Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Preliminaries and Related Work Key Bottlenecks in PC Parallelization Harnessing Block-Based PC Parallelization 4.1. Fully Connected Sum Layers 4.2. Generalizing To Practical Sum Layers 4.3. Efficient Implementations by Compiling PC Layers 4.4. Analysis: IO and Computation Overhead Optimizing Backpropagation with PC Flows Experiments 6.1. Faster Models with PyJuice 6.2. Better PCs At Scale 6.3. Benchmarking Existing PCs Conclusion, Acknowledgements, Impact Statement, and References Preliminaries and Related Work Preliminaries and Related Work Preliminaries and Related Work Key Bottlenecks in PC Parallelization Key Bottlenecks in PC Parallelization Key Bottlenecks in PC Parallelization Harnessing Block-Based PC Parallelization 4.1. Fully Connected Sum Layers 4.2. Generalizing To Practical Sum Layers 4.3. Efficient Implementations by Compiling PC Layers 4.4. Analysis: IO and Computation Overhead Harnessing Block-Based PC Parallelization 4.1. Fully Connected Sum Layers 4.1. Fully Connected Sum Layers 4.2. Generalizing To Practical Sum Layers 4.2. Generalizing To Practical Sum Layers 4.3. Efficient Implementations by Compiling PC Layers 4.3. Efficient Implementations by Compiling PC Layers 4.4. Analysis: IO and Computation Overhead 4.4. Analysis: IO and Computation Overhead Optimizing Backpropagation with PC Flows Optimizing Backpropagation with PC Flows Optimizing Backpropagation with PC Flows Experiments 6.1. Faster Models with PyJuice 6.2. Better PCs At Scale 6.3. Benchmarking Existing PCs Experiments Experiments 6.1. Faster Models with PyJuice 6.1. Faster Models with PyJuice 6.2. Better PCs At Scale 6.2. Better PCs At Scale 6.3. Benchmarking Existing PCs 6.3. Benchmarking Existing PCs Conclusion, Acknowledgements, Impact Statement, and References Conclusion, Acknowledgements, Impact Statement, and References Conclusion, Acknowledgements, Impact Statement, and References A. Algorithm Details A. Algorithm Details B. Additional Technical Details B. Additional Technical Details C. Experimental Details C. Experimental Details D. Additional Experiments D. Additional Experiments 6.3. Benchmarking Existing PCs We adopt two PD structures (i.e., PD-mid with 107M edges and PD-large with 405M edges) as well as two HCLT structures (i.e., HCLT-mid with 40M edges and HCLT-large with 174M edges). Details of the adopted models are described in Appendix C.4. We experiment with different optimization strategies and adopt full-batch EM as it yields consistently better performance across models and datasets. Specifically, the computed PC flows are accumulated across all samples in the training set before doing one EM step. Results are shown in Table 3. Notably, we achieve better results compared to previous papers. For example, Liu et al. (2023a) reports 4.82 bits-per-dimension (bpd) for HCLT on ImageNet32, while we achieved 4.33 bpd. The performance improvements stem from more training epochs and the ability to do more hyperparameter search thanks to the speedup. We highlight that the goal of this section is not to set new records for tractable deep generative models, but to establish a set of baselines that can be easily reproduced to track the progress of developments in PC modeling and learning. In Appendix C.4, we include additional benchmark results on the WikiText dataset (Merity et al., 2016). 7. Conclusion We proposed PyJuice, a novel system that supports training and inference of probabilistic circuits. PyJuice is orders of magnitude faster and much more memory efficient than even very recent baselines. 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Authors: (1) Anji Liu, Department of Computer Science, University of California, Los Angeles, USA (liuanji@cs.ucla.edu); (2) Kareem Ahmed, Department of Computer Science, University of California, Los Angeles, USA; (3) Guy Van den Broeck, Department of Computer Science, University of California, Los Angeles, USA; Authors: Authors: (1) Anji Liu, Department of Computer Science, University of California, Los Angeles, USA (liuanji@cs.ucla.edu); (2) Kareem Ahmed, Department of Computer Science, University of California, Los Angeles, USA; (3) Guy Van den Broeck, Department of Computer Science, University of California, Los Angeles, USA; This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv
