All simulations were based on pytorch [5]. For the nonlinear neuroscience tasks, we applied the gradient descent method "Adam" [4] to the recurrent weights W as well as to the input and output vectors mi, wi. We checked that our results did not depend qualitatively on the choice of the "Adam" algorithm over plain gradient descent; however, training converged more easily for this choice of algorithm. We also checked that restricting training to W only (as for the simple model) did not alter our results qualitatively (although, with this restriction, training on the Romo task for small values of g did not converge). Code for reproducing our results can be found on https://github.com/frschu/neurips_

The lack of publicly available high-quality and accurately labeled datasets has long been a major bottleneck for singing voice synthesis (SVS). To tackle this problem, we present M4Singer, a free-to-use Multi-style, Multi-singer Mandarin singing collection with elaborately annotated Musical scores as well as its benchmarks. Specifically, 1) we construct and release a large high-quality Chinese singing voice corpus, which is recorded by 20 professional singers, covering 700 Chinese pop songs as well as all the four SATB types (i.e., soprano, alto, tenor, and bass); 2) we take extensive efforts to manually compose the musical scores for each recorded song, which are necessary to the study of the prosody modeling for SVS. 3) To facilitate the use and demonstrate the quality of M4Singer, we conduct four different benchmark experiments: score-based SVS, controllable singing voice (CSV), singing voice conversion (SVC) and automatic music transcription (AMT).

Autonomous Driving (AD) vehicles still struggle to exhibit human - like behavior in highly dynamic and interactive traffic scenarios. The key challenge lies in AD's limited ability to interact with surrounding vehicles, largely due to a lack of understandi ng the underlying mechanisms of social interaction. To address this issue, we introduce MPCFormer, an explainable socially - aware autonomous driving approach with physics - informed and data - driven coupled social interaction dynamics. In this model, the dynam ics are formulated into a discrete space - state representation, which embeds physics priors to enhance modeling explainability. The dynamics coefficients are learned from naturalistic driving data via a Transformer - based encoder - decoder architecture. To the best of our knowledge, MPCFormer is the first approach to explicitly model the dynamics of multi - vehicle social interactions. The learned social interaction dynamics enable the planner to generate manifold, human - like behaviors when interacting with surro unding traffic. By leveraging the MPC framework, the approach mitigates the potential safety risks typically associated with purely learning - based methods. Open - looped evaluation on NGSIM dataset demonstrates that MPCFormer achieves superior social interac tion awareness, yielding the lowest trajectory p red iction errors compared with other state - of - the - art approach. The prediction achieves an ADE as low as 0.86 m over a long prediction horizon of 5 seconds. Close - looped experiments in highly intense interact ion scenarios, where consecutive lane changes are required to exit an off - ramp, further validate the effectiveness of MPCFormer. Results show that MPCFormer achieves the highest planning success rate of 94.67%, improves driving efficiency by 15.75%, and re duces the collision rate from 21.25% to 0.5%, outperforming a frontier Reinforcement Learning (RL) based planner. A. Research motivation During recent years, Autonomous Driving (AD) has demonstrated significant progress within transportation systems [1] [2] . However, AD vehicles still face significant challenges in exhibiting human - like behavior in highly dynamic and interactive traffic scenarios such as off - ramp and unprotected left turns [3] [4] . One critical reason is that AD vehic les lack the understanding of the underlying mechanisms of social interaction between surrounding vehicles.

We would like to thank the reviewers for their comments and feedback. Janzing et al. [9] write down the same equation, but We will follow the reviewer's The decomposition for conditional SVs follows by replacing "conditioning The decomposition is introduced in Section 3 to assist our illustration of how the different SVs attribute a model's SVs. Unlike conditional (asymmetric) SVs, causal SVs provide the right intuition in the case of common confounding. See also the previous paragraph. SVs appear to fare better than the reviewer suggests.

However, the reliability and generalisation properties of this approach are unknown.

We would like to thank the reviewers for their comments and feedback. Janzing et al. [9] write down the same equation, but We will follow the reviewer's The decomposition for conditional SVs follows by replacing "conditioning The decomposition is introduced in Section 3 to assist our illustration of how the different SVs attribute a model's SVs. Unlike conditional (asymmetric) SVs, causal SVs provide the right intuition in the case of common confounding. See also the previous paragraph. SVs appear to fare better than the reviewer suggests.