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Kushal Chakrabarti

Publications and source records attributed to Kushal Chakrabarti.

At least 19 recordsLinked to original sources

On-the-go Forgetting without Explicit Unlearning via ERASE

Existing unlearning approaches typically rely on post hoc weight adaptation or distillation, leading to duplicated memory costs, degraded generalization, and limited scalability. In this work, we introduce ERASE, Erasure via Reconstructive Adversarial Signal Editing, a framework for on-the-go forgetting that suppresses the observable influence of private data without modifying model weights. ERASE leverages structured, class-conditioned input perturbations to induce selective forgetting during inference, eliminating the need for retraining, fine-tuning, or model copies. We rigorously characterize sufficient conditions when ERASE provably achieves functional forgetting of designated subclasses while preserving predictions across other subclasses within the same superclass. This analysis offers a principled foundation for inference-time forgetting under mild regularity assumptions. Across diverse architectures and benchmark datasets, ERASE maintains the best observed balance between forgetting efficacy, computational efficiency, and retention fidelity over recent unlearning-based methods. By reimagining data removal as forgetting without unlearning, our work establishes a scalable, regulation-aligned pathway for continual, privacy-conscious learning.

cs.LG

Why Does CLAUDE.md Keep Growing? Catastrophic Remembering in Agentic Coding

Agentic coding READMEs like CLAUDE.md grow without bound in real repositories, stopping only when the repository retires or someone rewrites the file wholesale. We trace this to imperfect recall: appending an instruction is always cheap, but once an instruction's rationale is gone, deleting it without risking a correctness regression costs O(2^|D|) in a prompt of |D| instructions. We name the resulting divergence catastrophic remembering, the inverse of catastrophic forgetting around which continual learning is organized. First, we characterize this phenomenon across 247,694 instruction lifetimes in 1,867 repositories: agentic prompts grow without bound, more than tripling over their lifetime (+226%), gaining +4.9 net instructions every commit; further, the older an instruction gets, the less likely it is to be deleted (log-hazard -0.032/commit). Then, we show that prompt comments can halt the growth: inverting IFEval yields verifiable worlds whose optimal prompts are known, and there comments encoding latent reasoning remove 99.3% of excess instructions (+211.3% to +1.4%). Finally, applying the same inversion to WildIFEval, we show that prompt comments can improve real-world agentic instruction-following by up to 23.1%. If English is the new code, why don't we have comments yet?

cs.AI

Reliability Scales Inversely: Hallucinations Snowball Faster in Bigger Language Models

Bigger language models are less reliable. Across three families, three benchmarks and six rungs, including in-the-wild chat logs, scaling closes the start-of-response knowledge gap up to $7\times$ while within-response knowledge degradation grows up to $39\times$. We trace that residual to one variable, the per-position disagreement $\delta = \log p_M - \log p_O$ against a stronger oracle, whose second moment splits exactly into bias$^2$ $\mathrm{KL}(p_M \,\|\, p_O)^2$ and decoding risk $\mathrm{Var}[\delta]$. That split is an interpretability statement before it is a statistical one: the model's self-readable uncertainty $H(p_M)$ enters only the bias term, so the risk term has no model-readable component. Risk also takes a growing share of the squared error with scale, $31\%$ to $49\%$ from $1.7$B to $14$B. At a fabrication $H(p_M)$ relaxes within one token while risk persists up to $23\times$ longer, leaving a confident-but-precarious regime that bridges consecutive fabrications ($+69\%$ at $14$B). Contracting that risk at fixed $\mathrm{KL}$ removes $35$-$74\%$ of web-verified hallucinations across six rungs and three families. Semantic entropy fires $\approx$$30\%$ less on that branch ($p\!<\!10^{-16}$) though it carries nearly $4\times$ the fabrications. Bigger models snowball mistakes faster, through a failure mode that is dominant, self-perpetuating, causal and invisible to the model itself.

cs.LG

Quantized Stochastic Primal-Dual Methods for Distributed Optimization under Relaxed Global Geometry

We study distributed optimization with stochastic gradients and finite-bit communication modeled by random (unbiased) quantization. We propose q-PDGD, a quantized stochastic primal-dual method, and analyze it under relaxed global geometry. Under restricted secant inequality (RSI), a constant step-size yields linear contraction to an explicit neighborhood determined by gradient noise, quantization distortion, and network connectivity, while a diminishing step-size achieves O(1/k) convergence without shared-minimizer assumptions. Under Polyak-Lojasiewicz (PL) inequality, we obtain linear-to-neighborhood convergence in the same stochastic quantized setting. Our results match the best-known centralized stochastic rates in oracle complexity, and are supported by experiments demonstrating the predicted tradeoffs between quantization level, step-size choice, and graph structure.

math.OC

Enhancing Robustness of Federated Learning via Server Learning

This paper explores the use of server learning for enhancing the robustness of federated learning against malicious attacks even when clients' training data are not independent and identically distributed. We propose a heuristic algorithm that uses server learning and client update filtering in combination with geometric median aggregation. We demonstrate via experiments that this approach can achieve significant improvement in model accuracy even when the fraction of malicious clients is high, even more than $50\%$ in some cases, and the dataset utilized by the server is small and could be synthetic with its distribution not necessarily close to that of the clients' aggregated data.

cs.LG

Multi-Head Attention Is a Multi-Player Game

Modern transformer attention is internally multi-agent -- heads compete and coordinate -- yet we train it as if it were a monolithic optimizer. We formalize this gap: cross-entropy training induces an implicit potential game among heads, and gradient descent converges to Nash equilibria with potentially unbounded inefficiency due to unpriced externalities (redundancy, correlated errors). Our main result bounds the Price of Anarchy by $\Gamma(G)$, the off-diagonal mass of a head interaction matrix capturing weight and gradient coupling. Under mild smoothness assumptions, we prove that both \emph{excess hallucination probability} and \emph{excess head redundancy} scale with PoA, unifying two distinct failure modes into a single mechanism. The bound is prescriptive: regularization that reduces $\Gamma(G)$ provably tightens PoA. We instantiate this as GAME-LoRA, combining Barlow Twins decorrelation with log-determinant coordination pressure. Experiments validate the theory: $\Gamma(G)$ predicts hallucination ($p{<}0.05$), emergent coalitions exhibit selective coordination, and GAME-LoRA achieves up to 18\% hallucination reduction (8\% average) with no knowledge degradation -- a Pareto improvement inaccessible to methods ignoring the game structure.

cs.AI

Neural Diversity Regularizes Hallucinations in Language Models

Language models continue to hallucinate despite increases in parameters, compute, and data. We propose neural diversity -- decorrelated parallel representations -- as a principled mechanism that reduces hallucination rates at fixed parameter and data budgets. While existing mitigation strategies largely target accuracy, we provide the first formal tail bounds for hallucination probability in ensembled language models, reframing it as a second-moment reliability problem and explaining 94.3% of empirical reliability variation seen across parallel configurations. We introduce ND-LoRA (Neural Diversity Low-Rank Adaptation), combining parallel LoRA adapters with Barlow Twins regularization, and reduce hallucinations by up to 25.6% (and 14.6% on average) while preserving general accuracy. Ablations show LoRA adapters and regularization act synergistically, causal interventions prove neurodiversity as the mediating factor and correlational studies indicate scale: a 0.1% neural correlation increase is associated with a 3.8% hallucination increase. Finally, task-dependent optimality emerges: different tasks require different optimal amounts of neurodiversity. Together, our results highlight neural diversity as a third axis of scaling -- orthogonal to parameters and data -- to improve the reliability of language models at fixed budgets.

cs.CL

On Model Protection in Federated Learning against Eavesdropping Attacks

In this study, we investigate the protection offered by federated learning algorithms against eavesdropping adversaries. In our model, the adversary is capable of intercepting model updates transmitted from clients to the server, enabling it to create its own estimate of the model. Unlike previous research, which predominantly focuses on safeguarding client data, our work shifts attention protecting the client model itself. Through a theoretical analysis, we examine how various factors, such as the probability of client selection, the structure of local objective functions, global aggregation at the server, and the eavesdropper's capabilities, impact the overall level of protection. We further validate our findings through numerical experiments, assessing the protection by evaluating the model accuracy achieved by the adversary. Finally, we compare our results with methods based on differential privacy, underscoring their limitations in this specific context.

cs.CR

Trapped-ion quantum simulation of the Fermi-Hubbard model as a lattice gauge theory using hardware-aware native gates

The Fermi-Hubbard model (FHM) is a simple yet rich model of strongly interacting electrons with complex dynamics and a variety of emerging quantum phases. These properties make it a compelling target for digital quantum simulation. Trotterization-based quantum simulations have shown promise, but implementations on current hardware are limited by noise, necessitating error mitigation techniques like circuit optimization and post-selection. A mapping of the FHM to a Z2 LGT was recently proposed that restricts the dynamics to a subspace protected by additional symmetries, and its ability for post-selection error mitigation was verified through noisy classical simulations. In this work, we propose and demonstrate a suite of algorithm-hardware co-design strategies on a trapped-ion quantum computer, targeting two key aspects of NISQ-era quantum simulation: circuit compilation and error mitigation. In particular, a novel combination of iteratively preconditioned gradient descent (IPG) and subsystem von Neumann Entropy compression reduces the 2-qubit gate count of FHM quantum simulation by 35%, consequently doubling the number of simulatable Trotter steps when used in tandem with error mitigation based on conserved symmetries, debiasing and sharpening techniques. Our work demonstrates the value of algorithm-hardware co-design to operate digital quantum simulators at the threshold of maximum circuit depths allowed by current hardware, and is broadly generalizable to strongly correlated systems in quantum chemistry and materials science.

quant-ph

Distributed Optimization via Energy Conservation Laws in Dilated Coordinates

Continuous-time models can reveal accelerated structures in distributed optimization, but their rates need not survive direct discretization. We introduce a second-order primal--dual flow for smooth convex distributed optimization and construct an exactly conserved energy that yields an $\mathcal O(t^{-2})$ rate for both the aggregate objective gap and the squared consensus error. We then prove a horizon-wise $\Omega(k^{-1})$ lower bound for a broad class of single-loop finite-memory primal--dual discretizations, ruling out a $\mathcal O(k^{-2})$ aggregate-objective guarantee within this class. Motivated by this barrier, we develop a double-loop method that combines finite-step polynomial consensus with an accelerated outer update. It uses one gradient evaluation and at most $m-1$ communication rounds per outer iteration, $m$ being the number of agents, maintains exact consensus and achieves an $\mathcal O(k^{-2})$ aggregate-objective rate. Numerical comparisons with representative distributed methods support the theory and quantify the communication cost of acceleration.

math.OC

A Methodology Establishing Linear Convergence of Adaptive Gradient Methods under PL Inequality

Adaptive gradient-descent optimizers are the standard choice for training neural network models. Despite their faster convergence than gradient-descent and remarkable performance in practice, the adaptive optimizers are not as well understood as vanilla gradient-descent. A reason is that the dynamic update of the learning rate that helps in faster convergence of these methods also makes their analysis intricate. Particularly, the simple gradient-descent method converges at a linear rate for a class of optimization problems, whereas the practically faster adaptive gradient methods lack such a theoretical guarantee. The Polyak-{\L}ojasiewicz (PL) inequality is the weakest known class, for which linear convergence of gradient-descent and its momentum variants has been proved. Therefore, in this paper, we prove that AdaGrad and Adam, two well-known adaptive gradient methods, converge linearly when the cost function is smooth and satisfies the PL inequality. Our theoretical framework follows a simple and unified approach, applicable to both batch and stochastic gradients, which can potentially be utilized in analyzing linear convergence of other variants of Adam.

cs.LG

On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer

This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This paper presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. Our assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of the IPG observer with the Newton observer, which was only hypothesized earlier.

math.OC

On Linear Convergence of PI Consensus Algorithm under the Restricted Secant Inequality

This paper considers solving distributed optimization problems in peer-to-peer multi-agent networks. The network is synchronous and connected. By using the proportional-integral (PI) control strategy, various algorithms with fixed stepsize have been developed. Two notable among them are the PI algorithm and the PI consensus algorithm. Although the PI algorithm has provable linear or exponential convergence without the standard requirement of (strong) convexity, a similar guarantee for the PI consensus algorithm is unavailable. In this paper, using Lyapunov theory, we guarantee exponential convergence of the PI consensus algorithm for global cost functions that satisfy the restricted secant inequality, with rate-matching discretization, without requiring convexity. To accelerate the PI consensus algorithm, we incorporate local pre-conditioning in the form of constant positive definite matrices and numerically validate its efficiency compared to the prominent distributed convex optimization algorithms. Unlike classical pre-conditioning, where only the gradients are multiplied by a pre-conditioner, the proposed pre-conditioning modifies both the gradients and the consensus terms, thereby controlling the effect of the communication graph on the algorithm.

math.OC

Quantum Circuit Optimization through Iteratively Pre-Conditioned Gradient Descent

For typical quantum subroutines in the gate-based model of quantum computing, explicit decompositions of circuits in terms of single-qubit and two-qubit entangling gates may exist. However, they often lead to large-depth circuits that are challenging for noisy intermediate-scale quantum (NISQ) hardware. Additionally, exact decompositions might only exist for some modular quantum circuits. Therefore, it is essential to find gate combinations that approximate these circuits to high fidelity with potentially low depth, for example, using gradient-based optimization. Traditional optimizers often run into problems of slow convergence requiring many iterations, and perform poorly in the presence of noise. Here we present iteratively preconditioned gradient descent (IPG) for optimizing quantum circuits and demonstrate performance speedups for state preparation and implementation of quantum algorithmic subroutines. IPG is a noise-resilient, higher-order algorithm that has shown promising gains in convergence speed for classical optimizations, converging locally at a linear rate for convex problems and superlinearly when the solution is unique. Specifically, we show an improvement in fidelity by a factor of $10^4$ for preparing a 4-qubit W state and a maximally entangled 5-qubit GHZ state compared to other commonly used classical optimizers tuning the same ansatz. We also show gains for optimizing a unitary for a quantum Fourier transform using IPG, and report results of running such optimized circuits on IonQ's quantum processing unit (QPU). Such faster convergence with promise for noise-resilience could provide advantages for quantum algorithms on NISQ hardware, especially since the cost of running each iteration on a quantum computer is substantially higher than the classical optimizer step.

quant-ph

Iteratively Preconditioned Gradient-Descent Approach for Moving Horizon Estimation Problems

Moving horizon estimation (MHE) is a widely studied state estimation approach in several practical applications. In the MHE problem, the state estimates are obtained via the solution of an approximated nonlinear optimization problem. However, this optimization step is known to be computationally complex. Given this limitation, this paper investigates the idea of iteratively preconditioned gradient-descent (IPG) to solve MHE problem with the aim of an improved performance than the existing solution techniques. To our knowledge, the preconditioning technique is used for the first time in this paper to reduce the computational cost and accelerate the crucial optimization step for MHE. The convergence guarantee of the proposed iterative approach for a class of MHE problems is presented. Additionally, sufficient conditions for the MHE problem to be convex are also derived. Finally, the proposed method is implemented on a unicycle localization example. The simulation results demonstrate that the proposed approach can achieve better accuracy with reduced computational costs.

math.OC

A Control Theoretic Framework for Adaptive Gradient Optimizers in Machine Learning

Adaptive gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been proposed to enhance Adam's poor generalization ability compared to the classical stochastic gradient method. This paper develops a generic framework for adaptive gradient methods that solve non-convex optimization problems. We first model the adaptive gradient methods in a state-space framework, which allows us to present simpler convergence proofs of adaptive optimizers such as AdaGrad, Adam, and AdaBelief. We then utilize the transfer function paradigm from classical control theory to propose a new variant of Adam, coined AdamSSM. We add an appropriate pole-zero pair in the transfer function from squared gradients to the second moment estimate. We prove the convergence of the proposed AdamSSM algorithm. Applications on benchmark machine learning tasks of image classification using CNN architectures and language modeling using LSTM architecture demonstrate that the AdamSSM algorithm improves the gap between generalization accuracy and faster convergence than the recent adaptive gradient methods.

cs.LG

On Accelerating Distributed Convex Optimizations

This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a server, and there is no inter-agent communication. The agents' goal is to learn a parameter vector that optimizes the aggregate of their local costs without revealing their local data points. In principle, the agents can solve this problem by collaborating with the server using the traditional distributed gradient-descent method. However, when the aggregate cost is ill-conditioned, the gradient-descent method (i) requires a large number of iterations to converge, and (ii) is highly unstable against process noise. We propose an iterative pre-conditioning technique to mitigate the deleterious effects of the cost function's conditioning on the convergence rate of distributed gradient-descent. Unlike the conventional pre-conditioning techniques, the pre-conditioner matrix in our proposed technique updates iteratively to facilitate implementation on the distributed network. In the distributed setting, we provably show that the proposed algorithm converges linearly with an improved rate of convergence than the traditional and adaptive gradient-descent methods. Additionally, for the special case when the minimizer of the aggregate cost is unique, our algorithm converges superlinearly. We demonstrate our algorithm's superior performance compared to prominent distributed algorithms for solving real logistic regression problems and emulating neural network training via a noisy quadratic model, thereby signifying the proposed algorithm's efficiency for distributively solving non-convex optimization. Moreover, we empirically show that the proposed algorithm results in faster training without compromising the generalization performance.

math.OC

Generalized AdaGrad (G-AdaGrad) and Adam: A State-Space Perspective

Accelerated gradient-based methods are being extensively used for solving non-convex machine learning problems, especially when the data points are abundant or the available data is distributed across several agents. Two of the prominent accelerated gradient algorithms are AdaGrad and Adam. AdaGrad is the simplest accelerated gradient method, which is particularly effective for sparse data. Adam has been shown to perform favorably in deep learning problems compared to other methods. In this paper, we propose a new fast optimizer, Generalized AdaGrad (G-AdaGrad), for accelerating the solution of potentially non-convex machine learning problems. Specifically, we adopt a state-space perspective for analyzing the convergence of gradient acceleration algorithms, namely G-AdaGrad and Adam, in machine learning. Our proposed state-space models are governed by ordinary differential equations. We present simple convergence proofs of these two algorithms in the deterministic settings with minimal assumptions. Our analysis also provides intuition behind improving upon AdaGrad's convergence rate. We provide empirical results on MNIST dataset to reinforce our claims on the convergence and performance of G-AdaGrad and Adam.

cs.LG