Abstract
Large Language Models (LLMs) have demonstrated remarkable capabilities in natural language understanding and generation, and their integration with Extended Reality (XR) is poised to transform how users interact with immersive environments. This survey provides a comprehensive review of recent developments at the intersection of LLMs and XR, offering a structured organization of research along both technical and application dimensions. We propose a taxonomy of LLM-enhanced XR systems centered on key technical paradigms -- such as interactive agent control, XR development toolkits, and generative scene synthesis -- and discuss how these paradigms enable novel capabilities in XR. In parallel, we examine how LLM-driven techniques support practical XR applications across diverse domains, including immersive education, clinical healthcare, and industrial manufacturing. By connecting these technical paradigms with application frontiers, our survey highlights current trends, delineates design considerations, and identifies open challenges in building LLM-augmented XR systems. This work provides insights that can guide researchers and practitioners in advancing the state of the art in intelligent XR experiences.

Abstract
Over the past few years, the size of language models has grown exponentially, as has the computational cost to train these large models. This rapid growth has motivated researchers to develop new techniques aimed at enhancing the efficiency of the training process. Despite these advancements, optimally predicting the model size or allocating optimal resources remains a challenge. Several efforts have addressed the challenge by proposing different scaling laws, but almost all of them are architecture-specific (dense or sparse). In this work we revisit existing scaling laws and propose a generalized scaling law to provide a unified framework that is applicable to both dense and sparse large language models. We evaluate and compare our proposed scaling law with existing scaling laws to demonstrate its effectiveness.

Abstract
A fundamental challenge in the theory of deep learning is to understand whether gradient-based training in high-dimensional parameter spaces can be captured by simpler, lower-dimensional structures, leading to so-called implicit bias. As a stepping stone, we study when a gradient flow on a high-dimensional variable $\theta$ implies an intrinsic gradient flow on a lower-dimensional variable $z = \phi(\theta)$, for an architecture-related function $\phi$. We express a so-called intrinsic dynamic property and show how it is related to the study of conservation laws associated with the factorization $\phi$. This leads to a simple criterion based on the inclusion of kernels of linear maps which yields a necessary condition for this property to hold. We then apply our theory to general ReLU networks of arbitrary depth and show that, for any initialization, it is possible to rewrite the flow as an intrinsic dynamic in a lower dimension that depends only on $z$ and the initialization, when $\phi$ is the so-called path-lifting. In the case of linear networks with $\phi$ the product of weight matrices, so-called balanced initializations are also known to enable such a dimensionality reduction; we generalize this result to a broader class of {\em relaxed balanced} initializations, showing that, in certain configurations, these are the \emph{only} initializations that ensure the intrinsic dynamic property. Finally, for the linear neural ODE associated with the limit of infinitely deep linear networks, with relaxed balanced initialization, we explicitly express the corresponding intrinsic dynamics.

Abstract
This paper establishes a comprehensive approximation result for deep fully-connected neural networks with commonly-used and general activation functions in Sobolev spaces $W^{n,\infty}$, with errors measured in the $W^{m,p}$-norm for $m < n$ and $1\le p \le \infty$. The derived rates surpass those of classical numerical approximation techniques, such as finite element and spectral methods, exhibiting a phenomenon we refer to as \emph{super-convergence}. Our analysis shows that deep networks with general activations can approximate weak solutions of partial differential equations (PDEs) with superior accuracy compared to traditional numerical methods at the approximation level. Furthermore, this work closes a significant gap in the error-estimation theory for neural-network-based approaches to PDEs, offering a unified theoretical foundation for their use in scientific computing.

Abstract
This paper presents a comprehensive comparative survey of TensorFlow and PyTorch, the two leading deep learning frameworks, focusing on their usability, performance, and deployment trade-offs. We review each framework's programming paradigm and developer experience, contrasting TensorFlow's graph-based (now optionally eager) approach with PyTorch's dynamic, Pythonic style. We then compare model training speeds and inference performance across multiple tasks and data regimes, drawing on recent benchmarks and studies. Deployment flexibility is examined in depth - from TensorFlow's mature ecosystem (TensorFlow Lite for mobile/embedded, TensorFlow Serving, and JavaScript support) to PyTorch's newer production tools (TorchScript compilation, ONNX export, and TorchServe). We also survey ecosystem and community support, including library integrations, industry adoption, and research trends (e.g., PyTorch's dominance in recent research publications versus TensorFlow's broader tooling in enterprise). Applications in computer vision, natural language processing, and other domains are discussed to illustrate how each framework is used in practice. Finally, we outline future directions and open challenges in deep learning framework design, such as unifying eager and graph execution, improving cross-framework interoperability, and integrating compiler optimizations (XLA, JIT) for improved speed. Our findings indicate that while both frameworks are highly capable for state-of-the-art deep learning, they exhibit distinct trade-offs: PyTorch offers simplicity and flexibility favored in research, whereas TensorFlow provides a fuller production-ready ecosystem - understanding these trade-offs is key for practitioners selecting the appropriate tool. We include charts, code snippets, and more than 20 references to academic papers and official documentation to support this comparative analysis

Abstract
Multimodal classification requires robust integration of visual and textual signals, yet common fusion strategies are brittle and vulnerable to modality-specific noise. In this paper, we present \textsc{FLUID}-Flow-Latent Unified Integration via Token Distillation for Expert Specialization, a principled token-level pipeline that improves cross-modal robustness and scalability. \textsc{FLUID} contributes three core elements: (1) \emph{Q-transforms}, learnable query tokens that distill and retain salient token-level features from modality-specific backbones; (2) a two-stage fusion scheme that enforces cross-modal consistency via contrastive alignment and then performs adaptive, task-aware fusion through a gating mechanism and a \emph{Q-bottleneck} that selectively compresses information for downstream reasoning; and (3) a lightweight, load-balanced Mixture-of-Experts at prediction time that enables efficient specialization to diverse semantic patterns. Extensive experiments demonstrate that \textsc{FLUID} attains \(91\%\) accuracy on the GLAMI-1M benchmark, significantly outperforming prior baselines and exhibiting strong resilience to label noise, long-tail class imbalance, and semantic heterogeneity. Targeted ablation studies corroborate both the individual and synergistic benefits of the proposed components, positioning \textsc{FLUID} as a scalable, noise-resilient solution for multimodal product classification.

Abstract
Multimodal learning enables various machine learning tasks to benefit from diverse data sources, effectively mimicking the interplay of different factors in real-world applications, particularly in agriculture. While the heterogeneous nature of involved data modalities may necessitate the design of complex architectures, the model interpretability is often overlooked. In this study, we leverage the intrinsic explainability of Transformer-based models to explain multimodal learning networks, focusing on the task of crop yield prediction at the subfield level. The large datasets used cover various crops, regions, and years, and include four different input modalities: multispectral satellite and weather time series, terrain elevation maps and soil properties. Based on the self-attention mechanism, we estimate feature attributions using two methods, namely the Attention Rollout (AR) and Generic Attention (GA), and evaluate their performance against Shapley-based model-agnostic estimations, Shapley Value Sampling (SVS). Additionally, we propose the Weighted Modality Activation (WMA) method to assess modality attributions and compare it with SVS attributions. Our findings indicate that Transformer-based models outperform other architectures, specifically convolutional and recurrent networks, achieving R2 scores that are higher by 0.10 and 0.04 at the subfield and field levels, respectively. AR is shown to provide more robust and reliable temporal attributions, as confirmed through qualitative and quantitative evaluation, compared to GA and SVS values. Information about crop phenology stages was leveraged to interpret the explanation results in the light of established agronomic knowledge. Furthermore, modality attributions revealed varying patterns across the two methods compared.[...]

Abstract
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To efficiently compute the reverse sample likelihood, a quasi-likelihood is considered to approximate each reverse transition density by a Gaussian distribution with matched conditional mean and covariance, respectively. The score and Hessian functions for the diffusion generation are estimated by maximizing the quasi-likelihood, ensuring a consistent matching of both the first two transitional moments between every two time points. A stochastic sampler is introduced to facilitate computation that leverages on both the estimated score and Hessian information. We establish consistency of the quasi-maximum likelihood estimation, and provide non-asymptotic convergence guarantees for the proposed sampler, quantifying the rates of the approximation errors due to the score and Hessian estimation, dimensionality, and the number of diffusion steps. Empirical and simulation evaluations demonstrate the effectiveness of the proposed Likelihood Matching and validate the theoretical results.

Abstract
Diffusion Transformers (DiTs) have demonstrated remarkable performance in visual generation tasks. However, their low inference speed limits their deployment in low-resource applications. Recent training-free approaches exploit the redundancy of features across timesteps by caching and reusing past representations to accelerate inference. Building on this idea, TaylorSeer instead uses cached features to predict future ones via Taylor expansion. However, its module-level prediction across all transformer blocks (e.g., attention or feedforward modules) requires storing fine-grained intermediate features, leading to notable memory and computation overhead. Moreover, it adopts a fixed caching schedule without considering the varying accuracy of predictions across timesteps, which can lead to degraded outputs when prediction fails. To address these limitations, we propose a novel approach to better leverage Taylor-based acceleration. First, we shift the Taylor prediction target from the module level to the last block level, significantly reducing the number of cached features. Furthermore, observing strong sequential dependencies among Transformer blocks, we propose to use the error between the Taylor-estimated and actual outputs of the first block as an indicator of prediction reliability. If the error is small, we trust the Taylor prediction for the last block; otherwise, we fall back to full computation, thereby enabling a dynamic caching mechanism. Empirical results show that our method achieves a better balance between speed and quality, achieving a 3.17x acceleration on FLUX, 2.36x on DiT, and 4.14x on Wan Video with negligible quality drop. The Project Page is \href{https://cg-taylor-acce.github.io/CG-Taylor/}{here.}

Abstract
We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in parameter space. By analyzing the rank constraints on the network outputs within each activation region, we derive polynomial equations that characterize the functions representable by the network. We further investigate conditions under which these varieties attain their expected dimension, providing insight into the expressive and structural properties of ReLU networks.

Abstract
Deep learning approaches are increasingly relevant for time series forecasting tasks. Methods such as N-BEATS, which is built on stacks of multilayer perceptrons (MLPs) blocks, have achieved state-of-the-art results on benchmark datasets and competitions. N-BEATS is also more interpretable relative to other deep learning approaches, as it decomposes forecasts into different time series components, such as trend and seasonality. In this work, we present N-BEATS-MOE, an extension of N-BEATS based on a Mixture-of-Experts (MoE) layer. N-BEATS-MOE employs a dynamic block weighting strategy based on a gating network which allows the model to better adapt to the characteristics of each time series. We also hypothesize that the gating mechanism provides additional interpretability by identifying which expert is most relevant for each series. We evaluate our method across 12 benchmark datasets against several approaches, achieving consistent improvements on several datasets, especially those composed of heterogeneous time series.