arXiv subjects

Sanjit Dandapanthula

Publications and source records attributed to Sanjit Dandapanthula.

7 recordsLinked to original sources

arXiv2026

Are we really tilting? The mechanics of reward guidance in flow and diffusion models

Reward guidance algorithms steer a learned generative process toward the reward-tilted measure at inference time. While empirically powerful, these methods are prone to reward hacking: the guided model over-optimizes the reward at the cost of fidelity to the learned distribution. Prior work has attributed this to the complexity of neural reward functions or implicit biases in diffusion training, but its fundamental origins remain poorly understood. We show that reward hacking arises from an approximation made in most practical implementations of reward-guided diffusion -- finite-particle plug-in estimation of the Doob h-function -- even in the simplest non-trivial settings of Gaussian and Gaussian mixture targets with quadratic rewards. In closed form, we isolate two distinct failure modes of the plug-in estimator: it leads to reward hacking within each mode and it cannot select high-reward modes. We propose a closed-form reward damping schedule that corrects the within-mode bias with no additional compute, and clarify the role of best-of-n sampling in compensating for the mode selection failure. Experiments on Gaussian mixture targets, a 2D checkerboard, and FLUX.1 text-to-image generation confirm that our theoretical insights carry over to practical settings.

cs.LG↗

arXiv2026

Offline changepoint localization using a matrix of conformal p-values

Changepoint localization is the problem of estimating the index at which a change occurred in the data generating distribution of an ordered list of data, or declaring that no change occurred. We present the broadly applicable MCP algorithm, which uses a matrix of conformal p-values to produce a confidence interval for a (single) changepoint under the mild assumption that the pre-change and post-change distributions are each exchangeable. We prove a novel conformal Neyman-Pearson lemma, motivating practical classifier-based choices for our conformal score function. Finally, we exemplify the MCP algorithm on a variety of synthetic and real-world datasets, including using black-box pre-trained classifiers to detect changes in sequences of images, text, and accelerometer data.

math.ST↗

arXiv2026

Downscaling land surface temperature data using edge detection and block-diagonal Gaussian process regression

Accurate and high-resolution estimation of land surface temperature (LST) is crucial in estimating evapotranspiration, a measure of plant water use and a central quantity in agricultural applications. In this work, we develop a novel statistical method for downscaling LST data obtained from NASA's ECOSTRESS mission, using high-resolution data from the Landsat 8 mission as a proxy for modeling agricultural field structure. Using the Landsat data, we identify the boundaries of agricultural fields through edge detection techniques, allowing us to capture the inherent block structure present in the spatial domain. We propose a block-diagonal Gaussian process (BDGP) model that captures the spatial structure of the agricultural fields, leverages independence of LST across fields for computational tractability, and accounts for the change of support present in ECOSTRESS observations. We use the resulting BDGP model to perform Gaussian process regression and obtain high-resolution estimates of LST from ECOSTRESS data, along with uncertainty quantification. Our results demonstrate the practicality of the proposed method in producing reliable high-resolution LST estimates, with potential applications in agriculture, urban planning, and climate studies.

stat.AP↗

arXiv2026

Gradient descent for deep equilibrium single-index models

Deep equilibrium models (DEQs) have recently emerged as a powerful paradigm for training infinitely deep weight-tied neural networks that achieve state of the art performance across many modern machine learning tasks. Despite their practical success, theoretically understanding the gradient descent dynamics for training DEQs remains an area of active research. In this work, we rigorously study the gradient descent dynamics for DEQs in the simple setting of linear models and single-index models, filling several gaps in the literature. We prove a conservation law for linear DEQs which implies that the parameters remain trapped on spheres during training and use this property to show that gradient flow remains well-conditioned for all time. We then prove linear convergence of gradient descent to a global minimizer for linear DEQs and deep equilibrium single-index models under appropriate initialization and with a sufficiently small step size. Finally, we validate our theoretical findings through experiments.

cs.LG↗

arXiv2025

Optimal Transportation and Alignment Between Gaussian Measures

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets -- tasks ubiquitous in data science and machine learning. Because these frameworks are computationally expensive, large-scale applications often rely on closed-form solutions for Gaussian distributions under quadratic cost. This work provides a comprehensive treatment of Gaussian, quadratic cost OT and inner product GW (IGW) alignment, closing several gaps in the literature to broaden applicability. First, we treat the open problem of IGW alignment between uncentered Gaussians on separable Hilbert spaces by giving a closed-form expression up to a quadratic optimization over unitary operators, for which we derive tight analytic upper and lower bounds. If at least one Gaussian measure is centered, the solution reduces to a fully closed-form expression, which we further extend to an analytic solution for the IGW barycenter between centered Gaussians. We also present a reduction of Gaussian multimarginal OT with pairwise quadratic costs to a tractable optimization problem and provide an efficient algorithm to solve it using a rank-deficiency constraint. To demonstrate utility, we apply our results to knowledge distillation and heterogeneous clustering on synthetic and real-world datasets.

cs.LG↗

arXiv2025

Anytime-valid FDR control with the stopped e-BH procedure

The recent e-Benjamini-Hochberg (e-BH) procedure for multiple hypothesis testing is known to control the false discovery rate (FDR) under arbitrary dependence between the input e-values. This paper points out an important subtlety when applying the e-BH procedure with e-processes, which are sequential generalizations of e-values (where the data are observed sequentially). Since adaptively stopped e-processes are e-values, the e-BH procedure can be repeatedly applied at every time step, and one can continuously monitor the e-processes and the rejection sets obtained. One would hope that the "stopped e-BH procedure" (se-BH) has an FDR guarantee for the rejection set obtained at any stopping time. However, while this is true if the data in different streams are independent, it is not true in full generality, because each stopped e-process is an e-value only for stopping times in its own local filtration, but the se-BH procedure employs a stopping time with respect to a global filtration. This can cause information to leak across time, allowing one stream to know its future by knowing past data of another stream. This paper formulates a simple causal condition under which local e-processes are also global e-processes and thus the se-BH procedure does indeed control the FDR. The condition excludes unobserved confounding from the past and is met under most reasonable scenarios including genomics.

stat.ME↗

arXiv2025

Multiple testing in multi-stream sequential change detection

Multi-stream sequential change detection involves simultaneously monitoring many streams of data and trying to detect when their distributions change, if at all. Here, we theoretically study multiple testing issues that arise from detecting changes in many streams. We point out that any algorithm with finite average run length (ARL) must have a trivial worst-case false detection rate (FDR), family-wise error rate (FWER), per-family error rate (PFER), and global error rate (GER); thus, any attempt to control these Type I error metrics is fundamentally in conflict with the desire for a finite ARL (which is typically necessary in order to have a small detection delay). One of our contributions is to define a new class of metrics which can be controlled, called error over patience (EOP). We propose algorithms that combine the recent e-detector framework (which generalizes the Shiryaev-Roberts and CUSUM methods) with the recent e-Benjamini-Hochberg procedure and e-Bonferroni procedures. We prove that these algorithms control the EOP at any desired level under very general dependence structures on the data within and across the streams. In fact, we prove a more general error control that holds uniformly over all stopping times and provides a smooth trade-off between the conflicting metrics. Additionally, if finiteness of the ARL is forfeited, we show that our algorithms control the worst-case Type I error.

math.ST↗