arXiv subjects

Aranyak Acharyya

Publications and source records attributed to Aranyak Acharyya.

10 recordsLinked to original sources

arXiv2026

Concentration bounds on response-based vector embeddings of black-box generative models

Generative models, such as large language models or text-to-image diffusion models, can generate relevant responses to user-given queries. Response-based vector embeddings of generative models facilitate statistical analysis and inference on a given collection of black-box generative models. The Data Kernel Perspective Space embedding is one particular method of obtaining response-based vector embeddings for a given set of generative models, already discussed in the literature. In this paper, under appropriate regularity conditions, we establish high probability concentration bounds on the sample vector embeddings for a given set of generative models, obtained through the method of Data Kernel Perspective Space embedding. Our results tell us the required number of sample responses needed in order to approximate the population-level vector embeddings with a desired level of accuracy. The algebraic tools used to establish our results can be used further for establishing concentration bounds on Classical Multidimensional Scaling embeddings in general, when the dissimilarities are observed with noise.

stat.ML↗

arXiv2026

Optimal control of the future via prospective learning with control

Optimal control of the future is the next frontier for AI. Current approaches to this problem are typically rooted in reinforcement learning (RL). RL is mathematically distinct from supervised learning, which has been the main workhorse for the recent achievements in AI. Moreover, RL typically operates in a stationary environment with episodic resets, limiting its utility. Here, we extend supervised learning to address learning to control in non-stationary, reset-free environments. Using this framework, called ''Prospective Learning with Control'' (PLuC), we prove that under certain fairly general assumptions, empirical risk minimization (ERM) asymptotically achieves the Bayes optimal policy. We then consider a specific instance of prospective learning with control: foraging, a canonical task relevant to both natural and artificial agents. We illustrate that modern RL algorithms, which assume stationarity, struggle in these non-stationary reset-free environments. Even with time-aware modifications, they converge orders of magnitude slower than our prospective foraging agents on a simple 1-D foraging benchmark. Code is available at: https://github.com/neurodata/procontrol.

stat.ML↗

arXiv2026

Recovering manifold structure in LLM responses through a joint Euclidean mirror

Understanding the behavior of black-box large language models and determining effective means of comparing their performance is a key task in modern machine learning. We consider how large language models respond to a specific query by analyzing how the distributions of responses vary over different values of tuning parameters. We frame this problem in a general mathematical setting, treating the mapping from model parameters to response distributions as a structured family of probability measures, endowed with a geometry via a dissimilarity measure. We show how dissimilarities between response distributions can be represented in low-dimensional Euclidean space through a joint Euclidean mirror surface encoding the underlying geometry, which permits both qualitative and quantitative analysis of large language models and provides insight into predicting response distributions for different values of tuning parameters. We propose an estimation procedure for the underlying joint Euclidean mirror based on observed samples from the response distributions, and we prove its asymptotic properties. Additionally, we propose a statistically consistent procedure to infer the value of an unknown model parameter based on samples from the corresponding response distribution and the estimated joint Euclidean mirror. In an experimental setting with large language models, we find that changes in different tuning parameter values correspond to distinct directions in the embedding space, making it possible to estimate the tuning parameters that were used to generate a given response.

stat.ME↗

arXiv2025

Testing for LLM response differences: the case of a composite null consisting of semantically irrelevant query perturbations

Given an input query, generative models such as large language models produce a random response drawn from a response distribution. Given two input queries, it is natural to ask if their response distributions are the same. While traditional statistical hypothesis testing is designed to address this question, the response distribution induced by an input query is often sensitive to semantically irrelevant perturbations to the query, so much so that a traditional test of equality might indicate that two semantically equivalent queries induce statistically different response distributions. As a result, the outcome of the statistical test may not align with the user's requirements. In this paper, we address this misalignment by incorporating into the testing procedure consideration of a collection of semantically similar queries. In our setting, the mapping from the collection of user-defined semantically similar queries to the corresponding collection of response distributions is not known a priori and must be estimated, with a fixed budget. Although the problem we address is quite general, we focus our analysis on the setting where the responses are binary, show that the proposed test is asymptotically valid and consistent, and discuss important practical considerations with respect to power and computation.

math.ST↗

arXiv2025

Statistical inference on black-box generative models in the data kernel perspective space

Generative models are capable of producing human-expert level content across a variety of topics and domains. As the impact of generative models grows, it is necessary to develop statistical methods to understand collections of available models. These methods are particularly important in settings where the user may not have access to information related to a model's pre-training data, weights, or other relevant model-level covariates. In this paper we extend recent results on representations of black-box generative models to model-level statistical inference tasks. We demonstrate that the model-level representations are effective for multiple inference tasks.

cs.LG↗

arXiv2025

Consistent estimation of generative model representations in the data kernel perspective space

Generative models, such as large language models and text-to-image diffusion models, produce relevant information when presented a query. Different models may produce different information when presented the same query. As the landscape of generative models evolves, it is important to develop techniques to study and analyze differences in model behaviour. In this paper we present novel theoretical results for embedding-based representations of generative models in the context of a set of queries. In particular, we establish sufficient conditions for the consistent estimation of the model embeddings in situations where the query set and the number of models grow.

cs.LG↗

arXiv2025

Convergence guarantees for response prediction for latent structure network time series

In this article, we propose a technique to predict the response associated with an unlabeled time series of networks in a semisupervised setting. Our model involves a collection of time series of random networks of growing size, where some of the time series are associated with responses. Assuming that the collection of time series admits an unknown lower dimensional structure, our method exploits the underlying structure to consistently predict responses at the unlabeled time series of networks. Each time series represents a multilayer network on a common set of nodes, and raw stress embedding, a popular dimensionality reduction tool, is used for capturing the unknown latent low dimensional structure. Apart from establishing theoretical convergence guarantees and supporting them with numerical results, we demonstrate the use of our method in the analysis of real-world biological learning circuits of larval Drosophila.

stat.ME↗

arXiv2024

Consistent response prediction for multilayer networks on unknown manifolds

Our paper deals with a collection of networks on a common set of nodes, where some of the networks are associated with responses. Assuming that the networks correspond to points on a one-dimensional manifold in a higher dimensional ambient space, we propose an algorithm to consistently predict the response at an unlabeled network. Our model involves a specific multiple random network model, namely the common subspace independent edge model, where the networks share a common invariant subspace, and the heterogeneity amongst the networks is captured by a set of low dimensional matrices. Our algorithm estimates these low dimensional matrices that capture the heterogeneity of the networks, learns the underlying manifold by isomap, and consistently predicts the response at an unlabeled network. We provide theoretical justifications for the use of our algorithm, validated by numerical simulations. Finally, we demonstrate the use of our algorithm on larval Drosophila connectome data.

stat.ME↗

arXiv2023

Discovering a change point and piecewise linear structure in a time series of organoid networks via the iso-mirror

Recent advancements have been made in the development of cell-based in-vitro neuronal networks, or organoids. In order to better understand the network structure of these organoids, a super-selective algorithm has been proposed for inferring the effective connectivity networks from multi-electrode array data. In this paper, we apply a novel statistical method called spectral mirror estimation to the time series of inferred effective connectivity organoid networks. This method produces a one-dimensional iso-mirror representation of the dynamics of the time series of the networks which exhibits a piecewise linear structure. A classical change point algorithm is then applied to this representation, which successfully detects a change point coinciding with the neuroscientifically significant time inhibitory neurons start appearing and the percentage of astrocytes increases dramatically. This finding demonstrates the potential utility of applying the iso-mirror dynamic structure discovery method to inferred effective connectivity time series of organoid networks.

stat.AP↗

arXiv2021

On Variable Screening in Multiple Nonparametric Regression Model

In this article, we study the problem of variable screening in multiple nonparametric regression model. The proposed methodology is based on the fact that the partial derivative of the regression function with respect to the irrelevant variable should be negligible. The Statistical property of the proposed methodology is investigated under both cases : (i) when the variance of the error term is known, and (ii) when the variance of the error term is unknown. Moreover, we establish the practicality of our proposed methodology for various simulated and real data related to interdisciplinary sciences such as Economics, Finance and other sciences.

stat.ME↗