arXiv subjects

Anuj Kumar

Publications and source records attributed to Anuj Kumar.

At least 37 records · Page 2Linked to original sources

arXiv2025

On well-posedness of a mildly dissipative family of active scalar equations in borderline Sobolev spaces

This paper considers a family of active scalar equations which modify the generalized surface quasi-geostrophic (gSQG) equations through its constitutive law and a dissipative perturbation. These modifications are characteristically mild in the sense that they are logarithmic. The problem of well posedness, in the sense of Hadamard, is then studied in a borderline setting of regularity in analogy to the scaling-critical spaces of the gSQG equations. A novelty of the system considered is the nuanced form of smoothing provided by the proposed mild form of dissipation, which is able to support global well-posedness at the Euler endpoint, but in a setting where the inviscid counterpart is known to be ill-posed. A novelty of the analysis lies in the simultaneous treatment of modifications in the constitutive law, dissipative mechanism, and functional setting, which the existing literature has typically treated separately. A putatively sharp relation is identified between each of the distinct system-modifiers that is consistent with previous studies that considered these modifications in isolation. This unified perspective is afforded by the introduction of a linear model equation, referred to as the protean system, that successfully incorporates the more delicate commutator structure collectively possessed by the gSQG family and upon which each facet of well-posedness can effectively be reduced to its study.

math.AP↗

arXiv2025

WearVQA: A Visual Question Answering Benchmark for Wearables in Egocentric Authentic Real-world scenarios

We introduce WearVQA, the first benchmark specifically designed to evaluate the Visual Question Answering (VQA) capabilities of multi-model AI assistant on wearable devices like smart glasses. Unlike prior benchmarks that focus on high-quality, third-person imagery, WearVQA reflects the unique challenges of ego-centric interaction-where visual inputs may be occluded, poorly lit, unzoomed, or blurry, and questions are grounded in realistic wearable use cases. The benchmark comprises 2,520 carefully curated image-question-answer triplets, spanning 7 diverse image domains including both text-centric and general scenes, 10 cognitive task types ranging from basic recognition to various forms of reasoning, and 6 common wearables-specific image quality issues. All questions are designed to be answerable using only the visual input and common senses. WearVQA is paired with a rigorous LLM-as-a-judge evaluation framework with 96% labeling accuracy. Open-source and proprietary multi-model LLMs achieved a QA accuracy as low as 24-52% on WearVQA, with substantial drops on lower-quality images and reasoning-heavy tasks. These observations position WearVQA as a comprehensive and challenging benchmark for guiding technical advancement towards robust, real-world multi-model wearables AI systems.

cs.AI↗

arXiv2025

MobileLLM-Pro Technical Report

Efficient on-device language models around 1 billion parameters are essential for powering low-latency AI applications on mobile and wearable devices. However, achieving strong performance in this model class, while supporting long context windows and practical deployment remains a significant challenge. We introduce MobileLLM-Pro, a 1-billion-parameter language model optimized for on-device deployment. MobileLLM-Pro achieves state-of-the-art results across 11 standard benchmarks, significantly outperforming both Gemma 3-1B and Llama 3.2-1B, while supporting context windows of up to 128,000 tokens and showing only minor performance regressions at 4-bit quantization. These improvements are enabled by four core innovations: (1) implicit positional distillation, a novel technique that effectively instills long-context capabilities through knowledge distillation; (2) a specialist model merging framework that fuses multiple domain experts into a compact model without parameter growth; (3) simulation-driven data mixing using utility estimation; and (4) 4-bit quantization-aware training with self-distillation. We release our model weights and code to support future research in efficient on-device language models.

cs.LG↗

arXiv2025

CRAG-MM: Multi-modal Multi-turn Comprehensive RAG Benchmark

Wearable devices such as smart glasses are transforming the way people interact with their surroundings, enabling users to seek information regarding entities in their view. Multi-Modal Retrieval-Augmented Generation (MM-RAG) plays a key role in supporting such questions, yet there is still no comprehensive benchmark for this task, especially regarding wearables scenarios. To fill this gap, we present CRAG-MM -- a Comprehensive RAG benchmark for Multi-modal Multi-turn conversations. CRAG-MM contains a diverse set of 6.5K (image, question, answer) triplets and 2K visual-based multi-turn conversations across 13 domains, including 6.2K egocentric images designed to mimic captures from wearable devices. We carefully constructed the questions to reflect real-world scenarios and challenges, including five types of image-quality issues, six question types, varying entity popularity, differing information dynamism, and different conversation turns. We design three tasks: single-source augmentation, multi-source augmentation, and multi-turn conversations -- each paired with an associated retrieval corpus and APIs for both image-KG retrieval and webpage retrieval. Our evaluation shows that straightforward RAG approaches achieve only 32% and 43% truthfulness on CRAG-MM single- and multi-turn QA, respectively, whereas state-of-the-art industry solutions have similar quality (32%/45%), underscoring ample room for improvement. The benchmark has hosted KDD Cup 2025, attracting about 1K participants and 5K submissions, with winning solutions improving baseline performance by 28%, highlighting its early impact on advancing the field.

cs.CV↗

arXiv2025

VisualLens: Personalization through Task-Agnostic Visual History

Existing recommendation systems either rely on user interaction logs, such as online shopping history for shopping recommendations, or focus on text signals. However, item-based histories are not always accessible, and are not generalizable for multimodal recommendation. We hypothesize that a user's visual history -- comprising images from daily life -- can offer rich, task-agnostic insights into their interests and preferences, and thus be leveraged for effective personalization. To this end, we propose VisualLens, a novel framework that leverages multimodal large language models (MLLMs) to enable personalization using task-agnostic visual history. VisualLens extracts, filters, and refines a spectrum user profile from the visual history to support personalized recommendation. We created two new benchmarks, Google-Review-V and Yelp-V, with task-agnostic visual histories, and show that VisualLens improves over state-of-the-art item-based multimodal recommendations by 5-10% on Hit@3, and outperforms GPT-4o by 2-5%. Further analysis shows that VisualLens is robust across varying history lengths and excels at adapting to both longer histories and unseen content categories.

cs.CV↗

arXiv2025

On Turbulent Behavior of the Generalized Surface Quasigeostrophic Equations

Turbulent behavior of the two-parameter family of generalized surface quasigeostrophic equations is examined both rigorously and numerically. We adapt a cascade mechanism argument to derive an energy spectrum that scales as $κ^{2β/3-3}$ where $β$ controls the regularity of the velocity ($β=1$ in the special case of the SQG). Direct numerical simulations indicate that this fits better than $κ^{β/3-3}$ which was derived in earlier work. Guided by earlier work on the 2D Navier-Stokes equations, we prove a certain condition implies a direct cascade of enstrophy, as well as an upper bound on the enstrophy dissipation rate, and sharp bounds on a dissipation wavenumber. The dependence of these rigorous results on the two parameters is demonstrated numerically.

physics.flu-dyn↗

arXiv2025

AssoMem: Scalable Memory QA with Multi-Signal Associative Retrieval

Accurate recall from large scale memories remains a core challenge for memory augmented AI assistants performing question answering (QA), especially in similarity dense scenarios where existing methods mainly rely on semantic distance to the query for retrieval. Inspired by how humans link information associatively, we propose AssoMem, a novel framework constructing an associative memory graph that anchors dialogue utterances to automatically extracted clues. This structure provides a rich organizational view of the conversational context and facilitates importance aware ranking. Further, AssoMem integrates multi-dimensional retrieval signals-relevance, importance, and temporal alignment using an adaptive mutual information (MI) driven fusion strategy. Extensive experiments across three benchmarks and a newly introduced dataset, MeetingQA, demonstrate that AssoMem consistently outperforms SOTA baselines, verifying its superiority in context-aware memory recall.

cs.CL↗

arXiv2025

Statistical Estimates for 2D stochastic Navier-Stokes Equations

The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{E} [\varepsilon ]$ and enstrophy dissipation rates $\mathbb{E} [χ] $ for 2D flows sustained by a variety of stochastic driving forces. We show that $$\mathbb{E} [ \varepsilon ] \rightarrow 0 \hspace{0.5cm}\mbox{and} \hspace{0.5cm} \mathbb{E} [ χ] \lesssim \mathcal{O}(1)$$ in the inviscid limit, consistent with the dual-cascade in 2D turbulence.

physics.flu-dyn↗

arXiv2025

Stream RAG: Instant and Accurate Spoken Dialogue Systems with Streaming Tool Usage

End-to-end speech-in speech-out dialogue systems are emerging as a powerful alternative to traditional ASR-LLM-TTS pipelines, generating more natural, expressive responses with significantly lower latency. However, these systems remain prone to hallucinations due to limited factual grounding. While text-based dialogue systems address this challenge by integrating tools such as web search and knowledge graph APIs, we introduce the first approach to extend tool use directly into speech-in speech-out systems. A key challenge is that tool integration substantially increases response latency, disrupting conversational flow. To mitigate this, we propose Streaming Retrieval-Augmented Generation (Streaming RAG), a novel framework that reduces user-perceived latency by predicting tool queries in parallel with user speech, even before the user finishes speaking. Specifically, we develop a post-training pipeline that teaches the model when to issue tool calls during ongoing speech and how to generate spoken summaries that fuse audio queries with retrieved text results, thereby improving both accuracy and responsiveness. To evaluate our approach, we construct AudioCRAG, a benchmark created by converting queries from the publicly available CRAG dataset into speech form. Experimental results demonstrate that our streaming RAG approach increases QA accuracy by up to 200% relative (from 11.1% to 34.2% absolute) and further enhances user experience by reducing tool use latency by 20%. Importantly, our streaming RAG approach is modality-agnostic and can be applied equally to typed input, paving the way for more agentic, real-time AI assistants.

cs.CL↗

arXiv2025

Knowledge Extraction on Semi-Structured Content: Does It Remain Relevant for Question Answering in the Era of LLMs?

The advent of Large Language Models (LLMs) has significantly advanced web-based Question Answering (QA) systems over semi-structured content, raising questions about the continued utility of knowledge extraction for question answering. This paper investigates the value of triple extraction in this new paradigm by extending an existing benchmark with knowledge extraction annotations and evaluating commercial and open-source LLMs of varying sizes. Our results show that web-scale knowledge extraction remains a challenging task for LLMs. Despite achieving high QA accuracy, LLMs can still benefit from knowledge extraction, through augmentation with extracted triples and multi-task learning. These findings provide insights into the evolving role of knowledge triple extraction in web-based QA and highlight strategies for maximizing LLM effectiveness across different model sizes and resource settings.

cs.CL↗

arXiv2025

Memory-QA: Answering Recall Questions Based on Multimodal Memories

We introduce Memory-QA, a novel real-world task that involves answering recall questions about visual content from previously stored multimodal memories. This task poses unique challenges, including the creation of task-oriented memories, the effective utilization of temporal and location information within memories, and the ability to draw upon multiple memories to answer a recall question. To address these challenges, we propose a comprehensive pipeline, Pensieve, integrating memory-specific augmentation, time- and location-aware multi-signal retrieval, and multi-memory QA fine-tuning. We created a multimodal benchmark to illustrate various real challenges in this task, and show the superior performance of Pensieve over state-of-the-art solutions (up to 14% on QA accuracy).

cs.AI↗

arXiv2025

PrismRAG: Boosting RAG Factuality with Distractor Resilience and Strategized Reasoning

Retrieval-augmented generation (RAG) often falls short when retrieved context includes confusing semi-relevant passages, or when answering questions require deep contextual understanding and reasoning. We propose an efficient fine-tuning framework, called PrismRAG, that (i) trains the model with distractor-aware QA pairs mixing gold evidence with subtle distractor passages, and (ii) instills reasoning-centric habits that make the LLM plan, rationalize, and synthesize without relying on extensive human engineered instructions. Evaluated across 12 open-book RAG QA benchmarks spanning diverse application domains and scenarios, PrismRAG improves average factuality by 5.4%, outperforming state-of-the-art solutions.

cs.CL↗

arXiv2025

Proactive Assistant Dialogue Generation from Streaming Egocentric Videos

Recent advances in conversational AI have been substantial, but developing real-time systems for perceptual task guidance remains challenging. These systems must provide interactive, proactive assistance based on streaming visual inputs, yet their development is constrained by the costly and labor-intensive process of data collection and system evaluation. To address these limitations, we present a comprehensive framework with three key contributions. First, we introduce a novel data curation pipeline that synthesizes dialogues from annotated egocentric videos, resulting in \dataset, a large-scale synthetic dialogue dataset spanning multiple domains. Second, we develop a suite of automatic evaluation metrics, validated through extensive human studies. Third, we propose an end-to-end model that processes streaming video inputs to generate contextually appropriate responses, incorporating novel techniques for handling data imbalance and long-duration videos. This work lays the foundation for developing real-time, proactive AI assistants capable of guiding users through diverse tasks. Project page: https://pro-assist.github.io/

cs.AI↗

arXiv2025

A simple proof of linear instability of shear flows with application to vortex sheets

We consider the construction of linear instability of parallel shear flows, which was developed by Zhiwu Lin (SIAM J. Math. Anal. 35(2), 2003). We give an alternative simple proof in Sobolev setting of the problem, which exposes the mathematical role of the Plemelj-Sochocki formula in the emergence of the instability, as well as does not require the cone condition. Moreover, we localize this approach to obtain an approximation of the Kelvin-Helmholtz instability of a flat vortex sheet.

math.AP↗

arXiv2025

A convex integration scheme for the continuity equation past the Sobolev embedding threshold

We introduce a convex integration scheme for the continuity equation in the context of the Di Perna-Lions theory that allows to build incompressible vector fields in $C_{t}W^{1,p}_x$ and nonunique solutions in $C_{t} L^{q}_x$ for any $p,q$ with $\frac{1}{p} + \frac{1}{q} > 1 + \frac{1}{d}- δ$ for some $δ>0$. This improves the previous bound, corresponding to $δ=0$, or equivalently $q' > p^*$, obtained with convex integration so far, and critical for those schemes in view of the Sobolev embedding that guarantees that solutions are distributional in the opposite range.

math.AP↗

arXiv2025

Upper bounds on the dimension of the global attractor of the 2D Navier-Stokes equations on the $β-$plane

This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $β$-plane. Previous results in this setting by M.A.H. Al-Jaboori and D. Wirosoetisno (2011) had proved that the global attractor collapses to a single point that depends only the longitudinal coordinate, i.e., zonal flow, when the rotation is sufficiently fast. However, an explicit quantification of the complexity of the global attractor in terms of $β$ had remained open. In this paper, such estimates are established which are valid across a wide regime of rotation rates and are consistent with the dynamically degenerate regime previously identified. Additionally, a decomposition of solutions is established detailing the asymptotic behavior of the solutions in the limit of large rotation.

math.AP↗

arXiv2024

CRAG -- Comprehensive RAG Benchmark

Retrieval-Augmented Generation (RAG) has recently emerged as a promising solution to alleviate Large Language Model (LLM)'s deficiency in lack of knowledge. Existing RAG datasets, however, do not adequately represent the diverse and dynamic nature of real-world Question Answering (QA) tasks. To bridge this gap, we introduce the Comprehensive RAG Benchmark (CRAG), a factual question answering benchmark of 4,409 question-answer pairs and mock APIs to simulate web and Knowledge Graph (KG) search. CRAG is designed to encapsulate a diverse array of questions across five domains and eight question categories, reflecting varied entity popularity from popular to long-tail, and temporal dynamisms ranging from years to seconds. Our evaluation of this benchmark highlights the gap to fully trustworthy QA. Whereas most advanced LLMs achieve <=34% accuracy on CRAG, adding RAG in a straightforward manner improves the accuracy only to 44%. State-of-the-art industry RAG solutions only answer 63% of questions without any hallucination. CRAG also reveals much lower accuracy in answering questions regarding facts with higher dynamism, lower popularity, or higher complexity, suggesting future research directions. The CRAG benchmark laid the groundwork for a KDD Cup 2024 challenge and attracted thousands of participants and submissions. We commit to maintaining CRAG to serve research communities in advancing RAG solutions and general QA solutions. CRAG is available at https://github.com/facebookresearch/CRAG/.

cs.CL↗

arXiv2024

EgoQR: Efficient QR Code Reading in Egocentric Settings

QR codes have become ubiquitous in daily life, enabling rapid information exchange. With the increasing adoption of smart wearable devices, there is a need for efficient, and friction-less QR code reading capabilities from Egocentric point-of-views. However, adapting existing phone-based QR code readers to egocentric images poses significant challenges. Code reading from egocentric images bring unique challenges such as wide field-of-view, code distortion and lack of visual feedback as compared to phones where users can adjust the position and framing. Furthermore, wearable devices impose constraints on resources like compute, power and memory. To address these challenges, we present EgoQR, a novel system for reading QR codes from egocentric images, and is well suited for deployment on wearable devices. Our approach consists of two primary components: detection and decoding, designed to operate on high-resolution images on the device with minimal power consumption and added latency. The detection component efficiently locates potential QR codes within the image, while our enhanced decoding component extracts and interprets the encoded information. We incorporate innovative techniques to handle the specific challenges of egocentric imagery, such as varying perspectives, wider field of view, and motion blur. We evaluate our approach on a dataset of egocentric images, demonstrating 34% improvement in reading the code compared to an existing state of the art QR code readers.

cs.CV↗