We would like to thank all the reviewers for their effort, and their thoughtful comments. Being formal, it should be "the gradient associated to the pullback of f along exp". We will change it to "on which standard convergence results still apply". Thm 4.3 We will change "is equivalent" to The same can be said about higher order methods. We chose not to mention them in the main paper for simplicity.

Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have shown that regularizing the dynamics of the ODE can partially alleviate this. In this paper we propose a new regularization technique: randomly sampling the end time of the ODE during training. The proposed regularization is simple to implement, has negligible overhead and is effective across a wide variety of tasks. Further, the technique is orthogonal to several other methods proposed to regularize the dynamics of ODEs and as such can be used in conjunction with them. We show through experiments on normalizing flows, time series models and image recognition that the proposed regularization can significantly decrease training time and even improve performance over baseline models.

Posterior sampling for reinforcement learning (PSRL) is an effective method for balancing exploration and exploitation in reinforcement learning. Randomised value functions (RVF) can be viewed as a promising approach to scaling PSRL. However, we show that most contemporary algorithms combining RVF with neural network function approximation do not possess the properties which make PSRL effective, and provably fail in sparse reward problems. Moreover, we find that propagation of uncertainty, a property of PSRL previously thought important for exploration, does not preclude this failure. We use these insights to design Successor Uncertainties (SU), a cheap and easy to implement RVF algorithm that retains key properties of PSRL. SU is highly effective on hard tabular exploration benchmarks. Furthermore, on the Atari 2600 domain, it surpasses human performance on 38 of 49 games tested (achieving a median human normalised score of 2.09), and outperforms its closest RVF competitor, Bootstrapped DQN, on 36 of those.

Inspired by the two-way fixed effects regression model widely used in the panel data literature, we propose a two-way unmeasured confounding assumption to model the system dynamics in causal reinforcement learning and develop a two-way deconfounder algorithm that devises a neural tensor network to simultaneously learn both the unmeasured confounders and the system dynamics, based on which a model-based estimator can be constructed for consistent policy value estimation. We illustrate the effectiveness of the proposed estimator through theoretical results and numerical experiments.

Motion forecasting for agents in autonomous driving is highly challenging due to the numerous possibilities for each agent's next action and their complex interactions in space and time. In real applications, motion forecasting takes place repeatedly and continuously as the self-driving car moves. However, existing forecasting methods typically process each driving scene within a certain range independently, totally ignoring the situational and contextual relationships between successive driving scenes. This significantly simplifies the forecasting task, making the solutions suboptimal and inefficient to use in practice. To address this fundamental limitation, we propose a novel motion forecasting framework for continuous driving, named RealMotion. It comprises two integral streams both at the scene level: (1) The scene context stream progressively accumulates historical scene information until the present moment, capturing temporal interactive relationships among scene elements.

A.1 General training details All models studied in the paper are trained with squared loss and l

For a certain scaling of the initialization of stochastic gradient descent (SGD), wide neural networks (NN) have been shown to be well approximated by reproducing kernel Hilbert space (RKHS) methods. Recent empirical work showed that, for some classification tasks, RKHS methods can replace NNs without a large loss in performance. On the other hand, two-layers NNs are known to encode richer smoothness classes than RKHS and we know of special examples for which SGDtrained NN provably outperform RKHS. This is true even in the wide network limit, for a different scaling of the initialization. How can we reconcile the above claims?

We thank the reviewers for their time and appreciate the feedback. General problem, area of active research"; "seems significant and We will include all plots (k = 10, 20,.., 50) to Quantitive results appears in Table 2 and Figure 3. I'd appreciate standard error We will follow the suggestions about the clarity.

There was a time when certain shops would resemble nightclubs at about midnight: a long queue of excitable people, some of them perhaps too young to be out that late, discussing the excitement that awaits inside. The sight of throngs of gamers looking to get their hands on the latest hardware when the clock strikes 12 is growing increasingly rare. But if you happen to walk by a Smyths toy shop at midnight on 4 June, you may encounter a blast from the past: excitable people, most in their teens or 20s, possibly discussing Mario Kart. They will be waiting to buy the Nintendo Switch 2, the first major games console launch since 2020 and potentially the biggest of all time. What's particularly notable about this launch isn't the queues but just how few there will be.

Scores are calculated by giving a weight of 1 for applicable, 0.5 for conditionally applicable, and 0 for incorrect responses. The values are presented as percentages, calculated by the number of responses that satisfy the criteria divided by the total number of responses. The country with the highest percentage is marked in bold, and the second highest is underlined.