arXiv subjects

Ravi Ranjan

Publications and source records attributed to Ravi Ranjan.

At least 19 recordsLinked to original sources

arXiv2026

Infinite families and sporadic solutions of the equation $φ(n)=c+α\sum_{p\mid n}φ(p)$

Ranjan and Singh proved that for every composite $n$ which is not twice an odd prime, $φ(n)$ is at least one plus the sum of $φ$ over the prime divisors of $n$, with equality exactly for $n=4,12,30$. \new{We study the weighted equation $φ(n)=c+α\sum_{p\mid n}φ(p)$. We determine the parameters $(c,α)$ admitting infinite families of solutions, prove that all remaining solutions are finite in number and arise from an explicit linear mechanism, and compute them exactly in a range of parameters; the finiteness of $\{4,12,30\}$ becomes a special case. We also settle the analogous equations for the divisor functions $τ$ and $σ$ and for the Jordan totients, and, from known results on the sum of the prime divisors, derive the full asymptotic expansion of the average deficiency.} \K{In the range $|c|\le10$, $1\leα\le6$ the composite solution set is determined completely\V{, and the number and the size of the sporadic solutions are shown to be bounded by polynomials in $|c|+α$}.} \B{Finally, replacing the prime values $φ(p)$ by their iterates $φ^{(k)}(p)$, we determine all solutions of $φ(n)=1+\sum_{p\mid n}φ^{(k)}(p)$: the solution sets are $\{1,4,12,30\}$, $\{1,3,4,10\}$ and, for every $k\ge3$, $\{1,3,4\}$; for the weighted iterated equation we exhibit an infinite family governed by the safe primes.

math.NT↗

arXiv2026

Beyond MSE: Rician Likelihood Denoising for Self-Supervised Cardiac $T2$ and $T1ρ$ MRI

Magnetic resonance imaging involves an inherent trade-off among spatial resolution, acquisition time, and noise. This trade-off contributes to long scan times and high cost. Deep learning has improved image denoising, but cardiac MRI remains difficult because high-resolution, rapid acquisitions generally lack corresponding low-noise ground truth. Self-supervised denoising offers a potential solution by learning from noisy image pairs or even single noisy acquisitions. However, we show that Noise2Void-style blind-spot denoising, which uses a mean squared error (MSE) loss and assumes zero-mean, independent and identically distributed (i.i.d.) noise, is poorly suited to MR magnitude images. When applied to short-axis $T2$-weighted and $T1ρ$-weighted cardiac MRI with synthetic Rician noise, it produces biased denoised images and biased parametric maps of $T2$ and $T1ρ$. To address this limitation, we formulate self-supervised denoising as maximum likelihood estimation under a known Rician noise model. This yields unbiased denoisers that are competitive with supervised baselines.

eess.IV↗

arXiv2026

DePICT: Decision-Preserving Interface for Constrained Downstream Tasks

A constrained optimization problem may involve a parameter in its objective and active constraints, yet the final decision may remain insensitive to small changes in that parameter. This raises a fundamental question: which inputs does a decision making system truly depend on? Building on this question, we introduce DePICT, a procedure for constructing decision preserving interfaces by ranking context directions according to the optimizer's solution sensitivity and aggregating them across an operating regime. We study this problem in a high dimensional setting where primitive context parameterizes a constrained task and the downstream agent observes only a selected subset of context directions. For locally regular constrained programs, we derive a Karush Kuhn Tucker (KKT) based characterization of when a context direction is optimizer relevant. Our analysis shows that appearing in the active optimization problem does not necessarily imply that a variable affects the final decision. Some context directions can alter the KKT conditions while leaving the optimal solution unchanged because their effect is absorbed by the dual variables. DePICT is designed to remove exactly these directions. In a controlled diagnosis, it recovers the decision relevant interface exactly and reduces linear predictor regret to 0.009, compared with 0.475 for the strongest competing baseline.

cs.LG↗

arXiv2026

RippleCP: Measuring Counterfactual Checkpoint Advantage in Coding Agents

Agent checkpoint systems decide what state is recovery-relevant, how to snapshot it, and whether rollback is admissible. None decides which of the safe boundaries they expose are worth materializing. We formulate this as counterfactual checkpoint advantage, the reduction in future recovery cost obtained by checkpointing a candidate rather than skipping it, and measure it by driving a CP branch and a SKIP branch to the same logical failure and recovering both under matched model, tool, verifier, and stopping conditions. On a frozen pilot of 12 SWE-bench Verified tasks and 106 real recovery branches, checkpointing saves 49.4 s per task, and that figure resolves into two regimes two orders of magnitude apart. The first checkpoint returns 100.0 s on 156.5 s of protected work, a conversion of 0.64; a second one step later returns-1.1 s on 41.8 s, a conversion of -0.03. Recovery is a re-derivation rather than a replay, so preserved work is a poor guide to saved work, and the classical elapsed-work rule misprices the second checkpoint by its full nominal cost. We identify where placement can pay, and set the bar a placement policy must clear.

cs.AI↗

arXiv2026

Forgetting Only What Matters: Layer-Selective Unlearning toward Robust LLMs

Large Language Models (LLMs) can memorize and reproduce sensitive, copyrighted, or otherwise undesirable training content, creating privacy, safety, and regulatory concerns. Machine unlearning offers a practical alternative to full retraining, but many existing methods apply broad or fixed parameter updates that can degrade utility and remain brittle under deployment changes such as post-training quantization, where forgotten knowledge may partially re-emerge. We propose Forgetting Only What Matters via Unlearning Layers (FOM-UL), a layer-level unlearning framework that selects transformer layers using a forget-to-retain significance score. This score identifies layers with high influence on the forget set and low sensitivity to the retain set, allowing FOM-UL to concentrate updates where they are most effective while leaving most of the model unchanged. This targeted update strategy improves the forgetting-utility trade-off and provides an empirical path toward quantization-resilient unlearning by reducing the chance that small, diffuse updates are erased by low-bit rounding. Across TOFU, KnowUnDo, and MUSE-style evaluations, FOM-UL reduces residual memorization compared with strong GA, NPO, KLD, SURE, ReLearn, and LUNAR-based baselines while preserving retain-set utility close to the vanilla model. Under 8-bit and 4-bit post-training quantization, FOM-UL maintains stronger memorization suppression and utility preservation than competing methods, and adversarial prompt evaluations show lower recovery of forgotten content. Overall, FOM-UL provides an efficient unlearning strategy that improves targeted forgetting, utility preservation, and deployment robustness without claiming formal guarantees of erasure.

cs.LG↗

arXiv2026

SafeCommit: Certifying When Memory-Grounded Agents May Safely Act

Long-horizon agents increasingly use persistent memory and tools to take actions with external side effects. A central failure mode is premature commitment: an agent acts before resolving whether its memory grounding is stale, conflicting, incomplete, or corrupted. We formalize this problem as safe commitment under memory uncertainty and introduce SafeCommit, a risk controlled layer between agent reasoning and external execution. The layer constructs a calibrated set of plausible latent worlds from memory, observations, tool outputs, provenance, and policy constraints. It permits a side effectful action only when a conformal action certificate shows that the action is safe in every retained world. Otherwise, it selects a low-side-effect probe that targets the worlds blocking certification, or returns a conservative fallback. Under calibrated world coverage, the probability of an unsafe certified commit is at most the target level α; with imperfect world proposal, the bound separates calibration and representation error. A dependency-free controlled simulator illustrates the safety-utility tradeoff and reproduces all reported results with one command. The goal is to offer a concrete approach for deciding not only what an agent should do, but when the available evidence is sufficient to safely do it.

cs.AI↗

arXiv2026

Listening with Attention: Entropy-Guided Explainability for Transformer-Based Audio Models

Transformer-based automatic speech recognition (ASR) models such as Whisper are highly accurate, but their predictions remain difficult to interpret. Existing explainable AI (XAI) methods often lack faithfulness and precise temporal grounding. We propose Listening with Entropy-guided Attention for Faithful explainability (LEAF-X), a model-intrinsic XAI framework for transformer-based ASR. LEAF-X combines entropy-guided attention weighting, multi-layer attention rollout, and optional causal ablations to identify low-entropy, high-impact heads and layers, producing sparse token-to-frame attributions. Unlike perturbation-based explainers or raw attention maps, LEAF-X exploits the internal structure of encoder-decoder and speech-augmented decoder-only models to generate explanations that better reflect model computation. Results show 32% improved faithfulness, 35-39% stronger locality/sparsity, and the most stable attributions, supporting more transparent and auditable ASR.

cs.SD↗

arXiv2026

PERSA: Reinforcement Learning for Professor-Style Personalized Feedback with LLMs

Large language models (LLMs) can provide automated feedback in educational settings, but aligning an LLMs style with a specific instructors tone while maintaining diagnostic correctness remains challenging. We ask how can we update an LLM for automated feedback generation to align with a target instructors style without sacrificing core knowledge? We study how Reinforcement Learning from Human Feedback (RLHF) can adapt a transformer-based LLM to generate programming feedback that matches a professors grading voice. We introduce PERSA, an RLHF pipeline that combines supervised fine-tuning on professor demonstrations, reward modeling from pairwise preferences, and Proximal Policy Optimization (PPO), while deliberately constraining learning to style-bearing components. Motivated by analyses of transformer internals, PERSA applies parameter efficient fine-tuning. It updates only the top transformer blocks and their feed-forward projections, minimizing global parameter drift while increasing stylistic controllability. We evaluate our proposed approach on three code-feedback benchmarks (APPS, PyFiXV, and CodeReviewQA) using complementary metrics for style alignment and fidelity. Across both Llama-3 and Gemma-2 backbones, PERSA delivers the strongest professor-style transfer while retaining correctness, for example on APPS, it boosts Style Alignment Score (SAC) to 96.2% (from 34.8% for Base) with Correctness Accuracy (CA) up to 100% on Llama-3, and Gemma-2. Overall, PERSA offers a practical route to personalized educational feedback by aligning both what it says (content correctness) and, crucially, how it says it (instructor-like tone and structure).

cs.AI↗

arXiv2026

VLA-Forget: Vision-Language-Action Unlearning for Embodied Foundation Models

Vision-language-action (VLA) models are emerging as embodied foundation models for robotic manipulation, but their deployment introduces a new unlearning challenge: removing unsafe, spurious, or privacy-sensitive behaviors without degrading perception, language grounding, and action control. In OpenVLA-style policies, behavior is produced through a fused visual encoder, a cross-modal projector, and a language backbone that predicts tokenized robot actions, so undesirable knowledge can be distributed across perception, alignment, and reasoning/action layers rather than confined to a single module. Consequently, partial unlearning applied only to the vision stack or only to the language backbone is often insufficient, while conventional unlearning baselines designed for standalone vision or language models may leave residual forgetting or incur unnecessary utility loss in embodied settings. We propose VLA-Forget, a hybrid unlearning framework that combines ratio-aware selective editing for perception and cross-modal specificity with layer-selective reasoning/action unlearning for utility-preserving forgetting. VLA-Forget jointly optimizes three objectives: targeted forgetting, perceptual preservation, and reasoning retention, through staged updates over the visual encoder, projector, and upper action-generating transformer blocks. Across forget-set behavior probes and retain-task evaluations, VLA-Forget improves forgetting efficacy by 10%, preserves perceptual specificity by 22%, retains reasoning and task success by 9%, and reduces post-quantization recovery by 55% relative to strong unlearning baselines.

cs.CV↗

arXiv2026

On the Independence Number of the Prime-Coprime Graph of a Finite Group

The prime-coprime graph $Θ(G)$ of a finite group $G$ is the simple graph with vertex set $G$, where two distinct elements are adjacent whenever the greatest common divisor of their orders is either $1$ or a prime. We characterize all finite groups $G$ for which $Θ(G)$ is a split graph. We establish a general lower bound for the independence number of $Θ(G)$ of an arbitrary finite group $G$. Moreover, we explicitly compute the independence number of $Θ(G)$ for several distinguished families of finite groups, including cyclic, dihedral, dicyclic, and semidihedral groups.

math.GR↗

arXiv2026

AC-MIL: Weakly Supervised Atrial LGE-MRI Quality Assessment via Adversarial Concept Disentanglement

High-quality Late Gadolinium Enhancement (LGE) MRI can be helpful for atrial fibrillation management, yet scan quality is frequently compromised by patient motion, irregular breathing, and suboptimal image acquisition timing. While Multiple Instance Learning (MIL) has emerged as a powerful tool for automated quality assessment under weak supervision, current state-of-the-art methods map localized visual evidence to a single, opaque global feature vector. This black box approach fails to provide actionable feedback on specific failure modes, obscuring whether a scan degrades due to motion blur, inadequate contrast, or a lack of anatomical context. In this paper, we propose Adversarial Concept-MIL (AC-MIL), a weakly supervised framework that decomposes global image quality into clinically defined radiological concepts using only volume-level supervision. To capture latent quality variations without entangling predefined concepts, our framework incorporates an unsupervised residual branch guided by an adversarial erasure mechanism to strictly prevent information leakage. Furthermore, we introduce a spatial diversity constraint that penalizes overlap between distinct concept attention maps, ensuring localized and interpretable feature extraction. Extensive experiments on a clinical dataset of atrial LGE-MRI volumes demonstrate that AC-MIL successfully opens the MIL black box, providing highly localized spatial concept maps that allow clinicians to pinpoint the specific causes of non-diagnostic scans. Crucially, our framework achieves this deep clinical transparency while maintaining highly competitive ordinal grading performance against existing baselines. Code to be released on acceptance.

cs.CV↗

arXiv2026

G-Drift MIA: Membership Inference via Gradient-Induced Feature Drift in LLMs

Large language models (LLMs) are trained on massive web-scale corpora, raising growing concerns about privacy and copyright. Membership inference attacks (MIAs) aim to determine whether a given example was used during training. Existing LLM MIAs largely rely on output probabilities or loss values and often perform only marginally better than random guessing when members and non-members are drawn from the same distribution. We introduce G-Drift MIA, a white-box membership inference method based on gradient-induced feature drift. Given a candidate (x,y), we apply a single targeted gradient-ascent step that increases its loss and measure the resulting changes in internal representations, including logits, hidden-layer activations, and projections onto fixed feature directions, before and after the update. These drift signals are used to train a lightweight logistic classifier that effectively separates members from non-members. Across multiple transformer-based LLMs and datasets derived from realistic MIA benchmarks, G-Drift substantially outperforms confidence-based, perplexity-based, and reference-based attacks. We further show that memorized training samples systematically exhibit smaller and more structured feature drift than non-members, providing a mechanistic link between gradient geometry, representation stability, and memorization. In general, our results demonstrate that small, controlled gradient interventions offer a practical tool for auditing the membership of training-data and assessing privacy risks in LLMs.

cs.LG↗

arXiv2026

CatRAG: Functor-Guided Structural Debiasing with Retrieval Augmentation for Fair LLMs

Large Language Models (LLMs) are deployed in high-stakes settings but can show demographic, gender, and geographic biases that undermine fairness and trust. Prior debiasing methods, including embedding-space projections, prompt-based steering, and causal interventions, often act at a single stage of the pipeline, resulting in incomplete mitigation and brittle utility trade-offs under distribution shifts. We propose CatRAG Debiasing, a dual-pronged framework that integrates functor with Retrieval-Augmented Generation (RAG) guided structural debiasing. The functor component leverages category-theoretic structure to induce a principled, structure-preserving projection that suppresses bias-associated directions in the embedding space while retaining task-relevant semantics. On the Bias Benchmark for Question Answering (BBQ) across three open-source LLMs (Meta Llama-3, OpenAI GPT-OSS, and Google Gemma-3), CatRAG achieves state-of-the-art results, improving accuracy by up to 40% over the corresponding base models and by more than 10% over prior debiasing methods, while reducing bias scores to near zero (from 60% for the base models) across gender, nationality, race, and intersectional subgroups.

cs.CL↗

arXiv2026

Embodied Foundation Models at the Edge: A Survey of Deployment Constraints and Mitigation Strategies

Deploying foundation models in embodied edge systems is fundamentally a systems problem, not just a problem of model compression. Real-time control must operate within strict size, weight, and power constraints, where memory traffic, compute latency, timing variability, and safety margins interact directly. The Deployment Gauntlet organizes these constraints into eight coupled barriers that determine whether embodied foundation models can run reliably in practice. Across representative edge workloads, autoregressive Vision-Language-Action policies are constrained primarily by memory bandwidth, whereas diffusion-based controllers are limited more by compute latency and sustained execution cost. Reliable deployment therefore depends on system-level co-design across memory, scheduling, communication, and model architecture, including decompositions that separate fast control from slower semantic reasoning.

cs.RO↗

arXiv2026

Unrolled Reconstruction with Integrated Super-Resolution for Accelerated 3D LGE MRI

Accelerated 3D late gadolinium enhancement (LGE) MRI requires robust reconstruction methods to recover thin atrial structures from undersampled k-space data. While unrolled model-based networks effectively integrate physics-driven data consistency with learned priors, they operate at the acquired resolution and may fail to fully recover high-frequency detail. We propose a hybrid unrolled reconstruction framework in which an Enhanced Deep Super-Resolution (EDSR) network replaces the proximal operator within each iteration of the optimization loop, enabling joint super-resolution enhancement and data consistency enforcement. The model is trained end-to-end on retrospectively undersampled preclinical 3D LGE datasets and compared against compressed sensing, Model-Based Deep Learning (MoDL), and self-guided Deep Image Prior (DIP) baselines. Across acceleration factors, the proposed method consistently improves PSNR and SSIM over standard unrolled reconstruction and better preserves fine cardiac structures, leading to improved LA (left atrium) segmentation performance. These results demonstrate that integrating super-resolution priors directly within model-based reconstruction provides measurable gains in accelerated 3D LGE MRI.

cs.CV↗

arXiv2026

RAZOR: Ratio-Aware Layer Editing for Targeted Unlearning in Vision Transformers and Diffusion Models

Transformer based diffusion and vision-language models have achieved remarkable success; yet, efficiently removing undesirable or sensitive information without retraining remains a central challenge for model safety and compliance. We introduce Ratio-Aware Zero/One-step Optimized Retentive unlearning (RAZOR), a lightweight, model-agnostic unlearning framework that generalizes forgetting updates to coordinated multi-layer and multi-head edits within transformer backbones. RAZOR identifies the most important layers and attention heads by measuring how much they contribute to forgetting the target data while preserving useful knowledge. Then, it updates these parts of the model using a carefully regularized rule to avoid harming overall performance. The set of edited components grows gradually, ensuring precise unlearning without over-editing or damaging unrelated capabilities. We evaluate RAZOR on CLIP, Stable Diffusion, and vision-language models (VLMs) using widely adopted unlearning benchmarks covering identity, style, and object erasure tasks. Our results show that RAZOR achieves highly accurate and stable forgetting, even under quantization. This approach offers stronger retention and better efficiency than prior methods. Notably, it also operates significant faster than conventional techniques. These results demonstrate that RAZOR is a practical and scalable solution for safe, adaptive unlearning in transformer-based vision models.

cs.CV↗

arXiv2026

Position: LLMs Must Use Functor-Based and RAG-Driven Bias Mitigation for Fairness

Biases in large language models (LLMs) often manifest as systematic distortions in associations between demographic attributes and professional or social roles, reinforcing harmful stereotypes across gender, ethnicity, and geography. This position paper advocates for addressing demographic and gender biases in LLMs through a dual-pronged methodology, integrating category-theoretic transformations and retrieval-augmented generation (RAG). Category theory provides a rigorous, structure-preserving mathematical framework that maps biased semantic domains to unbiased canonical forms via functors, ensuring bias elimination while preserving semantic integrity. Complementing this, RAG dynamically injects diverse, up-to-date external knowledge during inference, directly countering ingrained biases within model parameters. By combining structural debiasing through functor-based mappings and contextual grounding via RAG, we outline a comprehensive framework capable of delivering equitable and fair model outputs. Our synthesis of the current literature validates the efficacy of each approach individually, while addressing potential critiques demonstrates the robustness of this integrated strategy. Ensuring fairness in LLMs, therefore, demands both the mathematical rigor of category-theoretic transformations and the adaptability of retrieval augmentation.

cs.CL↗

arXiv2025

On prime coprime graphs of certain finite groups

The prime coprime graph $Θ(G)$ of a finite group $G$ is the graph whose vertex set is $G$ and any two distinct vertices are adjacent if the greatest common divisor of their orders is either $1$ or a prime. In this paper, we investigate Hamiltonicity, clique number, and vertex degree of $Θ(G)$ for cyclic, dihedral, and dicyclic groups $G$. We establish that $Θ(G)$ admits a $(k,1)$-partition for cyclic, dihedral, and dicyclic groups $G$ of specified orders.

math.GR↗