact terms.

A 600-Mb/s rate-1/2 (128,3,6) LDPC convolutional code encoder and decoder was implemented in a 90-nm CMOS process. The encoder operates at 1.1 GHz and includes built-in all-phase termination. The decoder design maximizes throughput while minimizing the number of memory banks and delivering an information throughput of 1 bit per clock cycle. The size of the decoder controller is minimized by sharing it among an arbitrary number of decoder processors. The decoder dissipates 0.61 nJ of energy per decoded information bit at an SNR of 2.0 and a throughput of 600 Mb/s. An integrated test system enables accurate power measurements for various SNR settings.

The Hurst parameter characterizes the degree to which a time series is long range dependent (LRD). The value of this parameter can be used as an input to algorithms for bandwidth allocation, buffer sizing and congestion control. However, for these algorithms to be effective over the long run they must change their actions when the value of the Hurst parameter changes. We demonstrate a new technique which uses a wavelet decomposition to detect a change in the Hurst parameter. Our technique tests the variance structure of the wavelet coefficients at multiple scales and uses changes in variance to signal a change in the value of the Hurst parameter. The efficacy of the proposed technique is demonstrated by comparing its performance to that of another recently proposed method for change detection. The performance tests were conducted using artificially generated data sets which contain changes in the Hurst parameter of known position, magnitude and sign.

Low-density parity-check convolutional codes (LDPC-CCs) have been shown to have similar capacity-approaching performance to LDPC block codes. Their encoder structure is simple and efficient. However, the encoder termination, which is required when applied to finite length data frames, increases the encoder complexity and reduces the effective code rate. The LDPC-CC encoding and termination problems are discussed in this paper. A novel all-phase termination scheme is proposed with less implementation complexity and less loss in code rate, compared to existing methods. Finally a system architecture for the LDPC-CC encoder with all-phase termination is given with some analyses.

Low-density parity-check convolutional codes offer the same good error-correcting performance as low-density parity-check block codes while having the ability to encode and decode arbitrary lengths of data. This makes these codes well suited to certain applications, such as forward error control on packet switching networks. In this paper we propose a decoder architecture for low-density parity-check convolutional codes with very large memories. These codes have very good error correcting properties and as such may be applicable in wireless sensor networks and space communication systems. We discuss a realization of this architecture for a (2048,3,6) code implemented on a field-programmable gate-array.

Low-density parity-check convolutional codes combine the good bit error rate performance of low-density parity-check block codes with the ability to encode and decode arbitrary lengths of data. This makes them attractive in applications where the data unit to be encoded varies in length. In this paper we discuss the parallelization of encoders for low-density parity-check convolutional code. We then present results to show how this parallelism impacts on the area and throughput of VLSI implementations of these encoders. We show how this technique can be used to implement encoders with throughputs suitable for next-generation communication standards and other high-speed applications.

In this paper, the application of low-density parity-check convolutional codes (LDPC-CCs) to packet based communication systems is studied. By presenting analysis of encoder and decoder design as well as simulation results for such systems, we show that LDPC-CCs are more suited to packet based applications than LDPC block codes (LDPC-BCs). This is due to their ability to operate on arbitrary lengths of data, lower encoder complexity and the performance gain of presetting and termination. Moreover, in this paper, we propose an algorithm for terminating the LDPC-CC encoder from any state to the all-zero state.

In this paper we derive an unbiased estimator for the number of direct connections (edges or neighbors) in 2 and 3 dimensional ad hoc networks. We show how this estimator is based on a minimal number of assumptions regarding the topology of the network and is a good estimator for both sparse and dense networks. We then develop a relationship between the number of edges in the network and the probability of that network being strongly connected. We show for realistically sized networks, that if the nodes have, on average, just under 10 neighbors that the network is completely connected with high probability. This is a so called "magic number" which is the subject of some dispute in the literature at present. We go on to develop a simple algorithm that uses the prior results to construct strongly connected sensor or smart-dust networks. This algorithm is attractive as it is very robust whilst requiring only communication between adjacent nodes. We compare the performance of our algorithm against the shortest path algorithm.

In this paper the effective bandwidths of stable distributions are studied. Effective bandwidths are being heavily promoted as the most appropriate method for call admission control (CAC) and resource allocation within ATM networks. Previous work in teletraffic modelling has suggested that models based on stable distributions provide an efficient mechanism for capturing the long range dependence and infinite variance associated with teletraffic data (the Joseph and Noah effects; see Willinger et al. 1997). This has potentially serious implications for effective bandwidths and we show how the effective bandwidth of such data is theoretically infinite. We then present two approximate methods for estimating the effective bandwidth of data based on stable distribution.