In many applications, observations are naturally grouped into different classes.

Our approach is purely based on 2D convolutions. Nevertheless, it3 outperforms or performs comparably to many more costly 3D models. We thank the reviewers for pointing out some related (or missing) references. The12 Timeception layers involve group convolutions at different time scales while our TAM layers only use depthwise13 convolution. As a result, the Timeception has significantly more parameters than the TAM (10% vs. 0.1% of the14 totalmodelparameters).

The original CLUTRR data generation framework made sure that each testproof is not in the training set in order to test whether a model is able to generalize to unseen proofs. Initial results on the original CLUTRR test sets resulted in strong model performance ( 99%) on levels seen during training (2, 4, 6) but no generalization at all ( 0%) to other levels. The models are given as input " [story] [query] " and asked to generate the proof and answer. Models are trained on levels2,4,6only. In our case, the entity names are important to evaluate systematic generalization.

Withoutrequiring repeatable trials, itcanflexibly capture covariate-dependent jointSCDs, andprovide interpretable latent causes underlying the statistical dependencies between neurons.

ItisshownthatQKFormer achieves significantly superior performance over existing state-of-the-art SNN models on various mainstream datasets.

Conventional models prepare a large embedding matrix whose size depends on the vocabulary size. Therefore, storing these models in memory and disk storage is costly.

This problem involves identifying a density function that accurately represents the distribution of a given dataset.

A.1 PCNtraining We basically follow the same PCN training method by Wu et al.[1] but replace the AlphaZero algorithm with the Gumbel AlphaZero algorithm [2], where the simulation count is set to 322 in self-play and starts by sampling 16 actions. The architecture of the PCN contains three residual blocks with 256 hidden channels. Atotal of400,000 self-play games are generated for the whole training. During optimization, the learning rate is fixed at 0.02, and the batch size is set to 1,024. A.3 Workerdesign The worker is itself a Killall-Go solver. Thus,tofullyutilize GPU resources, we implement batch GPU inferencing to accelerate PCN evaluations for workers.