Cutting-Edge AI Research Analysis
Causal Masking on Spatial Data: An Information-Theoretic Case for Learning Spatial Datasets with Unimodal Language Models
Authors: Jared Junkin, Samuel Nathanson
Publication Date: October 30, 2025
Abstract: Language models are traditionally designed around causal masking. In domains with spatial or relational structure, causal masking is often viewed as inappropriate, and sequential linearizations are instead used. Yet the question of whether it is viable to accept the information loss introduced by causal masking on nonsequential data has received little direct study, in part because few domains offer both spatial and sequential representations of the same dataset. In this work, we investigate this issue in the domain of chess, which naturally supports both representations. We train language models with bidirectional and causal self-attention mechanisms on both spatial (board-based) and sequential (move-based) data. Our results show that models trained on spatial board states - even with causal masking - consistently achieve stronger playing strength than models trained on sequential data. While our experiments are conducted on chess, our results are methodological and may have broader implications: applying causal masking to spatial data is a viable procedure for training unimodal LLMs on spatial data, and in some domains is even preferable to sequentialization.
Executive Impact: Unlocking New LLM Capabilities for Spatial Data
Our research demonstrates that training unimodal language models with causal masking directly on spatial data, like chess FEN, leads to superior performance (2630 ELO) compared to traditional sequentialization (PGN). This challenges conventional wisdom and highlights the viability and advantage of spatially-aware causal masking, opening new avenues for efficient LLM training on structured domains.
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Grandmaster ELO
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Best Move Accuracy (Causal FEN)
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ELO Improvement over PGN
Deep Analysis & Enterprise Applications
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Methodology Comparison
Performance Breakthrough
Strategic Advantages
Implementation Insights
Information Processing Differences
Our core hypothesis centers on the inherent efficiency gains when models directly process spatial information, even with causal masking, compared to inferring spatial structures from sequential inputs.
Enterprise Process Flow
PGN Model Ingests Sequential Data
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Implicit Spatial Reconstruction (G)
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Maps Latent Spatial to Moves (F→S)
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Outputs Next Move (ΠP: G◦(F→S))
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Versus FEN Model Ingests Spatial Data
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Directly Maps Spatial to Moves (F→S)
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Outputs Next Move (ΠF: F→S)
Achieving Grandmaster-Level Chess Play
Our Llama model, even when applying causal masking directly to spatial FEN data, achieved an estimated ELO rating that positions it firmly within the grandmaster tier of human chess players.
2630
Estimated ELO Rating (Causal FEN)
Comparative Performance of Masking Strategies
A direct comparison of models trained with different data representations and masking strategies clearly illustrates the significant advantages of applying causal masking to spatial FEN data.
| Metric | PGN (Causal Masking) | FEN (Causal Masking) | FEN (Bidirectional) |
|---|---|---|---|
| Estimated ELO Rating | 2000 | 2630 | 2680 |
| Best Move Accuracy (Stockfish) | 40.7% | 58.2% | 61.6% |
| Syntactically Valid Moves Rate | 99.7% | 99.945% | 100.0% |
| Legal Moves Rate | 99.7% | 99.914% | 100.0% |
Key Lessons for Spatial LLM Development
Our findings provide crucial insights for adapting pretrained LLMs to structured, spatial domains, emphasizing the importance of aligning tokenization and prompting with the underlying data structure.
Context
Our findings provide crucial insights for adapting pretrained LLMs to structured, spatial domains, emphasizing the importance of aligning tokenization and prompting with the underlying data structure.
The Challenge
Default tokenizers often create ambiguous merges (e.g., 'pk' for pawn-king) for FEN strings, hindering training stability and performance. Improper prompting can also limit the model's ability to leverage spatial information effectively.
Our Solution
We implemented character-level tokenization for FEN and flattened run-length encodings to ensure consistent representation. Templated prompts embedding FEN, legal moves, and best moves significantly stabilized training and improved convergence, allowing LLMs to exploit explicit spatial features.
The Result
These methodological choices enabled our causal-masked Llama model to achieve grandmaster-level performance and demonstrated that careful preprocessing and prompt engineering are critical, not just technical afterthoughts, when adapting LLMs to new domains.
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