Large language models (LLMs) are usually evaluated in chess by how closely their position evaluations agree with a strong engine, but such agreement does not show that a model evaluates equivalent positions consistently. We apply metamorphic relations to chess evaluation: a 180-degree rotation of pawnless positions, left-right mirroring, color swapping, position pairs one move apart, conversion between Forsyth-Edwards Notation and a natural-language description, and illegal positions. Six LLMs (Claude Sonnet 4.5, DeepSeek Chat, Gemini 2.5 Flash, GPT-5.1, Grok 4.1 Fast and Kimi K2 Turbo) evaluated seven test sets of 500 items each, with Stockfish 16.1 as the reference. All six models failed on rotation: at most 10.6% of the 500 rotated pairs received evaluations within 300 centipawns (cp) of each other, and the models often declared the legal rotated positions illegal. On the other four transformations, stability ranked the models as accuracy did except for the first two places: GPT-5.1 had the lowest mean stability error (186.17 cp) and Claude Sonnet 4.5 the lowest accuracy error (330.41 cp). Rejection rates for illegal positions ranged from 44.2% to 96.0%. Stability should be reported with the share of consistent pairs, because means over answered pairs concealed most rotation failures.
The success of the transformer architecture is in large part due to its use of attention layers. An attention layer follows the standard neural network paradigm: it takes the residual stream as input and thereby produces context-dependent query, key, and value vectors. However, we find that model performance meaningfully improves when deeper layers learn only a context-free value vector to preserve the original token information, without drawing on any context from the residual stream. When the model has access to this context-free value vector, adding back the context-dependent component provides little additional benefit for aggregate benchmark performance. Such context-free value vectors can be stored as sparse model parameters, eliminating the need to recompute or persistently cache these values. Through systematic ablations on the key design choices for such context-free value vectors, we propose Bank of Values (BoV), a new way of computing value vectors in attention by learning a lookup table of token-specific value vectors for each of the last third of layers. Across 135M and 780M models, BoV improves validation loss over standard attention and, at 780M, the average score across 21 benchmarks, matching the previous best method that adds token information to the value vector with less compute and memory.