We study the low-degree hardness of broadcasting on trees.Broadcasting on trees has been extensively studied in statistical physics, in computational biology in relation to phylogenetic reconstruction and in statistics and computer science in the context of block model inference, and as a simple data model for algorithms that may require depth for inference. The inference of the root can be carried by celebrated Belief Propagation (BP) algorithm which achieves Bayes-optimal performance. Despite the fact that this algorithm runs in linear time (using real operations), recent works indicated that this algorithm in fact requires high level of complexity. Moitra, Mossel and Sandon constructed a chain for which estimating the root better than random (for a typical input) is $NC1$ complete. Kohler and Mossel constructed chains such that for trees with $N$ leaves, recovering the root better than random requires a polynomial of degree $N^{\Omega(1)}$. Both works above asked if such complexity bounds hold in general below the celebrated {\em Kesten-Stigum} bound. In this work, we prove that this is indeed the case for low degree polynomials. We show that for the broadcast problem using any Markov chain on trees with $N$ leaves, below the Kesten Stigum bound, any $O(\log N)$ degree polynomial has vanishing correlation with the root. Our result is one of the first low-degree lower bound that is proved in a setting that is not based or easily reduced to a product measure.

Three-dimensional rigid-body transforms, i.e. rotations and translations, are central to modern differentiable machine learning pipelines in robotics, vision, and simulation. However, numerically robust and mathematically correct implementations, particularly on SO(3), are error-prone due to issues such as axis conventions, normalizations, composition consistency and subtle errors that only appear in edge cases. SciPy's spatial$.$transform module is a rigorously tested Python implementation. However, it historically only supported NumPy, limiting adoption in GPU-accelerated and autodiff-based workflows. We present a complete overhaul of SciPy's spatial$.$transform functionality that makes it compatible with any array library implementing the Python array API, including JAX, PyTorch, and CuPy. The revised implementation preserves the established SciPy interface while enabling GPU/TPU execution, JIT compilation, vectorized batching, and differentiation via native autodiff of the chosen backend. We demonstrate how this foundation supports differentiable scientific computing through two case studies: (i) scalability of 3D transforms and rotations and (ii) a JAX drone simulation that leverages SciPy's Rotation for accurate integration of rotational dynamics. Our contributions have been merged into SciPy main and will ship in the next release, providing a framework-agnostic, production-grade basis for 3D spatial math in differentiable systems and ML.

6G networks are envisioned to support on-demand AI model downloading to accommodate diverse inference requirements of end users. By proactively caching models at edge nodes, users can retrieve the requested models with low latency for on-device AI inference. However, the substantial size of contemporary AI models poses significant challenges for edge caching under limited storage capacity, as well as for the concurrent delivery of heterogeneous models over wireless channels. To address these challenges, we propose a fine-grained AI model caching and downloading system that exploits parameter reusability, stemming from the common practice of fine-tuning task-specific models from a shared pre-trained model with frozen parameters. This system selectively caches model parameter blocks (PBs) at edge nodes, eliminating redundant storage of reusable parameters across different cached models. Additionally, it incorporates coordinated multipoint (CoMP) broadcasting to simultaneously deliver reusable PBs to multiple users, thereby enhancing downlink spectrum utilization. Under this arrangement, we formulate a model downloading delay minimization problem to jointly optimize PB caching, migration (among edge nodes), and broadcasting beamforming. To tackle this intractable problem, we develop a distributed multi-agent learning framework that enables edge nodes to explicitly learn mutual influence among their actions, thereby facilitating cooperation. Furthermore, a data augmentation approach is proposed to adaptively generate synthetic training samples through a predictive model, boosting sample efficiency and accelerating policy learning. Both theoretical analysis and simulation experiments validate the superior convergence performance of the proposed learning framework.

We study the low-degree hardness of broadcasting on trees.Broadcasting on trees has been extensively studied in statistical physics, in computational biology in relation to phylogenetic reconstruction and in statistics and computer science in the context of block model inference, and as a simple data model for algorithms that may require depth for inference. The inference of the root can be carried by celebrated Belief Propagation (BP) algorithm which achieves Bayes-optimal performance. Despite the fact that this algorithm runs in linear time (using real operations), recent works indicated that this algorithm in fact requires high level of complexity. Moitra, Mossel and Sandon constructed a chain for which estimating the root better than random (for a typical input) is NC1 complete. Kohler and Mossel constructed chains such that for trees with N leaves, recovering the root better than random requires a polynomial of degree N {\Omega(1)} .

Recent estimates put the carbon footprint of Bitcoin and Ethereum at an average of 64 and 26 million tonnes of CO2 per year, respectively. To address this growing problem, several possible approaches have been proposed in the literature: creating alternative blockchain consensus mechanisms, applying redundancy reduction techniques, utilizing renewable energy sources, and employing energy-efficient devices, etc. In this paper, we follow the second avenue and propose an efficient approach based on reinforcement learning that improves the block broadcasting scheme in blockchain networks. The analysis and experimental results confirmed that the proposed improvement of the block propagation scheme could cleverly handle network dynamics and achieve better results than the default approach. Additionally, our technical integration of the simulator and developed RL environment can be used as a complete solution for further study of new schemes and protocols that use RL or other ML techniques.

Rep. Brandon Gill, R- Tex., got into a heated exchange with CNN host Pamela Brown over the Trump administration's crackdown on government spending, specifically for public broadcasting at PBS and NPR. By 1970, both PBS and NPR sprang forth from the CBP, and Americans were treated to the "News Hour," "Sesame Street," British comedies and science programming at a time when there were only three networks, cable TV was strictly for the boondocks, and VCRs were science fiction. A big part of the reason that programming was limited was that production costs for broadcasting were incredibly high. In David Grzybowski's book, 'The Big Story,' he cites Philadelphia news anchor Larry Kane talking about how hard it was during the 1979 Three Mile Island nuclear scare to just get a live TV shot from Harrisburg to Philly: "I know we had a live microwave, but the microwaves didn't go that far. I think we sought some satellite time. The satellite times in those days were 5,000 a minute."

In multimedia broadcasting, no-reference image quality assessment (NR-IQA) is used to indicate the user-perceived quality of experience (QoE) and to support intelligent data transmission while optimizing user experience. This paper proposes an improved no-reference light field image quality assessment (NR-LFIQA) metric for future immersive media broadcasting services. First, we extend the concept of depthwise separable convolution (DSC) to the spatial domain of light field image (LFI) and introduce "light field depthwise separable convolution (LF-DSC)", which can extract the LFI's spatial features efficiently. Second, we further theoretically extend the LF-DSC to the angular space of LFI and introduce the novel concept of "light field anglewise separable convolution (LF-ASC)", which is capable of extracting both the spatial and angular features for comprehensive quality assessment with low complexity. Third, we define the spatial and angular feature estimations as auxiliary tasks in aiding the primary NR-LFIQA task by providing spatial and angular quality features as hints. To the best of our knowledge, this work is the first exploration of deep auxiliary learning with spatial-angular hints on NR-LFIQA. Experiments were conducted in mainstream LFI datasets such as Win5-LID and SMART with comparisons to the mainstream full reference IQA metrics as well as the state-of-the-art NR-LFIQA methods. The experimental results show that the proposed metric yields overall 42.86% and 45.95% smaller prediction errors than the second-best benchmarking metric in Win5-LID and SMART, respectively. In some challenging cases with particular distortion types, the proposed metric can reduce the errors significantly by more than 60%.

The broadcasting industry is increasingly adopting IP techniques, revolutionising both live and pre-recorded content production, from news gathering to live music events. IP broadcasting allows for the transport of audio and video signals in an easily configurable way, aligning with modern networking techniques. This shift towards an IP workflow allows for much greater flexibility, not only in routing signals but with the integration of tools using standard web development techniques. One possible tool could include the use of live audio tagging, which has a number of uses in the production of content. These include from automated closed captioning to identifying unwanted sound events within a scene. In this paper, we describe the process of containerising an audio tagging model into a microservice, a small segregated code module that can be integrated into a multitude of different network setups. The goal is to develop a modular, accessible, and flexible tool capable of seamless deployment into broadcasting workflows of all sizes, from small productions to large corporations. Challenges surrounding latency of the selected audio tagging model and its effect on the usefulness of the end product are discussed.

We propose a simple modification to the conventional attention mechanism applied by Transformers: Instead of quantifying pairwise query-key similarity with scaled dot-products, we quantify it with the logarithms of scaled dot-products of exponentials. Our modification linearizes attention with exponential kernel feature maps, whose corresponding feature function is infinite dimensional. We show that our modification is expressible as a composition of log-sums of exponentials, with a latent space of constant size, enabling application with constant time and space complexity per token. We implement our modification, verify that it works in practice, and conclude that it is a promising alternative to conventional attention.

A uniform $k$-{\sc dag} generalizes the uniform random recursive tree by picking $k$ parents uniformly at random from the existing nodes. It starts with $k$ ''roots''. Each of the $k$ roots is assigned a bit. These bits are propagated by a noisy channel. The parents' bits are flipped with probability $p$, and a majority vote is taken. When all nodes have received their bits, the $k$-{\sc dag} is shown without identifying the roots. The goal is to estimate the majority bit among the roots. We identify the threshold for $p$ as a function of $k$ below which the majority rule among all nodes yields an error $c+o(1)$ with $c<1/2$. Above the threshold the majority rule errs with probability $1/2+o(1)$.