King Charles tells Congress UK and US'have always found ways to come together' during historic address James Comey indicted AGAIN by Trump's Justice Department over seashell social media'assassination' accusation Justin Baldoni says he's not to blame for Blake Lively's downfall as lawyers brand her a'bully' with a history of flop business ventures at pre-trial hearing How to turbocharge your Ozempic and Mounjaro: Exact time, day of week and WHERE to inject on body... 'rotation' trick and other doctor-approved steps to lose MORE weight and avoid side effects I'm a urologist: Men worried about having a small penis need to know they CAN grow it I tried this 45-minute new size-boosting treatment myself Small print on page 26 of Newsom's billionaire's bill that reveals his real plans and how everyone could be hit Every woman who uses retinol must read this. You won't believe these beauty influencer claims they're just so damaging: DR SHEILA NAZARIAN Matt Damon's wife, 49, is accused of ...

What are Russia's gains from the Iran war? 'We are not losers; we are winners' Ukrainian drones strike Russia's Tuapse refinery for third time NewsFeed Ukrainian drones strike Russia's Tuapse refinery for third time Ukraine has targeted a major Russian oil refinery in the Black Sea port city of Tuapse for the third time in less than two weeks, setting off a fresh blaze and prompting authorities to evacuate local residents. Qatar says using Hormuz Strait as political weapon is'unacceptable' Australia's top diplomat visits China to talk energy security

Kernel design is a pivotal but challenging aspect of time series analysis, especially in the context of small datasets. In recent years, Reservoir Computing (RC) has emerged as a powerful tool to compare time series based on the underlying dynamics of the generating process rather than the observed data. However, the performance of RC highly depends on the hyperparameter setting, which is hard to interpret and costly to optimize because of the recurrent nature of RC. Here, we present a new kernel for time series based on the recently established equivalence between reservoir dynamics and Nonlinear Vector AutoRegressive (NVAR) processes. The kernel is non-recurrent and depends on a small set of meaningful hyperparameters, for which we suggest an effective heuristic. We demonstrate excellent performance on a wide range of real-world classification tasks, both in terms of accuracy and speed. This further advances the understanding of RC representation learning models and extends the typical use of the NVAR framework to kernel design and representation of real-world time series data.

Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial dependencies between groups of more than two variables can play a significant role in the analysis and modelling of such systems, yet extracting such high-order interactions from data remains challenging. Here, we introduce a hierarchy of d-order interaction measures, increasingly inclusive of possible factorisations of the joint probability distribution, and define non-parametric, kernel-based tests to establish systematically the statistical significance of d-order interactions. We also establish mathematical links with lattice theory, which elucidate the derivation of the interaction measures and their composite permutation tests; clarify the connection of simplicial complexes with kernel matrix centring; and provide a means to enhance computational efficiency. We illustrate our results numerically with validations on synthetic data, and through an application to neuroimaging data.

We consider a Bayesian forecast aggregation model where nexperts, after observing private signals about an unknown binary event, report their posterior beliefs about the event to a principal, who then aggregates the reports into a single prediction for the event. The signals of the experts and the outcome of the event follow a joint distribution that is unknown to the principal, but the principal has access to i.i.d. "samples" from the distribution, where each sample is a tuple of the experts' reports (not signals) and the realization of the event. Using these samples, the principal aims to find an ε-approximately optimal aggregator, where optimality is measured in terms of the expected squared distance between the aggregated prediction and the realization of the event. We show that the sample complexity of this problem is at least Ω(mn 2/ε) for arbitrary discrete distributions, where m is the size of each expert's signal space. This sample complexity grows exponentially in the number of experts n. But, if the experts' signals are independent conditioned on the realization of the event, then the sample complexity is significantly reduced, to O(1/ε2), which does not depend on n. Our results can be generalized to non-binary events. The proof of our results uses a reduction from the distribution learning problem and reveals the fact that forecast aggregation is almost as difficult as distribution learning.

Since the proposal of transformers (Vaswani et al., 2017), these models have been limited to bounded input lengths, because of their need to attend to every token in the input. In this work, we propose Unlimiformer: a general approach that wraps any existing pretrained encoder-decoder transformer, and offloads the cross-attention computation to a single k-nearest-neighbor (kNN) index, while the returned kNN distances are the attention dot-product scores. This kNN index can be kept on either the GPU or CPU memory and queried in sub-linear time; this way, we can index practically unlimited input sequences, while every attention head in every decoder layer retrieves its top-k keys, instead of attending to every key. We evaluate Unlimiformer on several long-document and book-summarization benchmarks, showing that it can process even 500k token-long inputs from the BookSum dataset, without any input truncation at test time. We demonstrate that Unlimiformer improves pretrained models such as BART (Lewis et al., 2020a) and Longformer (Beltagy et al., 2020) by extending them to unlimited inputs without additional learned weights and without modifying their code. Our code and models are publicly available, and support LLaMA-2 as well2.

The answer may already be in your home. To achieve a smart home, you need a voice assistant to run it. A smart home assistant, usually folded into a smart speaker, will let you command your smart home with your voice and run your various routines. It also acts as a center for every gadget you want to add to your home. And you can add almost anything these days, from smart garage control to even voice-commanding your blinds .

Valve's £85 Steam Controller divides gamers ahead of May launch Valve has announced its new Steam Controller will be available to order from 4 May, and will cost £85 in the UK and $99 in the US - prices that have raised eyebrows among some gamers. The second generation of the gamepad, it will be compatible with PCs and Valve's handheld console, the Steam Deck. It is also designed to work with the company's own upcoming gaming PC, the Steam Machine. The Steam Controller may be more expensive than the standard controllers from Nintendo, Xbox and PlayStation, but we do live in a time where companies including Sony and Microsoft are selling premium controllers for £150-£200, said Chris Scullion deputy editor of Video Games Chronicle. There has been a negative reaction from some gamers on social media though.