Thank you for your comment. Our response addresses two main points:
1. Coherence is the central motivation of our work, not just a post-hoc observed outcome.
2. Hermes ensures better coherence than the baselines through its unified, parameter-sharing approach.
**Coherence as central motivation**
We emphasize that coherence is not only observed post-training--it is the central motivation of our work. The third sentence of the Abstract states "Critical to achieving this goal, however, is coherently modeling human behavior at various skill levels." (L5). The central limitation of previous work, and the motivation for our present work, articulated in the Introduction is Maia's lack of coherence (paragraph starting on L48: "Maia models players at different skill levels completely independently...Viewed as a whole, [Maia's predictions] are volatile", "In order to serve as algorithmic teachers or learning aids, our models of human behavior must be coherent"). The first sentence of the Discussion summarizes our contribution as "Hermes is a unified model architecture that can accurately and coherently capture human decision-making in chess across a broad spectrum of skill levels." (L383). We hope that situating coherence as the central idea of our paper in the Abstract, Introduction, and Discussion makes it sufficiently clear that coherence is what we are aiming for, instead of something we stumbled upon, but we would also be happy to implement any suggestions you have in order to make this point clearer.
**Architecture intuition**
As for why Hermes ensures better coherence than the baselines, we are happy to provide some intuition (which we will certainly incorporate into our revision to make sure this is as clear as possible). In one sentence, Hermes uses a **unified, parameter-sharing modeling approach** instead of Maia’s independent parameters as a way to regularize across skill levels.
To explain more fully, the root cause of Maia's lack of coherence is that Maia models learn 9 sets of independent parameters for each of the 9 skill levels. This means that there is no mechanism to encourage or enforce consistency (i.e. coherence) across skill levels. Maia 1400 and Maia 1500, for example, are distinct models with completely separate training data and zero parameter overlap. As a result, Maia often outputs dramatically different predictions for neighboring skill levels on the same position, which leads to a lack of coherence. In contrast, in Hermes we learn a unified set of parameters to predict human decisions conditioned on skill level. This ensures that the conditional prediction will always be based on the shared knowledge in the one and only parameter space that we learn---therefore decisions made by 1500-rated players are partially informed by what 1400-rated and 1600-rated (etc.) players do. In other words, Hermes is implicitly regularized by the shared parameters across all skill levels, without over-optimizing towards any particular skill level. Neighboring skill levels will yield similar predictions, e.g., P(y|position, skill level_{i}) \approx P(y|position, skill level_{i+1}), unless Hermes recognizes some condition to switch to another prediction is satisfied. This unified modeling approach ensures **coherence by design**.
In addition, our skill-aware attention module enables Hermes to learn non-trivial interactions between positions and skill levels. The skill-aware attention module plays a crucial role in maintaining coherence. Whereas the various Maia models learn different representations of the position for each skill level, Hermes first learns the same unified representation that it uses for all skill levels, and then the skill-aware attention module learns how different skill levels interact with the position to produce a move. By learning a unified representation of the position first, and then adjusting based on skill level, Hermes ensures that all skill levels are informed by a consistent understanding of the position. This decomposition---learning position representation separately from skill-level interaction---naturally encourages coherence across skill levels.
**Summary**
In summary, our central motivation is to develop a model capable of coherent and accurate human move prediction. Our unified modeling approach is deliberately chosen to solve Maia's parameter independence problem, and our skill-level attention module is specifically designed to maintain a shared position representation across all skill levels while better modeling the interactions between position and skill level. We hope this addresses your concern.
If this explanation clarifies that coherence is our central motivation and why Hermes's design encourages coherence, along with the other points we addressed in our first response, would you be open to considering raising your score?