arXiv subjects

Anuj Kumar

Publications and source records attributed to Anuj Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Existence of weak solutions to the generalized SQG equations in Sobolev spaces

We consider the two-dimensional dissipative generalized surface quasi-geostrophic equations given by \[\partial_t \theta+u\cdot \nabla \theta+\nu (-\Delta)^{\alpha}\theta=0,\quad u=\nabla^{\perp}\Lambda^{\beta-2}\theta\] and establish global existence of weak solutions with initial data in $\dot{H}^{\frac{\beta}{2}-1}(\mathbb{R}^2)$. Our result extends the framework of Marchand's solutions (Comm. Math. Phys. 277 (2008), no. 1, 45-67) to this larger family of active scalar equations.

math.AP↗

arXiv2026

Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processing

Recent mesh-based simulation advances have, in no small part, relied on neural surrogates of two distinct families: global models that route information through a small set of latent tokens, and local models that perform message passing across mesh edges. Consistent with both classes is the inability to perform beyond low-dimensional problems and small-scale or oversimplified meshes, the simulation regimes where industrial problems reside. Our work shows this explicitly and presents a unified formulation. In global approaches, latent-token attention acts as a spatial low-pass filter, while local message passing lacks the global reach necessary to propagate information across large mesh spaces. Viewed through the error, the two operators are the halves of a multigrid cycle: one corrects errors at the lower end of the spectrum, the other at the higher end, and neither can do the other's job. We introduce Read-Write-Relax (RWR), which interleaves latent attention with message-passing relaxation under a unified formulation. The interleaved processor lowers error across the entire spectrum, making RWR the most accurate model in nearly every comparison across our industrial and public benchmarks. It is also markedly data-efficient in the scarce-data regimes, accurate on the engineering quantities of interest, and scales full-field predictions to challenging, large-scale problems.

cs.LG↗

arXiv2026

MoE-ViE: Mixture of Experts Vision Encoder for Efficient Image and Video Understanding

Vision encoders are a critical component of vision-language models, and scaling their capacity effectively improves performance. However, dense scaling increases compute cost and inference latency. Mixture-of-Experts (MoE) architectures offer a compelling alternative, having enabled efficient scaling in LLMs, yet the MoE design space for CLIP-style vision encoders remains underexplored at State-of-the-Art (SOTA) levels. In this work, we systematically study MoE designs for vision encoder scaling and find that fine-grained MoE topologies yield substantial gains over both dense and standard MoE counterparts. We further propose an auxiliary-loss-free balancing variant for better expert utilization, and design a specialized MoE kernel to mitigate inference latency overhead. To enhance video capabilities while preserving image knowledge, we introduce frame-level distillation paired with a novel freezing mechanism. We pretrain a series of Mixture-of-Experts Vision Encoders (MoE-ViE) across a range of sizes, all consistently outperforming their dense counterparts. Our largest model matches the zero-shot performance of a SOTA encoder 1.7x its size at 76% of its latency. When aligned with an LLM, MoE-ViE surpasses all compared encoders on image and video benchmarks, including those with up to 5x more activated parameters. Code is available at https://github.com/facebookresearch/moe_vie.

cs.CV↗

arXiv2026

Inviscid and fast rotation limit for dispersive generalized SQG equations

We consider the dissipative generalized surface quasi-geostrophic equations with a dispersive forcing term and study the behavior of solutions in the limit of vanishing viscosity. Using the approach of relative energy inequality, we prove convergence results in different dispersive regimes that extend the results obtained by Kosloff et al. (Appl. Math. Lett. (2019) 88 243-249) to more singular active scalar equations.

math.AP↗

arXiv2026

R3D: Quantitative 3D Spatial Reasoning for Egocentric Wearables

Quantitative 3D spatial reasoning from egocentric RGB-D video is a critical capability for next-generation wearable assistants. Yet existing benchmarks do not reflect the challenges of handling (1) natural egocentric video, (2) posed RGB-D video inputs, and (3) challenging quantitative 3D spatial reasoning Q&A. To fill this gap, we introduce R3D-Bench (Reasoning in 3D), a benchmark of 3,033 quantitative spatial reasoning questions across 15 types -- spanning multiple-choice, distance-based, and volumetric reasoning questions -- built on top of 57 egocentric video sequences from Aria Digital Twin. To set a strong baseline on this dataset, we introduce R3D, a model-agnostic spatial tool-calling framework. In contrast to existing approaches that directly embed 3D information into the model's input representation, R3D constructs a 3D scene from video using segmentation and depth-lifted object representations. It provides this information to an LLM through eight composable spatial tools. On R3D-Bench, R3D with Qwen3-VL 235B achieves 73.5% mean relative accuracy, substantially outperforming the best depth-enabled baseline (CuTR+Tools, 61.9%) and the best RGB-only baseline (Gemini 3 Flash, 46.5%).

cs.CV↗

arXiv2026

BluTrain: A C++/CUDA Framework for AI Systems

Progress in deep learning is, at scale, more a matter of systems engineering than of modelling: the behaviour of a model in training (its throughput, its memory footprint, and the numerical fidelity of the result) is determined less by the architecture itself than by how that architecture is expressed on the hardware. To achieve absolute control over this hardware expression while abstracting away systems complexity to make modelling seamless and eliminating the need for repetitive orchestration logic, BluTrain was architected from first principles as a robust, lightweight, and architecture-general training framework in standard C++ and the core CUDA programming model. Every layer is implemented natively: a typed tensor module with reverse-mode autograd, a linear-algebra library, a caching allocator, a multi-mode distributed-execution module, and an MLIR-based deep-learning compiler. In formal evaluations training a 124M-parameter GPT-2 baseline in FP32 on an 8-GPU 6000 Ada system, BluTrain outperforms industry-standard baselines in both throughput (sustaining an average of 407K tokens/s versus PyTorch's 395K tokens/s) and memory efficiency (achieving up to a 22% footprint reduction), while strictly preserving numerical fidelity and converging to a marginally lower final validation loss. With every layer explicitly open to native tuning, the performance ceiling is the framework's own to raise.

cs.AI↗

arXiv2026

Plan, Watch, Recover: A Benchmark and Architectures for Proactive Procedural Assistance

We envision a proactive multi-modal assistant system which gives users real-time step-by-step guidance on a procedural task, autonomously deciding \textit{when} to interrupt, and \textit{how} to coach. However, progress is limited by the absence of large-scale, cross-domain benchmarks that reflect realistic conditions, particularly the common case in which users deviate from the expected step sequence. We address this gap with four contributions: \textbf{(1)}~we release \textbf{EgoProactive}, a large-scale wearable-egocentric dataset for proactive procedural assistance with explicit Out-of-Plan (OOP) annotations and recovery steps; \textbf{(2)}~we augment five established benchmarks (Ego4D, EPIC-KITCHENS, EgoExo4D, HoloAssist, HowTo100M) into \textbf{Pro\textsuperscript{2}Bench} under a unified proactive-guidance schema; \textbf{(3)}~we propose a \textbf{decoupled planner--interaction architecture} specialized for procedural state, visual cues, and recovery injection; \textbf{(4)}~we introduce a post-training recipe that transfers across model families, validated by cross-backbone replication on Llama~4 and Qwen-3.6-VL. In extensive experiments, our trained Llama-4 system substantially improves objective intervention quality over strong proprietary baselines (Claude Opus~4.6, Gemini~3.1~Pro, GPT~5.2) and open-weight baselines (Qwen3~VL~235B) baselines across all six datasets. Oracle-plan experiments further show that, when plan quality is controlled, the trained duplex model produces high-quality guidance and large gains on Out-of-Plan recovery.

cs.CV↗

arXiv2026

SaliMory: Orchestrating Cognitive Memory for Conversational Agents

Conversational agents that serve as lifelong companions must maintain persistent memory across all interactions. However, simply expanding context windows with raw retrieval degrades reasoning quality, while training memory agents via standard reinforcement learning creates a severe credit assignment bottleneck in a multi-stage pipeline. To solve this, we introduce SALIMORY, a framework that trains a single language model to manage a cognitively-structured memory-spanning user facts, preferences, and working memory. By introducing a hierarchical stage-wise process reward and reward-decomposed contrastive refinement, SALIMORY provides isolated supervision for distinct memory operations (selective filtering, consolidation, and cue-driven recall) end-to-end. SALIMORY cuts memory-attributed failures by one-third, outperforms the state-of-the-art by over 10% in end-to-end accuracy, and more than doubles the Good Personalization rate.

cs.CL↗

arXiv2026

Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition

We introduce "Courant", a Perceiver-based encoder-processor-decoder surrogate model that has latent features exhibiting adaptive specialization and local support in the physical space, enabling functionality akin to an adaptive hp-refinement scheme, an attribute that is highly desirable in traditional numerical solvers and scientific machine learning broadly. The proposed architecture combines a shared random Fourier feature coordinate embedding, state-adapted latent queries, and a light-weight decoder. Courant is trained end-to-end with steady or transient simulation data and only a standard L_2 prediction loss in the physical space, achieving competitive accuracy on benchmarks. We demonstrate that Courant's inductive biases yield latents that are interpretable by design: they develop multiscale geometric specialization in the simulation domain and track coherent structures in the time-dependent case, acting analogously to time-evolving spatial basis functions and allowing for decoding a compact, geometry-anchored, partition-of-unity-like decomposition of the simulated field.

cs.LG↗

arXiv2026

Mixing and Small-Scale Formation in a Passive Divergence-Free Vector Field

We study mixing for a divergence-free passive vector field $u$ transported by another divergence-free vector field $U$, where $u$ evolves according to $ \partial_t u + (U \cdot \nabla) u + \nabla p = 0.$ In recent years, a lot of attention has been given to the question of optimal mixing in the scalar case, where there is a Sobolev constraint on the advecting velocity. In the vector setting considered here, however, the pressure term introduces substantial difficulties, since the simple Lagrangian perspective available in the scalar case is no longer applicable. In this paper, we investigate mixing on a torus $\mathbb{T}^d$ under the assumption that the field $U$ satisfies $ \|U(t)\|_{W^{1,q}} \leq C $ and we quantify mixing through the decay of the homogeneous $ H^{-\alpha}$ norm of $u$. We start with establishing conditions on $U$ that guarantee existence and uniqueness of solutions. We then derive lower bounds on the mixing rate for various ranges of $q$ and $\alpha$. In addition, we carry out numerical simulations of mixing by choosing, at each time instant, a field $U$ that maximizes the instantaneous decay of the $ H^{-\alpha}$ norm. These simulations provide evidence that the optimal mixing rate is at least exponential in time. More broadly, we view the present model and its diffusive analogue, as a useful framework for probing mechanisms of small-scale formation in divergence-free vector fields and for formulating simplified versions of open questions related to the incompressible Euler and Navier--Stokes equations.

math.AP↗

arXiv2026

Asymptotic study of supercritical generalized SQG equations in critical Sobolev spaces

We study the long time behavior of regular solutions of the supercritical gSQG equations in the fully nonlinear regime. More precisely, under the assumption of small initial data in the critical Sobolev norm, we prove the existence of the unique global solution that satisfies the energy inequality (1.3) and for which the critical norm $||{\theta(t)}||_{H^{1+\beta-2\alpha}}$ decays to 0 as time goes to infinity.

math.AP↗

arXiv2026

Aligning Paralinguistic Understanding and Generation in Speech LLMs via Multi-Task Reinforcement Learning

Speech large language models (LLMs) observe paralinguistic cues such as prosody, emotion, and non-verbal sounds--crucial for intent understanding. However, leveraging these cues faces challenges: limited training data, annotation difficulty, and models exploiting lexical shortcuts over paralinguistic signals. We propose multi-task reinforcement learning (RL) with chain-of-thought prompting that elicits explicit affective reasoning. To address data scarcity, we introduce a paralinguistics-aware speech LLM (PALLM) that jointly optimizes sentiment classification from audio and paralinguistics-aware response generation via a two-stage pipeline. Experiments demonstrate that our approach improves paralinguistics understanding over both supervised baselines and strong proprietary models (Gemini-2.5-Pro, GPT-4o-audio) by 8-12% on Expresso, IEMOCAP, and RAVDESS. The results show that modeling paralinguistic reasoning with multi-task RL is crucial for building emotionally intelligent speech LLMs.

cs.CL↗

arXiv2026

Pixel-Grounded Retrieval for Knowledgeable Large Multimodal Models

Visual Question Answering (VQA) often requires coupling fine-grained perception with factual knowledge beyond the input image. Prior multimodal Retrieval-Augmented Generation (MM-RAG) systems improve factual grounding but lack an internal policy for when and how to retrieve. We propose PixSearch, the first end-to-end Segmenting Large Multimodal Model (LMM) that unifies region-level perception and retrieval-augmented reasoning. During encoding, PixSearch emits tokens to trigger retrieval, selects query modalities (text, image, or region), and generates pixel-level masks that directly serve as visual queries, eliminating the reliance on modular pipelines (detectors, segmenters, captioners, etc.). A two-stage supervised fine-tuning regimen with search-interleaved supervision teaches retrieval timing and query selection while preserving segmentation ability. On egocentric and entity-centric VQA benchmarks, PixSearch substantially improves factual consistency and generalization, yielding a 19.7% relative gain in accuracy on CRAG-MM compared to whole image retrieval, while retaining competitive reasoning performance on various VQA and text-only QA tasks.

cs.CV↗

arXiv2026

Sharpness of the Osgood Criterion for the Continuity Equation with Divergence-free Vector Fields

For any modulus of continuity $\omega$ that fails the Osgood condition, we construct a divergence-free velocity field $v \in C_t C^\omega_x$ for which the associated ODE admits at least two distinct flow maps. In other words, non-uniqueness does not occur merely for a single or even finitely many trajectories, but instead on a set of initial conditions $E$ of positive Lebesgue measure. In fact, the set $E$ has full measure inside a cube where the construction is supported. Moreover, we also construct a divergence-free velocity field $v \in C_{t}C^\omega_x$ for which the associated continuity equation admits two distinct solutions $\mu^1$ and $\mu^2$ which are absolutely continuous with respect to Lebesgue measure for almost every time, and start from the same initial datum $\bar \mu \ll \mathscr{L}^{d}$. Our construction introduces two novel ideas: (i) We introduce the notion of "parallelization", where at each time, the velocity field consists of simultaneous motion across multiple nested spatial scales. This differs from most explicit constructions in the literature on mixing or anomalous dissipation, where the velocity on different scales acts at separate times. This is crucial to cover the whole class of non-Osgood moduli of continuity. (ii) Inspired by a recent work of Bru\`e, Colombo and Kumar, we develop a new fixed-point framework that naturally incorporates the parallelization mechanism. This framework allows us to construct anomalous solutions of the continuity equation that belong to $L^1(\mathbb{R}^d)$ a.e. in time.

math.AP↗

arXiv2025

WearVox: An Egocentric Multichannel Voice Assistant Benchmark for Wearables

Wearable devices such as AI glasses are transforming voice assistants into always-available, hands-free collaborators that integrate seamlessly with daily life, but they also introduce challenges like egocentric audio affected by motion and noise, rapid micro-interactions, and the need to distinguish device-directed speech from background conversations. Existing benchmarks largely overlook these complexities, focusing instead on clean or generic conversational audio. To bridge this gap, we present WearVox, the first benchmark designed to rigorously evaluate voice assistants in realistic wearable scenarios. WearVox comprises 3,842 multi-channel, egocentric audio recordings collected via AI glasses across five diverse tasks including Search-Grounded QA, Closed-Book QA, Side-Talk Rejection, Tool Calling, and Speech Translation, spanning a wide range of indoor and outdoor environments and acoustic conditions. Each recording is accompanied by rich metadata, enabling nuanced analysis of model performance under real-world constraints. We benchmark leading proprietary and open-source speech Large Language Models (SLLMs) and find that most real-time SLLMs achieve accuracies on WearVox ranging from 29% to 59%, with substantial performance degradation on noisy outdoor audio, underscoring the difficulty and realism of the benchmark. Additionally, we conduct a case study with two new SLLMs that perform inference with single-channel and multi-channel audio, demonstrating that multi-channel audio inputs significantly enhance model robustness to environmental noise and improve discrimination between device-directed and background speech. Our results highlight the critical importance of spatial audio cues for context-aware voice assistants and establish WearVox as a comprehensive testbed for advancing wearable voice AI research.

cs.CL↗

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↗