Learning to Imitate with Less: Efficient Individual Behavior Modeling in Chess
Authors: Zhenwei Tang
Difan Jiao
Eric Xue
Reid McIlroy-Young
Jon Kleinberg
Siddhartha Sen
Ashton Anderson
Venue: Accepted by TMLR ()

Abstract: As humans seek to collaborate with, learn from, and better understand artificial intelligence systems, developing AIs that can accurately emulate individual decision-making becomes increasingly important. Chess, a long-standing AI benchmark with precise skill measurement, offers an ideal testbed for human-AI alignment. However, existing approaches to modeling human behavior require prohibitively large amounts of data from each individual, making them impractical for new or sparsely represented users. In this work, we introduce Maia4All, a framework designed to learn and adapt to individual decision-making styles efficiently, even with limited data. Maia4All achieves this through a two-stage optimization process: (1) an enrichment step, which bridges population and individual-level human behavior modeling with a prototype-enriched model, and (2) a democratization step, which leverages ability levels or user prototypes to initialize and refine individual embeddings with minimal data. Our experimental results show that Maia4All can accurately predict individual moves and profile behavioral patterns with high fidelity, establishing a new standard for personalized human-like AI behavior modeling in chess. Maia4All achieves individual human behavior modeling in chess with only 20 games, compared to the 5,000 games required previously, representing a significant improvement in data efficiency. Our work provides an example of how population AI systems can flexibly adapt to individual users using a prototype-enriched model as a bridge. This approach extends beyond chess, as shown in our case study on idiosyncratic LLMs, highlighting its potential for broader applications in personalized AI adaptation.

Published in Transactions on Machine Learning Research (01/2026)
Learning to Imitate with Less: Efficient Individual Behavior Modeling in Chess
Zhenwei Tang
josephtang@essttrnnto.ddd
University of Toronto
Difan Jiao University of Toronto
difanjian@tes.trronto..tt
Eric Xue University of Toronto
scuue@mail.utoroonooo..
Reid Sellroy-Young
reidmcy@@seas.hrroordd edu
Harvard University
Jon Kleinberg Cornell University
Meinbery@eornelll.eh
Siddhartha Sen Microsoft Research
sidsen@microsoft..com
Ashton Anderson University of Toronto
ashton@cs. edu
Reviewed OpenReview: httpp:://openreviaau net/ forum? id= tm4kjcu319
Abstract
As humans seek to collaborate with, learn from, and better understand artificial intelligence systems, developing AIs that accurately emulate individual docision-making becomes increasingly important. Chess, a long-standing AI benchmark with precise skill measurement, offers an ideal testbed for human-Al alignment. However, existing approaches to modeling human behavior require prohibitively large amounts of data from each individual, making them impractical for new or sparsely represented users. this work, we introduce Maia4All, a framework designed learn and adapt to individual decision-making styles efficiently, even with limited data. Maia4All achieves this through two-stage optimization process: (1) an enrichment step, which bridges population and individual-level human behavior modeling with a prototype-enriched model, and (2) a democratization step, which leverages ability levels or user prototypes to initialize and refine individual embeddings with minimal data. Our experimental results show that Maia4All can accurately predict individual moves and profile behavioral patterns with high fidelity, establishing a new standard for personalized human-like Al behavior modeling in chess. Maia4All achieves individual human behavior modeling in chess with only games, compared to the 5,000 games required previously, representing a significant improvement in data efficiency. Our work provides an example of how population Al systems can flexibly adapt to individual users using prototype-enriclan bridge. This approach extends beyond chess, shown in our case study on idiosyncratic LLMs, highlighting its potential for broader applications in personalized AI adaptation. Maia4All implementation available at httph::////// https:///iihub... https//b....omSSSsaaaaaaaaaallll
model as

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Published in Transactions on Machine Learning Research (01/2026)
1 Introduction
The rise of artificial intelligence (AT) systems that rival or surpass human ability in domains where people remain active has introduced the possibility of collaborating with and learning from AI agents. A line of research has pursued this vision in the model system of chess, in which AI became superhuman 20 years ago, people vary widely in their ability, and vast detailed datasets of action traces abound. Since capturing human docision-making style is a prerequisite to wwwpgthhmiialll--fffaaaea
tcaching and collaboration, previous work has focused on creating AT agents that mimic human play (Mellroy- (Mellroy-Young et al.] 2020 2022 Jacob et al. 2022] Tang et al. 2024). Further, since capturing individual prrision-mmaiin style is a prerequisite to personally tailored algorithmic instruction, rescarchers have developed models of how specific people play chess, surpassing population models in their accuracy rates their target individual's decisions (MeIlroy- Young
et al. 2022
However, these fine-tuning-based models of individual decision-making require extraordinary amounts of data per person to function. When Maia, a human-like chess engine, was fine-tuned to play like specific individuals, gains accuracy over base Maia were only achieved when the player had 5,000 games worth of data (Mellroy- Young et al. 2022). This is an immense amount of game-playing; typical person would take around 1,000 hours to play this many games, which is equivalent to almost 25 weeks of full-time work at 40 hours per week. To put this in perspective, less than 1% of players on Lichess, a popular online chess platform, have played at least 5,000 games. Therefore, existing approaches for modcling individual behavior fall short of being full solutions to the problem, because they don't work for the vast majorily of people. In order for everyone to benefit from need another way to capture individual decision-making style-one that works in a much more data-cfficient manner.
halhmmmiiaall--ifommeee teaching, learning, and collaboration, we first
How could we go about modeling individual-level prcision-makinge behavior for the everyday person with much more modest amounts of data available? This is difficult task for two reasons. First, existing models for modeling human meaksinn-making, such as Maia and Maia-2 (Mellroy-Young et al. 2022 Tang et al. 2024), are population models. This, as we will see, makes direct fine-tuning ineffective, especially for low-resource players. Second, human action prediction is formulated as a generative task to predict the next move that requires a model with strong generalization capabilities, which is particularly hard to achieve in a low-resource environment.
In this work, we propose novel approach that produces Maia4All, model that overcomes both of these challenges. Strikingly, Maia4All can model successfully individual-level play with only 20 games of data, in stark contrast to the previous requirement of at least 5,000 games. While Maia-2 shows virtually no progress when given 20 games of data played by a specific individual, and Maia fine-tuned with 1,000 games even gets worse than a base model, Maia4All siguificantly rises in accuracy from a baseline of 51.4% to 53.2% a comparable rise to the accuracy gains reported in previous work using 5,000 games per player (Mellroy- Young let al. 2022). By this measure, our approach is 250 times more data-efficient than prior methods.
We achieve data-efficient modeling of individual behavior in chess with two methodological contributions. First, after showing that straightforward fine-tuning fails, we design a novel two-stage fine-tuning approach. First, we enrich Maia-2 by fine-tuning it to a diverse set of prototype players with rich game histories in order to adapt the model parameters from population-level modeling to individual-level modeling. Empirically, this makes it easier for the model to further adapt to low-resource players. In the second stage, we further finc-tune this prototype-infused model with low-rcsource player data. This two-stage approach is surprisingly effective fine-tuning directly on low-resource players doesn't 't work, but first enriching the model with a carefulll--seleceed set of prototype player data is key to our eventual success. Our second contribution is to start with a discriminative task instoad of attempting the difficult generative task directly; we first find the most similar prototype player to the target player we want to model with a prototype-matching meta-nel Once we've identified a suitable prototype player, we initialize the target player's embedding with the prototype's embedding, and fine-tune on their limited data with this much better initialization.
Our framework provides state-of-the-art individual behavior modeling in chess, which can open the door to personalized chess teaching and learning. Beyond chess, our novel two-stage design has potential to
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benefit other domains that require data-efficient adaptation to individual behavior. To demonstrate its broader applicability, we include a case study on idiosyneratic LLMs, showing how our two-stage optimization framework enables LLMs to mimic individual writers effectively from limited data.
2
Methodology
Our methodology consists of two major steps. Starting from a base model (Maia-2 in our case), we first conduct an enrichment step that enables the model to better capture individual-lovel patterns. Second, we perform democratiaation step that adapts the model to work unseen players with limited data. We present preliminary details about the base model followed by our two-step methodology.
2.1 Base Model: Maia-2
Choosing Base Model. Maia-2 (Tang et al. 2024) is a state-of-the-art human-like chess Al designed to predict human moves across skill levels using a unified transformer architecture. Unlike traditional chess Als such as AlphaGo (Silver et al. 2016) and AlphaZero (Silver et al. 2017). which focus on best-move prediction and optimal play, Maia-2 is explicitly trained to model human prcision-making making it a strong foundation for our work. Maia-2 improves upon its predecessor, Maia (Mellroy- Young et al. 2020), by learning a unified parameter space where move prediction is modulated through skill-level embeddings, rather than relying on separate models for different skill levels. This design makes Maia-2 an ideal base model for fine-tuning toward individual behavior modeling, its skill-level embeddings, initially trained on population-level data, can be further adapted to capture the unique patterns that characterize individual-level play. Allie (Zhang et al. 2024) is another approach to human move-nat which introduced an adaptive Monte-Carlo Tree Search with pondering time prodiction method. We chose Maia-2 as our base model for two reasous specific to individual modeling. First, Allie models skill levels with linear interpolation between a weak and strong control token, which may be inadequate for capturing playing style that is beyond strength non-lincar in nature. Unlike Maia-2's skill-level emboddings that can be fine-tuned from population-level representations to adapt to individuals, Allie's interpolation mechanism does not provide straightforward path for individual adapiation. Second, Allie requires a complete move history from the starting position for prediction, whereas Maia-2 operates on single board positions, which is more widely applicable in cases such as modeling individual puzzle solving, where move history from the starting position is often unavailable.
Architecture. We first present a concise overview of Maia-2's architecture. As shown in Figure ! Maia-2 consists of chess position encoder, a skill encoder, and transformer-base skill-aware blocks. The model takes chess position p, represented as a multi-channel tensor, along with skill levels of the aclive player r(a) and the opponent player r(o) as inputs, where r(.) denotes the mapping from a player to its skill level. Following the original design of Maia-2, when modeling only the behavior of the active player without considering variations in opponent strength, we set r(a) = r(o) to ensure a consistent skill representation. We denote the policy head prediction of Maia-2 for player i as:
a a= )=)(pr(()1))
(1)
where 0 represents the trainable parameters in Maia-2. A ResNet-bbaed (He et al., 2016) position encoder first encodes chess positions into position embeddings. The position embeddings then undergo channel-wise patching and linear transformation (Tang et al. 2024). and are fed into the residual flows of transformer blocks. Within these blocks, Maia-2 performs skill-aware attention to fuse skill embeddings with the position encodings. Maia-2 applics a vanilla ViT feed-forward network and Add & Norm component to obtain the output of each block and add it back to the model's residual stream. The model's output includes a policy head for move prediction, a value head for game outcome prediction, and an auxiliary information head for accelerating game rule learning from objective training goals. We focus exclusively on the policy head, as it is responsible for modeling individual player behavior, whereas the value and auxiliary heads in Maia-2 are mainly used as proxy rewards to guide the model.
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Historical Positions Before Action
Feature Extractor
Still inceder for Populatonn Individral
Historical Posttions After
Historical
Skill-Amare Altumiiun
+
Qaery
Fexd
Prototype Embeddings Ey
Transformer
Valual
Query
History Emb
Weighted Aggregation
ReaNet
Fenture Extractor
wise pucchngg
Forward
Similar Prototypes with Weights
Player Emb
Protetype Matching
Policy Heed
Auxiliary Head
Value Heed
Figure (Left) The architeclure of our base model Maia-2, which uses population embeddings to adapt. to different skill levels. We enrich Maia-2 by extending population embeddings to individual embeddings. (Right) The procedure of Profotype-Informeed Initialization and the architecture of the Prototype Matching Network.
2.2 Enrichment Step
The first step of our methodology is an enrichment step that adapts the base model so it can capture individual-level behavior instead of only aggregated population-level patterns.
Population Modeling in Maia-2. Chess players can be meaningfully grouped by skill level (Mellroy- Young
et al. 2020 2022). which is quantified using widely adopted rating systems (Elo 1967 1978) Maia-2's skill encoder lollows this norm and is designed for player populations at different skill levels. Let Ep E R|ErIx be the matrix of population embeddings, where each row corresponds to the embedding with dimension d of a group of players that share similar strength:
Ep [e00,1000 1(1100,1200) ... @(2000
(2)
Given player of skill level r(i), we look up the embedding matrix Ep by rows to map the player skill level to its embedding e, Er[r(()]. We decompose pre-trained Maia-2 parameters 0 = { Ep} for clarity:
a = f ri)] Er),
where & denotes the model parameters except for the population embedding matrix. Given the universal set of parameters o, Maia-2 adapts to different player populations by dynamically selecting the corresponding population embedding, allowing the model to account for variations in player skill levels.
To extend Maia-2 beyond population-level modeling, generalize population embed- dings (e.g. one entry per entire rating range of players) to individual embeddings (c.g. one entry per player), enabling the model to capture variations in individual player behavior much more precisely. Given a set of individual players (the choice of which still to be determined), we denote their embedding matrix as E, E g E, [xd where each row corresponds to a specific player. Given a player E I, we look up E, by rows to obtain the corresponding embedding, which initialized with the player's population embodding before the enrichment step: e; Eyli] +- Ep(r(i)). The enriched Maia-2 model retains the same universal parameters as Maia-2 at initialization:
Enriching Maia-2.
= fp,
(4)
Since has already been trained to model diverse groups of players, serves as strong foundation for fine-tuning toward capturing ledividual-evel variation. To enrich the model it captures individual-level
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Prototype Enriched Mala-2 with I
Mals4All: Democratization for it
All Players
Universal Puranesess
Universal Paruneters
Prototype Selaction
Population Emn =1100
Procotope 1 Emb
Unsen Player Emih 40
Pepulation Fash 1100-1199
Ep R3
Procotype 2 Farb
Protetypo
I
Uneass Playa=
Population 23000
Prontype K Emb
Profeegpe-nffemedd Intialiioiion
Strengh-lnfeeme Intallaztion
Figure 2: Overview of our proposed framework.
behavior, we minimize the following training objective:
L(o = - ELEr IPAl
1
ΣΣ iET PEP:
log P(a" P(a"I ((,,
(5)
where P. denotes the set of historical positions of player i and a" is the ground-truth move made by the player. After fine-tuning, the model refines both & and E,, producing updated parameters d' and E2 in the Enrichod Maia-2 model:
f(p, ild', Et)
(6)
Prototype Selection. While this enriched model can be directly used to model the behaviors of a pre-defined set of players I, it is unrealistic to include all players (e.g., the 11 million players on Lichess). Firstly, learning separate embeddings for massive sets of players is challenging for computational and model Icarnability reasons. But even more importantly, most players haven't played enough games to support an accurately learned embedding for them. Furthermore, there are always new chess players, who would require constant re-training to support. Therefore, this enrichment step produces crucial intermediate but incomplete model the way towards our goal of truly efficient and effective individual behavior modeling. It will help facilitate further adaptation to all individual players, particularly those with sparse data.
Which individual players should be in our set !? This extensibility requirement guided us to carefully select players for this enrichment step with two key criteria. First, players should have sufficient historical data (i.e. completed games) to ensure that. their decision-making styles can be well learned in E,, and so ø' will not be corrupted by under-trained embeddings. Second, the player set should be balanced across different skill levels to prevent the model from being biased toward any particular skill level. Ensuring diverse distribution of players helps this enriched model learn well-calibrated set of parameters o' that generalizes effectively across individual players with varying levels of expertise. We refer to these carefully selected players as prototypes, and the enriched model trained on these prototypes as Prototype-Enrichee Maia-2, which serves as a foundation for further adaptation to a much broader range of individual players.
2.3 Democratization Step
The enrichment step transitions model parameters ø' from being optimized for population-level modeling to being optimized for individual-level modeling. As previously discussed, it is infeasible to use the enriched model directly on all players, but it is now much more adaptable than the base model to unseen players U-any one of the vast majority of players who were not selected as prototypes. The key reason for this adaptability is that ø' becomes more responsive to individual embeddings, enabling more precise modulation of move predictions. This effect arises because the skill embeddings, initially constrained to 11 population embeddings in the base model Maia-2, have been expanded to much larger set of individual embeddings spanning a diverse player distribution, requiring the model to distinguish players with greater sensitivity.
We use Prototype-Enrichee Maia-2 as an intermediate model to efficiently adapt to unseen individual players even those with minimal data to learn from. This second and final step in our methodology democratizes Maia-2 and Prototype-Enrte Enriched Maia-2, making individual behavior modeling accessible to all players, not just. those with extensive historical data. We call this model Maia4All.
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To adapt to an unseen player u from the intermediate model, we minimize the loss function:
((e,) = PPal
Σ PEPu
log P(a")s(rlo''ee))
(7)
where Pa. denotes the set of historical positions of unseen player a' is the ground-truth move made by u, and e, denotes the individual embedding for u. Thus, ey is optimized towards modeling denoted as e', and the policy head prodiction is given by: a f
(8)
Strengtt--nformedd Initialization. Although ø' lays a strong foundation for democratizing Maia-2 to unseen players, an effective initialization strategy for unseen player embeddings is crucial for data-efficient adaptation. To address this, we propose to initialize unseen player embeddings using prior knowledge, enabling more efficient parameter updates. A natural source of prior knowledge is player strength, as reflected by their ratings. In chess, decision-making style is strongly influenced by player's strength. For example, novice is unlikely to employ the deep strategic insights characteristic of more advanced players. Therefore, player strength serves as a natural reference point for initializing player embeddings:
Initialize
Eplr(u)]-
(9)
However, player strength is only one dimension of a richer space of behavior. People not only vary in the overall quality of their play, but also in their decision-making style. In chess, people can tend towards being more aggressive or defensive, positional or tactical, intuitive or calculating, etc. Although overall quality metrics like ratings capture a lot of variation, it is likely that decision-making style is more variable and requires more careful initialization. Therefore, we aim to initialize the unseen player embedding e, with similar player embeddings.
Prototype-Inforned Initialization. Beyond the more responsive universal parameters inherited from the intermediate model, the learned prototype embeddings E, also play a crucial role in prior-informed initialization by leveraging similarities with existing prototypes. Since our prototype selection ensures a balanced distribution across skill levels, the prototype set I should idcally cover the diverse player styles across skill levels. Furthermore, because prototypes are chosen from players with extensive game histories, their embeddings will be well-trained and serve reliable references for initializing new player emboddings.
We train a transformer-based mela-nelwork for protolype matching, i.e., given unseen player, identifying similar prototypes that will be useful for initialization. As shown in Figure [ (Right), during training, given a collection of historical moves from a prototype player i E I, we extract position features before and after the player's ground-truth actions using ResNel-based lowers pre-trained by Maia-2. To encode player style, we apply stacked Transformer layers with mean pooling to aggregate historical action embeddings into a single history embedding. This embedding is then fed into a classification head with [I] outputs, designed to identify the corresponding prototype player. Since we use prototype players for training, the true identity of the player generating the history is naturally available, allowing us to train the [Z|-class classifier using a cross-entropy loss. We refer to this model as the Prototype Matching Network (PMN).
During inference, we input the historical moves of an unseen player u E l into PMN to assess the similarity between the player's style and the prototype players. The model's predictions are passed through a softmax function, and the top-k most similar prototypes are selected. Their embeddings are then combined using a weighted average to serve as the protolype-informed initialization of e..
Note that both prototype matching and our final task human move prediction exploit the same set of historical behaviors of unseen players. However, prototype matching is a much casier task than the latter. This is because ype matching is essentially discriminalive task against a fixed set of classes (prolotypes), and human move prediction is a next-move generative task that requires a deeper understanding of the player's docision-making style. Therefore, we initialize the player embedding with the casier prototype matching task to get a rough understanding of how similar players behave and further calibrate the player embedding with human move prediction loss.
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3
Experiments
We now conduct extensive experiments to evaluate how our novel two-step methodology for efficient individual- level behavior modeling performs and compares with strong baseline methods.
3.1
Experimental Settings
Datasets. Online chess platforms feature variety of game types, including blitz, rapid, and classical, each representing games played at different time controls (amount of time given to each player for the whole game). We use data derived from the jopnn database provided by Lichess) a well-known large open-source chess platform. In Lichess, since each game type is given a separate rating, ratings across different game types are not comparable (e.g. a rating of 1800 in "Rapid" is significantly weaker than rating of 1800 in "Blitz" on Lichess). We focus Blitz games because it is data-rich, and do not mix with other game types to ensure the ratings are meaningfully comparable. For protolype players, we use their game history in 2023 to compromise between the changing player strengths and styles over time and the availability of rich historical data. We follow Maia-2 by dividing players into 11 bins: under 1100, over 2000, and nine 100-point wide strength bins from 1100 to 2000, i.., |Epl= = 11. During training for Poototype-Enricher Maia-2, we use the game history of the N most frequent players in each strength level, i..., E = 11N. For testing, we use 10 prototype players and 10 unseen players per strength level. To simulate unseen players with limited game history, restrict their training positions to the first M positions while evaluating their performance the last 2048 positions recorded in 2023. This results in test datasets containing 225,280 positions for both prototype and unseen players.
Implementation Details. To maintain a consistent perspective from both sides of players, we used board flipping during both training and testing; that is, positions with black to move were mirrored so that all analyses could be conducted from the white side's viewpoint. Consistent with prior work, we further refined our dataset through game and position filtering, selecting games with available clock information and disregarding the initial 10 plies of each game as well as positions where either player had less than 30 seconds remaining. This filtering procedure mitigates the noise introduced by decisions made under extreme time pressure, which could skew the true representation of a player's strength and style. We report all hyperparameters involved in training in Table in the Appendix.
Evaluation Protocol. We evaluate our method with top-1 move-matching accuracy, which is essentially an extensive human study: observe what humans would play in natural situations recorded by the Lichess Database, and see if it matches the predicted move of our system. We also measure the perplexity of move predictions, which reflects the model's confidence in its predictions. A lower perplexity indicates the model is more confident and accurate in human move prediction, as it corresponds to a higher likelihood (lower log-likelihood) of the correct human move. We report the results with three categories: Skilled (Blitz rating up to 1600, which slightly excoods the initial rating of 1500), Advanced (Blitz rating between 1600 and 2000), and Master (Blitz rating over 2000, roughly comprising the top 10% of players (Duplessis))
Baselines. Maia (Mllroy- Young et al. 2020 is a set of 9 separate models, each trained on a different set of players at different skill levels from 1100 to 1900. Maia-1100 models the weaker players, Maia-1500 the intermediate players, and Maia-1901 the higher-skill players. We choose one of the Maia models for each population such that it is the nearest to their strength level for fair comparison. Since Maia--nnividdul [Mcllroy] Young et al.) 2022) is designed for data-rich settings, the published results of Indiviuda indicate that it requires 5,000 games per player to show improvement over Maia. However, Maia4All, as a method specifically designed for low-resource individual behavior modeling, most has access to 100,000 positions (* 2,500 games). Therefore, we do not include Maia-Individus as a bascline, since it docs not apply to the sparser settings we consider (and which cover the vast majority of players on Lichess). Note that the goal of meta learning methods (Finn et al.) 2017 Nichol et al. 2018) is to optimize for the query set without emphasizing the performance on the support set (similar to prototype players). While in Maia4All, we consider all players equally, the separation of prototype and unseen players is for the purpose of democratizing the individual behavior modeling process for all players. Therefore, our work is not strictly under a meta-learning setting.
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Table 1: Performance on unseen players under low-resource settings.
Move Prediction Accuracy f
Move Prediction Perplexity +
# Positions
20,000
8000
2000
800
20,000
8000
2000
800
# Games
=500
2020
=50
=220
=500
=200
A50
=22
Maia
0.5132
0.5132
0.5132
0.5132
5,4530
5.4530
5.4530
5.4530
Maia-2
0.5146
0.5146
0.5146
0.5146
4.5316
4.5316
4.5316
4.5316
Maia-2- 2aia-2-Strength
0.5195
0.5196
0.5193
0.5189
4.4932
4.4939
4.4976
4.5022
MaiaaAll-Strenntth
0.5308
0.5298
0.5279
0.5249
4.3077
4.3238
4.3658
4.4151
Maia-All-Protooype
0.5365
0.5348
0.5334
0.5322
4.2295
4.2431
4.2669
4.2988
Furthermore, meta learning methods require split support and query sets (prototype and unseen players) beforehand. However, the process to separate prototypes and unseen players (prototype selection) is inherent methodological component in Maia4All. Therefore, it's challenging to isolate Maia4All completely to apply classic meta learning methods as baselines directly.
3.2 Results
Base model: Maia2. The key difference between Maia and Maia-2 lies in their approach to modeling player's skill levels. Maia requires the selection of the appropriate sub-model based on a player's strength. In contrast, Maia-2 employs unified modeling approach, allowing it to dynamically adapt to various skill levels within a single model. This adaptability is enabled by skill-aware attention, which modulates model predictions based on the corresponding skill embedding, which represents a population or an individual. For fair comparison, we select the sub-Maia model that matches each player's strength level. For Maia-2, skill embeddings are initialized using the corresponding population embedding that aligns with the player's strength level. As shown in Table D and Table 2 Maia-2 consistently outperforms Maia across all evaluation metrics and settings. While top-1 accuracy gains are important, they may overshadow more significant improvements in prediction quality. Such results show that Maia-2 can not only more accurately predict human behaviors but also be much more certain about its predictions. These results support our choice of adopting Maia-2 the base model.
Maia-2-Stee 2-Sten-St We developed version of MaiadAll that skips the enrichment step. Since the prototype embeddings are obtained within this step, prototype-nnfrmeed initialization is not available. Therefore, we apply strength-informed initialization for fair comparison. We refer to this model as Maia-2-Strengtth. As shown in Table I and Table 2 directly fine-tuning from the base model for population modeling barely improves human move prediction accuracy and perplexity under low-resource and relatively data-rich settings; low-rcsource move matching only improves by 0.5 percentage points (p.p.) over the base model. This demonstrates the need for our two-stage approach and prololype-informed initialization.
Prototype-Enriched Maia-2. Previous work (Mellroy- Young et al. 2022) has shown that fine-tuning population models to individual players requires a substantial amount of data. Specifically, the previous state-of the-art that--of sees performance improvements over the base population model emerge only after fine-tuning on 5,000-10,000 games (<x 200,000-400,000 positions) per player, whereas with only 1,000 games (x 40,000 positions), the fine-tuned model underperformed compared the base model. In contrast, Prototype-Ennichet Maia-2 significantly outperforms both Maia and Maia-2 across all evaluation metrics, where move prediction accuracy and perplexity are shown in Figure g Notably, our model achieves these improvements using maximum of 100,000 positions (~ 2,500 games) per player-an amount that lies between the thresholds where Maia fine-tuning is ineffective (1,000 games) and where it becomes beneficial (5,000 games). These results highlight the effectiveness of our enrichment step, demonstrating that Prototype-Ennnn Enriched Maia-2 requires far less historical data accurately model individual decision-malkn makiin styles while achieving superior performance. Furthermore, the strong results indicate that the universal parameters ø' successfully transition from population-level modeling to individual-level modeling, making them well-suited for the downstream
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Table Performance on unseen players with relatively rich histories (100,000 positions 2,500 games).
Move Prediction Accuracy 1
Move Prediction Perplexity
Skill Categorios
Skilled
Advanced
Master
Overall
Skilled
Advanced
Master
Overall
Maia
0.4996
0.5099
0.5285
0.5132
5.8687
5.4642
5.1300
5.4530
Maia-2
0.5008
0.5158
0.5364
0.5146
4.7900
4.4389
4.1936
4.5316
Maia-2-Strengee
0.5071
0.5212
0.5400
0.5199
4.7264
4.4113
4.1760
4.4903
MaiaaAAl-SStrentth
0.5226
0.5376
0.5478
0.5336
4.4504
4.1733
4.0291
4.2599
Maia4All-Proton
0.5261
0.5408
0.5554
0.5381
4.4018
4.1048
3.9219
4.1899
Prediction Accuracy
Prediction Perplexity
0.58
6.5
Move Prediction Accuracy
0.56
Mais
Move Prediction Terplexity
6.0
Maia
Protatype Enriched Maia 2
Prototype Enriched Maia
5.5
0.52
5.0
4.5
4.0
0.48
3.5-
0.46
3.0
Skilled
Intermediate
Master
Overall
Skilled
Intermediate
Master
Overall
Figure 3: Move prediction accuracy (Left) and perplexity (Right) prototype players.
democratization step to model unseen players. Additionally, these results support that the prototype embeddings are well-learned, ensuring they serve effective references for prototype-infrmmc initialization.
Maia4All. We limit the democratization step to access 100,000 historical moves demonstrate the reduced size of historical data needed for achieving sufficient improvement. As shown in Table g the best performing Maia4All variant, Maia4All-Prototyper outperforms Mais with over 2.5 percentage points in accuracy and around 1.2 in perplexity (whereas Maia-Individual barely shows any improvement at this amount of data). These results demonstrate Maia4All's capability to adapt to unseen players with relatively rich data, and the amount of data needed is significantly lower. In the human move prediction problem for amateur players, the ceiling accuracy is far below 100% given the randomness and diversity of their decisions even the same player won't always make the same decision when faced with the same position. Given this unpredictability, 2.5 percentage point gain significant. improvement-ane -roond half of the gain amateur human move matching between Stockfish, the world's strongest chess engine (which obviously plays much differently than amateur humans) and base Maia, model specifically designed to play like humans.
When even fewer historical behaviors are accessible, Maia4All can still adapt to unseen players with considerable improvement in move prediction accuracy and perplexity. In particular, with only 800 positions (20 games, which considered incredibly few for human behavior modeling in chess), Maia4All can transfer its predictions to unseen players with over 1.9 more percentage points and 1.1 lowered perplexity with prototype-informnt initialization. Note that the number of accessible positions is most 20,000 positions (worth 500 games), whereas fine-tuning Maia with 1,000 games actually results in negative improvement (Mellroy- Soelroy-Youngg et al., 2022 We also show that Maia4All remains effective under incremental learning in extremely low-resource settings, where game history is added gradually, starting from no history. Also, Maia4All data efficiency does not come at the cost of performance with rich data. More details are presented in Appendix A
Prototype-Informed Initialization. Strength-Init and Prototype-Init Table represent strength and prototype-informed initialization, respectively, without further adaptation in the democratization step. Prototype-Init consistently outperforms Strength-Tnit across all data settings, explaining the superior per-

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Published in Transactions on Machine Learning Research (01/2026)
Table 3: Performance of prior-informed initialization.
Move Prediction Accuracy
Move Prediction Perplexity
# #Positions
20,000
8,000
2,000
800
20,000
8,000
2,000
800
Strength-lnit
0.5008
0.5008
0.5008
0.5008
4.8344
4.8344
4.8344
4.8344
Prototype-Init
0.5180
0.5175
0.5173
0.5167
4.5360
4.5333
4.5400
4.5459
Skill Categories
Skilled
Intermediate
Master
t-SNE Dimension
-8
0
t-SNE Dimension 1
Figure 4: Visualization of pontotype-informed initialized unseen player embeddings.
Move Prediction
Prediction Perplexity
Move Prediction
Prototypa Matching
0.520
4.7
0.5925
Pestotype Accuracy
0.95-
0.5900
0.515
0.5275
Mowe predeiionn
Move Frediteen
4.5
0.5250
0.85
0.510
4.4-
0.5225
0.80
0.5200
0.500
Mid
Unilorm
4.2
High Protokype Distribution
Uniform
0.5150
19
100
150
0.70
50
150
Prototype Distribution
#Prototypes
Skill Level
4Prototypes Skill Level
[a]
(b)
(d)
Figure 5: Effects of the distribution of prototypes (a,b) and prototype quantity strength level (c,d).
formance of Maia4All-Prototyye over MaiadAll-Strenggi These results highlight the effectiveness of the Prototype Matching Network and reinforce the importance of better ionaliaation-ddmmonnttaann that a strong loundation learned from a discriminative task (prototype matching) can enhance the final performance of the generative task (next-move prediction).
We take a step further to examine the patterns of prototypo-informed initialized unseen player emboddings using (-SNE for dimensionality reduction. As shown in Figure 4 the embeddings exhibit linear structure in 2D space, with Skilled and Master players forming clusters at opposite ends and Intermediate players concentrated along the middle. This indicates that prototype-informed initialization effectively encodes player strength. Additionally, the dispersion of embeddings around cluster centers suggests that the prototype- informed initialization also captures variations individual playing styles.
Hyperparameter Study. The distribution of the prototypes be matched is a hyperparameter. As shown in Figure 3 (a) and (b), if only include the prototypes from biased distribution of the population, i.e,
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only select from htrmm/med//hhghhl-eeee players, it will result in lowered move prediction accuracy and raised perplexity compared to uniformly select N prototypes from each strength level. Such results support our design choices of selecting the prototypes uniformly to cover the population space.
The number of prototypes N per strength level is also a hyperparameter. Choosing an appropriate N needs to compromise between the representativeness of prototypes for each range, i.e, more prototypes can better cover the player embedding space, and the difficulty in prototype matching, i.e, more prototypes means more candidates to be classified against. This is evidenced by the results shown in Figure 5 (c) and (d). We evaluate the top 1 matching accuracy of prototypical players under low-resource settings (800 positions). Increasing N from 10 to 150 yields gradually lowered performance in prototype matching, while the best-performing
Maia4All is achieved with a trade-off between protolype matching accuracy and player embedding space coverage.
4 Related Work
Human Behavior Modeling in Chess. The challenge of creating a chess engine that can outplay any human was solved over 20 years ago. The research focus then shifted towards the problem of extracting useful knowledge from these superhuman systems. A direct way of doing this is probing AT chess engine in human representation space. Evidence of human chess concepts learned by AlphaZero can be found and measured by linear probes (McGrath et al. 2022;; furthermore, AlphaZero also encodes knowledge that extends beyond existing human Another direction is the creation of 'echavioral stylometry' models that can identify chess players from the moves they play (Mcllroy- Khellroy-YYuug et al., 2021). Moreover, efforts have been made towards creating systemss that strive for Haman--lkenee
but can be successfully taught to humans (Schut et al.] 2023
over sheer strength (Mellroy-Youul et al., 2020 Jacob et al. 2022 Tang et al., 2024; Zhang et al., (024)) in which models are trained to predict the next move human will play, instead of optimizing for winning the game. In addition to predicting human actions at the population level, the models have been fine-tuned for individual-level human behavior modeling in dala-rich settings (Mcllroy- Young et al., 2022 Recent work (Omi et al.) (2225) frames individual behavior modeling as multi-task learning, using parameter-efficicnt fino-tuning with shared LoRA adapters and per-player routing vectors; this approach focuses on generalization across domains (chess, Rocket League, and image generation) and style manipulation, rather than democratizing individual modeling to low-resource settings.
Few-shot Learning and Meta Learning. Few-shot learning focuses on the ability of models to learn and generalize from a very limited amount of labeled training data (Fei-Fei et al. 2006 Fink 2004 Wang et al., 2020). Modeling unseen players follows the few-shot learning paradigm, where players' behavioral patterns are revealed by a limited collection of historical behaviors. Mcta learning is a main approach to few-shot learning, aiming to improve novel lasks' performance by training on similar lasks. Meta learning can be categorized into metric-based methods (Vinyals et al.) 2016 [nell et al.] 20017] Koch et al. 2015 Sung et al.) 2018) that aim to learn similarity distance function over objects and represent the relationship between inputs and the task space, model-based methods (Santoro et al. 2016 Munkhdalai & Yu 2017 which focus on designing models with internal mechanisms to quickly adapt to new tasks, and optimization-baset methods (Ravi & Larochelle| 2016 Finn et al. 2017 Nichol et al. 2018 Raghu et al. 2019) that aim to learn an initialization such that the model can adapt faster with few examples from there.
In Maia4All, our enrichment step follows multi-task pretraining methodologies common in optimization- based meta-learning, where training across diverse tasks (in our case, prototype players) produces universal
parameters for rapid fine-tuning (Finn et al. 2017 Nichol et al., 2018 Wang et al. 2024). The democratization step combines two established techniques. First, context-only optimization: we freeze universal parameters and optimize only low-dimensional player embeddings, following the parameter-cfficicnt adaptation paradigm
demonstrated in meta-learning for context. adaptation and domain transfer (Zinkgral et al. 2019 Houlsby
et al. 2019). Second, prototype-baser initialization: we use a learned prototype matching network to initialize embeddings based on behavioral similarity, following metric-basod meta-learning approaches that leverage
prototypes for few-shot adaptation (Snell et al. 2017 Triantafillou et al. 2019 Rusu et al., 2018 Sung et al.
2018).
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Table Performance of MaiooAll- with optimized or frozen universal parameters 6'.
Accuracy f
Perplexity J
# Positions 20,000
800
20,000
800
Optimized
0.5395
0.5297
4.1949
4.3753
Frozen
0.5365
0.5322
4.2295
4.2988
While these techniques are established, figuring out how to successfully combine several techniques into a pipeline that works surprisingly well for individual behavior modeling in chess is challenging. Such a specific combination for modeling human behavior represents a novel contribution motivated by chess's two-dinensional behavioral structure (strength and style). We require enrichment because population- level embeddings cannot capture individual playing styles within rating bins; we require prototype- based initialization because stylistically similar players can exist across different skill levels, necessitating a learned matching mechanism beyond rating- based lookup; and require context-only optimization to preserve universal chess knowledge while adapting to each player's coordinates in the behavioral space under low data. To our knowledge, this is the first work that integrates prototype enrichment, learned prototype matching, and context optimization in a unified framework for individual behavior modeling in strategic decision-making domains.
Imitation Learning. Our work also be viewed related to the imitation learning literature, where models are trained to perform tasks after observing expert human demonstrations Schaal 1999 Zare et al. (2024); Wang et al. (2019). In the imitation learning context, the model is usually attempting to learn a value function (inverse RT) [gg et al. 20000, or to quickly learn an optimal solution to a given optimization problem (Schaal 1999). In this paper, we attempt to learn a flawed, human value function using non-expert demonstrations. Additionally, many imitation learning methods require the model to be the same, or similar, state to the demonstrated one (Ho & Ermon 2016 Zare et al. 2024) which is condition that is impossible to guarantee in choss outside of the carly game.
5 Discussion
Behavioral Stylometry. The prototype matching network can be directly used for behavioral stylome- try (Mellroy-Young et al. 2021), i.e., identifying players given their historical behaviors. Since we freeze the shared parameters ø' and only optimize player embeddings for unseen players, the player embeddings are directly comparable within the same embedding space. Therefore, our design supports behavioral stylometry off the shelf. As shown in Figure 5, with only 800 positions (around 20 games), our model can identify the player with 89% accuracy with shot from 1100 candidates (100 players per strength level with 11 levels).
Parameter Efficient Fine- Tuning During the democratization step, we freeze the universal parameters o' and optimize only the unseen player embedding c., Table 4 compares this approach with an alternative where o' is also optimized, revealing two key insights. First, when the unseen player has a very limited game history, freezing ø' leads to better performance, suggesting that acts as a form of normalization to prevent. overfitting, which is particularly beneficial in extremely low-resource settings. Second, when more historical data is thouug still within a low-resource optimiii & provides a marginal improvement over freezing it. However, fine-tuning only e,, remains significantly more parameter-efficient while achieving comparable results. This follows the principles of efffcitt tuning seen in the LLM literature, such as Crompt-Tuning (Lester et al., 2021) and Prefix-Tuning (Li & Liang 2021). Given these findings, our original design of freezing ø' ensures better scalability for democratizing large models to individuals with minimal computational overhead while maintaining strong performance.
Maia4All Generalization. To demonstrate the broader capability of our approach beyond chess, we explore the generalization towards Large Language Model (LLM) adaptation to low-resource authors, which we term
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Table 5: Performance comparison of prototype-enriched prompt tuning under different training settings for idiosyncratic LLM.
LM Loss +
Perplexity +
# Tokens
1000
2000 3000
1000
2000
3000
1-step
2.794
2.772
2.740
17.189
16.839
16.318
2-step
2.792
2.757 2.724
17.131
16.546
15.996
idiosyneratic LLM, case study. The key components of our method find natural analogs in this domain: chess positions correspond to text sequences, player styles to writing styles, and next-move predictions to next-token predictions.
Following our two-stage approach, we first select 100 authors with the richest text content from Project Gutenberg (Project Gutenberg Literary Archive Foundation, 2003) as prototypes. We then enrich a base LLaMA-3.1-BB (Meta Al 2024) model by extending its vocabulary with author-specific tokens and fine-tuning both the token embeddings and set of LoRA parameters (Hu el al. 2021 dedicated to individualizing writing styles. This process is analogous to how enrich Maia-2 with prototype player embeddings. Simultaneously, we train ModernBERT-baase identify stylistic similarities between Lext samples. For new authors, we initialize their token embeddings through prototype matching and fine-tune only these embeddings while keeping other parameters fixed, similar to the democratization step. We select test authors who are genuinely low-resource for the base model. Starting from authors with the most limited texts in Project Gutenberg, we further identify the authors for whom the base model exhibits higher language modeling loss than protolype-enrichel model's average validation loss. This criterion ensures we focus authors whose writing styles are sufficiently unfamiliar to the base model, resulting in pool of 30 challenging cases.
(Warner et al. 2024) Prototype Matching Network (PMN) that learns to
Table 5 shows consistent. improvements in language modeling loss and perplexity when tuning author emboddings with our prior-informed initialization (2-step) compared to direct tuning with base model (1-step), across different low-resource data settings from 1,000 3,000 tokens. These results suggest the effectiveness of our framework in capturing individual characteristics from limited data generalizes beyond its original domain in chess, demonstrating the potential in various domains requiring personalized behavior modeling. While use language modeling loss proxy for style adaptation, future work could explore more direct metrics for evaluating writing style transfer, such author-specific linguistic feat ures or evaluation of stylistic similarity from human expert. Details of our implementation and evaluation for this case study of idiosyncratic LLM can be found in Appendix
6 Conclusion
We introduce Maia4All, a data-efficient framework for modeling individual behavior through an enrichment step and democratization step. Maia4All can effectively capture individual playing styles even in extremely low-resource settings. The successful extension of our framework modeling individual writing styles in LLMs suggests that our proposed stralegy could polentially generalize beyond chess, offering a promising approach for personalizing Al systems in more domains.
7 Limitation
While our framework achieves significant improvements in data efficiency, it requires set of prototype players with rich historical data for the enrichment step. This dependency might limit its applicability in newer domains where such extensive behavioral traces are not yet. available. Additionally, although our LLM case study demonstrates potential generalizability, we primarily validate our approach in chess, where the action space discrete and well-defined. While Maia4All represents meaningful progress modeling human preision-making future work should demonstrate whether these gains translate practical benefits in downst ream applications, such as personalized teaching and human-Al collaboration.
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A Additional Experiments
# Position
# Games
Accuracy
Perplexity
0
0
0.5146
4.5316
100
2.5
0.5252
4.4158
200
5
0.5271
4.3733
300
7.5
0.5285
4.3435
400
10
0.5292
4.3331
500
12.5
0.5302
4.3209
600
15
0.5309
4.3119
700
17.5
0.5314
4.3078
Table Maia4all performance with gradually added history on the extremely low-resource setting.
Incremental Learning under Low- Now-Resource. We conduct additional experiments to show how perfor- mance evolves with gradually added history. In particular, we focus on the extremely low-resource setting, Since Maia4All operates on positions instead of games, we gradually add 100 positions 2.5 games) each time. As the results shown in Table with even very little game history, Maia4All could still adapt to individual players effectively with almost full percentage point gain (51.46% -> 52.52%). Furthermore, the improvement the base model monotonically increases. Therefore, it is feasible to do prototype matching with very few initial observations without strength initialization, especially with our design that focuses data-efficient learning: using the same set of historical positions for the easier discrimination (protolype matching for initialization) first, and for the harder move generation (Maia-2 fine-tuning afterward.
Individual Bchavior Modcling with Rich Data. Data efficiency does not come the cost of performance. We Maia4All with 5000 game histories and achieved 56.2%, an almost 5 percentage point gain from the base model performance of 51.4%. Note that fine-tuning Maia using 5000 games per player improved from 53.2% to 55.0% with 1.8 percentage point gain. These comparisons are meaningful but have the caveat that there is a test set mismatch caused by the reproducibility of Maia-Individual (McIlroy- Young et al. 2022). But we can still observe that Maia4All improved from a worse starting baseline (51.4% vs 53.2%) to a much better resulting performance (56.2% vs 55.0%).
Maia4All Reproductibility
Position Representation and Encoding. We follow the well-cstablished prior works (Mellroy Young al. 2020 Silver al.] 2017) to represent chess positions multi-channel 8 8 matrices, including:
Piece Representation: The first 12 channels categorize the board's pieces by lype and color, with channel each for white and black Pawns, Knights, Bishops, Rooks, Queens, and Kings. A cell is marked to denote the presence of piece in the corresponding location, and 0 otherwise.
Player's Turn A single channel (the 13th) indicates the current player's turn, filled entirely with is for white and Os for black, providing the model with context whose move is being evaluated.
Castling Rights: Four channels (14th 17th) encode the castling rights for both players, with the entire channel set to 1 if the right is available or otherwise.
En Passant Target: The final channel (18th) marks the square available for en passant capture, if any, with and Os clsewhere.
One important departure from previous work that we only use the current chess position, and not the last few chess positions that occurred in the game (models have typically incorporated the most recent positions in the game). Many games with perfect information, including chess, can be modeled alternating
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Table Hyperparameter Settings. We follow the notations from Maia-2
(Tang et al.
2024
Initial learning rate
le-1
Weight decay
le
Batch size (positions)
8192
Minimum move ply Maximum move ply
10
300
Remaining seconds threshold #Backbone blocks Konv # #Attention block Kttt
30
12
#Input channels Cinput
Intermediate channels Ciiid
256
# #nnodeed channels Cpttch Player embedding dimension d Attention head dimension dy, Attention intermediate dimension datt # Attention heads
8
128
64
1024
player per range N
100
1.55
0.54
1.50
Training Loss
Val Acc
Validation
0.52
Train Loss
1.45
1.40
1.35
50000
100000
150000
200000
Training Steps
Figure 6: Training dynamics of the Prorchepe-Enriched Maia-2 model
Silver al. 2016); where future states are independent of past states given the current game state. Therefore, the current chess position theoretically encapsulates all the information necessary to make future decisions. Although human decision-making in chess may sometimes subtly depend on the historical lead-up to the current position, these effects are anccdotally small.
Markov games (Littman 1994
In exchange, we gain two large practical benefits. First, modeling Al-human move matching in a Markovian way vastly improves training efficiency by reducing the computational load via significantly smaller data usage for each decision. Sccond, also enhances flexibility, enabling our resulting model to make prodictions even without historical data, which is particularly advantageous in siluations where only the current position is available, like chess training puzzles or any position that didn't necessarily occur in full game.
Enrichment Step Training Results. We present detailed training dynamics of our Protitype-Enriched Maia-2 model in Figure 6 The training process exhibits smooth optimization trajectory suggests that our enrichment. step successfully adapts the base model parameters to capture individual-level behavior patterns. The stable convergence particularly noteworthy given that we are simultancously training both the universal parameters and large set of individual embeddings E,, demonstrating the effectiveness of our protolype selection criteria in ensuring model stability.
Enriched
C Idiosyncratic LLM Reproducibility
Datasct. We use the Project Gutenberg dataset, which contains vast collection of public domain books. Each book preprocessed by cleaning line breaks and whitespace, then chunked into sequences of 2048 tokens with no overlap for efficient processing. We extract author information from the book metadata, filtering
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Published in Transactions on Machine Learning Research (01/2026)
Table 8: Hyperparameter Settings for Prototype-Enriched Training.
Base Model
LLaMA 3.1 8B
LoRA Rank
128
LoRA Target Modules
Attention + FFN
LoRA Alpha
32
LoRA Dropout
Learning Rate
lo-4
Embedding Learning Rate
5e-5
Weight Decay
0.01
Batch Size
16
Gradient Accumulation Steps
Training Epochs
Warmup Ratio
0.1
Max Soquence Length
2048
Table 9: Hyperparameter Settings for Idiosyncratic LLM.
Initial learning rate (base)
le
Weight decay
le
Number of prototypes
100
Number of Training Tokens
IK, 2K, 3K
Number of Testing Tokens
5K
Top-k prototypes for matching
2
Temperature for prototype matching
0.5
Training Steps
100
out anonymous works and those with ambiguous authorship. From all others in the dataset, we select. 100 prototypes based on two criteria:
having the largest amount of publications in Project Gutenberg to ensure prevalence
having sufficient text content (at least 1000 chunks) to ensure reliable style learning
Enrichment Step in LLM. We implement our two-stage framework using LLaMA 3.1 8B as the base model. Our implementation focuses on efficient adaptation while preserving the model's core capabilities. In the first stage, we extend the model's vocabulary with author-specific tokens (e.g., <author _ack London>), creating explicit anchor points for learning author-specific writing styles. We employ LoRA for parameter-effiiint fine-tuning, with hyperparameters listed in Table 8 The LoR. adaptation strategically targets key attention modules and feed-forwatt layers, allowing the model to learn author-specitt transformations while maintaining its general language understanding capabilities. The training dynamics shown in Figure 7 demonstrate steady convergence, which suggests effective learning of author-specific styles while maintaining the model's general language capabilities.
To enable the prototype matching mechanism analogous our chess implementation, we train ModemBERT- based Prototype Matching wetwork (PMN). The PMN learns to map lext sequences space where stylistic similarities between authors be effectively measured. By training chunks of 2048 tokens from each prototype author's works, the PMN achieves 94.7% accuracy prototype classification. This high accuracy, compared to the 1% random baseline with 100 prototype authors, demonstrates the network's 's strong capability in discriminating distinct writing styles.
More Experimental Results. As shown in Table 5 this two-stage approach consistently outperforms direct fine-tuning across different data settings. Across 1000 to 3000 tokens of training data, which can be
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Published in Transactions on Machine Learning Research (01/2026)
2.8
2.6
Training Loss
2.4
0.0
Epochs
Figure 7: Training dynamics of the Prorolype-Bariched Llama 3.1 8B.
Humin
R. [George Payne Rainsford) James
Jules Varne
Franz Oppenhelmer
Biet liarte
Giber: Parker
Jacob Abbott
William H. Hamby
George o. Smith
t-SNE Dimension 2
Virginia Tracy
bavid Blyth Hanna
Henry Jarean
John D. Sedding
Ernest Govett
Thomas Smith
t-SNE Dimension 1
Figure 8: (-SNE visualization of author embeddings. Prototype authors are shown as dots, while new authors (labeled) are positioned based on their weighted combinations of prototype embeddings. Thicker arrows indicate stronger prototype influences.
fairly regarded as low-resource settings for LLM style transfer, our method shows improved language modeling performance, mirroring the benefits we observed in chess with increasing numbers of games. Furthermore, Table shows the prototype matching results for new authors using 2000 training tokens. For each author, we list their top-2 matched prototypes and corresponding weights, alongside the language modeling loss with and without prototype initialization. The matches reveal interpretable stylistic connections that often align with historical and literary contexts. For instance, Herbert Strang and Richard Stead, who wrote adventure stories for young readers, is matched with Robert Louis Stevenson (57.2%) and Anthony Hope (42.8%). This pairing is particularly apt as Stevenson's 's adventure novels (like "Treasure Island') and Hope's romantic adventures (like 'The Prisoner of Zenda') closely align with the literary style and target audience of Herbert Strang and Richard Stead. The corresponding improvement in language modeling loss (from 2.51 to 2.4885) quantitatively validates this stylistic matching.
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Published in Transactions on Machine Learning Research (01/2026)
Table 10: Prototype Matching Results with 2000 Training Tokens.
New Author
w/o Proto w/ Proto
Matched Prototypes
Weights
George O. Smith
2.7725
2.7581
Richard Harding Davis, Jack London
0.540, 0.460
John Sedding
2.7847
2.7652
John Ruskin, Mrs. Humphey Ward
0.618, 0.382
Franz Oppenheimer
2.6181
2.6307
H. G. Wells, Upton Sinclair
0.544, 0.456
Virginia Tracy
2.9959
2.9599
Mrs. Humphry Ward, Edith Wharton
0.622, 0.377
Henry C. Merwin
2.4606
2.4401
William Dean Howells, Grant Allen
0.509, 0.490
Henry James Forman
2.7958
2.7781
Eugène Sue, Mór Jókai
0.556, 0.444
William H. Hamby
2.7050
2.6828
Emerson Hough, Allen Chapman
0.601, 0.399
A Pakeha Maori
2.6287
2.6290
Grant Allen, Hilaire Belloc
0.674, 0.326
Ernest Govett
2.5229
2.5238
John Ruskin, Richard F. Burton
0.826, 0.174
Vivia Hemphill
3.0065
2.9972
Bret Harte, Charles King
0.546, 0.454
Arthur Henry Chamberlain
2.6130
2.6210
Mór Jōkai, Hilaire Belloc
0.509, 0.491
Samuel T. Pickard
2.5931
2.5971
Laura E. Richards, Oliver Optic
0,689, 0.310
Ruby K. Polkinghorne et al.
2.5960
2.5691
August Strindberg, Angela Brazil
0.590, 0.410
Thomas Smith
2.6182
2.6006
The Chautauquan LSC, Sir Walter Scott
0.572, 0.428
William Q. Judge
2.7304
2.7389
Upton Sinclair, Grant Allen
0.534, 0.465
Edith A. Browne
2.5726
2.5113
Grant Allen, Mór Jókai
0.669, 0.331
Donald Allen Wollheim
2.6725
2.6612
Jack London, Hamlin Garland
0.502, 0.497
Susan Carleton Jones
2.7170
2.6796
Rudyard Kipling, Edmund Yates
0.645, 0.355
Wallace Irwin
3.8899
3.8506
H. G. Wells, Carolyn Wells
0.507, 0.493
Hector MacQuarrie
2.7740
2.7712
William Le Queux, Hilaire Belloc
0.567, 0.433
S. Pérez Triana
2.7608
2.7751
Hilaire Belloc, Grant Allen
0.554, 0.446
Frangois-Joseph Fétis
2.4629
2.4748
John Ruskin, William Dean Howells
0.506, 0.493
Herbert Strang and Richard Stead
2.5114
2,4885
Robert Louis Stevenson, Anthony Hope
0.572, 0.428
Matt Crim
2.4610
2.4246
Robert W. Chambers, Hamlin Garland
0.617, 0.383
William Chauncey Bartlett
3.1245
3.0846
Rudyard Kipling, Charles G. D. Roberts
0.581, 0.418
David Blyth Hanna
2.9310
2.9009
Authony Hope, Mrs. Humphry Ward
0.562, 0.438
Edith Elise Cowper
2.9251
2.9086
Authony Hope, L. T. Meade
0.504, 0.496
Ray Bradbury
3.1877
3.1587
Emerson Hough, August Strindberg
0.665, 0.335
Mary Flizabeth Hall
2.5879
2.5707
Margaret Vandercook, Grant Allen
0.513, 0.487
Dutton Payne
3.1498
3.1341
Laura Richards, James Grant
0.615, 0.385
21


Reviews:
[{"review_id": "aY0jv7iXdS", "reviewer": "Reviewer_hY4j", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces Maia4All, a framework for modeling individual chess-playing behavior with significantly reduced data requirements. Maia4All uses a two-stage approach: (1) an enrichment step that fine-tunes the base model on selected \"prototype\" players with rich game histories, adapting the model from population-level to individual-level modeling, and (2) a democratization step that uses a Prototype Matching Network to initialize embeddings for new players based on similar prototypes, then fine-tunes embeddings on limited data. The method achieves comparable accuracy gains with 20 games, vs the 5,000 games previously required. The authors include a supplementary case study on adapting LLMs to individual writing styles to demonstrate broader applicability.\n\nStrengths: \nWhile the components are known, the explicit framing of enrichment (population → individual-level parameters) + democratization (prototype-informed initialization) as a systematic approach to the cold-start problem in behavioral modeling is a nice conceptual contribution. Applying this to individual human behavior modeling in chess is an interesting direction. Experiments show a large scale of data efficiency gain (250×) in this specific domain.\n\nWeaknesses:\n1. As a non-expert in chess game modeling, the 1.8 percentage point gain (51.4% -> 53.2%) seems small in absolute terms. While the authors argue this is meaningful given human unpredictability, the practical impact for downstream applications (personalized teaching, collaboration) remains unclear.\n2. I wonder what happens between 2,500 and 5,000 games? Does Maia4All match or exceed Maia-Individual's performance? This is crucial for understanding whether data efficiency comes at the cost of performance.\n3. Prototypes are selected primarily by most frequent players, rather than style diversity. It would be interesting to see an analysis of prototype coverage in behavioral style space.\n4. The LLM case study is the only evidence for broader applicability, but the improvements are marginal. Therefore the claim of potential for broader applications is overstated given this limited validation.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The authors provide detailed experiment analysis and reported results with baseline comparisons. However there are concerns regarding whether the proposed framework has a significant improvement on the current methods. See weaknesses above.", "audience_yn": "Yes", "audience_explanation": "Applying the explicit framework of enrichment + democratization to individual human behavior modeling in chess is an interesting direction.  The authors claim the framework leads to a performance improvement and more efficient use of data, which could be of interest to the broader community.", "requested_changes": "Please see weaknesses above.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ZuvovvtMX8", "reviewer": "Reviewer_sV18", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces Maia4All, a  highly data-efficient framework for modeling individual human behavior in chess, addressing the critical limitation of previous methods that required prohibitively large amounts of data.\nThe main contributions can be summarized as follows:\n- A Two-Stage Optimization Framework: The core contribution is the two-stage methodology consisting of an Enrichment Step and a Democratization Step. The enrichment step first creates a model conditioned on individual styles using data-rich \"prototypes,\" and then leverages this model to rapidly personalize for new, low-data users.\n- Experimental results show nice improvement on the data efficiency: The paper demonstrates that Maia4All can achieve significant performance gains in individual move prediction with as few as 20 games of data. This represents a roughly 250-fold reduction in data requirement compared to prior work (e.g., fine-tuning Maia)", "claims_and_evidence_yn": "No", "claims_explanation": "My major concern is that the paper did not do a good job of discussing its relationship with previous work, especially that presented in the meta-learning domain, for instance, [1] also presents a prototype-based meta learning approach for the few-shot learning problem, which has many similarities with the procedures in the Prototype-Informed Initialization section. The embedding gradient descent (equ 7) in the Democratization Step is also not new, considering there are tons of work on optimizing context/low-dimensional parameters in gradient-based meta learning like [2]. The personalization pretraining described in the Enrichment Step is also closely related to the multi-task and meta-learning literature. \n\nThus, I'd prefer to treat this paper as a nice application paper, rather than something novel or proposed by the authors' claim. \n\n\n[1] Snell J, Swersky K, Zemel R. Prototypical networks for few-shot learning. Advances in neural information processing systems. 2017;30.\n[2] Zintgraf L, Shiarli K, Kurin V, Hofmann K, Whiteson S. Fast context adaptation via meta-learning. InInternational conference on machine learning 2019 May 24 (pp. 7693-7702). PMLR.", "audience_yn": "Yes", "audience_explanation": "The paper did a good job of leveraging the meta-learning technique to address the personalized chess policy problem—the high efficiency of the result (that 250x efficiency improvement is impressive), and it'd be pretty useful for both the chess and chess machine learning community. And as far as I know, this is the first literature working on few-shot learning in the chess domain, so I believe some audience may find it interesting.", "requested_changes": "1. A major update on the discussion of the related work. A few words in the related work section is not enough -- especially considering the similarities between those literature. I'd like to see more disucssion on detailed comparison of the proposed methods and exisiting literature, to better clarify what's new in the author's contritbution. I am fine even if the paper is not that new, as long as it is a good application paper. But it is important to properly clarify the contribution.\n\n2. The new LLM experiment in Section 5 is weird -- why suddenly switch to another domain if the title and main content are about chess? It'd be fine if the narrative starts with a general methods that can be applied in different domains. But considering that 95% is about chess, I'd rather move this section to the appendix and only mention a few words about this new exp.\n\n3. Considering this is a meta-learning setting, only comparing the method with one meta-learning variant and one non-meta learning baseline (basically all are Maia's variants) is not enough. There are tons of meta-learning or efficient tuning methods that can also be used as part of your contribution or comparing baselines.", "broader_impact_concerns": "Not available for this work.", "additional_comments": "Here I have some further questions and suggestions:\n1. I'd recommend also inviting human players to measure the model's performance. SInce the goal is to play like humans, then the players themself should be one of the golden metrics.\n2. I noticed that you chose N=100 in your hyperparameter, which results in 1100 dims of the embedding rows? Do I understand it correctly? If so, how do you choose this hyper-parameter? What will the performance look like if you scale this number? It'd be better if there were statistics about the number of Lichess human game play and the rationale behind this parameter.\n3. Another easy baseline could be context-based meta learning, so basically just add personalized experience into the context when training. This sounds like inherently generalizable because it also trains a network that can take in a new player's history. Why choose the embedding-based method + prototype matching instead of this method?", "extra_scores": {}, "extra_text": {}}, {"review_id": "ys3I8DVjqu", "reviewer": "Reviewer_UMFK", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces Maia4All, a framework for customizing the behavior of Maia-2 (a humanlke chess model) to users with very few chess games (~20). The approach uses a two-stage optimization process: (1) an enrichment step that fine-tunes Maia-2 on selected \"prototype\" players to teach models to make use of individual \"prototype\" embeddings, and (2) a democratization step that specializes a model to a small number of unseen player games.\n\nStrengths:\n- Sample efficiency (individual behavior modeling in 20 games)\n- Some evidence of generalization of the technique demonstrated through modeling author style with limited texts\n\nWeakness:\n- Modest improvements (51.4% -> 53.2%)\n- Experiment setup is somewhat unrealistic (a practical system requires continual learning / test-time training), though should be easily addressable", "claims_and_evidence_yn": "Yes", "claims_explanation": "**Sample Efficiency**\n\nPrior work (Maia-Individual) required 5,000 games per player to show improvement over base models, which would take months of game play and is completely unrealistic. The enrichment training + prototype-matching initialization approach enables fast (~20 games) adaptation to user behavior, a huge improvement over what was previously possible.\n\nAn additional benefit of the method is that the model is not tuned during the \"democratization\" stage. So the amount of information stored is just a single embedding per user.\n\n**Generalization**\n\nAppendix B reports encouraging results on generalization of the proposed method to language modeling.\nThe proposed method reduces perplexity on low-resource authors after initializing from embeddings of similar authors.\n\n**Limitations of Experimental Setup**\n\nThe evaluation assumes a batch learning scenario where all user games are available upfront for fine-tuning. Real-world deployment would likely require online/continual learning approach, where the model adapts incrementally as users play more games. While the strong performance with just 20 games suggests online adaptation should be feasible, the paper lacks analysis of:\n- How performance evolves with sequential game-by-game updates\n- Whether prototype matching remains reasonable effective with very few initial games (e.g., 1-5 games)", "audience_yn": "Yes", "audience_explanation": "Individual behavior modeling / continual learning is an important topic in machine learning. If the proposed technique generalizes, the paper should be valuable to a broad ML audience.", "requested_changes": "**Online learning experiment (minor)**\n\nReal deployment scenarios would likely involve incremental learning as a previously unknown user plays more moves. Add discussion or preliminary analysis of:\n- How performance evolves with move-by-move updates\n- Whether it's feasible to do prototype matching with very few initial observations, or whether blending prototype / strength initialization is required (since there are no moves for prototype matching network to classify initially)", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)