arXiv subjects

Anand Sarwate

Publications and source records attributed to Anand Sarwate.

11 recordsLinked to original sources

arXiv2026

Extreme Points of the $(0,δ)$-LDP Polytope with Small Input Size and Arbitrary Output Sizes

The structure of locally differentially private (LDP) mechanisms can be understood through the geometry of the corresponding privacy polytope. While the extreme points of the $ (ε,0)$-LDP polytope are well characterized (Kairouz \emph{et al.}, 2014; Holohan \emph{et al.}, 2017; Pensia \emph{et al.}, 2017), comparatively little is known for the $(ε,δ)$-LDP polytope with $δ>0$. Recent work (Elangovan and Jog, 2024) has shown that even in the special case $ε=0$, the $ (0,δ) $-LDP privacy polytope exhibits fundamentally different behaviour. In this work, we provide complete characterizations of the extreme points for the low-input-alphabet regime $k=2$ and $k=3$ and with arbitrary output alphabet size $m $. We also identify new extreme mechanisms for larger input alphabet sizes $k$, of the star configuration type, as introduced by Elangovan and Jog (2024).

cs.IT↗

arXiv2025

LSR-Adapt: Ultra-Efficient Parameter Tuning with Matrix Low Separation Rank Kernel Adaptation

Imposing an effective structural assumption on neural network weight matrices has been the major paradigm for designing Parameter-Efficient Fine-Tuning (PEFT) systems for adapting modern large pre-trained models to various downstream tasks. However, low rank based adaptation has become increasingly challenging due to the sheer scale of modern large language models. In this paper, we propose an effective kernelization to further reduce the number of parameters required for adaptation tasks. Specifically, from the classical idea in numerical analysis regarding matrix Low-Separation-Rank (LSR) representations, we develop a kernel using this representation for the low rank adapter matrices of the linear layers from large networks, named the Low Separation Rank Adaptation (LSR-Adapt) kernel. With the ultra-efficient kernel representation of the low rank adapter matrices, we manage to achieve state-of-the-art performance with even higher accuracy with almost half the number of parameters as compared to conventional low rank based methods. This structural assumption also opens the door to further GPU-side optimizations due to the highly parallelizable nature of Kronecker computations.

cs.LG↗

arXiv2025

Unraveling the Localized Latents: Learning Stratified Manifold Structures in LLM Embedding Space with Sparse Mixture-of-Experts

However, real-world data often exhibit complex local structures that can be challenging for single-model approaches with a smooth global manifold in the embedding space to unravel. In this work, we conjecture that in the latent space of these large language models, the embeddings live in a local manifold structure with different dimensions depending on the perplexities and domains of the input data, commonly referred to as a Stratified Manifold structure, which in combination form a structured space known as a Stratified Space. To investigate the validity of this structural claim, we propose an analysis framework based on a Mixture-of-Experts (MoE) model where each expert is implemented with a simple dictionary learning algorithm at varying sparsity levels. By incorporating an attention-based soft-gating network, we verify that our model learns specialized sub-manifolds for an ensemble of input data sources, reflecting the semantic stratification in LLM embedding space. We further analyze the intrinsic dimensions of these stratified sub-manifolds and present extensive statistics on expert assignments, gating entropy, and inter-expert distances. Our experimental results demonstrate that our method not only validates the claim of a stratified manifold structure in the LLM embedding space, but also provides interpretable clusters that align with the intrinsic semantic variations of the input data.

cs.LG↗

arXiv2024

Learning To Help: Training Models to Assist Legacy Devices

Machine learning models implemented in hardware on physical devices may be deployed for a long time. The computational abilities of the device may be limited and become outdated with respect to newer improvements. Because of the size of ML models, offloading some computation (e.g. to an edge cloud) can help such legacy devices. We cast this problem in the framework of learning with abstention (LWA) in which the expert (edge) must be trained to assist the client (device). Prior work on LWA trains the client assuming the edge is either an oracle or a human expert. In this work, we formalize the reverse problem of training the expert for a fixed (legacy) client. As in LWA, the client uses a rejection rule to decide when to offload inference to the expert (at a cost). We find the Bayes-optimal rule, prove a generalization bound, and find a consistent surrogate loss function. Empirical results show that our framework outperforms confidence-based rejection rules.

cs.LG↗

arXiv2024

LASERS: LAtent Space Encoding for Representations with Sparsity for Generative Modeling

Learning compact and meaningful latent space representations has been shown to be very useful in generative modeling tasks for visual data. One particular example is applying Vector Quantization (VQ) in variational autoencoders (VQ-VAEs, VQ-GANs, etc.), which has demonstrated state-of-the-art performance in many modern generative modeling applications. Quantizing the latent space has been justified by the assumption that the data themselves are inherently discrete in the latent space (like pixel values). In this paper, we propose an alternative representation of the latent space by relaxing the structural assumption than the VQ formulation. Specifically, we assume that the latent space can be approximated by a union of subspaces model corresponding to a dictionary-based representation under a sparsity constraint. The dictionary is learned/updated during the training process. We apply this approach to look at two models: Dictionary Learning Variational Autoencoders (DL-VAEs) and DL-VAEs with Generative Adversarial Networks (DL-GANs). We show empirically that our more latent space is more expressive and has leads to better representations than the VQ approach in terms of reconstruction quality at the expense of a small computational overhead for the latent space computation. Our results thus suggest that the true benefit of the VQ approach might not be from discretization of the latent space, but rather the lossy compression of the latent space. We confirm this hypothesis by showing that our sparse representations also address the codebook collapse issue as found common in VQ-family models.

cs.LG↗

arXiv2024

Faithful and Efficient Explanations for Neural Networks via Neural Tangent Kernel Surrogate Models

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer. Open source software allowing users to efficiently calculate kernel functions in the PyTorch framework is available (https://github.com/pnnl/projection\_ntk).

cs.LG↗

arXiv2023

Spectral Evolution and Invariance in Linear-width Neural Networks

We investigate the spectral properties of linear-width feed-forward neural networks, where the sample size is asymptotically proportional to network width. Empirically, we show that the spectra of weight in this high dimensional regime are invariant when trained by gradient descent for small constant learning rates; we provide a theoretical justification for this observation and prove the invariance of the bulk spectra for both conjugate and neural tangent kernels. We demonstrate similar characteristics when training with stochastic gradient descent with small learning rates. When the learning rate is large, we exhibit the emergence of an outlier whose corresponding eigenvector is aligned with the training data structure. We also show that after adaptive gradient training, where a lower test error and feature learning emerge, both weight and kernel matrices exhibit heavy tail behavior. Simple examples are provided to explain when heavy tails can have better generalizations. We exhibit different spectral properties such as invariant bulk, spike, and heavy-tailed distribution from a two-layer neural network using different training strategies, and then correlate them to the feature learning. Analogous phenomena also appear when we train conventional neural networks with real-world data. We conclude that monitoring the evolution of the spectra during training is an essential step toward understanding the training dynamics and feature learning.

cs.LG↗

arXiv2021

Privid: Practical, Privacy-Preserving Video Analytics Queries

Analytics on video recorded by cameras in public areas have the potential to fuel many exciting applications, but also pose the risk of intruding on individuals' privacy. Unfortunately, existing solutions fail to practically resolve this tension between utility and privacy, relying on perfect detection of all private information in each video frame--an elusive requirement. This paper presents: (1) a new notion of differential privacy (DP) for video analytics, $(ρ,K,ε)$-event-duration privacy, which protects all private information visible for less than a particular duration, rather than relying on perfect detections of that information, and (2) a practical system called Privid that enforces duration-based privacy even with the (untrusted) analyst-provided deep neural networks that are commonplace for video analytics today. Across a variety of videos and queries, we show that Privid achieves accuracies within 79-99% of a non-private system.

cs.CR↗

arXiv2020

Quadratically Constrained Myopic Adversarial Channels

We study communication in the presence of a jamming adversary where quadratic power constraints are imposed on the transmitter and the jammer. The jamming signal is allowed to be a function of the codebook, and a noncausal but noisy observation of the transmitted codeword. For a certain range of the noise-to-signal ratios (NSRs) of the transmitter and the jammer, we are able to characterize the capacity of this channel under deterministic encoding or stochastic encoding, i.e., with no common randomness between the encoder/decoder pair. For the remaining NSR regimes, we determine the capacity under the assumption of a small amount of common randomness (at most $2\log(n)$ bits in one sub-regime, and at most $Ω(n)$ bits in the other sub-regime) available to the encoder-decoder pair. Our proof techniques involve a novel myopic list-decoding result for achievability, and a Plotkin-type push attack for the converse in a subregion of the NSRs, both of which which may be of independent interest. We also give bounds on the secrecy capacity of this channel assuming that the jammer is simultaneously eavesdropping.

cs.IT↗

arXiv2018

Robust Privacy-Utility Tradeoffs under Differential Privacy and Hamming Distortion

A privacy-utility tradeoff is developed for an arbitrary set of finite-alphabet source distributions. Privacy is quantified using differential privacy (DP), and utility is quantified using expected Hamming distortion maximized over the set of distributions. The family of source distribution sets (source sets) is categorized into three classes, based on different levels of prior knowledge they capture. For source sets whose convex hull includes the uniform distribution, symmetric DP mechanisms are optimal. For source sets whose probability values have a fixed monotonic ordering, asymmetric DP mechanisms are optimal. For all other source sets, general upper and lower bounds on the optimal privacy leakage are developed and a necessary and sufficient condition for tightness are established. Differentially private leakage is an upper bound on mutual information (MI) leakage: the two criteria are compared analytically and numerically to illustrate the effect of adopting a stronger privacy criterion.

cs.IT↗

arXiv2016

Social Learning and Distributed Hypothesis Testing

This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The conditional distributions are known locally at the nodes, but the true parameter/hypothesis is not known. An update rule is analyzed in which nodes first perform a Bayesian update of their belief (distribution estimate) of the parameter based on their local observation, communicate these updates to their neighbors, and then perform a "non-Bayesian" linear consensus using the log-beliefs of their neighbors. In this paper we show that under mild assumptions, the belief of any node in any incorrect hypothesis converges to zero exponentially fast, and we characterize the exponential rate of learning which is given in terms of the network structure and the divergences between the observations' distributions. Our main result is the concentration property established on the rate of convergence.

math.ST↗