arXiv subjects

Pranav Singh

Publications and source records attributed to Pranav Singh.

At least 19 recordsLinked to original sources

arXiv2026

Critical initialization destabilizes higher input derivatives in wide scalar-input networks

The edge-of-chaos condition preserves first-order input perturbations in wide randomly initialized networks, but physics-informed losses, score matching and derivative regularization depend on higher input derivatives. For smooth scalar-input fully connected networks, using a joint Gaussianity of the finite derivative jet that holds in the infinite-width limit at each fixed depth, we derive mean-field recursions through third order that are exact at the variance fixed point, with finite-depth corrections that decay geometrically. At criticality, the first-derivative variance is depth-invariant, whereas the second-derivative variance grows linearly whenever the activation has nonzero curvature. The resulting third-order system closes on mean-field susceptibilities. For residual networks with branch scale L^{-1/2}, we prove that every fixed finite derivative order has uniformly bounded variance under explicit regularity assumptions. Simulations verify the critical growth laws, the residual bound, and the closed recursion. The results concern initialization, not trained-network performance.

stat.ML↗

arXiv2026

What Fixed-Rollout pass@k Evaluations Can Identify

Repeated-sampling evaluations increasingly extrapolate pass@k far beyond the number n of samples collected per problem. We show that, in the pooled/random-task conditional-Binomial model, fixed-n success counts identify only the n free moments of the latent per-task success distribution. Consequently, direct pass@k is identified for k <= n, but generic extrapolated pass@k, tail exponents, and tail constants are not identified for k > n, even with arbitrarily many exchangeable tasks at the same rollout budget. This is stronger than the observation that the usual estimator is undefined beyond n: it characterizes the information missing from the fixed-depth count-law experiment. We give exact count-law-preserving constructions with incompatible extrapolations, state the exceptional unique-extension case, and compute sharp population identified intervals through Hausdorff principal representations. On the public 10,000-rollout-per-problem release of Brown et al., counterfactual n = 16 evaluations leave failure at k = 1000 ambiguous by factors from 1.5 to over 2,600 across four MATH/GSM8K/CodeContests configurations. The calibration shows that intermediate-scale failure share alone does not determine width. Our result does not reject parametric inference-time scaling laws; it supplies the nonparametric baseline against which their assumptions can be evaluated. We give an exact, conservative one-coordinate finite-task confidence certificate and a reporting standard separating direct estimates, identified sets, and model-conditioned forecasts.

stat.ML↗

arXiv2026

When Does Belief-Based Agent Memory Help? Reliability-Conditional Updating and Provenance-Capped Poisoning Defense

We investigate when belief-based memory actually improves large language model (LLM) agents. Our vehicle is Nous, a long-term memory architecture that represents each entity-attribute pair as a categorical probability distribution updated through closed-form Bayesian inference, with information-theoretic surprise driving belief revision and entropy-based forgetting. A controlled ablation on the LoCoMo benchmark shows that Bayesian belief updating alone provides little benefit over naive last-write-wins because existing conversational memory benchmarks rarely contain contradictory or differently reliable evidence. We then introduce reliability-conditioned updating, estimating per-observation reliability from epistemic language, and show on a controlled contradiction benchmark that belief updating substantially outperforms last-write-wins and raw-memory retrieval when observations differ in trustworthiness. Because content-derived reliability is itself vulnerable to manipulation, we further propose provenance-capped belief updating, where trust is bounded by source provenance rather than textual confidence. Under controlled memory-poisoning experiments, this approach resists volumetric poisoning attacks while revealing the utility costs and implementation requirements of provenance-aware memory. Finally, we quantify a 27.5-point discrepancy between strict token-F1 and LLM-as-judge evaluation on identical outputs, highlighting important reproducibility concerns for long-term memory benchmarks. Our results suggest that probabilistic belief-based memory is most beneficial in environments requiring reasoning over conflicting and differently trustworthy evidence, rather than conventional conversational recall alone.

cs.AI↗

arXiv2026

BackFlush: Knowledge-Free Backdoor Detection and Elimination with Watermark Preservation in Large Language Models

In recent trends, one can observe Large Language Models (LLMs) are exposed to backdoor attacks where vicious triggers added during training or model editing to elicit harmful outputs on specific input patterns while maintaining clean performance on normal inputs. Legitimate watermarks used as ownership signatures share similar mechanisms to backdoors, creating a critical challenge: detecting and eliminating unknown backdoors without compromising watermark integrity. Existing defenses require prior knowledge of triggers or their payloads, depend on clean reference models, or sacrifice model utility without preserving the watermark. To address these limitations we introduce BackFlush and its variants, a unified framework for backdoor detection and elimination while preserving watermarks. We establish two novel observations: Backdoor Flushing Phenomenon, where injecting and unlearning auxiliary data eliminates pre established backdoors, and Backdoor Susceptibility Amplification, enabling constant time detection independent of vocabulary size. BackFlush employs Rotation based Parameter Editing (RoPE) Unlearning, a technique that preserves watermarks while eliminating backdoors by rotating the embeddings. Comprehensive evaluation across diverse trigger types over different architectures demonstrates BackFlush achieves approximately 1%Attack Success Rate (ASR), approximately 99% clean accuracy (CACC), and preserved watermarking capabilities in the realm where no existing method simultaneously provides these alongside maintaining model utility comparable to clean baselines. Codes are available at https://github.com/JagadeeshAI/BackFlush IJCNN.git.

cs.CR↗

arXiv2026

RePAIR: Interactive Machine Unlearning through Prompt-Aware Model Repair

Large language models (LLMs) inherently absorb harmful knowledge, misinformation, and personal data during pretraining on large-scale web corpora, with no native mechanism for selective removal. While machine unlearning offers a principled solution, existing approaches are provider-centric, requiring retraining pipelines, curated retain datasets, and direct intervention by model service providers (MSPs), thereby excluding end users from controlling their own data. We introduce Interactive Machine Unlearning (IMU), a new paradigm in which users can instruct LLMs to forget targeted knowledge through natural language at inference time. To realize IMU, we propose RePAIR, a prompt-aware model repair framework comprising (i) a watchdog model for unlearning intent detection, (ii) a surgeon model for generating repair procedures, and (iii) a patient model whose parameters are updated autonomously. At the core of RePAIR, we develop Steering Through Activation Manipulation with PseudoInverse (STAMP), a training-free, single-sample unlearning method that redirects MLP activations toward a refusal subspace via closed-form pseudoinverse updates. Its low-rank variant reduces computational complexity from O(d^3) to O(r^3 + r^2 * d), enabling efficient on-device unlearning with up to ~3x speedup over training-based baselines. Extensive experiments across harmful knowledge suppression, misinformation correction, and personal data erasure demonstrate that RePAIR achieves near-zero forget scores (Acc_f = 0.00, F-RL = 0.00) while preserving model utility (Acc_r up to 84.47, R-RL up to 0.88), outperforming six state-of-the-art baselines. These results establish RePAIR as an effective and practical framework for user-driven model editing, advancing transparent and on-device control over learned knowledge, with potential extensions to multimodal foundation models.

cs.AI↗

arXiv2025

Leveraging Language Prior for Infrared Small Target Detection

IRSTD (InfraRed Small Target Detection) detects small targets in infrared blurry backgrounds and is essential for various applications. The detection task is challenging due to the small size of the targets and their sparse distribution in infrared small target datasets. Although existing IRSTD methods and datasets have led to significant advancements, they are limited by their reliance solely on the image modality. Recent advances in deep learning and large vision-language models have shown remarkable performance in various visual recognition tasks. In this work, we propose a novel multimodal IRSTD framework that incorporates language priors to guide small target detection. We leverage language-guided attention weights derived from the language prior to enhance the model's ability for IRSTD, presenting a novel approach that combines textual information with image data to improve IRSTD capabilities. Utilizing the state-of-the-art GPT-4 vision model, we generate text descriptions that provide the locations of small targets in infrared images, employing careful prompt engineering to ensure improved accuracy. Due to the absence of multimodal IR datasets, existing IRSTD methods rely solely on image data. To address this shortcoming, we have curated a multimodal infrared dataset that includes both image and text modalities for small target detection, expanding upon the popular IRSTD-1k and NUDT-SIRST datasets. We validate the effectiveness of our approach through extensive experiments and comprehensive ablation studies. The results demonstrate significant improvements over the state-of-the-art method, with relative percentage differences of 9.74%, 13.02%, 1.25%, and 67.87% in IoU, nIoU, Pd, and Fa on the NUAA-SIRST subset, and 4.41%, 2.04%, 2.01%, and 113.43% on the IRSTD-1k subset of the LangIR dataset, respectively.

cs.CV↗

arXiv2024

Adaptive higher order reversible integrators for memory efficient deep learning

The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems.

math.NA↗

arXiv2024

Commutator-free Cayley methods

Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect important physical laws of the dynamical system, such as unitarity and energy conservation in the context of quantum dynamical systems, for instance. In this article we develop a high-order commutator free Lie group integrator for non-autonomous differential equations evolving on quadratic Lie groups. Instead of matrix exponentials, which are expensive to evaluate and need to be approximated by appropriate rational functions in order to preserve the Lie group structure, the proposed method is obtained as a composition of Cayley transforms which naturally respect the structure of quadratic Lie groups while being computationally efficient to evaluate. Unlike Cayley--Magnus methods the method is also free from nested matrix commutators.

math.NA↗

arXiv2024

Computation of some dispersive equations through their iterated linearisation

It is often the case that, while the numerical solution of the non-linear dispersive equation $\mathrm{i}\partial_t u(t)=\mathcal{H}(u(t),t)u(t)$ represents a formidable challenge, it is fairly easy and cheap to solve closely related linear equations of the form $\mathrm{i}\partial_t u(t)=\mathcal{H}_1(t)u(t)+\widetilde{\mathcal H}_2(t)u(t)$, where $\mathcal{H}_1(t)+\mathcal{H}_2(v,t)=\mathcal{H}(v,t)$. In that case we advocate an iterative linearisation procedure that involves fixed-point iteration of the latter equation to solve the former. A typical case is when the original problem is a nonlinear Schr\"odinger or Gross--Pitaevskii equation, while the `easy' equation is linear Schr\"odinger with time-dependent potential. We analyse in detail the iterative scheme and its practical implementation, prove that each iteration increases the order, derive upper bounds on the speed of convergence and discuss in the case of nonlinear Schr\"odinger equation with cubic potential the preservation of structural features of the underlying equation: the $\mathrm{L}_2$ norm, momentum and Hamiltonian energy. A key ingredient in our approach is the use of the Magnus expansion in conjunction with Hermite quadratures, which allows effective solutions of the linearised but non-autonomous equations in an iterative fashion. The resulting Magnus--Hermite methods can be combined with a wide range of numerical approximations to the matrix exponential. The paper concludes with a number of numerical experiments, demonstrating the power of the proposed approach.

math.NA↗

arXiv2024

Exploring Intrinsic Properties of Medical Images for Self-Supervised Binary Semantic Segmentation

Recent advancements in self-supervised learning have unlocked the potential to harness unlabeled data for auxiliary tasks, facilitating the learning of beneficial priors. This has been particularly advantageous in fields like medical image analysis, where labeled data are scarce. Although effective for classification tasks, this methodology has shown limitations in more complex applications, such as medical image segmentation. In this paper, we introduce Medical imaging Enhanced with Dynamic Self-Adaptive Semantic Segmentation (MedSASS), a dedicated self-supervised framework tailored for medical image segmentation. We evaluate MedSASS against existing state-of-the-art methods across four diverse medical datasets, showcasing its superiority. MedSASS outperforms existing CNN-based self-supervised methods by 3.83% and matches the performance of ViT-based methods. Furthermore, when MedSASS is trained end-to-end, covering both encoder and decoder, it demonstrates significant improvements of 14.4% for CNNs and 6% for ViT-based architectures compared to existing state-of-the-art self-supervised strategies.

cs.CV↗

arXiv2024

Free Form Medical Visual Question Answering in Radiology

Visual Question Answering (VQA) in the medical domain presents a unique, interdisciplinary challenge, combining fields such as Computer Vision, Natural Language Processing, and Knowledge Representation. Despite its importance, research in medical VQA has been scant, only gaining momentum since 2018. Addressing this gap, our research delves into the effective representation of radiology images and the joint learning of multimodal representations, surpassing existing methods. We innovatively augment the SLAKE dataset, enabling our model to respond to a more diverse array of questions, not limited to the immediate content of radiology or pathology images. Our model achieves a top-1 accuracy of 79.55\% with a less complex architecture, demonstrating comparable performance to current state-of-the-art models. This research not only advances medical VQA but also opens avenues for practical applications in diagnostic settings.

cs.CV↗

arXiv2023

Unitary rational best approximations to the exponential function

Rational best approximations (in a Chebyshev sense) to real functions are characterized by an equioscillating approximation error. Similar results do not hold true for rational best approximations to complex functions in general. In the present work, we consider unitary rational approximations to the exponential function on the imaginary axis, which map the imaginary axis to the unit circle. In the class of unitary rational functions, best approximations are shown to exist, to be uniquely characterized by equioscillation of a phase error, and to possess a super-linear convergence rate. Furthermore, the best approximations have full degree (i.e., non-degenerate), achieve their maximum approximation error at points of equioscillation, and interpolate at intermediate points. Asymptotic properties of poles, interpolation nodes, and equioscillation points of these approximants are studied. Three algorithms, which are found very effective to compute unitary rational approximations including candidates for best approximations, are sketched briefly. Some consequences to numerical time-integration are discussed. In particular, time propagators based on unitary best approximants are unitary, symmetric and A-stable.

math.NA↗

arXiv2023

Quantum simulation of highly-oscillatory many-body Hamiltonians for near-term devices

We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the Magnus expansion is the appearance of a commutator term which leads to prohibitively long circuits. We present a technique for eliminating this commutator and find that a single time-step of the resulting algorithm is only marginally costlier than that required for time-stepping with a time-independent Hamiltonian, requiring only three additional single-qubit layers. For a large class of Hamiltonians appearing in liquid-state nuclear magnetic resonance (NMR) applications, we further exploit symmetries of the Hamiltonian and achieve a surprising reduction in the expansion, whereby a single time-step of our fourth-order method has a circuit structure and cost that is identical to that required for a fourth-order Trotterized time-stepping procedure for time-independent Hamiltonians. Moreover, our algorithms are able to take time-steps that are larger than the wavelength of oscillation of the time-dependent Hamiltonian, making them particularly suited for highly-oscillatory controls. The resulting quantum circuits have shorter depths for all levels of accuracy when compared to first and second-order Trotterized methods, as well as other fourth-order Trotterized methods, making the proposed algorithm a suitable candidate for simulation of time-dependent Hamiltonians on near-term quantum devices.

quant-ph↗

arXiv2023

Shifting to Machine Supervision: Annotation-Efficient Semi and Self-Supervised Learning for Automatic Medical Image Segmentation and Classification

Advancements in clinical treatment are increasingly constrained by the limitations of supervised learning techniques, which depend heavily on large volumes of annotated data. The annotation process is not only costly but also demands substantial time from clinical specialists. Addressing this issue, we introduce the S4MI (Self-Supervision and Semi-Supervision for Medical Imaging) pipeline, a novel approach that leverages advancements in self-supervised and semi-supervised learning. These techniques engage in auxiliary tasks that do not require labeling, thus simplifying the scaling of machine supervision compared to fully-supervised methods. Our study benchmarks these techniques on three distinct medical imaging datasets to evaluate their effectiveness in classification and segmentation tasks. Notably, we observed that self supervised learning significantly surpassed the performance of supervised methods in the classification of all evaluated datasets. Remarkably, the semi-supervised approach demonstrated superior outcomes in segmentation, outperforming fully-supervised methods while using 50% fewer labels across all datasets. In line with our commitment to contributing to the scientific community, we have made the S4MI code openly accessible, allowing for broader application and further development of these methods.

cs.CV↗

arXiv2023

Enhancing Medical Image Segmentation: Optimizing Cross-Entropy Weights and Post-Processing with Autoencoders

The task of medical image segmentation presents unique challenges, necessitating both localized and holistic semantic understanding to accurately delineate areas of interest, such as critical tissues or aberrant features. This complexity is heightened in medical image segmentation due to the high degree of inter-class similarities, intra-class variations, and possible image obfuscation. The segmentation task further diversifies when considering the study of histopathology slides for autoimmune diseases like dermatomyositis. The analysis of cell inflammation and interaction in these cases has been less studied due to constraints in data acquisition pipelines. Despite the progressive strides in medical science, we lack a comprehensive collection of autoimmune diseases. As autoimmune diseases globally escalate in prevalence and exhibit associations with COVID-19, their study becomes increasingly essential. While there is existing research that integrates artificial intelligence in the analysis of various autoimmune diseases, the exploration of dermatomyositis remains relatively underrepresented. In this paper, we present a deep-learning approach tailored for Medical image segmentation. Our proposed method outperforms the current state-of-the-art techniques by an average of 12.26% for U-Net and 12.04% for U-Net++ across the ResNet family of encoders on the dermatomyositis dataset. Furthermore, we probe the importance of optimizing loss function weights and benchmark our methodology on three challenging medical image segmentation tasks

eess.IV↗

arXiv2023

Efficient Representation Learning for Healthcare with Cross-Architectural Self-Supervision

In healthcare and biomedical applications, extreme computational requirements pose a significant barrier to adopting representation learning. Representation learning can enhance the performance of deep learning architectures by learning useful priors from limited medical data. However, state-of-the-art self-supervised techniques suffer from reduced performance when using smaller batch sizes or shorter pretraining epochs, which are more practical in clinical settings. We present Cross Architectural - Self Supervision (CASS) in response to this challenge. This novel siamese self-supervised learning approach synergistically leverages Transformer and Convolutional Neural Networks (CNN) for efficient learning. Our empirical evaluation demonstrates that CASS-trained CNNs and Transformers outperform existing self-supervised learning methods across four diverse healthcare datasets. With only 1% labeled data for finetuning, CASS achieves a 3.8% average improvement; with 10% labeled data, it gains 5.9%; and with 100% labeled data, it reaches a remarkable 10.13% enhancement. Notably, CASS reduces pretraining time by 69% compared to state-of-the-art methods, making it more amenable to clinical implementation. We also demonstrate that CASS is considerably more robust to variations in batch size and pretraining epochs, making it a suitable candidate for machine learning in healthcare applications.

cs.LG↗

arXiv2023

Cross-Architectural Positive Pairs improve the effectiveness of Self-Supervised Learning

Existing self-supervised techniques have extreme computational requirements and suffer a substantial drop in performance with a reduction in batch size or pretraining epochs. This paper presents Cross Architectural - Self Supervision (CASS), a novel self-supervised learning approach that leverages Transformer and CNN simultaneously. Compared to the existing state-of-the-art self-supervised learning approaches, we empirically show that CASS-trained CNNs and Transformers across four diverse datasets gained an average of 3.8% with 1% labeled data, 5.9% with 10% labeled data, and 10.13% with 100% labeled data while taking 69% less time. We also show that CASS is much more robust to changes in batch size and training epochs than existing state-of-the-art self-supervised learning approaches. We have open-sourced our code at https://github.com/pranavsinghps1/CASS.

cs.CV↗

arXiv2022

CASS: Cross Architectural Self-Supervision for Medical Image Analysis

Recent advances in deep learning and computer vision have reduced many barriers to automated medical image analysis, allowing algorithms to process label-free images and improve performance. However, existing techniques have extreme computational requirements and drop a lot of performance with a reduction in batch size or training epochs. This paper presents Cross Architectural - Self Supervision (CASS), a novel self-supervised learning approach that leverages Transformer and CNN simultaneously. Compared to the existing state of the art self-supervised learning approaches, we empirically show that CASS-trained CNNs and Transformers across four diverse datasets gained an average of 3.8% with 1% labeled data, 5.9% with 10% labeled data, and 10.13% with 100% labeled data while taking 69% less time. We also show that CASS is much more robust to changes in batch size and training epochs. Notably, one of the test datasets comprised histopathology slides of an autoimmune disease, a condition with minimal data that has been underrepresented in medical imaging. The code is open source and is available on GitHub.

cs.CV↗