arXiv subjects

Abhradeep Thakurta

Publications and source records attributed to Abhradeep Thakurta.

At least 19 recordsLinked to original sources

arXiv2026

Adapting AlphaEvolve to Optimize Fully Homomorphic Encryption on TPUs

The deployment of Fully Homomorphic Encryption (FHE) at scale is hindered due to its heavy computational overhead. While specialized hardware accelerators like Google Tensor Processing Units (TPUs) can help, mapping complex cryptographic kernels onto such architectures remains a challenge. Efficient execution requires co-optimization between the systolic array-based Matrix Multiplication Unit (MXU) and Vector Processing Units (VPUs), as well as the orchestration of data movement across the vector register files. Existing compiler stacks often abstract low-level hardware utilization, requiring developers to adopt a manual trial-and-error process that often results in fragmented execution and underutilized resources. To accelerate this development process, we use AlphaEvolve to automate the exploration of hardware-aware cryptographic-kernel optimizations. We frame optimization as an evolutionary search problem, utilizing the closed-loop system provided by AlphaEvolve, that leverages LLM-driven code generation. We use real-world feedback from hardware execution and rigorous correctness testing to guide the evolution process. We evaluate AlphaEvolve optimization on primitives for both the TFHE (Jaxite) and CKKS (CROSS) FHE schemes on Google Cloud TPUv5e, a contemporary TPU architecture. Within 24 hours of automated exploration, AlphaEvolve discovered implementation-level optimizations that improve TFHE bootstrap latency by 2.5x and CKKS rotation and multiplication latency by 1.31x and 1.18x, respectively, relative to human-engineered state of the art. These results demonstrate that AlphaEvolve can be used to enable researchers to navigate the optimization trade-offs between cryptography, compilers, and hardware accelerators.

cs.CR↗

arXiv2026

Reinforced Generation of Combinatorial Structures: Ramsey Numbers

We present improved lower bounds for nine classical Ramsey numbers: $\mathbf{R}(3, 13)$ is increased from $60$ to $61$, $\mathbf{R}(3, 18)$ from $99$ to $100$, $\mathbf{R}(4, 13)$ from $138$ to $139$, $\mathbf{R}(4, 14)$ from $147$ to $148$, $\mathbf{R}(4, 15)$ from $158$ to $159$, $\mathbf{R}(4, 16)$ from $170$ to $174$, $\mathbf{R}(4, 18)$ from $205$ to $209$, $\mathbf{R}(4, 19)$ from $213$ to $219$, and $\mathbf{R}(4, 20)$ from $234$ to $237$. These results were achieved using AlphaEvolve, an LLM-based code mutation agent. Beyond these new results, we successfully recovered lower bounds for all Ramsey numbers known to be exact, and matched the best known lower bounds across many other cases. These include bounds for which previous work does not detail the algorithms used. Virtually all known Ramsey lower bounds are derived computationally, with bespoke search algorithms each delivering a handful of results. AlphaEvolve is a single meta-algorithm yielding search algorithms for all of our results.

math.CO↗

arXiv2026

Reinforced Generation of Combinatorial Structures: Hardness of Approximation

Can AI based methods help us make advances in complexity theory? We provide evidence towards answering this in the affirmative, using AlphaEvolve (an LLM code mutation agent) to obtain new results in three settings: a) We improve a recent result of Kunisky and Yu to obtain near-optimal upper and (conditional) lower bounds on certification algorithms for MAX-CUT and MAX-Independent Set on random 3- and 4-regular graphs. Our improved lower bounds are obtained by constructing nearly extremal Ramanujan graphs on as many as $163$ vertices, and our upper bounds are obtained via analytical arguments. b) We obtain new inapproximability results for MAX-4-CUT and MAX-3-CUT, proving that it is NP-hard to approximate them within factors of $0.987$ and $0.9649$ respectively, using AlphaEvolve to discover new gadget reductions. Our MAX-4-CUT result improves upon the SOTA of $0.9883$, and our MAX-3-CUT result improves on the current best gadget-based inapproximability result of $0.9853$, but falls short of the SOTA of $16/17$ that relies on a custom PCP (rather than a reduction from ``standard'' Håstad-style PCPs). c) Inapproximability for the metric Traveling Salesman Problem (TSP): We show that it is NP-hard to approximate the minimum cost tour within a factor of $111/110$ using AlphaEvolve to discover a new gadget, thus improving the SOTA of $117/116$. Along the way, we provide new modular soundness and completeness arguments that can be of independent interest. A key technical challenge we faced: verifying a candidate construction produced by AlphaEvolve is costly (sometimes requiring time exponential in the size of the construction). We used AlphaEvolve itself to evolve the verification procedure to be faster (sometimes by $10,000\times$ for our gadgets). Our results suggest that gadget based proofs would benefit from a pass through AI-based tools to obtain stronger results.

cs.LG↗

arXiv2025

Preserving Expert-Level Privacy in Offline Reinforcement Learning

The offline reinforcement learning (RL) problem aims to learn an optimal policy from historical data collected by one or more behavioural policies (experts) by interacting with an environment. However, the individual experts may be privacy-sensitive in that the learnt policy may retain information about their precise choices. In some domains like personalized retrieval, advertising and healthcare, the expert choices are considered sensitive data. To provably protect the privacy of such experts, we propose a novel consensus-based expert-level differentially private offline RL training approach compatible with any existing offline RL algorithm. We prove rigorous differential privacy guarantees, while maintaining strong empirical performance. Unlike existing work in differentially private RL, we supplement the theory with proof-of-concept experiments on classic RL environments featuring large continuous state spaces, demonstrating substantial improvements over a natural baseline across multiple tasks.

cs.CR↗

arXiv2025

The Attacker Moves Second: Stronger Adaptive Attacks Bypass Defenses Against Llm Jailbreaks and Prompt Injections

How should we evaluate the robustness of language model defenses? Current defenses against jailbreaks and prompt injections (which aim to prevent an attacker from eliciting harmful knowledge or remotely triggering malicious actions, respectively) are typically evaluated either against a static set of harmful attack strings, or against computationally weak optimization methods that were not designed with the defense in mind. We argue that this evaluation process is flawed. Instead, we should evaluate defenses against adaptive attackers who explicitly modify their attack strategy to counter a defense's design while spending considerable resources to optimize their objective. By systematically tuning and scaling general optimization techniques-gradient descent, reinforcement learning, random search, and human-guided exploration-we bypass 12 recent defenses (based on a diverse set of techniques) with attack success rate above 90% for most; importantly, the majority of defenses originally reported near-zero attack success rates. We believe that future defense work must consider stronger attacks, such as the ones we describe, in order to make reliable and convincing claims of robustness.

cs.LG↗

arXiv2025

On Design Principles for Private Adaptive Optimizers

The spherical noise added to gradients in differentially private (DP) training undermines the performance of adaptive optimizers like AdaGrad and Adam, and hence many recent works have proposed algorithms to address this challenge. However, the empirical results in these works focus on simple tasks and models and the conclusions may not generalize to model training in practice. In this paper we survey several of these variants, and develop better theoretical intuition for them as well as perform empirical studies comparing them. We find that a common intuition of aiming for unbiased estimates of second moments of gradients in adaptive optimizers is misguided, and instead that a simple technique called scale-then-privatize (which does not achieve unbiased second moments) has more desirable theoretical behaviors and outperforms all other variants we study on a small-scale language model training task. We additionally argue that scale-then-privatize causes the noise addition to better match the application of correlated noise mechanisms which are more desirable to use in practice.

cs.LG↗

arXiv2025

Correlated Noise Mechanisms for Differentially Private Learning

This monograph explores the design and analysis of correlated noise mechanisms for differential privacy (DP), focusing on their application to private training of AI and machine learning models via the core primitive of estimation of weighted prefix sums. While typical DP mechanisms inject independent noise into each step of a stochastic gradient (SGD) learning algorithm in order to protect the privacy of the training data, a growing body of recent research demonstrates that introducing (anti-)correlations in the noise can significantly improve privacy-utility trade-offs by carefully canceling out some of the noise added on earlier steps in subsequent steps. Such correlated noise mechanisms, known variously as matrix mechanisms, factorization mechanisms, and DP-Follow-the-Regularized-Leader (DP-FTRL) when applied to learning algorithms, have also been influential in practice, with industrial deployment at a global scale.

cs.LG↗

arXiv2025

Hush! Protecting Secrets During Model Training: An Indistinguishability Approach

We consider the problem of secret protection, in which a business or organization wishes to train a model on their own data, while attempting to not leak secrets potentially contained in that data via the model. The standard method for training models to avoid memorization of secret information is via differential privacy (DP). However, DP requires a large loss in utility or a large dataset to achieve its strict privacy definition, which may be unnecessary in our setting where the data curator and data owner are the same entity. We propose an alternate definition of secret protection that instead of targeting DP, instead targets a bound on the posterior probability of secret reconstruction. We then propose and empirically evaluate an algorithm for model training with this secret protection definition. Our algorithm solves a linear program to assign weights to examples based on the desired per-secret protections, and then performs Poisson sampling using these weights. We show our algorithm significantly outperforms the baseline of running DP-SGD on the whole dataset.

cs.CR↗

arXiv2025

Near Exact Privacy Amplification for Matrix Mechanisms

We study the problem of computing the privacy parameters for DP machine learning when using privacy amplification via random batching and noise correlated across rounds via a correlation matrix $\textbf{C}$ (i.e., the matrix mechanism). Past work on this problem either only applied to banded $\textbf{C}$, or gave loose privacy parameters. In this work, we give a framework for computing near-exact privacy parameters for any lower-triangular, non-negative $\textbf{C}$. Our framework allows us to optimize the correlation matrix $\textbf{C}$ while accounting for amplification, whereas past work could not. Empirically, we show this lets us achieve smaller RMSE on prefix sums than the previous state-of-the-art (SOTA). We also show that we can improve on the SOTA performance on deep learning tasks. Our two main technical tools are (i) using Monte Carlo accounting to bypass composition, which was the main technical challenge for past work, and (ii) a "balls-in-bins" batching scheme that enables easy privacy analysis and is closer to practical random batching than Poisson sampling.

cs.CR↗

arXiv2024

Optimal Rates for $O(1)$-Smooth DP-SCO with a Single Epoch and Large Batches

In this paper we revisit the DP stochastic convex optimization (SCO) problem. For convex smooth losses, it is well-known that the canonical DP-SGD (stochastic gradient descent) achieves the optimal rate of $O\left(\frac{LR}{\sqrt{n}} + \frac{LR \sqrt{p \log(1/δ)}}{εn}\right)$ under $(ε, δ)$-DP, and also well-known that variants of DP-SGD can achieve the optimal rate in a single epoch. However, the batch gradient complexity (i.e., number of adaptive optimization steps), which is important in applications like federated learning, is less well-understood. In particular, all prior work on DP-SCO requires $Ω(n)$ batch gradient steps, multiple epochs, or convexity for privacy. We propose an algorithm, Accelerated-DP-SRGD (stochastic recursive gradient descent), which bypasses the limitations of past work: it achieves the optimal rate for DP-SCO (up to polylog factors), in a single epoch using $\sqrt{n}$ batch gradient steps with batch size $\sqrt{n}$, and can be made private for arbitrary (non-convex) losses via clipping. If the global minimizer is in the constraint set, we can further improve this to $n^{1/4}$ batch gradient steps with batch size $n^{3/4}$. To achieve this, our algorithm combines three key ingredients, a variant of stochastic recursive gradients (SRG), accelerated gradient descent, and correlated noise generation from DP continual counting.

cs.LG↗

arXiv2024

Differentially Private Parameter-Efficient Fine-tuning for Large ASR Models

Large ASR models can inadvertently leak sensitive information, which can be mitigated by formal privacy measures like differential privacy (DP). However, traditional DP training is computationally expensive, and can hurt model performance. Our study explores DP parameter-efficient fine-tuning as a way to mitigate privacy risks with smaller computation and performance costs for ASR models. Through extensive experimentation and progressive optimization, we achieve 4.6%/8.1% word error rate on LibriSpeech clean/other test-sets, setting a new performance benchmark while maintaining (10, 3.52e-6)-DP in fine-tuning a large ASR model with over 600M parameters.

cs.CR↗

arXiv2024

Training Large ASR Encoders with Differential Privacy

Self-supervised learning (SSL) methods for large speech models have proven to be highly effective at ASR. With the interest in public deployment of large pre-trained models, there is a rising concern for unintended memorization and leakage of sensitive data points from the training data. In this paper, we apply differentially private (DP) pre-training to a SOTA Conformer-based encoder, and study its performance on a downstream ASR task assuming the fine-tuning data is public. This paper is the first to apply DP to SSL for ASR, investigating the DP noise tolerance of the BEST-RQ pre-training method. Notably, we introduce a novel variant of model pruning called gradient-based layer freezing that provides strong improvements in privacy-utility-compute trade-offs. Our approach yields a LibriSpeech test-clean/other WER (%) of 3.78/ 8.41 with ($10$, 1e^-9)-DP for extrapolation towards low dataset scales, and 2.81/ 5.89 with (10, 7.9e^-11)-DP for extrapolation towards high scales.

cs.SD↗

arXiv2024

Recycling Scraps: Improving Private Learning by Leveraging Intermediate Checkpoints

In this work, we focus on improving the accuracy-variance trade-off for state-of-the-art differentially private machine learning (DP ML) methods. First, we design a general framework that uses aggregates of intermediate checkpoints \emph{during training} to increase the accuracy of DP ML techniques. Specifically, we demonstrate that training over aggregates can provide significant gains in prediction accuracy over the existing state-of-the-art for StackOverflow, CIFAR10 and CIFAR100 datasets. For instance, we improve the state-of-the-art DP StackOverflow accuracies to 22.74\% (+2.06\% relative) for $ε=8.2$, and 23.90\% (+2.09\%) for $ε=18.9$. Furthermore, these gains magnify in settings with periodically varying training data distributions. We also demonstrate that our methods achieve relative improvements of 0.54\% and 62.6\% in terms of utility and variance, on a proprietary, production-grade pCVR task. Lastly, we initiate an exploration into estimating the uncertainty (variance) that DP noise adds in the predictions of DP ML models. We prove that, under standard assumptions on the loss function, the sample variance from last few checkpoints provides a good approximation of the variance of the final model of a DP run. Empirically, we show that the last few checkpoints can provide a reasonable lower bound for the variance of a converged DP model. Crucially, all the methods proposed in this paper operate on \emph{a single training run} of the DP ML technique, thus incurring no additional privacy cost.

cs.LG↗

arXiv2024

Differentially Private Stream Processing at Scale

We design, to the best of our knowledge, the first differentially private (DP) stream aggregation processing system at scale. Our system -- Differential Privacy SQL Pipelines (DP-SQLP) -- is built using a streaming framework similar to Spark streaming, and is built on top of the Spanner database and the F1 query engine from Google. Towards designing DP-SQLP we make both algorithmic and systemic advances, namely, we (i) design a novel (user-level) DP key selection algorithm that can operate on an unbounded set of possible keys, and can scale to one billion keys that users have contributed, (ii) design a preemptive execution scheme for DP key selection that avoids enumerating all the keys at each triggering time, and (iii) use algorithmic techniques from DP continual observation to release a continual DP histogram of user contributions to different keys over the stream length. We empirically demonstrate the efficacy by obtaining at least $16\times$ reduction in error over meaningful baselines we consider. We implemented a streaming differentially private user impressions for Google Shopping with DP-SQLP. The streaming DP algorithms are further applied to Google Trends.

cs.CR↗

arXiv2024

Correlated Noise Provably Beats Independent Noise for Differentially Private Learning

Differentially private learning algorithms inject noise into the learning process. While the most common private learning algorithm, DP-SGD, adds independent Gaussian noise in each iteration, recent work on matrix factorization mechanisms has shown empirically that introducing correlations in the noise can greatly improve their utility. We characterize the asymptotic learning utility for any choice of the correlation function, giving precise analytical bounds for linear regression and as the solution to a convex program for general convex functions. We show, using these bounds, how correlated noise provably improves upon vanilla DP-SGD as a function of problem parameters such as the effective dimension and condition number. Moreover, our analytical expression for the near-optimal correlation function circumvents the cubic complexity of the semi-definite program used to optimize the noise correlation matrix in previous work. We validate our theory with experiments on private deep learning. Our work matches or outperforms prior work while being efficient both in terms of compute and memory.

cs.LG↗

arXiv2024

Efficient and Near-Optimal Noise Generation for Streaming Differential Privacy

In the task of differentially private (DP) continual counting, we receive a stream of increments and our goal is to output an approximate running total of these increments, without revealing too much about any specific increment. Despite its simplicity, differentially private continual counting has attracted significant attention both in theory and in practice. Existing algorithms for differentially private continual counting are either inefficient in terms of their space usage or add an excessive amount of noise, inducing suboptimal utility. The most practical DP continual counting algorithms add carefully correlated Gaussian noise to the values. The task of choosing the covariance for this noise can be expressed in terms of factoring the lower-triangular matrix of ones (which computes prefix sums). We present two approaches from this class (for different parameter regimes) that achieve near-optimal utility for DP continual counting and only require logarithmic or polylogarithmic space (and time). Our first approach is based on a space-efficient streaming matrix multiplication algorithm for a class of Toeplitz matrices. We show that to instantiate this algorithm for DP continual counting, it is sufficient to find a low-degree rational function that approximates the square root on a circle in the complex plane. We then apply and extend tools from approximation theory to achieve this. We also derive efficient closed-forms for the objective function for arbitrarily many steps, and show direct numerical optimization yields a highly practical solution to the problem. Our second approach combines our first approach with a recursive construction similar to the binary tree mechanism.

cs.DS↗

arXiv2024

Privacy Amplification for Matrix Mechanisms

Privacy amplification exploits randomness in data selection to provide tighter differential privacy (DP) guarantees. This analysis is key to DP-SGD's success in machine learning, but, is not readily applicable to the newer state-of-the-art algorithms. This is because these algorithms, known as DP-FTRL, use the matrix mechanism to add correlated noise instead of independent noise as in DP-SGD. In this paper, we propose "MMCC", the first algorithm to analyze privacy amplification via sampling for any generic matrix mechanism. MMCC is nearly tight in that it approaches a lower bound as $ε\to0$. To analyze correlated outputs in MMCC, we prove that they can be analyzed as if they were independent, by conditioning them on prior outputs. Our "conditional composition theorem" has broad utility: we use it to show that the noise added to binary-tree-DP-FTRL can asymptotically match the noise added to DP-SGD with amplification. Our amplification algorithm also has practical empirical utility: we show it leads to significant improvement in the privacy-utility trade-offs for DP-FTRL algorithms on standard benchmarks.

cs.LG↗

arXiv2024

Advancing Differential Privacy: Where We Are Now and Future Directions for Real-World Deployment

In this article, we present a detailed review of current practices and state-of-the-art methodologies in the field of differential privacy (DP), with a focus of advancing DP's deployment in real-world applications. Key points and high-level contents of the article were originated from the discussions from "Differential Privacy (DP): Challenges Towards the Next Frontier," a workshop held in July 2022 with experts from industry, academia, and the public sector seeking answers to broad questions pertaining to privacy and its implications in the design of industry-grade systems. This article aims to provide a reference point for the algorithmic and design decisions within the realm of privacy, highlighting important challenges and potential research directions. Covering a wide spectrum of topics, this article delves into the infrastructure needs for designing private systems, methods for achieving better privacy/utility trade-offs, performing privacy attacks and auditing, as well as communicating privacy with broader audiences and stakeholders.

cs.CR↗