Cross-Attention and Encoder-Decoder Transformers: A Logical Characterization

Researchers present a novel logical framework for understanding encoder-decoder transformers using temporal logic extended with counting and past modalities. The work provides theoretical foundations for how these architectures process information across attention mechanisms, with implications for LLM interpretability and design.

This research addresses a fundamental gap in transformer architecture understanding by formalizing how encoder-decoder models process sequential information. The temporal logic framework introduces counting operations over encoder inputs and past-focused operations for decoder inputs, creating a mathematically rigorous model of attention mechanisms. This theoretical contribution matters because it bridges the gap between practical deep learning implementations and formal computational theory, enabling researchers to reason precisely about transformer behavior rather than relying on empirical observations alone.

The work extends beyond conventional transformer analysis by operating in the practical domain of floating-point arithmetic and soft attention, making the characterization relevant to actual systems rather than idealized versions. The distributed automata characterization provides an alternative lens for understanding these systems, suggesting multiple valid mathematical frameworks can describe the same architecture. This flexibility indicates the theory accommodates architectural variations, including different masking strategies, which reflects how transformers evolve in practice.

For the AI research community, this logical characterization could accelerate development of more interpretable models and enable formal verification of transformer properties. Developers building encoder-decoder systems for multimodal or cross-attention tasks gain theoretical guarantees about information flow. The autoregressive setting analysis proves particularly relevant for large language models, where understanding token generation sequences directly impacts performance optimization and safety considerations.

The significance lies in establishing a foundation for future work on transformer verification, safety guarantees, and efficiency improvements grounded in formal mathematics rather than intuition.

• →Temporal logic framework formalizes encoder-decoder transformer behavior with counting and past modalities
• →Theory operates in practical floating-point and soft-attention settings rather than idealized abstractions
• →Distributed automata characterization provides alternative mathematical lens for transformer analysis
• →Framework accommodates architectural variations including different masking strategies
• →Results enable formal reasoning about transformer properties critical for LLM interpretability and safety