Multi-distribution or collaborative learning involves learning a single predictor that works well across multiple data distributions, using samples from each during training. Recent research on multi-distribution learning, focusing on binary loss and finite VC dimension classes, has shown near-optimal sample complexity that is achieved with oracle efficient algorithms. That is, these algorithms are computationally efficient given an efficient ERM for the class. Unlike in classical PAC learning, where the optimal sample complexity is achieved with deterministic predictors, current multi-distribution learning algorithms output randomized predictors. This raises the question: can these algorithms be derandomized to produce a deterministic predictor for multiple distributions? Through a reduction to discrepancy minimization, we show that derandomizing multi-distribution learning is computationally hard, even when ERM is computationally efficient. On the positive side, we identify a structural condition enabling an efficient black-box reduction, converting existing randomized multi-distribution predictors into deterministic ones.

Abstract-- Intra-cardiac Echocardiography (ICE) is a crucial imaging modality used in electrophysiology (EP) and structural heart disease (SHD) interventions, providing realtime, high-resolution views from within the heart. Despite its advantages, effective manipulation of the ICE catheter requires significant expertise, which can lead to inconsistent outcomes, particularly among less experienced operators. To address this challenge, we propose an AIdriven closed-loop view guidance system with human-inthe-loop feedback, designed to assist users in navigating ICE imaging without requiring specialized knowledge. Our method models the relative position and orientation vectors between arbitrary views and clinically defined ICE views in a spatial coordinate system, guiding users on how to manipulate the ICE catheter to transition from the current view to the desired view over time. Overview of the proposed view guidance system. The primary use cases of the ICE imaging involve visualizing target anatomy, detecting and tracking therapeutic devices, and validating treatments in real-time. HE Intra-cardiac Echocardiography (ICE) is a sophisticated imaging modality that offers real-time, highresolution have significant expertise in interpreting anatomical views views from within the heart, making it an invaluable via ICE images and skillfully maneuvering the ICE catheter tool in both electrophysiology (EP) and structural heart disease using two knobs (anterior-posterior, right-left) and the rotating/translating (SHD) interventions.

Zelenskyy rejected the China-Brazil six-point plan to end Russia's war and questioned'true' intent. Ukrainian President Volodymyr Zelenskyy took to the podium at the 79th United Nations General Assembly (UNGA) for the third time since Russia's deadly invasion began more than two and half years ago, though this time he took direct aim at nations aiding Moscow: China, North Korea and Iran. Zelenskyy – who has long toed the line when it comes to maintaining murky geopolitical relations amid the war – for the first time called out not only the nations supplying direct arms to Moscow, but those who have remained complacent in their refusal to back Ukraine's demands that Russian President Vladimir Putin withdraw his troops. "We need to make it clear the war is over. This is the peace formula – what part of this could be unacceptable to anyone who upholds the U.N. Charter?" he questioned.

As world leaders gather in New York City for the United Nations General Assembly, there's a lot to get done, with just six years left to achieve the bold ambitions laid out for the world's 2030 agenda. When world governments agreed to the 2030 plan back in 2015, a decade and a half seemed like plenty of time to achieve the 17 Sustainable Development Goals (SDGs) designed to create a more prosperous, safe and fair global society. While amazing progress has been made, we are in danger of falling short. I believe the U.N.'s goals can be attained through a collaborative commitment to make digital networks available to everybody in the world. Mobility, broadband and the cloud are the infrastructure of 21st century life and everybody should have that opportunity.

B.1 Conditional convergence in distribution Suppose (X, d The proof of this Lemma is identical to the portmanteau lemma for weak convergence by replacing probabilities/expectations with conditional probabilities/expectations (for example, see [38, Section 2.1]). Lemma B.2. Suppose X, X X as m, and X is a constant a.s., then X A, where A is a constant. We can exchange the expectation and limit by the dominated convergence theorem. The result follows by taking ϵ 0. 4. Since X is a.s. For any K > 0, we have x x K is a bounded and continuous function. R. Because f g: X is a bounded and A. We now show that (X The result follows by an application of the continuous mapping theorem with the function (x, A) Ax. B.2 Model assumptions The following sets of assumptions are only used to prove the large-data limit results of Proposition 3.1, Proposition 3.2, and Proposition 3.3. We will always use a subscript m to indicate that the quantity is dependent on the data. For the remainder of this section we will assume the following regularity conditions.

Detecting and answering ambiguous questions has been a challenging task in open-domain question answering. Ambiguous questions have different answers depending on their interpretation and can take diverse forms. Temporally ambiguous questions are one of the most common types of such questions. In this paper, we introduce TEMPAMBIQA, a manually annotated temporally ambiguous QA dataset consisting of 8,162 open-domain questions derived from existing datasets. Our annotations focus on capturing temporal ambiguity to study the task of detecting temporally ambiguous questions. We propose a novel approach by using diverse search strategies based on disambiguated versions of the questions. We also introduce and test non-search, competitive baselines for detecting temporal ambiguity using zero-shot and few-shot approaches.

The goal of this work is to serve as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. By studying these spaces from a mathematical perspective, we expect to gain more insight into how to build better algorithms to solve decision problems. Therefore, we focus on presenting the connection between the Banach fixed point theorem and the convergence of reinforcement learning algorithms, and we illustrate how the insights gained from this can practically help in designing more efficient algorithms. Before doing so, however, we first introduce relevant concepts such as metric spaces, normed spaces and Banach spaces for better understanding, before expressing the entire reinforcement learning problem in terms of Markov decision processes. This allows us to properly introduce the Banach contraction principle in a language suitable for reinforcement learning, and to write the Bellman equations in terms of operators on Banach spaces to show why reinforcement learning algorithms converge. Finally, we show how the insights gained from the mathematical study of convergence are helpful in reasoning about the best ways to make reinforcement learning algorithms more efficient.

We propose a new operator defined between two tensors, the broadcast product. The broadcast product calculates the Hadamard product after duplicating elements to align the shapes of the two tensors. Complex tensor operations in libraries like \texttt{numpy} can be succinctly represented as mathematical expressions using the broadcast product. Finally, we propose a novel tensor decomposition using the broadcast product, highlighting its potential applications in dimensionality reduction.

Reinforcement Learning from Human Feedback aligns the outputs of Large Language Models with human values and preferences. Central to this process is the reward model (RM), which translates human feedback into training signals for optimising LLM behaviour. However, RMs can develop biases by exploiting spurious correlations in their training data, such as favouring outputs based on length or style rather than true quality. These biases can lead to incorrect output rankings, sub-optimal model evaluations, and the amplification of undesirable behaviours in LLMs alignment. This paper addresses the challenge of correcting such biases without additional data and training, introducing the concept of Post-hoc Reward Calibration. We first propose an intuitive approach to estimate the bias term and, thus, remove it to approximate the underlying true reward. We then extend the approach to a more general and robust form with the Locally Weighted Regression. Focusing on the prevalent length bias, we validate our proposed approaches across three experimental settings, demonstrating consistent improvements: (1) a 3.11 average performance gain across 33 reward models on the RewardBench dataset; (2) enhanced alignment of RM rankings with GPT-4 evaluations and human preferences based on the AlpacaEval benchmark; and (3) improved Length-Controlled win rate of the RLHF process in multiple LLM--RM combinations. Our method is computationally efficient and generalisable to other types of bias and RMs, offering a scalable and robust solution for mitigating biases in LLM alignment. Our code and results are available at https://github.com/ZeroYuHuang/Reward-Calibration.

We introduce SeaSplat, a method to enable real-time rendering of underwater scenes leveraging recent advances in 3D radiance fields. Underwater scenes are challenging visual environments, as rendering through a medium such as water introduces both range and color dependent effects on image capture. We constrain 3D Gaussian Splatting (3DGS), a recent advance in radiance fields enabling rapid training and real-time rendering of full 3D scenes, with a physically grounded underwater image formation model. Applying SeaSplat to the real-world scenes from SeaThru-NeRF dataset, a scene collected by an underwater vehicle in the US Virgin Islands, and simulation-degraded real-world scenes, not only do we see increased quantitative performance on rendering novel viewpoints from the scene with the medium present, but are also able to recover the underlying true color of the scene and restore renders to be without the presence of the intervening medium. We show that the underwater image formation helps learn scene structure, with better depth maps, as well as show that our improvements maintain the significant computational improvements afforded by leveraging a 3D Gaussian representation.