arXiv subjects

Pulkit Grover

Publications and source records attributed to Pulkit Grover.

At least 19 recordsLinked to original sources

arXiv2026

Separating Intrinsic Ambiguity from Estimation Uncertainty in Deep Generative Models for Linear Inverse Problems

Recently, deep generative models have been used for posterior inference in inverse problems, including high-stakes applications in medical imaging and scientific discovery, where the uncertainty of a prediction can matter as much as the prediction itself. However, posterior uncertainty is difficult to interpret because it can mix ambiguity inherent to the forward operator with uncertainty propagated through inference. We introduce a structural decomposition of posterior uncertainty that isolates intrinsic ambiguity. A cascade formulation makes this ambiguity accessible for calibration analysis, enabling qualitative diagnostics and simulation-based calibration tests that reveal failure modes that remain hidden when models are selected by reconstruction quality alone. We first validate the approach on a Gaussian example with analytical posterior structure, then illustrate the decomposition on accelerated magnetic resonance imaging (MRI), and finally apply the calibration diagnostics to electroencephalography (EEG) source imaging.

cs.LG↗

arXiv2025

EEG-to-fMRI synthesis of task-evoked and spontaneous brain activity: addressing issues of statistical significance and generalizability

A growing interest has developed in the problem of training models of EEG features to predict brain activity measured using fMRI, i.e. the problem of EEG-to-fMRI synthesis. Despite some reported success, the statistical significance and generalizability of EEG-to-fMRI predictions remains to be fully demonstrated. Here, we investigate the predictive power of EEG for both task-evoked and spontaneous activity of the somatomotor network measured by fMRI, based on data collected from healthy subjects in two different sessions. We trained subject-specific distributed-lag linear models of time-varying, multi-channel EEG spectral power using Sparse Group LASSO regularization, and we showed that learned models outperformed conventional EEG somatomotor rhythm predictors as well as massive univariate correlation models. Furthermore, we showed that learned models were statistically significantly better than appropriate null models in most subjects and conditions, although less frequently for spontaneous compared to task-evoked activity. Critically, predictions improved significantly when training and testing on data acquired in the same session relative to across sessions, highlighting the importance of temporally separating the collection of train and test data to avoid data leakage and optimistic bias in model generalization. In sum, while we demonstrate that EEG models can provide fMRI predictions with statistical significance, we also show that predictive power is impaired for spontaneous fluctuations in brain activity and for models trained on data acquired in a different session. Our findings highlight the need to explicitly consider these often overlooked issues in the growing literature of EEG-to-fMRI synthesis.

cs.LG↗

arXiv2025

HingePlace: Harnessing the neural thresholding behavior to optimize Transcranial Electrical Stimulation

Transcranial Electrical Stimulation (tES) is a neuromodulation technique that utilizes electrodes on the scalp to stimulate target brain regions. tES has shown promise in treating many neurological conditions, such as stroke rehabilitation and chronic pain. Several electrode placement algorithms have been proposed to optimize tES-based therapies by designing multi-electrode montages that create focal neural responses. We first extend a well-known unification result by Fernandez-Corazza et al. to unify all major traditional electrode placement algorithms. We utilize this unification result to identify a common restriction among traditional electrode placement algorithms: they do not harness the thresholding behavior of neural response. Consequently, these algorithms only partially harness the properties of neural response to optimize tES, particularly increasing the focality of neural response. We propose a new electrode placement algorithm, HingePlace, that utilizes a symmetrized hinge loss to harness the thresholding behavior of neural response. We extensively compare the HingePlace algorithm with traditional electrode placement algorithms in two simulation platforms. Across both platforms, we find that HingePlace-designed montages consistently generate more focal neural responses -- by as much as 60% -- than the electrode montages designed by traditional electrode placement algorithms.

eess.SY↗

arXiv2024

Message-Relevant Dimension Reduction of Neural Populations

Quantifying relevant interactions between neural populations is a prominent question in the analysis of high-dimensional neural recordings. However, existing dimension reduction methods often discuss communication in the absence of a formal framework, while frameworks proposed to address this gap are impractical in data analysis. This work bridges the formal framework of M-Information Flow with practical analysis of real neural data. To this end, we propose Iterative Regression, a message-dependent linear dimension reduction technique that iteratively finds an orthonormal basis such that each basis vector maximizes correlation between the projected data and the message. We then define 'M-forwarding' to formally capture the notion of a message being forwarded from one neural population to another. We apply our methodology to recordings we collected from two neural populations in a simplified model of whisker-based sensory detection in mice, and show that the low-dimensional M-forwarding structure we infer supports biological evidence of a similar structure between the two original, high-dimensional populations.

q-bio.QM↗

arXiv2023

Computing Unique Information for Poisson and Multinomial Systems

Bivariate Partial Information Decomposition (PID) describes how the mutual information between a random variable M and two random variables Y and Z is decomposed into unique, redundant, and synergistic terms. Recently, PID has shown promise as an emerging tool to understand biological systems and biases in machine learning. However, computing PID is a challenging problem as it typically involves optimizing over distributions. In this work, we study the problem of computing PID in two systems: the Poisson system inspired by the 'ideal Poisson channel' and the multinomial system inspired by multinomial thinning, for a scalar M. We provide sufficient conditions for both systems under which closed-form expressions for many operationally-motivated PID can be obtained, thereby allowing us to easily compute PID for these systems. Our proof consists of showing that one of the unique information terms is zero, which allows the remaining unique, redundant, and synergistic terms to be easily computed using only the marginal and the joint mutual information.

cs.IT↗

arXiv2022

PATHFINDER: Designing Stimuli for Neuromodulation through data-driven inverse estimation of non-linear functions

There has been tremendous interest in designing stimuli (e.g. electrical currents) that produce desired neural responses, e.g., for inducing therapeutic effects for treatments. Traditionally, the design of such stimuli has been model-driven. Due to challenges inherent in modeling neural responses accurately, data-driven approaches offer an attractive alternative. The problem of data-driven stimulus design can be thought of as estimating an inverse of a non-linear ``forward" mapping, which takes in as inputs the stimulus parameters and outputs the corresponding neural responses. In most cases of interest, the forward mapping is many-to-one, and hence difficult to invert using traditional methods. Existing methods estimate the inverse by using conditional density estimation methods or numerically inverting an estimated forward mapping, but both approaches tend to perform poorly at small sample sizes. In this work, we develop a new optimization framework called PATHFINDER, which allows us to use regression methods for estimating an inverse mapping. We use toy examples to illustrate key aspects of PATHFINDER, and show, on computational models of biological neurons, that PATHFINDER can outperform existing methods at small sample sizes. The data-efficiency of PATHFINDER is especially valuable in stimulus design as collecting data is expensive in this domain.

stat.AP↗

arXiv2022

Extracting Unique Information Through Markov Relations

We propose two new measures for extracting the unique information in $X$ and not $Y$ about a message $M$, when $X, Y$ and $M$ are joint random variables with a given joint distribution. We take a Markov based approach, motivated by questions in fair machine learning, and inspired by similar Markov-based optimization problems that have been used in the Information Bottleneck and Common Information frameworks. We obtain a complete characterization of our definitions in the Gaussian case (namely, when $X, Y$ and $M$ are jointly Gaussian), under the assumption of Gaussian optimality. We also examine the consistency of our definitions with the partial information decomposition (PID) framework, and show that these Markov based definitions achieve non-negativity, but not symmetry, within the PID framework.

cs.IT↗

arXiv2022

Quantifying Feature Contributions to Overall Disparity Using Information Theory

When a machine-learning algorithm makes biased decisions, it can be helpful to understand the sources of disparity to explain why the bias exists. Towards this, we examine the problem of quantifying the contribution of each individual feature to the observed disparity. If we have access to the decision-making model, one potential approach (inspired from intervention-based approaches in explainability literature) is to vary each individual feature (while keeping the others fixed) and use the resulting change in disparity to quantify its contribution. However, we may not have access to the model or be able to test/audit its outputs for individually varying features. Furthermore, the decision may not always be a deterministic function of the input features (e.g., with human-in-the-loop). For these situations, we might need to explain contributions using purely distributional (i.e., observational) techniques, rather than interventional. We ask the question: what is the "potential" contribution of each individual feature to the observed disparity in the decisions when the exact decision-making mechanism is not accessible? We first provide canonical examples (thought experiments) that help illustrate the difference between distributional and interventional approaches to explaining contributions, and when either is better suited. When unable to intervene on the inputs, we quantify the "redundant" statistical dependency about the protected attribute that is present in both the final decision and an individual feature, by leveraging a body of work in information theory called Partial Information Decomposition. We also perform a simple case study to show how this technique could be applied to quantify contributions.

cs.LG↗

arXiv2021

Can Information Flows Suggest Targets for Interventions in Neural Circuits?

Motivated by neuroscientific and clinical applications, we empirically examine whether observational measures of information flow can suggest interventions. We do so by performing experiments on artificial neural networks in the context of fairness in machine learning, where the goal is to induce fairness in the system through interventions. Using our recently developed $M$-information flow framework, we measure the flow of information about the true label (responsible for accuracy, and hence desirable), and separately, the flow of information about a protected attribute (responsible for bias, and hence undesirable) on the edges of a trained neural network. We then compare the flow magnitudes against the effect of intervening on those edges by pruning. We show that pruning edges that carry larger information flows about the protected attribute reduces bias at the output to a greater extent. This demonstrates that $M$-information flow can meaningfully suggest targets for interventions, answering the title's question in the affirmative. We also evaluate bias-accuracy tradeoffs for different intervention strategies, to analyze how one might use estimates of desirable and undesirable information flows (here, accuracy and bias flows) to inform interventions that preserve the former while reducing the latter.

cs.IT↗

arXiv2021

A Minimal Intervention Definition of Reverse Engineering a Neural Circuit

In neuroscience, researchers have developed informal notions of what it means to reverse engineer a system, e.g., being able to model or simulate a system in some sense. A recent influential paper of Jonas and Kording, that examines a microprocessor using techniques from neuroscience, suggests that common techniques to understand neural systems are inadequate. Part of the difficulty, as a previous work of Lazebnik noted, lies in lack of formal language. We provide a theoretical framework for defining reverse engineering of computational systems, motivated by the neuroscience context. Of specific interest are recent works where, increasingly, interventions are being made to alter the function of the neural circuitry to both understand the system and treat disorders. Starting from Lazebnik's viewpoint that understanding a system means you can ``fix it'', and motivated by use-cases in neuroscience, we propose the following requirement on reverse engineering: once an agent claims to have reverse-engineered a neural circuit, they subsequently need to be able to: (a) provide a minimal set of interventions to change the input/output (I/O) behavior of the circuit to a desired behavior; (b) arrive at this minimal set of interventions while operating under bounded rationality constraints (e.g., limited memory) to rule out brute-force approaches. Under certain assumptions, we show that this reverse engineering goal falls within the class of undecidable problems. Next, we examine some canonical computational systems and reverse engineering goals (as specified by desired I/O behaviors) where reverse engineering can indeed be performed. Finally, using an exemplar network, the ``reward network'' in the brain, we summarize the state of current neuroscientific understanding, and discuss how computer-science and information-theoretic concepts can inform goals of future neuroscience studies.

cs.IT↗

arXiv2020

Fairness Under Feature Exemptions: Counterfactual and Observational Measures

With the growing use of ML in highly consequential domains, quantifying disparity with respect to protected attributes, e.g., gender, race, etc., is important. While quantifying disparity is essential, sometimes the needs of an occupation may require the use of certain features that are critical in a way that any disparity that can be explained by them might need to be exempted. E.g., in hiring a software engineer for a safety-critical application, coding-skills may be weighed strongly, whereas name, zip code, or reference letters may be used only to the extent that they do not add disparity. In this work, we propose an information-theoretic decomposition of the total disparity (a quantification inspired from counterfactual fairness) into two components: a non-exempt component which quantifies the part that cannot be accounted for by the critical features, and an exempt component that quantifies the remaining disparity. This decomposition allows one to check if the disparity arose purely due to the critical features (inspired from the business necessity defense of disparate impact law) and also enables selective removal of the non-exempt component if desired. We arrive at this decomposition through canonical examples that lead to a set of desirable properties (axioms) that a measure of non-exempt disparity should satisfy. Our proposed measure satisfies all of them. Our quantification bridges ideas of causality, Simpson's paradox, and a body of work from information theory called Partial Information Decomposition. We also obtain an impossibility result showing that no observational measure can satisfy all the desirable properties, leading us to relax our goals and examine observational measures that satisfy only some of them. We perform case studies to show how one can audit/train models while reducing non-exempt disparity.

cs.IT↗

arXiv2019

CodeNet: Training Large Scale Neural Networks in Presence of Soft-Errors

This work proposes the first strategy to make distributed training of neural networks resilient to computing errors, a problem that has remained unsolved despite being first posed in 1956 by von Neumann. He also speculated that the efficiency and reliability of the human brain is obtained by allowing for low power but error-prone components with redundancy for error-resilience. It is surprising that this problem remains open, even as massive artificial neural networks are being trained on increasingly low-cost and unreliable processing units. Our coding-theory-inspired strategy, "CodeNet," solves this problem by addressing three challenges in the science of reliable computing: (i) Providing the first strategy for error-resilient neural network training by encoding each layer separately; (ii) Keeping the overheads of coding (encoding/error-detection/decoding) low by obviating the need to re-encode the updated parameter matrices after each iteration from scratch. (iii) Providing a completely decentralized implementation with no central node (which is a single point of failure), allowing all primary computational steps to be error-prone. We theoretically demonstrate that CodeNet has higher error tolerance than replication, which we leverage to speed up computation time. Simultaneously, CodeNet requires lower redundancy than replication, and equal computational and communication costs in scaling sense. We first demonstrate the benefits of CodeNet in reducing expected computation time over replication when accounting for checkpointing. Our experiments show that CodeNet achieves the best accuracy-runtime tradeoff compared to both replication and uncoded strategies. CodeNet is a significant step towards biologically plausible neural network training, that could hold the key to orders of magnitude efficiency improvements.

cs.IT↗

arXiv2019

Information Flow in Computational Systems

We develop a theoretical framework for defining and identifying flows of information in computational systems. Here, a computational system is assumed to be a directed graph, with "clocked" nodes that send transmissions to each other along the edges of the graph at discrete points in time. We are interested in a definition that captures the dynamic flow of information about a specific message, and which guarantees an unbroken "information path" between appropriately defined inputs and outputs in the directed graph. Prior measures, including those based on Granger Causality and Directed Information, fail to provide clear assumptions and guarantees about when they correctly reflect information flow about a message. We take a systematic approach---iterating through candidate definitions and counterexamples---to arrive at a definition for information flow that is based on conditional mutual information, and which satisfies desirable properties, including the existence of information paths. Finally, we describe how information flow might be detected in a noiseless setting, and provide an algorithm to identify information paths on the time-unrolled graph of a computational system.

cs.IT↗

arXiv2018

Coded Elastic Computing

Cloud providers have recently introduced new offerings whereby spare computing resources are accessible at discounts compared to on-demand computing. Exploiting such opportunity is challenging inasmuch as such resources are accessed with low-priority and therefore can elastically leave (through preemption) and join the computation at any time. In this paper, we design a new technique called coded elastic computing, enabling distributed computations over elastic resources. The proposed technique allows machines to leave the computation without sacrificing the algorithm-level performance, and, at the same time, adaptively reduce the workload at existing machines when new ones join the computation. Leveraging coded redundancy, our approach can achieve similar computational cost as the original (noiseless) method when all machines are present; the cost gracefully increases when machines are preempted and reduces when machines join. The performance of the proposed technique is evaluated on matrix-vector multiplication and linear regression tasks. In experimental validations, it can achieve exactly the same numerical result as the noiseless computation, while reducing the computation time by 46% when compared to non-adaptive coding schemes.

cs.IT↗

arXiv2018

An Application of Storage-Optimal MatDot Codes for Coded Matrix Multiplication: Fast k-Nearest Neighbors Estimation

We propose a novel application of coded computing to the problem of the nearest neighbor estimation using MatDot Codes [Fahim. et.al. 2017], that are known to be optimal for matrix multiplication in terms of recovery threshold under storage constraints. In approximate nearest neighbor algorithms, it is common to construct efficient in-memory indexes to improve query response time. One such strategy is Multiple Random Projection Trees (MRPT), which reduces the set of candidate points over which Euclidean distance calculations are performed. However, this may result in a high memory footprint and possibly paging penalties for large or high-dimensional data. Here we propose two techniques to parallelize MRPT, that exploit data and model parallelism respectively, by dividing both the data storage and the computation efforts among different nodes in a distributed computing cluster. This is especially critical when a single compute node cannot hold the complete dataset in memory. We also propose a novel coded computation strategy based on MatDot codes for the model-parallel architecture that, in a straggler-prone environment, achieves the storage-optimal recovery threshold, i.e., the number of nodes that are required to serve a query. We experimentally demonstrate that, in the absence of straggling, our distributed approaches require less query time than execution on a single processing node, providing near-linear speedups with respect to the number of worker nodes. Through our experiments on real systems with simulated straggling, we also show that our strategy achieves a faster query execution than the uncoded strategy in a straggler-prone environment.

cs.IT↗

arXiv2018

A Unified Coded Deep Neural Network Training Strategy Based on Generalized PolyDot Codes for Matrix Multiplication

This paper has two contributions. First, we propose a novel coded matrix multiplication technique called Generalized PolyDot codes that advances on existing methods for coded matrix multiplication under storage and communication constraints. This technique uses "garbage alignment," i.e., aligning computations in coded computing that are not a part of the desired output. Generalized PolyDot codes bridge between Polynomial codes and MatDot codes, trading off between recovery threshold and communication costs. Second, we demonstrate that Generalized PolyDot can be used for training large Deep Neural Networks (DNNs) on unreliable nodes prone to soft-errors. This requires us to address three additional challenges: (i) prohibitively large overhead of coding the weight matrices in each layer of the DNN at each iteration; (ii) nonlinear operations during training, which are incompatible with linear coding; and (iii) not assuming presence of an error-free master node, requiring us to architect a fully decentralized implementation without any "single point of failure." We allow all primary DNN training steps, namely, matrix multiplication, nonlinear activation, Hadamard product, and update steps as well as the encoding/decoding to be error-prone. We consider the case of mini-batch size $B=1$, as well as $B>1$, leveraging coded matrix-vector products, and matrix-matrix products respectively. The problem of DNN training under soft-errors also motivates an interesting, probabilistic error model under which a real number $(P,Q)$ MDS code is shown to correct $P-Q-1$ errors with probability $1$ as compared to $\lfloor \frac{P-Q}{2} \rfloor$ for the more conventional, adversarial error model. We also demonstrate that our proposed strategy can provide unbounded gains in error tolerance over a competing replication strategy and a preliminary MDS-code-based strategy for both these error models.

cs.IT↗

arXiv2018

Straggler-Resilient and Communication-Efficient Distributed Iterative Linear Solver

We propose a novel distributed iterative linear inverse solver method. Our method, PolyLin, has significantly lower communication cost, both in terms of number of rounds as well as number of bits, in comparison with the state of the art at the cost of higher computational complexity and storage. Our algorithm also has a built-in resilience to straggling and faulty computation nodes. We develop a natural variant of our main algorithm that trades off communication cost for computational complexity. Our method is inspired by ideas in error correcting codes.

cs.IT↗

arXiv2018

Coded FFT and Its Communication Overhead

We propose a coded computing strategy and examine communication costs of coded computing algorithms to make distributed Fast Fourier Transform (FFT) resilient to errors during the computation. We apply maximum distance separable (MDS) codes to a widely used "Transpose" algorithm for parallel FFT. In the uncoded distributed FFT algorithm, the most expensive step is a single "all-to-all" communication. We compare this with communication overhead of coding in our coded FFT algorithm. We show that by using a systematic MDS code, the communication overhead of coding is negligible in comparison with the communication costs inherent in an uncoded FFT implementation if the number of parity nodes is at most $o(\log K)$, where $K$ is the number of systematic nodes.

cs.IT↗