KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI (2410.11415v3)

Abstract: A popular approach to neurosymbolic AI involves mapping logic formulas to arithmetic circuits (computation graphs consisting of sums and products) and passing the outputs of a neural network through these circuits. This approach enforces symbolic constraints onto a neural network in a principled and end-to-end differentiable way. Unfortunately, arithmetic circuits are challenging to run on modern AI accelerators as they exhibit a high degree of irregular sparsity. To address this limitation, we introduce knowledge layers (KLay), a new data structure to represent arithmetic circuits that can be efficiently parallelized on GPUs. Moreover, we contribute two algorithms used in the translation of traditional circuit representations to KLay and a further algorithm that exploits parallelization opportunities during circuit evaluations. We empirically show that KLay achieves speedups of multiple orders of magnitude over the state of the art, thereby paving the way towards scaling neurosymbolic AI to larger real-world applications.

• The paper introduces Knowledge Layers (KLay) to efficiently parallelize arithmetic circuit evaluations on GPUs.
• It presents a layerization algorithm that organizes circuit nodes into parallelizable layers using unary nodes for consistency.
• The approach handles multi-rooted circuits via node deduplication with Merkle hashes, achieving multiple orders of magnitude speedup on benchmarks.

Accelerating Neurosymbolic AI with KLay

The paper "KLay: Accelerating Neurosymbolic AI" addresses a critical computational challenge in neurosymbolic AI, specifically the inefficient processing of arithmetic circuits on modern AI accelerators due to their irregular sparsity. By introducing Knowledge Layers (KLay), the authors propose a novel data structure that significantly optimizes arithmetic circuit evaluations on GPUs.

Neurosymbolic AI aims to integrate symbolic reasoning with neural networks, enhancing reasoning capabilities, safety, and interpretability. These models often include dense neural components and sparse symbolic components, complicating efficient computation, especially on AI accelerators like GPUs.

Core Contributions

1. Knowledge Layers (KLay): A new data structure that represents arithmetic circuits for efficient parallelization. KLay exploits GPU capabilities by transforming circuit evaluations into index and scatter operations, allowing computational efficiency akin to tensor libraries such as PyTorch and Jax.
2. Layerization Algorithm: The paper proposes an algorithm to map traditional circuit nodes into parallelizable layers. Nodes are organized by height, and unary nodes are introduced where necessary to maintain layer consistency, enabling layer-wise evaluation.
3. Multi-Rooted Circuit Handling: The research extends to multi-rooted circuits common in batched inference settings. By deduplicating nodes using Merkle hashes, KLay efficiently compiles circuits to reduce redundancy, further optimizing parallel computation.
4. Empirical Validation: KLay achieves multiple orders of magnitude speedup over existing methods, as demonstrated by experiments on synthetic benchmarks and neurosymbolic tasks. This performance underlines KLay’s potential to scale neurosymbolic AI to more complex real-world applications.

Numerical Results and Analysis

The proposed method exhibits substantial improvement over previous state-of-the-art implementations, especially in scalability and efficiency. On synthetic benchmarks, KLay outperformed baseline methods significantly, including customized hardware implementations that traditionally relied on CPU evaluations due to the complexity of GPU processing. This highlights KLay's capacity to execute large-scale arithmetic circuits effectively without requiring hardware-specific implementations.

Implications and Future Directions

KLay presents a pivotal advancement in the neurosymbolic AI framework by resolving one of its primary computational bottlenecks. It enables the broader deployment of neurosymbolic models across various applications, significantly expanding their utility and scope.

Looking forward, KLay could stimulate further exploration into optimizing sparse computational graphs on general-purpose hardware. By enhancing the integration of symbolic logic with deep learning architectures, KLay fosters a more rich interaction between symbolic and sub-symbolic paradigms. Future work could investigate extending KLay to accommodate different types of symbolic knowledge representations or incorporating dynamic circuit generation capabilities.

In conclusion, KLay offers a substantial stride towards harmonizing the strengths of symbolic reasoning with the scalability of neural networks. Its capacity to deploy efficiently on widely available hardware accelerates the adoption of neurosymbolic AI in diverse domains, potentially leading to innovative applications and developments.