ALTA: Compiler-Based Analysis of Transformers (2410.18077v2)

Abstract: We propose a new programming language called ALTA and a compiler that can map ALTA programs to Transformer weights. ALTA is inspired by RASP, a language proposed by Weiss et al. (2021), and Tracr (Lindner et al., 2023), a compiler from RASP programs to Transformer weights. ALTA complements and extends this prior work, offering the ability to express loops and to compile programs to Universal Transformers, among other advantages. ALTA allows us to constructively show how Transformers can represent length-invariant algorithms for computing parity and addition, as well as a solution to the SCAN benchmark of compositional generalization tasks, without requiring intermediate scratchpad decoding steps. We also propose tools to analyze cases where the expressibility of an algorithm is established, but end-to-end training on a given training set fails to induce behavior consistent with the desired algorithm. To this end, we explore training from ALTA execution traces as a more fine-grained supervision signal. This enables additional experiments and theoretical analyses relating the learnability of various algorithms to data availability and modeling decisions, such as positional encodings. We make the ALTA framework -- language specification, symbolic interpreter, and weight compiler -- available to the community to enable further applications and insights.

• The paper introduces ALTA, a novel compiler framework that compiles symbolic programs into Transformer weights, enabling length-invariant algorithm representation.
• It details how ALTA supports dynamic control flows and loops, outperforming earlier methods by efficiently mapping attention and MLP operations.
• The study analyzes learnability challenges and demonstrates that trace supervision bridges the gap between algorithm expressibility and practical Transformer training.

Analysis of ALTA: Compiler-Based Analysis of Transformers

The paper introduces a novel programming language and compiler framework, ALTA, which aims to map symbolic programs to Transformer model weights. ALTA draws inspiration from previous works like RASP and Tracr, offering extensions and enhancements such as supporting loops and compiling to Universal Transformers. This framework provides a structured method to investigate the expressive capabilities of Transformers, particularly in representing length-invariant algorithms without intermediate decoding steps. Furthermore, ALTA brings new tools for analyzing algorithm expressibility and model learnability, providing a significant addition to the corpus of computational frameworks for Transformers.

Key Contributions and Results

1. Symbolic Program Compilation: ALTA provides a seamless path for converting symbolic programs into Transformer weights. The language supports dynamic control flow operations, distinguishing it from previous efforts like Tracr, which depended on autoregressive decoders for similar tasks. The compilation process involves mapping attention and MLP operations into Transformer parameters, optimizing through techniques like shared layer weights.
2. Expressibility Demonstrations: Central to the paper are new results on the expressibility of Universal Transformers. ALTA constructs models capable of executing algorithms like parity, addition, and solving SCAN tasks without relying on intermediate representations. In particular, the Sequential (Relative) program demonstrates significant length invariance, showcasing ALTA's ability to highlight expressive possibilities in Transformer architectures.
3. Learnability Analysis: The paper explores the gap between expressibility and learnability, proposing trace supervision as a method to bridge this divide. By leveraging execution traces from ALTA programs, the authors examine scenarios where additional supervision signals aid in training models to better match desired algorithmic behavior. For instance, the task of computing parity highlighted cases where trace supervision provided clarity on Transformers' failure modes under traditional training paradigms.
4. Theoretical Insights: ALTA introduces the concept of program minimality, analytically evaluating conditions under which specific algorithms can be learned from given datasets. Through rigorous theorems, the authors connect minimal program criteria with local optima of the reconstruction loss, suggesting that correctly framed learning objectives align closely with compiled Transformer implementations.

Implications for AI and Future Directions

The implications of ALTA are considerable for both theoretical and practical domains. The framework enhances understanding of how Transformers can represent and learn symbolic processes, potentially guiding improvements in model architectures and training paradigms. By offering a way to integrate symbolic reasoning within deep learning models, ALTA opens pathways for exploring more interpretable and efficient AI systems.

Practically, the availability of ALTA's framework in open-source format invites community contributions and expansions. It could serve as a testbed for further interpretability tools, algorithmic efficiency studies, or even novel applications in software verification and reasoning.

Future trajectories might involve integrating ALTA's approach with other model forms beyond Transformers, exploring how dynamic program compilation can benefit architectures like graph neural networks or recurrent models. Furthermore, expanding the framework to incorporate probabilistic or fuzzy logic representations might enhance its utility in broader AI applications, ensuring it stays at the forefront of computational innovation.

In summary, ALTA represents a comprehensive toolkit for advancing the understanding and application of Transformers in complex algorithmic tasks. Its blend of expressibility analysis and theoretical insight positions it as a valuable contribution to the ongoing evolution of machine learning and computational linguistics.