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Football (soccer) is a sport that is characterised by complex game play, where players perform a variety of actions, such as passes, shots, tackles, fouls, in order to score goals, and ultimately win matches. Accurately forecasting the total number of each action that each player will complete during a match is desirable for a variety of applications, including tactical decision-making, sports betting, and for television broadcast commentary and analysis. Such predictions must consider the game state, the ability and skill of the players in both teams, the interactions between the players, and the temporal dynamics of the game as it develops. In this paper, we present a transformer-based neural network that jointly and recurrently predicts the expected totals for thirteen individual actions at multiple time-steps during the match, and where predictions are made for each individual player, each team and at the game-level. The neural network is based on an \emph{axial transformer} that efficiently captures the temporal dynamics as the game progresses, and the interactions between the players at each time-step. We present a novel axial transformer design that we show is equivalent to a regular sequential transformer, and the design performs well experimentally. We show empirically that the model can make consistent and reliable predictions, and efficiently makes $\sim$75,000 live predictions at low latency for each game.

Large language models (LLMs) have demonstrated impressive capabilities and are receiving increasing attention to enhance their reasoning through scaling test--time compute. However, their application in open--ended, knowledge--intensive, complex reasoning scenarios is still limited. Reasoning--oriented methods struggle to generalize to open--ended scenarios due to implicit assumptions of complete world knowledge. Meanwhile, knowledge--augmented reasoning (KAR) methods fail to address two core challenges: 1) error propagation, where errors in early steps cascade through the chain, and 2) verification bottleneck, where the explore--exploit tradeoff arises in multi--branch decision processes. To overcome these limitations, we introduce ARise, a novel framework that integrates risk assessment of intermediate reasoning states with dynamic retrieval--augmented generation (RAG) within a Monte Carlo tree search paradigm. This approach enables effective construction and optimization of reasoning plans across multiple maintained hypothesis branches. Experimental results show that ARise significantly outperforms the state--of--the--art KAR methods by up to 23.10%, and the latest RAG-equipped large reasoning models by up to 25.37%. Our project page is at https://opencausalab.github.io/ARise.

John McGinn believes Aston Villa's Europa Conference League campaign has been a "learning curve" despite suffering a semi-final exit to Olympiakos. Unai Emery's side missed out on a place in the final after going down 6-2 on aggregate against the Greek side. Villa travelled to the Karaiskakis Stadium needing a memorable turnaround, having lost the first leg 4-2 on home soil, but were unable to overturn the deficit. "I think it has been a big learning curve for us," McGinn told TNT Sports. "It's not been a smooth journey. "We got to the semi-final and were down to the bare bones a wee bit.