Personalized Decision Modeling: Utility Optimization or Textualized-Symbolic Reasoning
Authors: Yibo Zhao
Yang Zhao
Hongru Du
Hao Frank Yang
Venue: NeurIPS 2025 spotlight ()
Keywords: Personalized Decision Making
Symbolic Regression
LLM
Primary area: machine_learning_for_sciences

Abstract: Decision-making models for individuals, particularly in high-stakes scenarios like vaccine uptake, often diverge from population optimal predictions. This gap arises from the uniqueness of the individual decision-making process, shaped by numerical attributes (e.g., cost, time) and linguistic influences (e.g., personal preferences and constraints). Developing upon Utility Theory and leveraging the textual-reasoning capabilities of Large Language Models (LLMs), this paper proposes an Adaptive Textual-symbolic Human-centric Reasoning framework (ATHENA) to address the optimal information integration. ATHENA uniquely integrates two stages: First, it discovers robust, group-level symbolic utility functions via LLM-augmented symbolic discovery; Second, it implements individual-level semantic adaptation, creating personalized semantic templates guided by the optimal utility to model personalized choices. Validated on real-world travel mode and vaccine choice tasks, ATHENA consistently outperforms utility-based, machine learning, and other LLM-based models, lifting F1 score by at least 6.5\% over the strongest cutting-edge models.  Further, ablation studies confirm that both stages of ATHENA are critical and complementary, as removing either clearly degrades overall predictive performance. By organically integrating symbolic utility modeling and semantic adaptation, ATHENA provides a new scheme for modeling human-centric decisions. The project page can be found at https://yibozh.github.io/Athena.

Personalized Decision Modeling: Utility Optimization or Textualized-Symbolic Reasoning
Yibo Zhao
Yang Zhao
Department of Civil and Systems Engineering Johns Hopkins University
Department of Civil and Systems Engineering Johns Hopkins University
Hongru Du i
Department of Systems and Information Engineering
University of Virginia
hongrudu@virginia.edd
Hao Frank Yang
Department of Civil and Systems Engineering Johns Hopkins Data Science and Al Institute
Johns Hopkins University
haofrankyangejun edu
Abstract
Decision-making models for individuals, particularly in high-stakes scenarios like vaceine uptake, often diverge from population optimal predictions. This gap arises from the uniqueness of the individual decision-making process, shaped by numeri- cal attributes (c.g., cost, time) and linguistic influences (e.g., personal preferences and constraints). Developing upon Utility Theory and leveraging the textual- reasoning capabilities of Large Language Models (LLMs), this paper proposes an Adaptive Textual-syme -ymbolli Human-centric Reasoning framework (ATHENA) to address the optimal information integration. ATHENA uniquely integrates two stages: First, discovers robust, group-level symbolic utility functions via LLM- augmented symbolic discovery; Second, it implements individual-level semantic adaptation, creating personalized semantic templates guided by the optimal utility to model personalized choices. Validated on real-world travel mode and vaccine choice tasks, ATHENA consistently outperforms utility-basedd machine learning, and other LLM-bascd models, lifting Fl score by at least 6.5% over the strongest cutting-edge models. Further, ablation studies confirm that both stages ATHENA are critical and complementary, removing either clearly degrades overall predic- tive performance. By organically integrating symbolic utility modeling and seman- tie adaptation, ATHENA provides new scheme for modeling human-centn centric deci- sions. The project page can found at httpt::://// //yiboz// .ii.hbb........... io/ Athena
1 Introduction
Consider the widely debated vaccine dilenma [1. from a population-level perspective aimed at opti- mizing collective well-being (e.g., achieving herd immunity minimal societal cost), models would invariably predict near-universal vaccine adoption. However, this population optimum consistently
"This work was completed while Hongru Du was at Johns Hopkins University.
i "ooresponndecce Hongru Du and Hao Frank Yang.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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fails to predict actual individual behavior. The reality is a broad spectrum of personal choices, because each individual undertakes their own unique cognitive calculus: balancing a vaccine's perceived efficacy and protection against its perceived risks 21, all filtered through their personal beliefs, constraints, and even considerations of potential "free-riding" on the immunity of others R. This divergence between the theoretical population optimum and observed individual actions highlights a critical limitation: models designed to maximize collective outcomes do not adequately explain or predict individuals' choices. Instead, individual choices are profoundly shaped by who we are, when the decision is made, and the unique constraints we face. This internal 'cognitive calculus', unique to each individual and situation, presents profound challenge for human decision modeling.
For decades, researchers have attempted model this 'cognitive calculus' with Utility Theory [4) which assumes individuals select options that maximize expected gain. Operationally, this involves defining a parametric utility function, denoted as / X' - R. that maps vector of structured attributes X' (e.g., monetary cost and time) for each option to a scalar utility score. Such pre-defined and explicit specifications of f are the basis for classic discrete choice models 77), which have been widely adopted across economics [8H10], transportation 7 and public policy [1416]. In these models, the utility scores derived from ff for each available option are used to probabilistically determine the likelihood of an individual selecting particular option. However, even these utility- based models encounter fundamental barriers when attempting to capture the full depth of human decision-makee making. Real-world human decisions, seen in the vaccine dilemma, frequently deviate from these mathematical formulations. Individuals exhibit behaviors that appear inconsistent or irrational [8), yet these often driven by subjective feelings and personal experiences. Such deviations reflect that traditional models, with their reliance on pre-specified functions, struggle to capture personalized decisions [9]. The clue for deciphering this deviation is covered within individual attributes, some of which are structured and quantifiable, while others are unstructured and semantic (e.g., individual preference and constraints).
Addressing these unstructured and semantic dimensions, which are pivotal for capturing personalized decision mechanisms, calls for new modeling paradigms. LLMs with their strong textual-reasoning capability offer a clear advance (20), providing new mechanisms for identifying the utility func- tion and for integrating semantic individual context directly into the decision modeling process. Specifically, LLMS enhance our ability to model human choice by: a) Guiding the discovery of more accurate and robust parametric forms for f- Through I.M--aummetted symbolic regression 23 it becomes feasible to identify data-driven mathematical structures that capture underlying group-level choice patterns more effectively than pre-specified forms. b) Enabling the infusion of individual-level textual information into the human decision modeling (24H26). By encoding personal preferences, constraints, and narratives, LLMs allow each decision to reflect the nuanced motivations and situational factors that traditional numeric features alone cannot convey.
This paper introduces Adaptive Textual-symbolic Human-centric Reasoning framework (ATHenA). ATHENA achieves personalized decision modeling by uniquely integrating two sequen- tially structured steps: First, at the group level. it focuses on discovering robust, symbolic utility functions. Second, it implements individual-level, L.L --owere semantic adaptation guided by optimal utility functions discovered in previous steps. The outcome is customized semantic template for each person, specifically designed to empower an LLM to model their choices by incorporating their unique preferences and constraints. We empirically validate ATHENA on two real-world human decision-making tasks: travel mode choice and vaccine uptake decisions. The model consistently outperforms traditional utility-based, machine learning, and LLM-based models, with at least 6.5% improvement in Fl score. Further ablation experiments reveal that removing either the group-level symbolic utility search or the individual semantic adapter lowers performance by at least 18% underscoring the merit of the full ATHENA framework.
2 Related Work
Utidety-based Decision-Making Models. Initial explorations into this complex domain were pre- dominantly by utility-basee models [0] These methods aim to capture human behavior within explicit mathematical functions, formulated from empirical data. Established methodologies such as Discrete Choice Models (DCMs) have been widely used, attributable to their interpretability
and robust statistical underpinnings 31 10
32 37 While offering tractability, they may also limit the ability to fully capture complex non-linear patterns and diverse preferences in modern high-dimensional data.

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Machine Learning-Driin Decision-Making Models. ML-driven decision Decision-making models aim to directly leam from rich, diverse features. Tree-based ensemble methods, including Random Forests (38] Gradient-Boosee Boosting Trees [39] XGBoost 44 41], and LightGBM [42], alongside neural network architectures [% exhibited a notable proficiency in fitring complex, non-additive interaction effects. These models effectively integrated large-scale data, but their Decision-making processes
often lacked transparency despite strong predictive performance. Efforts to enhance transparency via post-hoc explanation frameworks, for instance, SHAP [46)48] and Integrated Gradients [49] (50), have provided some insights for human behavior. A persistent challenge is these models' vulnerability to distribution shifts, lack of transparency, and limited ability provide symbolic, interpretable insights needed for personalized utility reasoning.
Symbolic Regression with LLMs Classical symbolic regression (SR) typically uses genetic programming to evolve populations of candidate equations via stochastic mutation and crossover [51]
53 The goal is to find formulas that balance simplicity, generalizability, and human interpretability
The recent rise of LLMs has revitalized symbolic regression, enabling new possibilities in scientific discovery when combined with advanced evolutionary algorithms [57]. For example,
54 56
LLM-SR integrates LLM with evolutionary symbolic regression by treating equations as executable programs. It leverages LLMs' scientific prior knowledge and code generation abilities to iteratively generate, refine, and optimize equation skeletons [22]. LASR integrated LLM-driven abstract textual concepts within evolutionary frameworks, achieving notable performance enhancements on benchmarks, such as the Feynman equation set [58]. The DiSciPLE framework extended these contributions by emphasizing the interpretability and reliability of generated scientific hypotheses, incorporating critical evaluation and simplification to ensure hypotheses are both scientifically rigorous and computationally efficient (59].
LLM--bssd Decision-Making Models. The advent of LLMs has offered a new opportunity, es- tablishing these models as human-like reasoning engines [60H65). Techniques such as instruction tuning [66-69], thain-of-thought reasoning 70 are elevating LLMs move beyond basic text generation to handle more complex tasks involving step-by-step reasoning and symbolic or numerical problem-solving 75 81. Within the specific domain of personalized decision making, preliminary findings suggest that zero-shot and few-shot prompting strategies can enhance the behavioral align- ment of LLMs 882 83 Because a model's knowledge is inherited from generic pre- pre-training priors, its reasoning defaults universally salient factors - e.g., cost and time in travel mode choice while overlooking personal preferences such as rail-pass loyalty or transfer aversion, thereby introducing systematic bias (84). Techniques like persona loading partially mitigate this gap by conditioning responses on inferred preference structures 2
85). Beyond basic prompting, decision- systems add explicit structure to improve reliability and transparency: DeLLMa enumerates plausible states, elicits utilities via pairwise comparisons, and maximizes expected utility: STRUX distills inputs into fact tables with self-reflective evidence; OptiGuide compiles natural- language "what-if" queries into optimization code and invokes solvers, Agent-Driver Driver coordinates tool calls, commonsense/cxpe- rience memory, and chain-of offthought planning; Personalized Oncology evaluations show chat-LLMs still trail experts, motivating structured, widence-groundee pipelines 90). Nevertheless, many deployments still treat LLMS as opaque scoring mechanisms, falling short of fully recovering explicit, personalized utility logic.
3 Methods
We consider a classic discrete choice problem, where an individual i faces a finite set of choices J [1,,,...,JJ] J.. where J = -JT.. The decision-making process assumes individuals select the option j that maximizes their utility. Each individual's is observed choice behavior is represented by a dataset D= {X,,, )) For each observation i, X, = {z.,, 1 represents the set of feature vectors, where Zig E IR captures the features for choice j and y: E J denotes the observed choice
The standard approach to modeling discrete choices is the Random Utility Maximization (RUM) framework [91. It assumes the latent utility for each alternative j is described by U.j = [XX,, +eejj where J(X.,)) is systematic component of utility and eaj is the random error. Assuming 6i are independently and identically drawn (i.i..)) and follow a Type Extreme Value distribution [92]. the probability of individual i choosing alternative j is given by:
3

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Figure 1: Overview of the proposed ATHENA framework. Group-level symbolic utility discovery: Symbolic & semantic constraints library feed an LLM-driven symbolic-optimization engine that iteratively proposes candidate utility functions, scores them with loss Lg. and prunes the search via analysis, crossover, and mutation. Red rings in the contour maps illustrate how the feasible solution space shrinks across iterations until the optimal formula fg selected. adaptation: The optimal group utility f seeds a personalized template space. For each individual i, TextGrad computes textual gradients of an individual loss and updates the template Pi into more personalized decision rule D4+11 Finally, the optimal P is used to predict personal decisions.
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A central challenge lies in specifying the systematic utility component f. Traditional applications of RUM often rely on pre-specified functional forms for using domain expertise and observed data 193) This approach may result in suboptimal representation of the decision mechanism, while also neglecting individual heterogeneity in choices. Furthermore, traditional decision-making models not designed to incorporate non-structured semantic information. To address these limitations, introduce ATHENA for personalized decision modeling designed to identify suitable utility function representations while simultaneously capturing individual-specits preferences. As shown in Fig. ATHENA structures the decision modeling process into two sequential stages:
Group-Level Symbolic Utility Discovery: This initial stage focuses on identifying optimal symbolic utility components that capture common decision patterns within distinct demographic groups. The discovery is achieved through a beddback-informan symbolic discovery process powered by LLMs.
Individual- Semantic Adaptation: Then, the optimal group-level utility functions serve as guidance for the LLM-driven optimization of personalized semantic templates. This adaptation process is designed to incorporate individual-specifi preferences and constraints, leveraging the rich semantic reasoning capabilities of LLMs.
3.1 Group-Level Symbolic Utility Discovery
The first stage aims to discover optimal parametric utility function, denoted f" for each demographic group g E G. This function f should be constructible from symbolic building blocks and optimally explain the group's choice behavior. Following the choice probability defined carlier

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Eq. ① the objective is to find the optimal fg and its associated parameters og such that:
ex
(fg. fg) org min (X( uc: ()) =-
log (X..)EEE,
Σ
(2)
EKEE ef(X
1.0
To automate the symbolic utility discovery of f we design an iterative, (eedback-informed generation process powered by LLMs. To effectively guide the automated discovery of utility functions, constructed two foundational libraries: domain knowledge concept library (C) and symbolic library (S). The library C, developed based on imput from domain experts, covers high-level conceptual knowledge about Nomain--peciffu human behavior. The library S provides the fundamental syntactic building blocks needed for constructing all candidate utility expressions.
Inspired by evolutionary algorithms [94). the core discovery process proceeds iteratively. In each iteration é for each demographic group g. the LLM samples set of K candidate symbolic utility
functions, { 1K This sampling is performed from the LLM's learned distribution & 120 955] conditioned on the group profile g. the domain concept C, the available symbolic building block S, - and feedback B from preceding iteration:
( ~
The feedback B is essential in refining the LLM's sampling strategy. Specifically, B constructed at the end of each iteration and comprises the best-performing and worst-performing candidate functions from that iteration:
B' Ug
where fg. arg Cg g,k. Dg) and fg. arg max Cg(fg g.k. Dg). Here Cg the group-level keK
kEK
loss function, with a similar format as Eq. 2 This feedback B is used to refine the LLM's sampling distribution á through stochastic mutation crossover [51453), pushing the generation towards more promising types functions. The iterative discovery process for group g is considered to have converged at iteration T if the absolute difference in the loss of the best-performing function from the current iteration and that of the previous iteration t falls below a predefined threshold
Lg Dg) Lo p,)l< 5.
Upon convergence at iteration T, the optimal group-level symbolic utility function (ft) de- termined as the function that achieved the minimum loss across all generated candidate functions throughout the entire iterative process:
1 arg min (J Dg): IEF,
(6)
where Fg = Ut 1K and T is the iteration at which convergence occurred. This discovered function 1 along with fitted parameters 0g serves as the learned representation the systematic utility for group g.
3.2 Individual-Level Semantic Adaptation
Following the determination of the group-level optimal symbolic utility functions fg. the framework transitions to the second stage, leveraging an LLM conditioned on f² to model individual choice behavior more accurately. While f captures the central tendencies of utility for group g. significant intra-group heterogeneity often persists. To account for this, we introduce an individual-level adaptation stage to personalize the utility representation by generating and refining an individual- specific semantic template.
For each individual g. the initial semantic template, denoted as p generated by the LLM (Ø). The generation of the initial semantic template is represented as a sampling process from the LLM's distribution: P of-1,,,,, C). In this formulation, Ø conditions on the optimal group-level symbolic function fÿ, the specific individual context i, and the high-level domain concepts from C to generate P.. This initial template P;O is semantic representation that is designed to be adaptable in
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subsequent optimization steps. Then, the semantic template Pf undergoes an iterative refinmmnn process for each individual i. This optimization is driven by TextGrad [96], which optimizes the template based on the individual's 's specific data D; = (Xi, W1). The update rule is given by:
p P D.).
(7)
The term (P; D₂) represents the "textual gradient" of the loss function with respect to the semantic template P.-- Since Pf is the textual template, this gradient not a vector of partial derivatives in the mathematical sense. Instead, indicates the direction and nature of textual modifications to P. that would lead to the most improvement in loss. This iterative refinement process continues until a maximum number of iterations T" is reached. Then the final optimal semantic template for individual i, denoted as P;, is determined. The predicted personalized choice y: is then represented as sampling from the LLM's output distribution:
Symbolic Utility Discovery
8 (X
(8)
Semantic Adapiation
The overall procedure of ATHENA is summarized in Algorithm I
Experiments
Algorithm 1 ATHENA Optimization Flow
Require: Demographic group dataset Dy. domain concept C, symbolic building block S
This section empirically validates the value of ATHENA, demonstrating its overall effectiveness personalized
1: Initialize Bo +- None
// Stage I: Group-Level Symbolic Utility Discovery
decision-making and its robust capa- bility to apply across diverse appli- cation domains. We break down our experimental findings to specifically showcase the distinct value added by each core component of the ATHENA framework: 1) group-level symbolic utility discovery and 2) personalized semantic template adaptation. Fig. 2 illustrates the full pipeline using the travel-mode choice as an example.
2: for = 1 to T do
3: Sample symbolic utility functions ( ~ Φ(-
C,
4: Update B < [J2++ using Eq. 4
5: Select best function fg arg minye., Lg Dz)
6: if stopping condition in Eq. (5) is met then break
7:
8: end if
9: end for
// Stage 2: Individual-Level Semantic Adaptation
10: for each individual i g do
11: Initialize semantic template 'P. ~ +b. fg Update p <- Pi LP, D.) using Eq.
12:
for t= 1 to T" do
4.1 Experimental Setup
13:
14: end for
Datasets. To test ATHENA's 's ability to generalize across different domains and to adapt to individual preferences, we selected two real-world tasks that reflect fundamentally different personalized decision scenarios: daily transportation choices and public health decisions. (1) Swissmetro Transportation Choice (Swissmetro): is widely used benchmark in travel mode choice modeling 97-1011. Each record details a trip between major Swiss cities and includes both traveler characteristics (e.g., income, age) and alternative-specifi attributes (e.g., travel time, cost). The dataset has a potential choice set of three transportation modes: Train, Car, and Metro. (2) COVID-19 Vaccination Choice (Vaccine): This dataset is derived from a large-scale international survey, conducted across multiple countries [102]. The survey was designed to understand factors influencing COVID-19 vaccine uptake and attitudes. For each participant, it captures demographies, prior beliefs about the vaccine, and their self-reported vaccination status. The modeled choices based on this information include: Unvaccinated, Vaccinated initial doses, booster, and Vaccinated initial doses plus booster.
end for
16: return (Pi predict decisions using Eq.
Experiment Configurations. To maintain a reasonable budget for the template-adaptation stage, we restricted the experimental sample to a representative subset of each dataset. Specifically, we used: (1) Swissmetro: 500 travelers, two trip records per person; (2) Vaceine: 300 respondents, one survey record per person. Within each dataset, we first identified key demographic dimensions (gender,

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Figure 2: ÂTHENA pipeline applied travel-mode choice example. Here we use Swissmetro as an example to illustrate ATHENA framework. The Initialization panel encodes conceptual constraints, a mixed semantic-numerical feature space, and a symbolic library of operations. In Group-level symbolic optimizution, an LLM samples, scores, and prunes candidate utility expressions for each alternative to produce compact formulas (fg that best explain group behavior. Individual semantic adaptation, each f seeds a group proup-specific prompt template Po, which refined to a personalized template via TextGrad to capture individual heterogeneity (P - P;).
age, and income), then sampled approximately balanced subsets across these strata from the full dataset. This ensures (i) comparable class priors between training and test splits, and (ii) that no demographic group dominates the symbolic-utility discovery process. The predefined demographic grouping follows established practice in choice modeling, supports interpretability, and improves robustness by avoiding the complexity and data requirements of latent clustering methods [103
Evaluation metrics. We report Accuracy, F1, AUC, and Cross-Entropp (CH). CE is included because ATHENA produces probabilistic predictions over choices. A lower CE means the model assigns higher probabilities to actual choices, while F1 and AUC capture classification performance; together, they provide complementary views on accuracy and calibration.
Models and baselines. Both stages of ATHENA, symbolic-utility discovery and individual seman- tic adaptation, run on the gpt-4o-mini- 2022-0202277 and gemini -2. 0-flash. To evaluate its performance, contrasted ATHENA with three baseline groups. (i) LLM-based methods: plain zero-shot method [106, [07]. a zero-shot chain-of- ofatnnof-thought method [106]. a five-example few-shot
method [108, [09 and TextGrad tuning [96). (ii) Classical discrete-choice models: Multinomial
Logit (MNL) 110). Conditional Logit (CLogit) 1111, and Latent-Class MNL [122] (ii) Standard
machine-learning classifiers: logistic regression, random forest, XGBoost [133, shallow two-layer
MLP 114, TabNet for tabular data [115). and a fine-tuned BERT classifier 116). This spectrum
ranges from end-to-end language-moder reasoning through discrete choice models to conventional predictive learners, providing a balanced reference for unique modeling capabilities.
4.2 Overall Performance Analysis
Performance and insights. As shown Table on the Swissmetro mode choice task, ATHENA with GPT-4o-mini notably outperforms evaluated baselines across Accuracy (Acc), F1-score (F1), and AUC. Over the strongest baseline, achieves gains of at least 6% in Ace and 6.5% in F1, respectively. Similar improvements are noted on the Vaccine dataset. Notably, our proposed method exhibits higher Cross-Entropy (CE) compared to baselines such as XGBoost. We attribute this the inherent design of ATHENA, which produces more conservative probability distributions rather than extreme certainties. Specifically, unlike models that might predict choice with > 90% confidence. ATHENA's 's framework is less prone to such high probabilities. This characteristic may better reflect the
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Table Performance comparison of LLM-based, classical choice, and machine learning methods on the three-class Swissmetro and three-class COVID- 19 Vaccine choice tasks.
Method
LLM Model
Swissmetro
Vaccino
Acc.1
Fl.1
CE.
ALC.1
Acc.t
Fl.-
CE.
AUC..
Zeroshot
gemini-2. 2.0 2.0-flas
GPT-1o-misi
0.5920
0.2940
0.2757
2.7258
0.9257
0.6561
0.5800
0.5433
0.5092
0.8328
0.7607
Zor
gemini-2.0--B 2.0--lshh
0,5880
0.3478
0.9415
0.6331
0.5800
0.5073
0.8436
0.7526
GPT- fo-mini
0.6120
0.2960
0.8957
0.6237
0.5500
0.5353
0.8510
0.7465
LLM- Rased
Fewshot
gemini-22 1.miini--.00-e 2.0-flash
0.7580
0.7027
8.7244
0.7956
0.5667
0.5740
12,0524
0.7053
GP 1-4e-mini
0.6815
0.4945
7.0029
0.7395
0.5067
0.5097
6.6110
0.6891
TextGrad
gomini-2 0-0-lash
1.2011
0,4241
0.4014
GP 1-40-mini
0.6500
0.3620
0.9079
0,5364
0.5084
0.4962
4,5412
0.6709
ATHENA
GP 1-4o-mini
gemini-2 2 flaassh
0.7679
0.8134
0.7222
0.7655
0.9041
1,0863
0,8387
0.8825
0.6797
0.7345
0.7161
0.5968
0.7610
0.7551
0.8704
0.8370
Utility
0.6101
0.3887
0.8383
0.7074
0,4150
0.1955
1,0510
0.430
Theory
Clggit
0,5714
0.2424
0.8916
0.5976
0.41.5
0.1955
1.05
0.5000
Latent Class
0.6101
0.3967
0.8175
0.7182
0.1950
0.1088
1.0986
0,5000
Logistic Regrassion
0.5620
0.5570
0,9310
0.6500
Random Forest
0.7100
0.7050
0.7380
(18810
0.6300)
0.6470
0.7290
0.8420
Machine
XGBoost
0.7080
0.7050
0.70-10
0,8810
0.6300
0.6180
1,1420
0.8150
Learning
BERT
0.7246
0.4994
0.7037
0.8811
0.6350
0.6541
0.7409
0.8168
TabNeet
0.6375
0.4060
0.77887
018810
0.6650
0.6684
0.8968
0.8147
0.6475
0.7626
0.6068
uncertain nature of human decision-making which our model designed to accommodate. Overall, the performance enhancements highlight ATIIENA's 's strength in combining symbolic structures with semantic adaptation for effective personalized decision modeling.
Disentangling Semantically Similar Choices. Prompt-only LLMs and classical choice models frequently fail to distinguish between superficially similar options. For example, the few-shot LLM misclassified 75% of true Car trips as the premium Metro service. By introducing symbolic-level structure and performing individual-level semantic adaptation, ATHENA more than doubled the number of correctly classified Car trips, while maintaining high recall for both Train and Metro. On the Vaccine task, its learned templates encode key interactions such as age-risk trade-off's and prior-infection hesitancy, allowing it to achieve the highest Fl score despite strong semantic similarity between fully vaccinated and booster options. In practice, these interpretable templates enable a better understanding of individual behavior, for instance, identifying who tends to decline vaccination and why, which is crucial for informing high-stakes decision-making maaiin.. See Appendix (A.3 for details.
Computational Complexity and Scalability. With T and T' fixed, ATHENA'S 's runtime is linear in the number of groups [g] and individuals N, scaled by the average L.M latency T:
[ + NT') T.ok).
Both stages parallelize naturally, as group-level searches run independently and individual-level re- finements can be batched or distributed. Detailed runtime measurements are provided in Appendix D
Extended backbone LLM comparisons. On 100-individual subset, we also tested larger reasoning RR-Distill-Quenn
LLMs (Qwen3-32B, larger reasoning models occasionally yield higher F1/Ace but exhibit volatile calibration (high CE), reflecting the lack of structural constraints. Under ATHENA, backbone differences shrink: the symbolic discovery plus semantic adaptation turns the task into constrained sampling and small, directed improvements, allowing lightweight models to reach near-maximal performance, while stronger reasoning models provide modest, consistent gains on harder interactions (e.g., vaccine risk- trade-offss. Full experimental details appear in Appendix for completeness.
GPT-40). With prompt-only baselines,
4.3 Ablation Study
We evaluate ATHENA's 's two components by (i) keeping only the group-level symbolic utility discovery and (ii) keeping only the individual-level semantic adaptation, under identical data and metrics. We do not include symbolic-only group-level discovery baseline (Stage without LLM), because the Concept Library accessible only via the LLM. Excluding it would reduce the hypothesis space to symbolic operators alone, changing the problem definition rather than providing a clean ablation.
Group-Level Symbolic Utility Discovery: necessary but not sufficient. When ATHENA retains only the group-level symbolic component, accuracy exceeds the classical MNL by 4.7% on Swissmetro
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indicating that only LLM -eneeaeeetttdd utilityy expressions can already encode broad demographic regularities. The accuracy trajectories of this symbolic discovery process over 30 iterations (Fig. 3 further demonstrate its effectiveness, illustrating the gradual learning of these group-level trends. Nevertheless, lower F1 score and AUC and elevated cross-entropy, reflecting limited discriminative capacity for similar alternatives. These results highlight the symbolic stage's s strength in pruning the hypothesis space to interpretable structures, but also expose its limitations in capturing much heterogeneity.
and 19% on Vaccine (Table 2),
Table 2: Component-wise ablation results on the Swissmetro and Vaccine choice tasks, comparing Symbolic Utility Discovery only, Semantic Adaptation only, MNL, and the full ATHENA pipeline.
Swissmelm
Vaccine
Variant
Acc.
F1.1
CE.
AUC.1
Acc.1
F1.1
CE
AUC.1
Symbollc Uuiliyy Discovery Only
0.6566
0.3785
2,6044
0,5687
0.6067
0.3596
1.0410
0.7294
Ablation Variants
Semantic Aduptation Only
0.6044
0.4950
2.2897
0.6872
0.5433
0.5348
0.8695
0.7535
MNL
0.6101
0.3967
0.8175
0.7182
0.5000
Full Pipeline
0.8134
0.7655
1.0863
0.8825
0.7345
0.7161
0.7551
0.8704
Young Above Nedian hncom
Wedee Above Modian tncome
Wide: Bolow treone
Ircome
Old Bolon Med treeme
10
15
20
25
10
15
20
10
3.5
30
35
Sanstion
Bactdd
Figure Accuracy trajectories of symbolic regression. As shown here, the accuracy keeps growing in 30 iterations for all four groups in the vaccine dataset. Each orange dot is the average accuracy at given iteration; the red dashed curve is fit showing the overall upward trend and convergence.
Individual-Leve Semantic Adaptation: powerful only with a solid starting point. Conversely, bypassing symbolic discovery and initiating TextGrad from random templates leads to noteworthy degraded performance: As shown in Table 2 accuracy drops to 60.4% on the Swissmetro dataset and 54.3% on the Vaccine dataset; Swissmetro' CE more than doubles (2.29), and AUC falls below 0.70. Without sound starting point, gradients are likely to converge to local optima and yield erratic probability outputs, reaffirming the unreliability of unguided adaptation in multi-choice settings.
Take-away. The two stages of ATHEEA complementary: symbolic discovery supplies an interpretable, well-regularized search space, while semantic adaptation injects the individual-level nuance that symbolic rules alone miss.
4.4 Symbolic Utility Discovery Fragment Analysis
Equation (8) shows that individual prediction is influenced by group-level symbolic utility f (X;; (r) In this section, we demonstrate the building blocks of those utilities are both behaviorally meaningful and reusable across groups. As shown in Fig, 4 each symbolic utility is decomposed into atomic fragments (591, .......) } and their global importance is quantified.
Fragment score. For every group we retain the top-K (K 3) utilities ranked by held-out accuracy Af.(f). The importance score of a fragment Pm is then
K
Score (1mm)
[smm C (fg Acc (fz.
gES k=1
So fragment points whenever it (i) appears in the top-ranked utilities of many groups and (ii) embedded in highly predictive expressions.
Fig. 4 visualizes the fragment scores for both datasets. Only small fraction of fragments dominate, confirming that ATHENA converges a compact and interpretable symbolic basis. For example, in Vaccine, of the leading fragment 107 VAge (Trust Govemment Trust Science) softens

---

Arnull hones Level
16-
Hesdoueyinn
Sender
Belsmmtto Ticket Cost
% Firt Class Traveler
24
Timelmin)
Tidee Poyer Type
Inse Cos|Chll
Tram Travel ConelChl)
Numban of luagagee
bugins 4.0)
# 1.5
7 3g
Kest
R
Ke + sytrsa
x
(a) Swissmetro travel-mode choice dataset
1.0
Levaccivatdd
Viccinos Safl to Me
boodarr
is rigrouu health
0.8
Rias of CDVID 19 in Risk of voccine prevented
Iegertaee 6000
Age
Government
Trunt Science
fymily
0.2
Cct.pitionn hure
Veccine CoVV-
Ky. Occopation - Healts Worker
g
g
33
t
logisca!
(b) COVID-19 vaccine-choice dataset
Figure 4: Aggregated fragment importance extracted from the learned symbolic utilities. For each task, we plot the top-ranked atomic fragments fm that appear in the three best group-level utility formulas and weight them by fragment importance score 9 Values shown here are the normalized scores in [0. 1]-
age's impact at higher values while amplifying it for individuals who trust government or science, precisely isolating the cohort most likely to take boosters.
Beyond fragment-level analysis, ATHENA also produces fully interpretable symbolic utilities. Repre- sentative full formulas and Nomain-relevan insights for both Swissmetro and Vaccine are provided in Appendix A.4
Conclusion
This research highlights the critical role of textual-semantee information in overcoming the limitations of traditional -tilityybased models for human decision- making. By introducing ATHENA, an adaptive textual-symbolic and human-centric reasoning framework is proposed that integrates group-level symbolic regression of utility functions with individual-level. LLW-powered semantic modeling, we offer more comprehensive and personalized view of choice behavior. Our experiments on transportation mode choice and vaccine uptake demonstrate that this co-design approach clearly outperforms three existing model zoos, including classical utility. machine learning, and purely LLM-based approach, underscoring the benefits of capturing both structured attributes and rich semantic context. These findings suggest that between theoretical utility optimization and real- world individual choices, paving the way for more adaptive and human-centric decision models.
reasoning can bridge the gap
Limitations. The current implementation of ATHENA has two limitations. 1) Computational Complexity: The proposed framework requires extra computational resources for textual gradient, particularly when scaling to larger populations. 2) Representation on Groups: ATHENA assumes that a shared symbolic utility function can effectively model each demographic group. However, groups with greater internal diversity may produce weaker or less reliable representations. 3) Result Stability: All reported results are based on single representative runs under fixed random seeds, given the computational cost of multi-stage adaptation. Future work will include multi-seed repetitions to further examine the stability of ATHENA'S 's performance.
10

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Acknowledgments
Yang Zhao acknowledges a fellowship from JHU Amazon Initiative for Interactive AL.
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Frank Kanayet, Frank Seide, Gabricla Medina Florez, Gabriclla Schwarz, Gada Badeer, Georgia Swee, Gil Halpern, Grant Herman, Grigory Sizov, Guangyi, Zhang. Guna Lakshminarayanan, Hakan Inan, Hamid Shojanazeri, Han Zou, Hannah Wang, Hanwen Zha, Haroun Habeeb, Harrison Rudolph, Helen Suk, Henry Aspegren, Hunter Goldman, Hongyuan Zhan, Ibrahim Damlaj, Igor Molybog, Igor Tufanov, Ilias Leontiadis, Irina-Elena Veliche, Itai Gat, Jake Weissman, James Geboski, James Kohli, Janice Lam, Japhet Asher, Jean-Baptiste Gaya, Jeff Marcus, Jeff Tang, Jennifer Chan, Jenny Zhen, Jeremy Reizenstein, Jeremy Teboul, Jessica Zhong, Jian Jin, Jingyi Yang, Joe Cummings, Jon Carvill, Jon Shepard, Jonathan McPhie, Jonathan Torres, Josh Ginsburg, Junjie Wang, Kai Wu, Kam Hou U, Karan Saxena, Kartikay Khandelwal, Katayoun Zand, Kathy Matosich, Kaushik Veeraraghavan, Kelly Michelena, Keqian Li, Kiran
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Jagadeesh, Kun Huang, Kunal Chawla, Kyle Huang, Lailin Chen, Lakshya Garg, Lavender A, Leandro Silva, Lee Bell, Lei Zhang, Liangpeng Guo, Licheng Yu, Liron Moshkovich, Luca Wehrstedt, Madian Khabsa, Manav Avalani, Manish Bhatt, Martynas Mankus, Matan Hasson, Matthew Lennie, Matthias Reso, Maxim Groshev, Maxim Naumov, Maya Lathi, Meghan Keneally, Miao Liu, Michael L. Seltzer, Michal Valko, Michelle Restrepo, Mihir Patel, Mik Vyatskov, Mikayel Samvelyan, Mike Clark, Mike Macey, Mike Wang, Miquel Jubert Hermoso, Mo Metanat, Mohammad Rastegari, Munish Bansal, Nandhini Santhanam, Natascha Parks, Natasha White, Navyata Bawa, Nayan Singhal, Nick Egebo, Nicolas Usunier, Nikhil Mehta, Nikolay Pavlovich Laptev, Ning Dong, Norman Cheng, Oleg Chernoguz, Olivia Hart, Omkar Salpekar, Ozlem Kalinli, Parkin Kent, Parth Parekh, Paul Saab, Pavan Balaji, Pedro Rittner, Philip Bontrager, Pierre Roux, Piotr Dollar, Polina Zvyagina, Prashant Ratanchan- dani, Pritish Yuvraj, Qian Liang, Rachad Alao, Rachel Rodriguez, Rafi Ayub, Raghotham Murthy, Raghu Nayani, Rahul Mitra, Rangaprabhu Parthasarathy, Raymond Li, Rehekkah Hogan, Robin Battey, Rocky Wang, Russ Howes, Ruty Rinott, Sachin Mehta, Sachin Siby, Sai Jayesh Bondu, Samyak Datta, Sara Chugh, Sara Hunt, Sargun Dhillon, Sasha Sidorov, Satadru Pan, Saurabh Mahajan, Saurabh Verma, Seiji Yamamoto, Sharadh Ramaswamy, Shaun Lindsay, Shaun Lindsay, Sheng Feng, Shenghao Lin, Shengxin Cindy Zha, Shishir Patil, Shiva Shankar, Shuqiang Zhang, Shuqiang Zhang, Sinong Wang, Sneha Agarwal, Soji Sajuyigbe, Soumith Chintala, Stephanie Max, Stephen Chen, Steve Kehoe. Steve Satterfield, Sudarshan Govindaprasad, Sumit Gupta, Summer Deng, Sungmin Cho. Sumny Virk. Suraj Subramanian, Sy Choudhury, Sydney Goldman, Tal Remez, Tamar Glaser, Tamara Best, Thilo Koehler, Thomas Robinson, Tianhe Li, Tianjun Zhang, Tim Matthews, Timothy Chou, Tzook Shaked, Varun Vontimitta, Victoria Ajayi, Victoria Montanez, Vijai Mohan, Vinay Satish Kumar, Vishal Mangla, Vlad lonescu, Vlad Poenaru, Vlad Tiberiu Mihailescu, Vladimir Ivanov, Wei Li, Wenchen Wang. Wenwen Jiang. Wes Bouaziz, Will Constable, Xiaocheng Tang. Xiaojian Wu, Xiaolan Wang, Xilun Wu, Xinbo Gao, Yaniv Kleinman, Yanjun Chen, Ye Hu, Ye Jia. Ye Qi, Yenda Li, Yilin Zhang, Ying Zhang, Yossi Adi, Youngjin Nam, Yu, Wang, Yu Zhao, Yuchen Hao, Yundi Qian, Yunlu Li, Yuzi He, Zach Rait, Zachary Vito, Zef Rosnbrick, Zhaoduo Wen, Zhenyu Yang, Zhiwei Zhao, and Zhiyu Ma. The llama 3 herd of models, 2024. URL attps://arzes //axxvv.. org/aagge wrg/abs////ee.. abs.//47 21783
[62] Albert Q Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, Lélio Renard Lavaud, Maric-Anne Lachaux, Pierre Stock, Teven Le Scao, Thibaut Lavril. Thomas Wang, Timothée Lacroix, and William El Sayed. Mistral 7b, 2023. URL fttps://arxivve www.//gg///////////o/o.o/eeeee// http/abs/231100000
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Jonathan Lai, Phil Crone, Bogdan Damoc, Lewis Ho, Sebastian Riedel, Karel Lene, Chan Yeh, Aakanksha Chowdhery, Yang Xu, Mehran Kazemi, Ehsan Amid, Anastasia Petrushkina, Kevin Swersky, Ali Khodaei, Gowoon Chen, Chris Larkin, Mario Pinto, Geng Yan, Adria Puig- domenech Badia, Piyush Patil, Steven Hansen, Dave Orr, Sebastien M. R. Arnold, Jordan Grimstad, Andrew Dai, Sholto Douglas, Rishika Sinha, Vikas Yadav, Xi Chen, Elena Gri- bovskaya, Jacob Austin, Jeffrey Zhao, Kaushal Patel, Paul Komarek, Sophia Austin, Sebastian Borgeaud, Linda Friso, Abhimanyu Goyal, Ben Caine, Kris Cao. Da-Woon Chung. Matthew Lamm, Gabe Barth-Maron, Thais Kagohara, Kate Olszewska, Mia Chen, Kaushik Shivakumar, Rishabh Agarwal, Harshal Godhia, Ravi Rajwar, Javier Snaider, Xerxes Dotiwalla, Yuan Liu, Aditya Barua, Victor Ungureanu, Yuan Zhang, Bat-Orgil Batsaikhan, Mateo Wirth, James Qin, Ivo Danihelka, Tulsee Doshi, Martin Chadwick, Jilin Chen, Sanil Jain, Quoe Le, Arjun Kar, Madhu Gurumurthy, Cheng Li, Ruoxin Sang. Fangyu Liu, Lampros Lamprou, Rich Munoz, Nathan Lintz, Harsh Mehta, Heidi Howard, Malcolm Reynolds, Lora Aroyo, Quan Wang. Lorenzo Blanco, Albin Cassirer, Jordan Griffith. Dipanjan Das, Stephan Lee, Jakub Sygnowski, Zach Fisher, James Besley, Richard Powell, Zafarali Ahmed, Dominik Paulus, David Reitter, Zalan Borsos, Rishabh Joshi, Aedan Pope. Steven Hand, Vittorio Selo, Vihan Jain, Nikhil Sethi, Megha Goel, Takaki Makino, Rhys May, Zhen Yang. Johan Schalkwyk, Christina Butterfield, Anja Hauth, Alex Goldin, Will Hawkins, Evan Senter, Sergey Brin, Oliver Woodman, Marvin Ritter, Eric Noland, Minh Giang, Vijay Bolina, Lisa Lee, Tim Blyth, Ian Mackinnon, Machel Reid, Obaid Sarvana, David Silver. Alexander Chen, Lily Wang, Loren Maggiore, Oscar Chang. Nithya Attaluri, Gregory Thomton, Chung- -Chnng Chiu, Oskar Bunyan, Nir Timothy Chung, Evgenii Eltyshev, Xiance Si, Timothy Lillicrap. Demetra Brady, Vaibhav Aggarwal, Boxi Wu, Yuanzhong Xu, Ross Mcllroy, Kartikeya Badola, Paramjit Sandhu, Erica Moreira, Wojciech Stokowiec, Ross Hemsley, Dong Li, Alex Tudor, Pranav Shyam, Elahe Rahimtoroghi, Salem Haykal, Pablo Sprechmann, Xiang Zhou, Diana Mineu, Yujia Li, Ravi Addanki, Kalpesh Krishna, Xiao Wu, Alexandre Frechette, Matan Eyal, Allan Dafoe, Dave Lacey, Whang. Thi Avrahami, Ye Zhang, Emanuel Taropa, Hanzhao Lin, Daniel Toyama, Eliza Rutherford, Motoki Sano, HyunJeong Choe, Alex Tomala, Chalence Safranek- -Shrader, Nora Kassner, Mantas Pajarskas, Matt Harvey, Sean Sechrist, Meire Fortunato, Christina Lyu, Gamaleldin Elsayed, Chenkai Kuang. James Lottes, Eric Chu, Chao Jia, Chih-Wei Chen, Peter Humphreys, Kate Baumli, Connie Tao, Rajkumar Samuel, Cicero Nogueira dos Santos, Anders Andreassen, Nemanja Rakićević, Dominik Grewe, Aviral Kumar, Stephanie Winkler, Jonathan Caton, Andrew Brock, Sid Dalmia, Hannah Sheahan, lain Barr, Yingjie Miao, Paul Natsev, Jacob Devlin, Feryal Behbahani, Flavien Prost, Yanhua Sun, Artiom Myaskovsky, Thanumalayan Sankaranarayana Pillai, Dan Hurt, Angeliki Lazaridou, Xi Xiong, Ce Zheng, Fabio Pardo, Xiaowei Li. Dan Horgan, Joe Stanton, Moran Ambar, Fei Xia, Alejandro Lince, Mingqiu Wang. Basil Mustafa, Albert Webson, Hyo Lee, Rohan Anil, Martin Wicke, Timothy Dozat, Abhishek Sinha, Enrique Piqueras, Elahe Dabir, Shyam Upadhyay, Anudhyan Boral, Lisa Anne Hendricks, Corey Fry. Josip Djolonga, Yi Su. Jake Walker, Jane Labanowski, Ronny Huang, Vedant Misra. Jeremy Chen, RJ Skerry-Ryan, Avi Singh, Shruti Rijhwani. Dian Yu, Alex Fastro-Ros, Beer Changpinyo, Romina Datta, Sumit Bagri, Amar Mar Hrafnkelsssn. Marcello Maggioni, Daniel Zheng, Yury Sulsky, Shaobo Hou, Tom Le Paine, Antoine Yang. Jason Riesa, Dominika Rogozinska, Dror Marcus, Dalia EI Badawy, Qiao Zhang, Luyu Wang. Helen Miller, Jeremy Greer, Lars Lowe Sjos, Azade Nova, Heiga Zen, Rahma Chaabouni, Mihaela Rosca, Jiepu Jiang, Charlie Chen, Ruibo Liu, Tara Sainath, Maxim Krikun, Alex Polozov, Jean-Baptiste Lespiau, Josh Newlan, Zeyncep Cankara, Soo Kwak, Yunhan Xu, Phil Chen, Andy Coenen, Clemens Meyer, Katerina Tsihlas, Ada Ma, Juraj Gottweis, Jinwei Xing, Chenjie Gu, Jin Miao, Christian Frank, Zeynep Cankara, Sanjay Ganapathy, Ishita Dasgupta, Steph Hughes-Fitt Fitt, Heng Chen, David Reid, Keran Rong. Hongmin Fan, Joost van Amersfoort, Vincent Zhuang, Aaron Cohen, Shixiang Shane Gu, Anhad Mohananey, Anastasija Ilie, Taylor Tobin, John Wieting, Anna Bortsova, Phocbe Thacker, Emma Wang, Emily Caveness, Justin Chiu, Eren Sezener, Alex Kaskasoli, Steven Baker, Katie Millican, Mohamed Elhawaty, Kostas Aisopos, Carl Lebsack, Nathan Byrd, Hanjun Dai, Wenhao Jia, Matthew Wiethoff, Elnaz Davoodi, Albert Weston, Lakshman Yagati, Arun Ahuja, Isabel Gao, Golan Pundak, Susan Zhang, Michael Azzam, Khe Chai Sim, Sergi Caelles, James Keeling, Abhanshu Sharma, Andy Swing, YaGuang Li, Chenxi Liu, Carrie Grimes Bostock, Yamini Bansal, Zachary Nado, Ankesh Anand, Josh Lipschultz, Abhijit Karmarkar, Lev Proleev, Abe Ittycheriah, Soheil Hassas Yeganeh, George Polovets, Aleksandra Faust, Jiao Sun, Alban Rrustemi, Pen Li. Rakesh Shivanna, Jeremiah Liu, Chris Welty, Federico Lebron, Anirudh
Levine.
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Baddepudi, Sebastian Krause, Emilio Parisotto, Radu Soricut, Zheng Xu, Dawn Bloxwich, Melvin Johnson, Behnam Neyshabur, Justin Mao-Jones, Renshen Wang, Vinay Ramasesh, Zaheer Abbas, Arthur Guez, Constant Segal, Due Dung Nguyen, James Svensson, Le Hou, Sarah York, Kieran Milan, Sophie Bridgers, Wiktor Gworek, Marco Tagliasacchi, James Lee-Thorp, Michael Chang, Alexey Guseynov, Ale Jakse Hartman, Michael Kwong, Ruizhe Zhao, Sheleem Kashem, Elizabeth Cole, Antoine Miech, Richard Tanburn, Mary Phuong, Filip Pavetic, Sebastien Cevey, Ramona Comanescu, Richard Ives, Sherry Yang, Cosmo Du, Bo Li, Zizhao Zhang, Mariko linuma, Clara Huiyi Hu, Aurko Roy, Shaan Bijwadia, Zhenkai Zhu, Danilo Martins, Rachel Saputro, Anita Gergely, Steven Zheng. Dawei Jia, loannis Antonoglou, Adam Sadovsky, Shane Gu, Yingying Bi, Alek Andreev, Sina Samangooei, Mina Khan, Tomas Kocisky, Angelos Filos, Chintu Kumar, Colton Bishop, Adams Yu, Sarah Hodkinson, Sid Mittal, Premal Shah, Alexandre Moufarek, Yong Cheng, Adam Bloniarz, Jaehoon Lee, Pedram Pejman, Paul Michel, Stephen Spencer, Vladimir Feinberg, Xuehan Xiong, Nikolay Savinov, Charlotte Smith, Siamak Shakeri, Dustin Tran, Mary Chesus, Bernd Bohnet, George Tucker, Tamara Glehn, Carrie Muir, Yiran Mao, Hideto Kazawa, Ambrose Slone, Kedar Soparkar, Disha Shrivastava, James Cobon-Kerr, Michael Sharman, Jay Pavagadhi, Carlos Araya, Karolis Misiunas, Nimesh Ghelani, Michael Laskin, David Barker, Qiujia Li, Anton Briukhov, Neil Houlsby, Mia Glaese Balaji Lakshminarayanan, Nathan Schucher, Yunhao Tang, Eli Collins, Hyeontaek Lim, Fangxiaoyu Feng, Adria Recasens, Guangda Lai, Alberto Magni, Nicola De Cao, Aditya Siddhant, Zoe Ashwood, Jordi Orbay, Mostafa Dehghani, Jenny Brennan, Yifan He, Kelvin Xu, Yang Gao, Carl Saroufim, James Molloy, Xinyi Wu, Seb Amold, Solomon Chang. Julian Schrittwieser, Elena Buchatskaya, Soroush Radpour, Martin Polacek, Skye Gior- dano, Ankur Bapna, Simon Tokumine, Vincent Hellendoorn, Thibault Sottiaux, Sarah Cogan, Aliaksei Severyn, Mohammad Saleh, Shantanu Thakoor, Laurent Shefey, Siyuan Qiao, Meenu Gaba, Shuo yiin Chang, Craig Swanson, Biao Zhang. Benjamin Lee, Paul Kishan Rubenstein, Gan Song, Tom Kwiatkowski, Anna Koop, Ajay Kannan, David Kao, Parker Schuh, Axel Stjerngren, Golnaz Ghiasi, Gena Gibson, Luke Vilnis, Ye Yuan, Felipe Tiengo Ferreira, Aish- warya Kamath, Ted Klimenko, Ken Franko, Kefan Xiao, Indro Bhattacharya, Miteyan Patel, Rui Wang, Alex Morris, Robin Strudel, Vivek Sharma, Peter Choy, Sayed Hadi Hashemi, Jessica Landon, Mara Finkelstein, Priya Jhakra, Justin Frye. Megan Barnes, Matthew Mauger, Dennis Daun, Khuslen Baatarsukh, Matthew Tung, Wael Farhan, Henryk Michalewski, Fabio Viola, Felix de Chaumont Quitry, Charline Le Lan, Tom Hudson, Qingze Wang, Felix Fischer, Ivy Zheng, Elspeth White, Anca Dragan, Jean baptiste Alayrac, Eric Ni, Alexander Pritzel, Adam Iwanicki, Michael Isard, Anna Bulanova, Lukas Zilka, Ethan Dyer, Devendra Sachan, Srivatsan Srinivasan, Hannah Muckenhirn, Honglong Cai, Amol Mandhane, Mukarram Tariq, Jack W. Rae, Gary Wang, Kareem Ayoub, Nicholas FitzGerald, Yao Zhao, Woohyun Han, Chris Alberti, Dan Garrette, Kashyap Krishnakumar, Mai Gimenez, Anselm Levskaya, Daniel Sohn, Josip Matak, Inaki Iturrate. Michael B. Chang, Jackie Xiang. Yuan Cao, Nishant Ranka, Geoff Brown, Adrian Hutter, Vahab Mirrokni, Nanxin Chen, Kaisheng Yao, Zoltan Egyed, Francois Galilee, Tyler Liechty, Praveen Kallakuri, Evan Palmer, Sanjay Ghemawat, Jasmine Liu, David Tao, Chloe Thornton, Tim Green, Mimi Jasarevic, Sharon Lin, Victor Cotruta, Yi-Xuan Tan, Noah Fiedel, Hongkun Yu, Ed Chi, Alexander Neitz, Jens Heitkaemper, Anu Sinha, Denny Zhou, Yi Sun, Charbel Kaed, Brice Hulse, Swaroop Mishra, Maria Georgaki, Sneha Kudugunta, Clement Farabet, Izhak Shafran, Daniel Vlasic, Anton Tsitsulin, Rajagopal Ananthanarayanan, Alen Carin, Guolong Su, Pei Sun, Shashank V. Gabriel Carvajal, Josef Broder, Iulia Comsa, Alena Repina, William Wong, Warren Weilun Chen, Peter Hawkins, Egor Filonov, Lucia Loher, Christoph Himschall, Weiyi Wang. Jingchen Ye, Andrea Burns, Hardie Cate, Diana Gage Wright, Federico Piccinini, Lei Zhang, Chu-Cheng Lin, Ionel Gog, Yana Kulizhskaya, Ashwin Sreevatsa, Shuang Song, Luis C. Cobo, Anand Iyer, Chetan Tekur, Guillermo Garrido, Zhuyun Xiao, Rupert Kemp, Huaixiu Steven Zheng, Hui Li, Ananth Agar- wal, Christel Ngani, Kati Goshvadi. Rebeca Santamaria-Femandezz Wojeiech Fica. Xinyun Chen, Chris Gorgolewski. Sean Sun, Roopal Garg, Xinyu Ye, S. M. Ali Eslami, Nan Hua, Jon Simon, Pratik Joshi, Yelin Kim, Ian Tenney, Sahitya Potluri, Lam Nguyen Thiet, Quan Yuan, Florian Luisier, Alexandra Chronopoulou, Salvatore Scellato, Praveen Srinivasan, Minmin Chen, Vinod Koverkathu, Valentin Dalibard, Yaming Xu, Brennan Saeta, Keith Anderson, Thibault Sellam, Nick Fernando, Fantine Huot, Junehyuk Jung, Mani Varadarajan, Michael Quinn, Amit Raul, Maigo Le, Ruslan Habalov, Jon Clark, Komal Jalan, Kalesha Bullard, Achintya Singhal, Thang Luong, Boyu Wang, Sujeevan Rajayogam, Julian Eisenschlos, John- son Jia, Daniel Finchelstein, Alex Yakubovich, Daniel Balle, Michael Fink, Sameer Agarwal,
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Jing Li, Dj Dvijotham, Shalini Pal, Kai Kang, Jaclyn Konzelmann, Jennifer Beattie, Olivier Dousse, Diane Wu, Remi Crocker, Chen Elkind, Siddhartha Reddy Jonnalagadda, Jong Lee, Dan Holtmann-Rice, Krystal Kallarackal, Rosanne Liu, Denis Vnukov, Neera Vats, Luca Invernizzi, Mohsen Jafari, Huanjie Zhou, Lilly Taylor, Jennifer Prendki, Mareus Wu, Tom Eccles, Tianqi Liu, Kavya Kopparapu, Francoise Beaufays, Christof Angermueller, Andreea Marzoca, Shourya Sarcar, Hilal Dib, Jeff Stanway, Frank Perbet, Nejc Trdin, Rachel Stemneck, Andrey Khorlin, Dinghua Li, Xihui Wu, Sonam Goenka, David Madras, Sasha Goldshtein, Willi Gierke, Tong Zhou, Yaxin Liu, Yannie Liang, Anais White, Yunjie Li, Shreya Singh, Sanaz Bahargam, Mark Epstein, Sujoy Basu, Li Lao, Adnan Ozturel, Carl Crous, Alex Zhai, Han Lu, Zora Tung, Neeraj Gaur, Alanna Walton, Lucas Dixon, Ming Zhang, Amir Globerson, Grant Uy Andrew Bolt, Olivia Wiles, Milad Nasr, Ilia Shumailov. Marco Selvi, Francesco Piccinno, Ricardo Aguilar, Sara McCarthy, Misha Khalman, Mrinal Shukla, Vlado Galic, John Carpenter, Kevin Villela, Haibin Zhang. Harry Richardson, James Martens, Matko Bosnjak, Shreyas Rammohan Belle, Jeff Seibert, Mahmoud Alnahlawi, Brian McWilliams, Sankalp Singh, Annie Louis, Wen Ding, Dan Popovici, Lenin Simicich, Laura Knight, Pulkit Mehta, Nishesh Gupta, Chongyang Shi, Saaber Fatehi, Jovana Mitrovic, Alex Grills, Joseph Pagadora, Tsendsuren Munkhdalai, Dessie Petrova, Danielle Eisenbud, Zhishuai Zhang, Damion Yates, Bhavishya Mittal, Nilesh Tripuraneni, Yannis Assael, Thomas Brovelli, Prateek Jain, Mihajlo Velimirovic, Canfer Akbulut, Jiaqi Mu, Wolfgang Macherey, Ravin Kumar, Jun Xu. Haroon Qureshi, Gheorghe Comanici, Jeremy Wiesner, Zhitao Gong. Anton Ruddock, Matthias Bauer, Nick Felt, Anirudh GP, Anurag Arnab, Dustin Zelle, Jonas Rothfuss, Bill Rosgen, Ashish Shenoy, Bryan Seybold, Xinjian Li, Jayaram Mudigonda, Goker Erdogan, Jiawei Xia, Jiri Simsa, Andrea Michi, Yi Yao, Christopher Yew, Steven Kan, Isaac Caswell, Carey Rade- baugh, Andre Elisseeff, Pedro Valenzuela, Kay McKinney, Kim Paterson, Albert Cui, Eri Caiorre-Chimoto, Solomon Kim, William Zeng. Ken Durden, Priya Ponnapalli, Tiberiu Sosea, Christopher A. Choquette-Choo, James Manyika, Brona Robenek, Harsha Vashisht, Sebastien Pereira, Hoi Lam, Marko Velic. Denese Owusu-Afriyie, Katherine Lee, Tolga Bolukbasi, Alicia Parrish, Shawn Lu, Jane Park, Balaji Venkatraman, Alice Talbert, Lambert Rosique, Yuchung Cheng, Andrei Sozanschi, Adam Paszke, Praveen Kumar, Jessica Austin, Lu Li, Khalid Salama, Bartek Perz. Wooycol Kim, Nandita Dukkipati. Anthony Baryshnikov, Christos Kaplanis, XiangHai Sheng, Yuri Chervonyi, Caglar Unlu, Diego de Las Casas, Harry Askham, Kathryn Tunyasuvunakool, Felix Gimeno, Siim Poder, Chester Kwak, Matt Miecnikowski, Va- hab Mirrokni, Alek Dimitriev, Aaron Parisi, Dangyi Liu, Tomy Tsai, Toby Shevlane, Christina Kouridi, Drew Garmon, Adrian Goedeckemeyer, Adam R. Brown, Anitha Vijayakumar, Ali Elqursh, Sadegh Jazayeri, Jin Huang, Sara Mc Carthy, Jay Hoover, Lucy Kim, Sandeep Kumar, Wei Chen, Courtney Biles, Garrett Bingham, Evan Rosen, Lisa Wang. Qijun Tan, David Engel, Francesco Pongetti, Dario de Cesare, Dongseong Hwang, Lily Yu, Jennifer Pullman, Srini Narayanan, Kyle Levin, Siddharth Gopal, Megan Li, Asaf Aharoni, Trieu Trinh, Jessica Lo, Norman Casagrande, Roopali Vij. Loic Matthey, Bramandia Ramadhana, Austin Matthews, CJ Carey, Matthew Johnson, Kremena Goranova. Rohin Shah, Shereen Ashraf, Kingshuk Dasgupta, Rasmus Larsen, Yicheng Wang, Manish Reddy Vuyyuru, Chong Jiang, Joana Ijazi, Kazuki Osawa, Celine Smith, Ramya Sree Boppana, Taylan Bilal, Yuma Koizumi, Ying Xu, Yasemin Altun, Nir Shabat, Ben Bariach, Alex Korchemniy, Kiam Choo, Olaf Ronneberger, Chimezie Iwuanyanwu, Shubin Zhao, David Soergel, Cho-Jui Hsieh, Irene Cai,, Shariq lqbal, Martin Sundermeyer, Zhe Chen, Elie Bursztein, Chaitanya Malaviya, Fadi Biadsy, Prakash Shroff, Inderjit Dhillon, Tejasi Latkar, Chris Dyer, Hannah Forbes, Massimo Nicosia, Vitaly Nikolaev, Somer Greene, Marin Georgiev, Pidong Wang, Nina Martin, Hanie Sedghi, John Zhang, Praseem Banzal, Doug Fritz, Vikram Rao, Xuezhi Wang. Jiageng Zhang, Viorica Patraucean, Dayou Du, Igor Mordatch, Ivan Jurin, Lewis Liu, Ayush Dubey, Abhi Mohan, Janck Nowakowski, Vlad-Doru Ion, Nan Wei, Reiko Tojo, Maria Abi Raad, Drew A. Hud- son, Vaishakh Keshava, Shubham Agrawal, Kevin Ramirez, Zhichun Wu, Hoang Nguyen, Ji Liu, Madhavi Sewak, Bryce Petrini, DongHyun Choi, Ivan Philips, Ziyue Wang, loana Bica, Ankush Garg, Jarek Wilkiewicz, Priyanka Agrawal, Xiaowei Li, Danhao Guo, Emily Xue, Naseer Shaik, Andrew Leach, Sadh MNM Khan, Julia Wiesinger, Sammy Jerome, Abhishek Chakladar, Alek Wenjiao Wang, Tina Ornduff, Folake Abu, Alireza Ghaffarkhah, Marcus Wainwright, Mario Cortes, Frederick Liu, Joshua Maynez, Andreas Terzis, Pouya Samangouei, Riham Mansour, Tomasz Kępa, TrraçoissXXvveer Aubet, Anton Algymr, Dan Banica, Agoston Weisz, Andras Orban, Alexandre Senges, Ewa Andrejezuk, Mark Geller, Niccolo Dal Santo, Valentin Anklin, Majd Al Merey, Martin Bacuml, Trevor Strohman, Junwen Bai, Slav Petrov.
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A Extended Analysis
A.1 Broader Societal Impacts
The introduction of ATHENA, a two-stage framework that first discovers group-level symbolic utility functions and then develops individual semantic templates, offers potential for positive societal contributions, By combining LLM reasoning with symbolic regression, ATHENA aims to deliver: (1) More inclusive public-policy insights: interpretable utility functions reveal group motivations behind choices in socially critical behaviors, enabling better targeted interventions and policy making. (2) Precise and equitable individual adaptation: reduce the oone-size-fits-al errors in some high-stake domains, like healthcare and education.
At the same time, ATHENA also brings concerns. (1) Potential Misuse: Because ATHENA can model fine-grained individual decisions, it could be deployed for manipulative ad advertising, political margo-targeting, or discriminatory dynamic pricing. Mitigations include restricted licensing and mandatory human oversight for high-impact deployments. (2) Bias and Faimnss:: The symbolic utility discovery stage may suffer from coarse group partitioning, which can ignore intra-group heterogeneity. Meanwhile, the semantic adaptation stage may inherit biases presented in the LLM's training data, thereby embedding historical stereotypes.
A.2 Qualitative Analysis and Case Study
Table 3: Qualitative study of ATHENA the Swissmetro dataset. This table contrasts four representative travelers' attributes, the candidate alternatives, the group-level symbolic utility functions learned in Stage- and the individualized decision rules refined in Stage-2.
Swissmetro
Case
Features X'
Age: between 54 and 65 years old
Gender: Male
Income: Over 100
Trip Purpose: business
Luggage: none of luggage
Payment Method: paid by oneself
Origin: St. Gallen
Destination: Bern
Alternatives
Metro: travel time 77 minutes, costing 74 CHF, with headway 30 minutes
T
Train:
travel time of 120 minutes, costing 64 CHF, with a headway of 120 minutes
Car:
travel time of 169 minutes, costing 60 CHF
Optimal
Train: K₃ - ttip_rpp purpose + K₂ (ynum luggage + Ci + C2) log
Group Utility f
Cs) + K3 time train + K4 vtrain headway min + K₃ (is first classsclsss- +
C₁) /Tooffncom + C³) + Cg
Car: K2 ruippeer + K₂ /num Sargnlllggggeeee + Ci log(age + C2) + K3
time_ Vlogfincome C3) + K₃ Vccost //ccostttrainntttttoeeeee Cyl + Ks-
service hhadwayyaaaaaaa Kg (is (is_first class + Cs) /log/income + Cb) + Cr
Metro:
Ki-trip trip_ppe K2- (num__g_lg C log(age + C2)+ K3 time_sm- Vincome Cg + K4- / costssmm + + KG (ticket_payer_tyye) + Ct) + Co
Optimal Personal-
As a business traveler, my travel decisions are guided by a dynamic scoring system that prioritizes speed, environmental impact, and cost. I often weigh these factors differently based on specific scenarios (e.g., major conferences vs. regular trips). Real-time traffic/weather and reflections on past trips refine preferences; I consider Swissmetro, trains, cars, buses, and rideshares, evaluating comfort, reliability, and amenities.
BALANCED:
ized
Decision Rule P
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Swissmetro
Case
Features
Age: between and 54 years old
Gender: Male
Income: between 50 and 100
Trip Purpose: leisure
Luggage: no luggage
Payment Method: paid by oneself
Origin: Graubünden
Destination: Bern
Alternatives
Metro: travel time 142 min, cost 123 CHF, headway 30 min
J
Train: travel time 180 min, cost 97 CHP, headway 60 min
Car: travel time 136 min, cost 149 CHF
Optimal
Train: K1. (ticket_payerr.ce
is_car sl_.availablee /age Ci + K2
Group
is_ fs_first_chee class log(age + C2)) K3 time_train K4. (incone +
Utility f
age + C3
time_car
num_luggage C4) K5
+ Co C7
age + +Cs
Car: K1 (aaee (ype-_ttppp__ is car avwiaaableeeaaeeeaaee + C1 + K2
time train
is first class) - Ky
+ K₃ -log(incoome + num luggage
age + C2
time_car
Kayage C3) Kg
Cs
Co
age C4
time_ sm
Metro: K1 (sm_headwwy
+ K2
log + C1)
(has lals_ga____ sa__ravel____ travel_pass / + C3)) C4
gender Tog(income + num huggaee +
Optimal
BALANCED, INFORMED, SUSTAINABLE, USER-CENTRIC,
Personal-
CONTEXT-ADAPTIE COMFORT-FOCUSIE Dynamically trades off time, cost, and scenic enjoyment. Fco-friendliness and comfort (leg-room, quiet cars) matter, even with longer trips higher prices; prior-trip feedback and real-time context refine recommendations.
ized
Decision
Rule P.
Swissmetro
Case
Features X
Age: between 39 and 54 years old
Gender: Male
Income: under 50
Trip Purpose: leisure
Luggage: no luggage
Payment Method: paid by unknown people
Origin: Zurich
Destination: Bern
Alternatives
Metro: travel time 56 min, cost 42 CHF, headway 10 min
Train: travel time min, cost 36 CHF, headway 30 min
Car: travel time 88 min, cost 60 CHF
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Optimal Group Utility fg
Train: C1 + K1 time train time carl (log (income + C2) +
agg + C3) (gender num luggage + C1 + is first class) + K2
trip_purpose
K3 cost cost_train trip_ supppurppse
V Vage C3 + Cs
Car: C₁ + K1 (num (nuum___ugaaaa Juggage trip_purpose [iog(income + C2)l (C3 + Vage + C4) + Vage + Cs [time _eneitrain-- time carl (Cg + is first crrss__class) K2-(C7 train service hateeeeeaawwwaaeaeee _in) + K3 K3-(income + Cs)
Metro: C + K
time sm trip purpose num luggage C3 log(income + C4)
Vage C5 + C.
K2-(cost_ssm (log(age + C7) is fifffist__che soffisst_lass)) (Cs + /tieetteeeeeeee car)
Optimal Personal-
COST_SAVING Prefers options at least 10% cheaper than peak-fare averages, values minimal transfers and amenities (Wi-Fi, food), uses gurbon-footprin data, and favors off off-peak scheduling; feedback refines future recommendations.
ized
Decision
Rule P.
Swissmetro
Case
Features X
Age: over 65 years old
Gender: Male
Income: over 100
Trip Purpose: shopping
Luggage: luggage
Payment Method: paid half-half
Origin: Vaud
Destination: Geneva
Alternatives
Metro: travel time min, cost 226 CHF, headway 10 min
T
Train: travel time 42 min, cost 209 CHF, headway 60 min
Car: travel time min, cost 67 CHF
Optimal
Train: (ii-(ttme_traii -aaieetraii--e num _uggaguuuaeeeeee age + age + time_ccepec _ame___rr____ + K2.
Group
(income is_first_class gender log(age C3)) + num num_luggage Co Cs
Utility f
Car: - + num _uggaee age + innomee firrst_cllassss class +
car por__tavel___e heavvelccsttehhff
num _lggauuuuggeeeee exp(age/Ca) /22) + +CB
Metro: K₁ -time_smmmmmmmt sm + K2. (c-ss sm + income (is first first_class, + gender)
exp(age C1) + num luggage age age + age/Cs) C4
Optimal Personal- ized
COMFORT SEEKING: Prioritizes spacious seating, quiet cars, and onboard services: willing to pay up to 20% premium. Prefers real-time updates and easy boarding for accessibility; social events may nudge to more social modes; feedback refines future recommendations.
Decision Rule P.
Table 4: Qualitative case study of ATHENA on the Vaccine dataset. This table contrasts four representative individuals' attributes, the candidate alternatives, the group-level symbolic utility functions learned in Stage-1, and the individualized decision rules refined Stage-2.
Vaccine
Case
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Features X
Age: 25
Gender: Male
Occupation: Nurse
Education: No university degree
Income: Above-median
COVID-19 Threat Perception: Moderate
Risk Perception: Disease risk vaccine risk
Trust in Government: Moderate
Trust in Science:
Moderate
Perceived Vaccine Safety: Fairly safe
Family COVID Infection: > yr ago
Attention to Vaccine News: Increased
Alternatives
Unvaccinated
J
Vaccinated_NNe Baainated_NoBBooore No_Booster
Booster
Optimal Group
Unvaccinated: Ci -cvovii__it (hriid_ttrea((222 + trust_oov trust_sci log(age + Ca))
_txxxxd___axx___ + te-ffmlll_covvii log(age + C4)
Utility fg
Vaccinated No_Booster: C1 "Gvvid____heeee threat C2- Va-vax_safe- + K₁ gtruttust_gov
trust sci more_ sure_attention v'ge C33)
Booster: " covid tiredtttrttttt wwwptprootttttte
Ca-vax_seea + K₃
(trust_gov irust_sci- nurse Vage C4)
Optimal Personal-
TRUSTING AUTHORITY: This persona represents cautiously informed healthcare worker who values evidence-base guidance and may favor "Vaccinated (No Booster)" given safety concerns, while remaining open updates as new data emerge; family and social influence are considered.
ized
Decision Rule P
Vaccine
Case
Features X
Age: 55
Gender: Male
Education: No university degree
Income: Below-median
COVID-19 Threat Perception: Moderate
Trust in Government Delivery: High
Trust in Science: Some
Risk Perception: Disease risk >> vaccine risk
Family COVID: None
Attention to Vaccine News: Decreased
Alternatives
Unvaccinated
Vaccinated No Booster
Booster
Optimal Group
Unvaccinated:
/iv/ovii_thhee cisbaattrrscccviiid st__d__g_vaaa_____ vax gender,/age Ci)
((trust_goy gov trust_sci)C: C3) K2- - Si-lowwjicomer +
Utility fg
has doss_eeereee-a trust_gov _ov trust_sci) sci) Css
Vaceinated Booster:
Kι-(vax safe trust gov-trust truuutuutstcce sci. V Vage + C₁ + income unknown C2 more_attention
Cz) + K₂ dess_attention + C22
Cs
Booster: - (familyymmooiii + physician trust_ trust_ (Vage + Ci C2) + nurse trust_sciv/age C3 + C4) + Cs
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Optimal
SKEPTICAL: Prefers conservative choices due perceived safety concerns; may remain unvaccinated unless convinced by trusted figures; open to "Vaccinated No Booster" or "Booster" if necessity and safety are clearly established.
Personal-
ized
Decision
Rule P.
Vaccine
Case
Features X'
Age: 86
Gender: Male
Education: No university degree
Income: Below-median
COVID-19 Threat View: Moderate
Perceived Vaccine Safety: High
Long-COVID Protection Belief: Uncertain
Family COVID: None
Attention Vaccine News: Increased
Alternatives
Unvaccinated
Vaceinated BetttteddNoBBBBooe No_Bter
Booster
Optimal Group Utility Sg
Unvaccinated:
C + Ki (covid ttreatt------- grust_oov trust_sci age (C3 hamily_covidle
K2 -riski fe--rriskccoidd___ gt__gg____aaaa__a vax + income unknown e Kg more atlentionn age
Vaccinated No. Booster: C1 K₃ (age Os (C3 low income)
trust_sci)) + K2 (vax-vvx__aa (vax_safe safe trust_gov (Cs + more attention age Cae ())
Booster: C1 +
+ (vvx__protect_lowe e (ago
family covid))
K3- coiss_sttention trust_sci (age/Ca))
Optimal
THREAT AVOIDING: Perceives high disease risk; ranks Booster > Vaccinated No Booster > Unvaccinated; considers logistics and side-effect concerns while relying on trusted sources.
Personal-
ized
Decision
Rule P.
Vaccine
Case
Features X
Age: 52
Gender: Male
Education: No university degree
Income: Below-medie
COVID-19 Threat Perception: Strong
Belief in Vaccine Prevention: Low
Trust in Science:
Moderate
Risk Perception: Disease risk >> vaccine risk
Attention to Vaccine News: Unchanged
Family COVID: None
Alternatives
Unvaccinated
Vaccinated _No___ooo____ Booster _N__oossterrrr
Booster
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Optimal
Unvaccinated: covid threat(risk covid gt_ genderragge C1)
Group Utility fg
((trust_go) gov must_sci)(== C3) K2 mmoee_ateention low income
1isllwwiicoom C4
has mas__eeree- trust_go trust_sci) + Cs.
Vaccinated_ Booster:
::oooserr
Ki-(vax_safee Lerax_safe+-tiiie trust covust_oo-trrust.teo trust_sci V Vage C1 income_unknowe C2
C3) + K2' more_attention
+ C3
less attentionno C4
Booster: (1-(family_cove covid physician grust_oov trust_sci (Vage + + C2) + nurse trust crust_scivagge C3 + C4) + Cs
Optimal Personal- ized Decision Rule ?
BALANCED: Cautious yet data-driven; moderate trust in authorities; open to boosters with clear evidence; weighs prior experiences and accessibility.
A.3 Semantically Similar Choices Analysis
As illustrated in Figure 5 ATHENA not only raises aggregated accuracy but also improves decision- critical boundaries, offering more reliable evidence for public-health and transport -policy planning.
A.4 Extended Interpretability Showcase
We provide representative full symbolic utilities discovered by ATHENA Swissmetro and Vaccine datasets. These examples illustrate how the symbolic structure translates into actionable insights for transportation and public health domains.
A.4.1
Representative Example - Swissmetro Dataset
Mode
Discovered symbolic utility
Train
K ((trainnttmme metro
metro <ht-:-/-gggeeeeeeee------e---e--
income) C3- (GA_pass
pass headway)
Car
(eccar_time + traiin_timeeetttttette + [ispaaghhouolessecoooe//e////o/r
C3 (GA (GA_pass + metro fare + is male)
fare K metro time luggage age m
Metro
GA pass male)
Feature:
Between 39 and 54 years old, identify as female, and have an income between 50 and 100.
Key take-aways for domain experts
Time dominates. Large negative coefficients on travel-time variables show this segment is highly time-sensitive - investments that shorten door-to-door time (e.g., skip-stop service) should shift demand [117.
Comfort premium. Positive weight (first class + income) across all modes indicates willing- ness to pay for comfort that scales with income - targeted upselling (seat reservations, quiet cars) is effective [188.
Luggage burden grows with age. The interaction luggage log(age + C1) reveals baggage becomes disproportionately painful for older travelers - facilities such luggage trolleys or porter services may raise train/metro share [119].
GA pass effect. Owning a GA pass biases travellers away from modes that still incur extra fares. Extending GA coverage to Swissmetro would therefore raise its relative appeal [20].
38

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Logistic Regression
Fewshot
Athena
No
No
Booster No Booster
Boaser No Boosler
63
34
12
51
@opstr
37
18
No
No Booster
Booster
No Booster
Booster
No
Booster
Booster
(a) Vaccine-uptake task. ATHENА removes all 34 cases in which the Vaccinated no
sal__o__ooooo_e booster class
was previously misclassified as Booster, thereby preserving the integrity of booster-demand estimates.
Random Forest
Fewshot
Athena
Car Swizsmetro Irain
Tain
219
Sufssmebro Tain
5B
Swissmettoo
56
187
97
607
535
Car
Car
69
mhann
Swissmetro
Car
Train
Swissmetro
Car
Train
Swiismmetro
Car
(b) Travel-mode choice task. ATHENA cuts the Swiismetrro-versus-CCo Car confusion from 83 to instances, refining forecasts of low-carbon rail adoption.
Figure 5: ATHENA yields improvements on the classes that matter most yet were previously hard to distinguish.
Mode
Discovered symbolic utility
Train
Ki purposse + [payer_type-Gi first_class- + |uggagel v /age
C2 |rain_timme time
C3l log(income + C.)) -c
Car
K1 [car faar_time=-a + C1l + caar time-tme---- train time + C2l |car_coss train C3 +
hhaddway Vincome + C4 C5
Metro
K1 [metro_timer time Ci meetr__cossssss cococccosstttt C2/+ / Jage + C3 log eeppeexxpino (C)) +
C5}
C5
Feature:
Male travelers younger than 24 years, annual income 50-100k.
Key take-aways for domain experts
Time still trumps money. Travel time appears in utilities, while fare only in Car/Metro. For under-25 travelers, each minute lost matters more than an extra franc prioritizing faster transfers or signal priority especially effective 1211.
Headway frustration fuels car use. The term headway Vincome shows that infrequent trains push young people toward cars, and irritation rises with income higher-frequency rail services can curb car switching [122
coefficient suggests little interest in upgrades -> amenities in standard class (Wi-Fi, gaming lounges) may more persuasive than premium seating [23]
First-class indifference. The negative
39

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A.4.2 Representative Example Vaccine Dataset
Mode
Discovered symbolic utility
Unvaccinated
C₁ covid threat
(C2 + gust__oovrmment trust_ rust_science
log(age (aa)) risk_of _o_eooo__ooooooooeeeeeeeeeeeeeee _o_oaed__reaater greater_than than_ vax
+ K
have_covid sick family_mme member log(age C4)
Vaccinated (no boaster)
Ci _arrddttttttt-tee + C2-vaccine satle_saf_____eeeeee so_tt___ee____ me + (trust government-
rrss_scciene more attention to_vat vax info vage + +3)
Booster
C1 eggo covid_threat
+ C3
vaccine_safe safe_to__ee K1 (trust_ gorus__gvvemmmnttt crust_science
nurse Vage + C4)
Feature:
Age 18-38, income above county median.
Key take-aways for domain experts
Risk trade-off in vaccination choice. The product captures a critical decision-making trade-off. Messaging must narrow this perceived risk gap, e.g., by emphasizing robust evidence vaccine safety [124]
oo_cc eeeeggrreeeaaaaae taaa_thaaaaaaaaaa vax
Booster demand rises steeply with age. The factor e generates a nonlinear effect: as age inereases, perceived vaceine benefit grows rapidly. This reflects age-associated increases in risk perception and vulnerabilities [125].
Prior belief' and healthcare occupation. The presence of vax_ protect_longe and nurse occu- pation in the booster equation means emphasizing extended protection and occupation will push this group further along the vaccination ladder [166]
Trust is pivotal for vaccine uptake. The multiplicative trust government x trust science term ap- pears in every vaccinated utility, signalling that confidence both institutions amplifies willingness
127
Mode
Discovered symbolic utility
Unvaccinated
Kry Krrycovid_theee threatt (risk of_oooovvviioo Leeeooodoeeateerrr._._e__eeeeee saarr_tthaaaa than_vax + inge-gender + CT).
((trust government
trust science)2
C2)
K₂
more attention vax info K3 (income below median have sete__niversity_dee Setillyddeeeeeeeeee (trust_ gonestsgvvemmett trtuttuuuuuuuuutttttt coutt_siencce) + C33 K1 saacine__safetto
Vaccinated (no booster)
+ trust rust_goovemment trust trust_science
V Vage - C1 www.innnccociieeeeeeeeeee a_t_aatnntin_to_va___ooo _o_ooo___________e
C2) + C4 less attention to__vxx____o info + Cs
K₂
Booster
K Kr[have_ coreeeeeeovvdeeeeeeeeeeeeee sick family mmcnbrr-plyysciinnuuttt..gm govermmet
trust (eaet_sceneee((((_
Ci ( (uuneeetrsssscieneee/ae C5))
+ C4
Feature:
Adults with varied trust, income, and education profiles.
Key take-aways for domain experts
Information atfention as lever. Positive weights on more_attention_to, cepttttiontt_vxx________ to__ooo__iineeeeeee inn_info indicate that engagement with vaccine information consistently increases uptake - interactive campaigns remain essential [128].
trust_science)² highlights a super-additive effect - boosting both trust dimensions together disproportionately reduces hesitancy [19
Nonlinear trust amplification. The squared term
40

---

Education buffers income hesitancy. The negative income effect is mitigated by education- trust interactions higher education plus trust can offset low-income hesitancy, pointing education- focused outreach 130
B Baseline Setup
B.1
Utility-Based Models
Table Utility-based models and key settings (train test = 0.8 0.2)
Model
Key (Non-default) Settings
SimpleMNL
intercept="itent ; optimizer="adam,
Conditionall Logit
optimizer="adan! added intercept for items 1 & 2
Latent Class MNL
p..laten__classese fit "ett_mmtho==mme"".
optimizer= "adam"; "adam" epochs=1000
B.2
Machine Learning Models
Table 11: Machine learning models and key settings (train test 0.8 0.2)
Model
Best hyper-parameterss
Logistic Regression
C=10, penalty=12, solver=saga
Random Forest
bootstrap-False, sin_ssamlees_slitee n_estimators=600
max_depth-None, min_ sin_ssamlee__eaae
XGBoost
bymmpeeebytree=0.8 Learming_rate=D..e max_depth=6, nLestimators=500, subsample=0.8
B.3
LLM-Based Models
Take Swissmetro dataset as example.
Prompt B.I: Swissmetro Zeroshot
[SYS] You are a decision assistant that predicts probability distribution over three travel modes, Swissmetro, Train, and Car, for single trip.
You will receive two blocks of text: details like trip purpose, luggage, payment, origin, destination
VTRI_INFOO
</TRIP INFO>
TRANSPORT OPTIONS>... ... list of modes with travel time, cost, headway ... </TRANS-
PORT OPTIONS>
** #Intrructions:**
1. Use only the information in <TRIP <TRIP_INFO> and <PRANSPORT
2. Estimate probability for each mode they sum 1.
**Output only** a JSON object, for example:
"'json "Swissmetro": <float between and 1>, "Train": <float between 0 and 1>, "Car":
<float between and 1> } ".
No additional text; just the JSON object with normalized probabilities.
[USR] <TRIP INFO> _NFO> (trip_info) </TRIP _TRIPPINFO>>>>>
2PTIONN <TRANSPORT OPTIONS> (transport_options) </TRANSPORT OPTIONS>
41

---

Prompt B.2: Swissmetro Zeroshot-CoT
[SYS] You are a decision assistant that predicts probability distribution over three travel modes, Swissmetro, Train, and Car, for single trip.
You will receive two blocks of text: details like trip purpose, luggage, payment, origin, destination
PTRIPINFFO
</RIP INFO>
TRANSPORT OPTIONS>... ... list of modes with travel time, cost, headway </TRANS-
TOR_OOPTION>>>
* #nstructionns: **
1. Use only the information in <TRIP <TRIP_INFO> and <IRAASSPOT.OPTTONS
Estimate probability for each mode so they sum 1.
3. **Output only** a JSON object, for example:
"jsonn "Swissmetro": <float between and 1>, "Train": <float between 0 and 1>, "Car":
<float between 0 and I> } "
No additional text; just the JSON object with normalized probabilities.
Let's think step-by-step.
[USR] <TRIP INFO> (trip_inff j__ </TRIP _NFO>>
CIAASPORT_OPPIONE (rransport_option)) O/TRANSSORTLOFTIONSS
42

---

Prompt B.3: Swissmetro Fewshot
[SYS] You are a decision assistant that predicts probability distribution over three travel Swiss-SSiismmerro, Train, and Car-for set of travel records.
You will receive multiple records. Each record consists of three blocks: <TRIP INFO> trip details: purpose, luggage, payment, origin, destination
</TRIP [IRIP_INFO>>
<TRANSPORT OPTIONS> each mode's travel time, cost, headway ... </TRANS- PORT OPTIONS> <CHOICE>.. either JSON object with probabilities (for examples), left empty for the record to predict... ... </CHOICE>
*Instructionss:* ** For records where <CHOICE> filled, treat them as examples. For the final record (with empty <CHOICE>), output **only** the JSON object of normalized probabilities (summing to 1), with no extra text.
[USR] <TRIP INFO> (trip info 1) </TRIP INFO> <IRANSPORT OPTIONS> (trans-
port_ port_option____ 1)
</TRANSPORT OPTIONS>
<CHOICE> [choice_11 1| </CHOICE>
<TRIP INFO>
(trip info 2 </TRIP INFO>
<TRANSPORT OPTIONS> (trans-
port_ cit_option__2 _
</TRANSPORT <ITRANSPORT_OPTIONS
<CHOICE> [choice_2] 2) </CHOICE>
<TRIP INFO>
(trip info 3) </TRIP INFO>
<TRANSPORT OPTIONS> (trans-
port_ Part_optios__3 33
</TRANSPORT LOPIIOO
<CHOICE> [choice_3) </CHOICE>
STRIP_INFO
(trip_ smp_info___ 4) </TRIP INNF>> DERRANSPORT_OPTIONS
<TRANSPORT OPTIONS> (trans-
port_options__
<CHOICE> [choice_44 _4 </CHOICE>
(trip_info_] </TRIP INFF>>
<TRANSPORT OPTIONS> (trans-
port options_ 5)
</TRANSPORT OPTIONS>
<CHOICE> [choice 5) </CHOICE>
<TRIP INFO>
(trip info </TRIP INFO> <TRANSPORT OPTIONS> (trans-
port options 6)
O <CHOICE> Please predict the travel mode for
this trip. </CHOICE>
Prompt B.4: Swissmetro TextGrad
[INITIAL FULL PROMPT SOLUTION] Task: Estimate the probability distribution over three travel modes (Swissmetro, Train, Car) for single trip.
<TRIP [IP_INFO>
CTTRIPINNFO
<TRANSPORT OPTIONS> | ttransport { </TRANSPORT OPTIONS>
Solution (JSON): ("Swissmetro": 0.333, "Train": 0.333, "Car": 0.334)
[GRADING PROMPT] You are a transport-economic expert. Given the trip info, transport options, and predicted probabilities in the user's 's message, output single line ONLY: Score: <float between 0 and 1> 1 = probabilities look highly reasonable, = implausible. Remember: THE PREDICTION MUST BE A JSON DICT.
43

---

C Additional Experiments: Reasoning LLMs and End-to-End Baselines
Purpose and setup. This section probes how much backbone model capacity matters on our tasks. For a controlled comparison, we randomly sample 100 individuals from the 500- person pool to form a compact evaluation subset (same preprocessing, metrics, and decoding settings as in the main experiments), For each individual, we randomly sample one record. evaluate ATHENA with five backbones: two state-of-the-art open-source reasoning mod- els (Qwen3-32B, DeepSek-RR-Distill--eee (GPT-40-mimi, GPT-4o, Gemini-2. O-Flash). Across both tasks, ATHENA attains state-of-the- classification performance among LLM-based Accuracy and FI, with AUC that competitive or superior to prompt-only LLM baselines (sce Tables 13 and
and three leading commercial offerings
delivering the highest
Structure dominates model size; stronger reasoning yiclds modest, consistent gains. Under ATHENA, swapping (PT-4o-ming for larger "reasoning" backbones (e.g., GPT-4o, Qwen3-32B, DeepSeek-R1) yields incremental but consistent improvements, especially on the more interaction- heavy Vaccine task. The effect is smaller on Swissmetro, where dominant explanatory factors (time/cost) are already well captured by the symbolic discovery - textual refinement pipeline. Intuitively, Stage 1 constrains the hypothesis space to interpretable utility forms, and Stage makes small, directed edits to those forms; this turns the problem into guided search plus local adjustments. As result, structural bias (symbolic utility discovery + semantic adaptation) shoulders most of the lift, while backbone capacity primarily fine-tunes edge cases (nonlinear interactions, atypical profiles), producing steady but not dramatic gain.
Prompt-only methods are brittle and poorly calibrated; ATHENA regularizes both decisions and probabilities. Zero-shot/ CoT / Few-shot prompting shows visible volatility across metrics: Accuracy/Fl can spike on one dataset yet drop on another, and AUC/CE often swing with decoding details (temperature, sampling count, score-to-probabile mapping). ATHENA markedly reduces this variance: the symbolic stage enforces cross-person consistency (shared operators, shared concept library), while the textual refinement stage adjusts within those constraints, leading to better class separability and more conservative probability mass. Empirically this manifests as stronger and more stable FI/AUC, with CE reflecting improved calibration compared to prompt-only baselines. In short, structure acts as regularization for both decisions and confidence.
End-to-end baselines trail on interpretability and robustness; ATHENA 's decomposition cap- tures heterogeneity with explicit utility logic. Machine leasning-based models be competitive on single metrics in isolated settings, but they do not expose explicit, policy-relevan utility functions and are less consistent across tasks/splits. They must implicitly learn both which attributes matter and how they combine, from scratch. ATHENA instead decouples the problem: Stage discovers globally interpretable utility structure (operators, interactions), and Stage 2 adapts those structures to individual semantics. This yields (i) stronger across-task consistency in Cecuracy/FI/AUG (ii)
end-to-end interpretability of the discovered utilities.
44

---

Table 13: Performance comparison across methods on Swissmetro and Vaccine datasets.
Method
LLM Model
Swissmetro
Vaccine
Acc.f
Fl1
CEU
AUC
Acc.1
CE
AUC
Zeroshot
gemini-2.0-ffas
0.5800
0.3046
0.9059
0.6829
0.6000
0,5386
0.8317
0.7433
GPT-4o-mini
0.6100
0.2763
0.9253
0.5556
0,5500
0.5302
0.8271
0.7500
GPT-4o
0.5900
0.3310
0.8646
0.6946
0.6000
0.5465
0.8052
0.7306
Qwen3
0,5900
0.4158
1.4047
0.6126
0.5400
0.5729
0.8676
0.7519
DeepSeek-rl
0.5900
0.4339
1.2473
0.6608
0.6300
0.6531
0.8244
0.7692
Zeroshot-CoT
gemini-2.0- O-flash
0.5300
0.2809
0.9858
0.6409
0.6100
0,5485
0.8128
0.7604
GPT-4o-mini
0.6100
0.2763
0.9109
0.6156
0.5900
0.5820
0.8161
0.7714
GPT-4o
0.5800
0.3162
0.9237
0.6404
0.6300
0.5717
0.7785
0.7700
Qwen3
0.6200
0.4632
1.7101
0.6284
0.5400
0.5843
0.9073
0.7364
DeepSeek-rl
0,5800
0,3018
0.9522
0.6173
0.5200
0,5492
0.8761
0.7373
Few-shot
gemini-2.0-flase
0.7200
0.6922
10.0922
0.7984
0,5300
0,5508
14,2531
0.6747
GPT-4o-mini
0.6800
0.5320
5,0402
0.7516
0.5200
0.5278
7.7066
0.6975
GPT-4o
0.7300
0.6654
3,9386
0.8423
0.5700
0.5967
5.6261
0.7467
Qwen3
0.7400
0.6760
7.0435
0.8033
0.5400
0.5487
9.5013
0.7060
DeepScck-rl
0.7000
0.6282
3.6154
0.8439
0.5500
0,5392
8.8895
0.6855
TextGrad
gemini-2.0-flash
0.5400
0,2432
1.1934
0.4718
0,5000
0,4511
4.1290
0.7345
GPT-4o-mini
0.5700
0.3111
0,9551
0.5292
0.5000
0.4686
4,7960
0.6460
GPT-4o
0,5600
0,3316
0,9441
0.6256
0.5600
0.5321
2.3468
0.6721
Qwen3
0.5100
0.3669
2.0180
0.5322
0.4600
0.4276
6,4994
0.6303
DeepSeek-rl
0.5800
0.3356
0.9631
0.6344
0.4300
0.4235
3. 3.1080
0.5948
ÂTHRNA (ours)
gemini-2.0-faase f.ahfahh
0.7900
0.7185
0.6121
0.9153
0.6500
0.5978
0.8305
0.7998
GPT-4o-mini
0.7600
0.7304
1.4208
0,8577
0.6500
0.6079
803033
0,8133
GPT-4o
0.7700
0.7085
1.0417
0.8697
0.6700
0.6213
0.7765
0.8279
Qwen3
0.7400
0.7040
4,9132
0.7754
0.5700
0.5650
1.1393
0.7637
DeepSeck-rl
0.7100
0.6612
0.8437
0.8353
0.6600
0.6501
0.8115
0.8212
D Empirical Scalability Evidence
We benchmarked wall-clock time and token usage using gpt-4o-mise on the Swissmetro subset.
D.1 Stage Individual adaptation
Table 14: Runtime and token usage for Stage 2 (individual-Ieva) semantic adaptation) under different iteration counts TV.
T
Time (s)
s/iter
tokens/iter
48.16
48.16
1079.6
3
176.89
58.96
1195.83
5
315.66
63.13
1249.28
D.2 Stage Group-level discovery
Table 15: Runtime and token usage for Stage 1 (group-level symbolic utility discovery) under different iteration counts
T
Time (min)
tokens total
5
30.61
215,281
15
36,69
251,974
30
65.64
479,751
These results confirm that runtime and token usage scale approximately linearly with the number of iterations, consistent with the theoretical analysis.
45

---

E
Prompts
Take Swissmetro dataset as example.
Prompt E.1: Swissmetro Symbolic Utility Initialization
Step 1:
[SYS] You are a transportation planner specializing in analyzing the relationships among vari- ous factors that influence travel behavior. You will be provided with two types of information: individual features (delimited by <FEATURES> and </FEATURES>) and preliminary travel mode knowledge (delimited by <KNNWWEDGGS> and </KNOWLEDGE>) Your task is to carefully review these inputs and in detailed sentence describe how the provided features interrelate. Ensure your response includes as many specific details as possible about the relationships, but do not propose any new features suggest modifications to the existing ones. Example: Time: quadratic. Cost: log, luggage: linear.
[USR] <GROUP DESCRIPTION ( (ddescriptioonn/GRRROOO TURES> </FEATURES>> <KNOWLEDGE> (
<FEA- DESCRIPTION
You should ONLY provide the relations between the features. YOU MUST return your assumption in this exact format: "[""reation__"" relation_""....
Step 2:
[SYS] You are helpful assistant that proposes mathematical expressions based on some provided suggestions. Your goal is to:
0. ** Generate utility functions for travel mode choice of group of (description).
1. **Use only the specified variables: (variables)
2. Reppeseent all constants** with the symbol "C", and all coefficients with the symbol "K".
**Restric*** yourself the following operators: operators
4. #*ror each group** suggest utility functions for train, car, and Swissmetro respectively. Your response must: Propose exactly **[N]* groups of expressions. MUST return in this exact format: ""[("e "(""expressions. _arr", "expressions s_tas__rrrn"___ "rainn,""xpressionn"" "expressions_ "iteessiossmmtto""" "), ...]",, replace expressions mode with your proposed expressions.
[USR] Suggestions:
(suggestions)
Prompt E.2: Swissmetro Results Analysis
[SYS] You are a creative and insightful mathematical research assistant. You have been provided with two sets of utility expressions: function group labeled "Good Expressions" and one labeled "Bad Expressions." Your objective is to hypothesize about the underlying assumptions principles that might generate the good expressions yet exclude the bad ones. Key Points:
1. Focus primarily the good expressions' mathematical structures and any connections they might have to physical or applied contexts.
2. Capital "C" in any expression is just arbitrary constant.
3. Do not discuss or compare the expressions terms of their simplicity or complexity.
4. Provide your reasoning step by step, but keep very concise and genuinely insightful. No more than 5 lines.
[USR] Good Expression 1: (train: [texprl). car: [cexpri), metro: [mexprl]) )), accuracy: [
Good Expression (train: (texpr2), car: (cexpr2), metro: (mexpr2)), accuracy: (acc2)
Bad Expression 1: (train: (bexprl), ), car: [bexpr2), metro: (bexpr3)). accuracy: (acc3)
Above expressions are travel mode choice utility functions of group (deseription). Propose
[N} hypotheses that would be appropriate given the expressions. Provide short commentary for each of your decisions. Do not talk about topics related to the simplicity or complexity the expressions. I want ideas that are unique and interesting enough to amaze the world's best mathematicians.
46

---

Prompt E.3: Swissmetro Crossover
[SYS] You are a helpful assistant that recombines two mathematical expressions based on some provided suggestions. Your goal is produce new expressions that:
1. Blend or merge elements from both reference expressions in a way that reflects the suggestions.
2.
Adhere to the following constraints:
You may only use the variables in library: [variables)
All constants must be represented with the symbol C
Only the following operators are allowed: {operators) Guidelines:
Propose exactly (N) new expressions.
Each new expression should integrate clements of both reference expressions. You also propose new terms with variables that are in the library but not in the old expressions. If any suggestions appear contradictory, reconcile them reasonably. MUST return in this exact format:
[(" ("expressions _arn" "expresss cxpresssions.. train", cespresssionsmmerro". ...] Replace expressions_ with your proposed expressions. [USR] Suggestion: (suggestions)
Reference Expression group I: (train: [texpr]), ), car: [cexprl), ), metro: [mexprl] })
Reference Expression group 2: (train: (texpr2), car: [cexpr2), metro: (mexpr2))
Propose (N) expressions that would be appropriate given the suggestions and refer- ences.
Prompt E.4: Swissmetro Mutation
[SYS] You a helpful assistant that generates mutated variants of **tippet*** of math- ematical expressions (car, train, metro) based on provided mutation strategies, Your goal is produce new expression triplets that: 1. Mutate the reference expressions by applying mutation operations (e.g., adjust coefficients, swap variables, alter operators) in a way that reflects the suggestions. 2. Adhere the following constraints: You may only use the variables in library: [variables] All constants must be represented with the symbol C Only the following operators are allowed: [operators]
Guidelines: Produce exactly (M) mutated **triplets** Within each triplet you must provide one mutated expression for **car** one for **train ** and one for m* mutation can modify any combination of variable, operator or constant, but each expression must remain syntactically valid under the constraints. MUST return in this exact format: [("mut_cari)
mmu__train"" "mut_metutt pout__metro"),
[USR] Generate (M) mutated variants of the following mathematical expression triplet according to these mutation strategies: You may only use variables from: (variables) - All constants must be written C- Only these operators are allowed: [operators) Mutation strategies: [suggestions)
Reference expressions: (car): (cexpr) (train): (texpr) (metro): (mexpr)
Please return exactly (M) new, syntactically valid triplets in the JSON list format shown above.
47

---

Prompt E.5: Swissmetro Semantic Adaptation Initialization
[SYS] You are travel-behavior preference selector. You will be given two blocks of information:
<DEMOGRPPICS>> <DDEOGRRPPHCCS> SUTILITY_FUNCTIO
</UTIL-
ITY FFUNCTION>>
Your goal: choose the single best-matching high-level preference template for this group # *exactly*** ** from the catalogue below and output **only** the template name (upperease).
CATALOGUE TIME EFFICIENYC travellers primarily minimise total travel time.
-COOT_SSVINN SAVING travellers primarily minimise direct monetary cost.
-OST
COMFORT SEEKING travellers value comfort/service frequency and dislike crowding. -BALANCED sensitivities are evenly distributed across factors.
...//OTHER POSSIBLE TEMPLATE
Return nothing else no commentary, no punctuation, just the template name.
[USR] <DEMOGRAPHICSS (ddeooocShseemm BeteemgggrraiiiiDDEDAAAAAAAAA //DEMOGRAPHICS <UTILITY (uNCTIINNsuulltty FUNCTTTNIO FUNCTION>
Prompt E.6: Swissmetro Semantic Adaptation Loss Function
Evaluate the travel mode prediction based the individual's profile and alternatives. Compare it to the actual choice and identify any discrepancies. Be concise and focus on why the prediction might be incorrect. Return 0 they match, otherwise.
Prompt E.7:
Swissmetro Prediction
[SYS] You are decision assistant that recommends the most suitable travel mode for an individual trip by estimating a probability distribution over three options: Swissmetro, Train,
and Car.
You will receive three blocks: <TEMPLATE> optimized preference template </TMM-
PLATE>
<PROFILES individual profile </PROFILE>
<ALTERNATIVES> ... attributes of Swissmetro, Train, and Car </ALTERNATIVES>
** *Instructionss 1. **U the <TEMPLATE> as a guide** for understanding the individual's
likely preference bias (e.g.. time efficiency, cost saving, comfort secking, balanced).
2. ** Analyze the <PROFILE>** (age, gender, income, trip details) #* **and the <ALTERNA-
TIVES> ** (travel time, cost, headway).
3. EEstimate and output probability** for each travel mode, such that all three probabilities sum to 1.
**Uupptt format (JSON only):* "'json { "Swissmetro". <float between 0 and 1>, "Train": <float between O and 1>, "Car": <float between O and 1> ... No additional text; just the
JSON object with normalized probabilities.
[USR] <TEMPLATE> template name //TMM/LATEE <PROFILE> (individual block] <PROFILE> <ALTERNATIVES>> [options] </ALTERNATIVES>
48


Reviews:
[{"review_id": "ZApfK0mo1S", "reviewer": "Reviewer_F7TL", "summary": "This paper proposes ATHENA (Adaptive Textual-symbolic Human-centric Reasoning), a framework for personalized decision modeling that combines symbolic utility discovery and LLM-powered semantic adaptation. The approach first uses LLM-augmented symbolic regression to derive interpretable group-level utility functions for predefined demographic groups, then refines these models at the individual level via TextGrad to capture personal preferences and constraints. Evaluations on transportation mode choice and COVID-19 vaccine uptake tasks show that ATHENA outperforms classical utility-based models, machine learning classifiers, and LLM baselines by at least 6.5% in F1 score. The method is notable for producing interpretable, human-centric models, but its reliance on manually specified demographic groupings limits its flexibility and raises questions about the robustness of these partitions across diverse domains.", "questions": "- Are $T$ and $T’$ two hyper-parameters? What are the chosen hyper-parameters for the experiments? For Figure 3, is the iteration (x-axis) showing $T$ or $T’$?\n\n## Suggestions\n\n- The “Stage 1” and “Stage 2” annotations in Algorithm 1 currently look like part of the code; consider changing their style (e.g., italics or actual comment syntax) so they visually appear as comments and are easier to distinguish.\n- Style-wise, the `enumerate` on line 133 could have **shorter left padding** to improve visual alignment and readability.\n- The inline citations on lines 235–238 are attached directly to the previous word; there should be **one space separating the citations** from the preceding text for proper formatting.\n- Include at least **one qualitative example in the main text** showcasing a discovered group-level symbolic utility formula, along with **proper takeaways or insights**. This is crucial to demonstrate the value of having an explainable model for informing domain experts (e.g., public health decision-makers).\n- Provide more context on why **Cross Entropy (CE)** is included as a metric for evaluating ATHENA. Given its meaning in probabilistic models, explain its relevance to your setting and why it complements metrics like F1 and AUC.", "limitations": "- Computational Complexity: Textual gradient optimization is resource-intensive, limiting scalability to large populations.\n- Predefined Group Assignment: Requires a priori demographic groups, which may oversimplify heterogeneity and miss latent patterns.\n- Group Significance: Lacks a principled method to verify whether demographic partitions are behaviorally meaningful, risking weak or biased utility functions.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n- **The paper is very well written** and easy to follow, with clear motivation, technical details, and experimental narrative.\n- **Visualizations are excellent**, effectively illustrating the two-stage ATHENA pipeline and the learned symbolic components.\n- The proposed framework combines symbolic utility modeling with LLM-driven semantic adaptation in a **conceptually elegant and technically sound way**.\n- **Premise is strong**: addressing the gap between population-level utility models and personalized decision-making is both timely and impactful.\n- **Performance is very good**, achieving ≥6.5% F1 score improvement over classical discrete choice models, machine learning baselines, and LLM-only approaches on real-world datasets.\n- The two-stage design (group-level symbolic utility discovery and individual-level semantic adaptation) is **well-motivated and validated** through ablation studies, demonstrating clear complementarity.\n- Produces **interpretable, human-centric decision models** with potential relevance for high-stakes applications such as public health policy and transportation planning.\n\n## Weaknesses\n\n- The framework relies on predefined demographic groups for the group-level symbolic utility discovery stage, which assumes these partitions are optimal and behaviorally meaningful. This is akin to providing the top-level splits in a decision tree without verifying their significance, limiting flexibility and potentially propagating bias.\n    - Is the baselines also provided the same grouping during the experiments?\n- There is no mechanism to automatically discover or validate significant groupings, which raises concerns about robustness in domains with high intra-group heterogeneity.\n- While the integration of symbolic regression and LLMs is novel, the individual components (symbolic regression, TextGrad) are adaptations of existing methods rather than fundamentally new techniques.\n- The paper could benefit from more qualitative analysis and takeaways from the synthesized group-level utility formulas. Since one of the main advantages of having an interpretable model is to derive actionable insights for domain experts (e.g., public health professionals), this feels like a missed opportunity to showcase the framework’s real-world utility beyond predictive performance.\n- (Minor) The paper has not discussed scalability of the method. When $T$ and $T'$ are treated as fixed hyper-parameters, and disregarding LLM inference time, is the methodology a constant time algorithm? Either a high level discussion or an empirical evaluation (including LLM invocation time) would be appreciated.\n\nI am happy to increase scores when the questions are well-addressed.", "was_revised": true, "final_justification": "This paper proposes ATHENA (Adaptive Textual-symbolic Human-centric Reasoning), a framework for personalized decision modeling that combines symbolic utility discovery and LLM-powered semantic adaptation. During review, I raised questions about the reliance on demographic groups and the derived symbolic representations. Through rebuttal, the authors have justified that such setting is reasonable, and provided qualitative analysis on symbolic representations. I'm happy that my concerns are resolved and that such changes are going to be made in the final version of the paper. I'm raising my rating of the paper (4 -> 5).", "rebuttal": "We thank you for your time and effort in reviewing our paper! We find your suggestions very helpful and we hereby address your questions:\n\n> **W1/W2 & L2/L3 – Predefined Demographic Grouping & Robustness**\n\nTo clarify, all baseline models received the same demographic features and groups. Our choice to use these groups (common demo-based group) was a deliberate decision motivated by:\n\n- **Theoretical Grounding**: It aligns with established practices in decision choice modeling researches that use demographics to explain behavioral heterogeneity [1-3].\n\n- **Interpretability**: It yields human-readable symbolic rules that translate directly into levers. E.g., for women aged 39-54 earning 50–100 k CHF, the rules reveal that shorter travel-time, premium comfort, and baggage assistance most sway their choice -- actionable insight that guides operators toward faster services, targeted upsells, and better luggage support for this segment.\n\n- **Robustness**: Automatically discovering behaviorally consistent latent clusters is a challenging task that typically requires large datasets. Given the scale of our experimental data, relying on established demographic priors provides a more robust initial partition. It mitigates the risk of overfitting and learning spurious patterns. Also, we don't want to increase complexity or introduce additional hyperparameters to make the model more difficult to use.\n\nCrucially, our ablation study shows that removing the group-level symbolic discovery stage causes a severe performance drop. This result underscores that a well-structured, group-informed prior is not a limitation but a necessary component for the model's success, preventing the unguided adaptation from converging to poor local optima.\n\nWhile we agree automated group discovery is a valuable direction for future research, our work demonstrates the marked effectiveness of this principled, two-stage approach.\n\n[1] Tymula, Agnieszka, et al. \"Adolescents’ risk-taking behavior is driven by tolerance to ambiguity.\" Proceedings of the National Academy of Sciences 109.42 (2012): 17135-17140.\n\n[2] De Bruijn, Ernst-Jan, and Gerrit Antonides. \"Poverty and economic decision making: a review of scarcity theory.\" Theory and Decision 92, no. 1 (2022): 5-37.\n\n[3] Croson, Rachel, and Uri Gneezy. \"Gender differences in preferences.\" Journal of Economic literature 47, no. 2 (2009): 448-474.\n\n> **W3: Component novelty**\n\nThe contribution should be evaluated on the end-to-end paradigm and its conceptual novelty, not on isolated components. As noted in Section 1, population-level models often overlook each person’s unique cognitive calculus -- the belief, the unique constraints and the context-specific trade-offs that drive real decisions. ATHENA captures this calculus through a novel two-stage pipeline: symbolic regression extracts compact, group-level utility laws, and TextGrad then personalizes them to each individual.\n- Symbolic regression for insight: Generates interpretable, domain-aware formulas that reveal feature relations far beyond merely black-box predictors.\n- Informed semantic optimization: Uses those formulas as data-driven priors, mitigating TextGrad’s sensitivity to initialization and yielding faster, more reliable convergence to personalized models.\n\n> **W4: Qualitative Analysis of symbolic representations**\n\nWe agree that deeper qualitative analysis and actionable takeaways from our group-level utility formulas would strengthen the manuscript. Below, we provide a detailed qualitative analysis of the example Swissmetro symbolic utilities. For a parallel example on the Vaccine dataset, see the “Q2: Explainability of ATHENA utilities” section in [Reviewer HnWo’s rebuttal](https://openreview.net/forum?id=RDt0crdC7N&noteId=STQUOcL5iO). These examples demonstrate that our group-level utilities are both interpretable and directly actionable for domain experts.\n\n- **Representative Example — Swissmetro Dataset**\n\n| Mode  | Discovered symbolic utility|\n|---|---|\n| **Train** | `K·(train_time + metro_time + luggage·log(age + 1) + age + is_male)  + C·(first_class + income)  − C·(GA_pass + headway)` |\n| **Car**   | `K·(car_time + train_time + luggage·log(age + 1) + age)             + C·(first_class + income)  − C·(GA_pass + metro_fare + is_male)` |\n| **Metro** | `K·(metro_time + luggage + age + is_male)                         + C·(first_class + income)  − C·(headway + GA_pass + is_male)` |\n\nFeature: Between 39 and 54 years old, identify as female, and have an income between 50 and 100.\n\n- **Key take-aways for domain experts**\n\n| Insight | Interpretation & policy relevance |\n|---|---|\n| **Time dominates** | Large negative coefficients on travel-time variables show this segment is **highly time-sensitive** → investments that shorten door-to-door time (e.g., skip-stop service) should shift demand [1]. |\n| **Comfort premium** | Positive weight on `(first_class + income)` across all modes indicates a willingness to pay for comfort that scales with income → targeted upselling (seat reservations, quiet cars) is effective [2]. |\n| **Luggage burden grows with age** | The interaction `luggage·log(age + 1)` reveals baggage becomes disproportionately painful for older travelers → facilities such as luggage trolleys or porter services may raise train/metro share [3]. |\n| **GA pass effect** | Owning a GA pass (the Swiss national annual travel pass) biases travellers away from modes that still incur extra fares (e.g. Car, premium metro segments). Extending GA coverage to Swissmetro would therefore raise its relative appeal [4].|\n\nThese insights translate raw coefficients into specific levers for service design and policy -- exactly the actionable value the reviewer is seeking. Taken together, these conclusions are highly valuable for practitioners and align closely with the extensive body of prior research on travel behavior and mode choice.\n\n[1] Shires, Jeremy D., and Gerard C. De Jong. \"An international meta-analysis of values of travel time savings.\" Evaluation and program planning 32, no. 4 (2009): 315-325.\n\n[2] Abrantes, Pedro AL, and Mark R. Wardman. \"Meta-analysis of UK values of travel time: An update.\" Transportation Research Part A: Policy and Practice 45, no. 1 (2011): 1-17.\n\n[3] Chang, Yu-Chun. \"Factors affecting airport access mode choice for elderly air passengers.\" Transportation research part E: logistics and transportation review 57 (2013): 105-112.\n\n[4] Weis, Claude, Kay W. Axhausen, Robert Schlich, and René Zbinden. \"Models of mode choice and mobility tool ownership beyond 2008 fuel prices.\" Transportation Research Record 2157, no. 1 (2010): 86-94.\n\n> **Q1: Hyper-parameter clarification**\n\nYes. In ATHENA both $T$ and $T’$ are user-set hyper-parameters:\n- $T$ – maximum iterations of Stage 1: Group-level Symbolic Utility Discovery.\n- $T’$ – maximum iterations of Stage 2: Individual-level Semantic Adaptation.\n\nFigure 3 tracks the symbolic-discovery loop, so its x-axis is $T$ (30 iterations in our runs).\n\n| Symbol | Role in ATHENA | Value used |\n| :---:  | --- | :--- |\n| LLMs | Backbone models (both stages) | `gpt-4o-mini`, `gemini-2.0-flash` |\n| $T$ | Iterations in Stage 1 (Fig. 3) | **30** |\n| $T'$ | Iterations in Stage 2 | **5** |\n| $K$ | Candidate utilities per Stage 1 iteration | **10** |\n\n> **W5 & L1: Scalability and parameter $T$ and $T'$**\n\n#### 1. Theoretical analysis\n\nWith $T$, $T'$ fixed, the algorithm is linear, not constant:\n\n$$\nt_{\\text{total}}\n= t_{\\text{Stage1}} + t_{\\text{Stage2}}\n\\sim\n\\underbrace{\\lvert\\mathcal{G}\\rvert\\cdot K\\cdot T}\\_{\\text{symbolic utility search}}\n+\n\\underbrace{N\\cdot T'}\\_{\\text{textual gradient refinement}}\n$$\n\nEach term is multiplied by the average LLM latency $\\tau$ (roughly linear in token count):\n\n$$\n\\mathcal{O}\\bigl((\\lvert\\mathcal{G}\\rvert K T + N T')\\,\\tau_{\\text{tok}}\\bigr)\\;.\n$$\n\nBoth stages can be parallelized:\n* **Stage 1:** symbolic searches for each demographic group run independently.  \n* **Stage 2:** TextGrad refinements for each individual can be batched or dispatched to separate workers.\n\n#### 2. Empirical evidence\nUsing **gpt-4o-mini**, we measured wall-clock time and token usage on the Swissmetro subset:\n\nStage 2 – Individual adaptation\n\n| $T'$ (iterations) | Stage-2 time (s) | s / iter | tokens / iter |\n|:---:|:---:|:---:|:---:|\n|1|48.16|48.16 | 1079.6 |\n|3|176.89|58.96| 1195.83 |\n|5|315.66|63.13| 1249.28 |\n\nStage 1 – Group-level discovery\n\n|$T$ (iterations)|Stage-1 time (min)|tokens total|\n|:---:|:---:|:---:|\n|5|30.61|215281.3|\n|15|36.69|251974.1|\n|30|65.64|479751.3|\n\nHere we can see runtime and tokens grow linearly with iterations: Stage 2: 48 s → 316 s (T′ 1 → 5); Stage 1: 31 min → 66 min (T 5 → 30)—so a full Swissmetro run (T = 30, T′ = 5) finishes in < 70 min and ≈ 0.5 M tokens on one worker, with near-perfect parallel speed-up.\n\n> **S1\\S2\\S3\\S4: Paper Writing**\n\nThank you for the helpful suggestions. We have revised all relevant instances in the manuscript. The updates are summarized below.\n\n|Position|Original | Revised|\n| :--- | :---| :---|\n|Algorithm 1, Near L198|**Stage 1:** …|*// Stage 1 – Group-Level Symbolic Discovery*|\n|Algorithm 1, Near L208|**Stage 2:** …|*// Stage 2 – Individual-Level Semantic Adaptation*|\n|Page 3, L133, L137| ` 1. …  2. ...`   | `1. … 2. ...` (reduced left padding)|\n|Page 7, L235–238| eg. \"…model [98,99] and…\", \"...few-shot method[100,101]\"...| \"…model [98, 99] and …\" (added spacing before citations), \"...few-shot method [100, 101]\"... |\n\n> **S5: Cross Entropy metric**\n\nCross-Entropy is important because the ATHENA models decision-making as a probabilistic choice, consistent with the Random Utility Maximization theory. A lower CE value shows the model assigns higher probabilities to the choices individuals actually make.\n\nWhile F1/AUC measures classification performance, CE provides a distinct and complementary evaluation of the model's confidence calibration. With all those metrics, we can better understand the model's performance and robustness."}, {"review_id": "YYTKf8bC8j", "reviewer": "Reviewer_HnWo", "summary": "This paper studies the problem of modeling human behaviour in complex domains where peoples idiosyncratic preferences may cause them to deviate from the global optima. As a solution to this problem the authors propose a two stage approach where first a global utility function is learned and then this function is tuned to each individuals unique characteristics. Both of these stages are implemented with the help of an LLM. They validate this approach on real world data showing this approach is performative and that both stages are important for success.", "questions": "In the experiment which tests the power of Individual-Level Semantic Adaptation alone, is it given a completely random starting point or the highest performing starting point out of a number of samples comparable to the amount that stage 1 generates? It seems unfair to attribute performance to step 1 that could be attributed to simply taking the best of N samples.\n\nOne of the primary goals of utility models, typically, is not to predict behaviour but to understand it. I see that in your fragment analysis some pieces of the predictive model are commonly reused but are any of the full models outputted by this procedure interpretable? Are the global functions interpretable?\n\nHave you tried any more powerful models? In particular I would be interested in whether reasoning models show improved performance.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 4, "strengths_and_weaknesses": "Strengths\n\n- This is a very interesting and original idea\n- The methodology seems sound \n- The paper is well written and easy to follow\n- The authors make a strong effort to ablate and interpret their results\n\nWeaknesses\n\n- The baselines compared against seem a little weak. Is there a reason why one couldnt train and end to end neural network?\n- It would have been nice to see an ablation on the LLM component of the model. How much is the model benefiting from an LLM versus some other sampling procedure in the evolutionary algorithm and is it worth the additional computation cost", "was_revised": true, "final_justification": "The authors rebuttal cleared up all of my concerns for the paper including comparing against stronger benchmarks and Ive therefore decided to bump my score to an accept.", "rebuttal": "We thank you for your time and effort in reviewing our paper! We find your suggestions very helpful and we address all your questions/comments as follows:\n\n> **W1/Q3: End-to-End Baseline Comparison & More Powerful Base Models**\n\nThank you for the suggestions of adding end-to-end baselines and more powerful base models. We've been paying close attention to new cutting-edge models and have supplemented our experiments accordingly.\n\n- End-to-end models: BERT, TabNet, 3-layer-MLP.\n- Additional LLMs: Qwen3-32b, DeepSeek-R1-Distill-Qwen-32B, GPT-4o.\n\nPlease see the updated results in the table published in rebuttal section of [Reviewer FBCn](https://openreview.net/forum?id=RDt0crdC7N&noteId=PIht69t6z8)\n\n> **Q2: Explainability of ATHENA utilities**\n\nWe agree that interpretability is crucial and confirm that ATHENA yields fully interpretable, end-to-end utility functions. Below is two representative segments from the Swissmetro and Vaccine dataset.\n\n- **Representative Example — Swissmetro Dataset**\n\n| Mode  | Discovered symbolic utility|\n|-------|------------------------------------------|\n| **Train** | `K·(train_time + metro_time + luggage·log(age + 1) + age + is_male)  + C·(first_class + income)  − C·(GA_pass + headway)` |\n| **Car**   | `K·(car_time + train_time + luggage·log(age + 1) + age)             + C·(first_class + income)  − C·(GA_pass + metro_fare + is_male)` |\n| **Metro** | `K·(metro_time + luggage + age + is_male)                         + C·(first_class + income)  − C·(headway + GA_pass + is_male)` |\n\nFeature: Between 39 and 54 years old, identify as female, and have an income between 50 and 100.\n\n- **Key take-aways for domain experts**\n\n| Insight | Interpretation & policy relevance |\n|---------|-----------------------------------|\n| **Time dominates** | Large negative coefficients on travel-time variables show this segment is **highly time-sensitive** → investments that shorten door-to-door time (e.g., skip-stop service) should shift demand [1]. |\n| **Comfort premium** | Positive weight on `(first_class + income)` across all modes indicates a willingness to pay for comfort that scales with income → targeted upselling (seat reservations, quiet cars) is effective [2]. |\n| **Luggage burden grows with age** | The interaction `luggage·log(age + 1)` reveals baggage becomes disproportionately painful for older travelers → facilities such as luggage trolleys or porter services may raise train/metro share [3]. |\n| **GA pass effect** | Owning a GA pass (the Swiss national annual travel pass) biases travellers away from modes that still incur extra fares (e.g. Car, premium metro segments). Extending GA coverage to Swissmetro would therefore raise its relative appeal [4].|\n\nThese insights translate raw coefficients into specific levers for service design and policy -- exactly the actionable value the reviewer is seeking. Taken together, these conclusions are highly valuable for practitioners and align closely with the extensive body of prior research on travel behavior and mode choice.\n\n[1] Shires, Jeremy D., and Gerard C. De Jong. \"An international meta-analysis of values of travel time savings.\" Evaluation and program planning 32, no. 4 (2009): 315-325.\n\n[2] Abrantes, Pedro AL, and Mark R. Wardman. \"Meta-analysis of UK values of travel time: An update.\" Transportation Research Part A: Policy and Practice 45, no. 1 (2011): 1-17.\n\n[3] Chang, Yu-Chun. \"Factors affecting airport access mode choice for elderly air passengers.\" Transportation research part E: logistics and transportation review 57 (2013): 105-112.\n\n[4] Weis, Claude, Kay W. Axhausen, Robert Schlich, and René Zbinden. \"Models of mode choice and mobility tool ownership beyond 2008 fuel prices.\" Transportation Research Record 2157, no. 1 (2010): 86-94.\n\n- **Representative Example — Vaccine Dataset**\n\n| Mode  | Discovered symbolic utility|\n|-------|------------------------------------------|\n| **Unvaccinated** | `C·covid_threat·(1 + trust_government·trust_science·log(age + 5))·risk_of_covid_greater_than_vax  +  K·have_covid_sick_family_member·log(age + 4)` |\n| **Vaccinated (no booster)**   | `C·covid_threat + C·vaccine_safe_to_me  +  K·(trust_government·trust_science·more_attention_to_vax_info·√(age + 4))` |\n| **Booster** | `C·e^{age^1.5}·covid_threat·√(vax_protect_long_yes)  +  C·vaccine_safe_to_me  +  K·(trust_government·trust_science·nurse·√(age + 7))` |\n\nFeature: Age 18–38, income above county median.\n\n- **Key take-aways for domain experts**\n\n| Insight | Interpretation & policy relevance |\n|---------|-----------------------------------|\n| **Risk trade-off in vaccination choice** | The product `covid_threat × risk_of_covid_greater_than_vax` captures a critical decision-making trade-off: individuals weigh the perceived risk of infection against their belief about vaccine safety. Effective messaging must work to narrow this perceived risk gap, for instance by emphasizing robust evidence on vaccine safety and the serious consequences of infection [5]. |\n| **Booster demand rises steeply with age** | The factor $e^{age^{1.5}}$ generates a nonlinear age effect: as age increases, the perceived benefit of taking the vaccine grows rapidly. This pattern likely reflects age-associated increases in risk perception and underlying health vulnerabilities [6]. |\n| **Prior belief and healthcare occupation** | The presence of `vax_protect_long_yes` and nurse occupation in the booster equation means emphasizing extended protection and occupation will push this group further along the vaccination ladder [7]. |\n| **Trust is pivotal for vaccine uptake** | The multiplicative `trust_government × trust_science` term appears in every vaccinated utility, signalling that confidence in both institutions—not just one—amplifies willingness [8].|\n\nThese findings convert raw symbolic coefficients into tailored interventions: age-targeted messaging, trust-building coalitions, and occupation-based booster incentives.\n\n[5] Green, Manfred S. \"Rational and irrational vaccine hesitancy.\" Israel Journal of Health Policy Research 12, no. 1 (2023): 11.\n\n[6] Noh, Yunha, Ju Hwan Kim, Dongwon Yoon, Young June Choe, Seung-Ah Choe, Jaehun Jung, Sang-Won Lee, and Ju-Young Shin. \"Predictors of COVID-19 booster vaccine hesitancy among fully vaccinated adults in Korea: a nationwide cross-sectional survey.\" Epidemiology and Health 44 (2022): e2022061.\n\n[7] Biswas, Nirbachita, Toheeb Mustapha, Jagdish Khubchandani, and James H. Price. \"The nature and extent of COVID-19 vaccination hesitancy in healthcare workers.\" Journal of community health 46, no. 6 (2021): 1244-1251.\n\n[8] Trent, Mallory, et al. \"Trust in government, intention to vaccinate and COVID-19 vaccine hesitancy: A comparative survey of five large cities in the United States, United Kingdom, and Australia.\" Vaccine 40.17 (2022): 2498-2505.\n\n\n> **W2: Ablation on the LLM component**\n\nThank you for the suggestion regarding an ablation of the LLM component. We appreciate the opportunity to clarify the role and necessity of the LLM in our framework. 1) Our LLM-based utility search relies on two distinct libraries: a Symbolic Library, which contains standard algebraic operators, and a Concept Library, which includes semantically rich, high-level terms derived from domain-specific text. The Concept Library is only accessible through the LLM. 2) Ablating the LLM would not simply remove a component of the model; it would eliminate access to the Concept Library entirely. This makes a clean ablation infeasible: any such comparison would conflate the removal of the LLM with the removal of high-level semantic concepts, thereby blurring the effect under study. 3) Traditional symbolic regression methods (e.g., GP, SRBench) rely solely on the Symbolic Library and therefore cannot propose or reason over high-level, text-derived concepts. As a result, their outputs often lack the semantic richness and real-world relevance that LLM-enhanced models provide. This is not an apples-to-apples comparison, and such a comparison would overlook the core novelty of our approach.\n\nIn short, the LLM is not just a computational enhancement; it is essential to the inclusion of semantically meaningful, multimodal domain knowledge in the search process. We hope this clarifies the role of the LLM and why a traditional ablation would not offer a fair ablation. That said, we are open to alternative suggestions for more targeted comparisons, should the reviewer have specific ideas in mind.\n\n> **Q1: Initialization in the *Stage-2-only* Ablation**\n\n**Paper setting.**\nFor the “Individual-Level Semantic Adaptation only” ablation we seeded TextGrad with **one** symbolic template drawn **uniformly at random**. No *best-of-N* filtering was applied.\n\n- **New control experiment: *best / median / worst* of all formulas after 30 iterations**\n\nWe sampled 10 individuals from Swissmetro datasets. We selected the best, median, and worst symbolic utility formula after 30 iterations of Stage 1. We then ran TextGrad on these formulas as initial seeds.\n\n| LLM                | Init‑seed | Swissmetro Acc. (mean ± std) | Swissmetro F1 (mean ± std) |\n|--------------------|-----------|---------------------------|--------------------------|\n| **GPT‑4o‑mini**    | best   | 0.8611 ± 0.1273 | 0.4127 ± 0.1803 |\n|                    | median | 0.8333 ± 0.2887 | 0.4074 ± 0.2313 |\n|                    | worst  | 0.6250 ± 0.2320 | 0.3558 ± 0.2319 |\n\n**Key Observation** After TextGrad refinement, median-quality seeds converge to within ≈ 3 pp Acc and ≈ 0.6 pp F1 of the best seed, while even the worst seed retains ≈ 73 % of the best accuracy. Hence Stage 2’s boost comes from gradient adaptation, not from simply picking the “best of N” start."}, {"review_id": "4Ip5iacRBA", "reviewer": "Reviewer_FBCn", "summary": "The authors introduce ATHENA that proposes to integrate group-level symbolic regression of utility functions with individual level, LLM-powered semantic modeling to offer a more comprehensive and personalized view of decision making behavior. The key innovation with this approach is the integration of symbolic utility modeling with LLM-powered semantic reasoning to create more accurate and interpretable personalized decision models. ATHENA is evaluated in two decision making tasks--travel mode and vaccine uptake--, and results show that it outperformed traditional utility-based models, machine learning approaches, and other LLM based models.", "questions": "What was the reason testing with GPT-4o-mini and Gemini-2.0-flash? Was there a hard computational constraint on using large models? What other models were considered for testing?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The presented idea would inspire other researchers in the field. While the two components, symbolic utility modeling and LLM-based semantic adaptation, both exist separately, their integration for personalized decision making is novel. This focus on individual-level adaptation aligns with every-increasing interest in personalized AI systems that can account for individual differences. \n\nBut the testing of ATHENA appears limited in scope because they only used two lightweight models: GPT-4o-mini and Gemini-2.0-flash. While these models are practical choices, the experiment section would be stronger if authors explained the rationale behind choosing these specific models. For example, GPT-4o-mini is considered to be strong at reasoning tasks, so it would be valuable to compare it against models known for different strengths. Testing with only two models provides limited view of how ATHENA's performance varies across different types of LLMs. Testing with at least one large model would help understand how model size affect performance, and whether the additional computational costs of larger models are justified by improved results.", "was_revised": true, "final_justification": "I thank the authors on clarifying their model choices. I adjusted my rating from 4 to 5.", "rebuttal": "We thank you for your time and effort in reviewing our paper! We appreciated for noting that “integrating symbolic utility modeling with LLM-powered semantic adaptation for personalized decision-making is novel and will inspire future work.” Your recognition of ATHENA’s ability to deliver accurate, interpretable, individual-level utility models is highly encouraging.\n\nWe are also gratified that the other reviewers independently highlighted the same strengths. Reviewer F7TL praised the “clear motivation, technically sound two-stage design” as well as our visualizations and writing clarity. Reviewer HnWo called the approach “very interesting and original,” commending the sound methodology and thorough ablations. Reviewer zWuZ valued the detailed formalism, the importance of combining LLMs with symbolic methods, and the originality of our neural-symbolic framework.\n\nTogether, the reviewers’ comments affirm that ATHENA makes a timely and impactful contribution to human-centric, interpretable personalized decision modeling.\n\nRegarding your concerns, we added below experiments:\n\n- End-to-end models: BERT, TabNet, MLP.\n- Additional LLMs: Qwen3-32b, DeepSeek-R1-Distill-Qwen-32B, GPT-4o.\n\nResults: Please see the table below. All new runs use a randomly selected subset (size of 100 individuals) from the dataset described in §4.1.\n\n| Category            | Method / Setting       | LLM Model          | Swiss Acc | Swiss F1 | Swiss CE  | Swiss AUC | Vaccine Acc | Vaccine F1 | Vaccine CE  | Vaccine AUC |\n|---------------------|------------------------|--------------------|-----------|----------|-----------|-----------|-------------|------------|-------------|-------------|\n| **LLM-Based**       | Zeroshot               | gemini-2.0-flash   | 0.5800    | 0.3046   | 0.9059    | 0.6829    | 0.6000      | 0.5386     | 0.8317      | 0.7433      |\n|                     |                        | GPT-4o-mini        | 0.6100    | 0.2763   | 0.9253    | 0.5556    | 0.5500      | 0.5302     | 0.8271      | 0.7500      |\n|                     |                        | GPT-4o             | 0.5900    | 0.3310   | 0.8646    | 0.6946    | 0.6000      | 0.5465     | 0.8052      | 0.7306      |\n|                     |                        | Qwen3              | 0.5900    | 0.4158   | 1.4047    | 0.6126    | 0.5400      | 0.5729     | 0.8676      | 0.7519      |\n|                     |                        | DeepSeek-r1        | 0.5900    | 0.4339   | 0.6608    | 1.2473    | 0.6300      | 0.6531     | 0.8244      | 0.7692      |\n|                     | Zeroshot-CoT           | gemini-2.0-flash   | 0.5300    | 0.2809   | 0.9858    | 0.6409    | 0.6100      | 0.5485     | 0.8128      | 0.7604      |\n|                     |                        | GPT-4o-mini        | 0.6100    | 0.2763   | 0.9109    | 0.6156    | 0.5900      | 0.5820     | 0.8161      | 0.7714      |\n|                     |                        | GPT-4o             | 0.5800    | 0.3162   | 0.9237    | 0.6404    | 0.6300      | 0.5717     | 0.7785      | 0.7700      |\n|                     |                        | Qwen3              | 0.6200    | 0.4632   | 1.7101    | 0.6284    | 0.5400      | 0.5843     | 0.9073      | 0.7364      |\n|                     |                        | DeepSeek-r1        | 0.5800    | 0.3018   | 0.9522    | 0.6173    | 0.5200      | 0.5492     | 0.8761      | 0.7373      |\n|                     | Few-shot               | gemini-2.0-flash   | 0.7200    | 0.6922   | 10.0922   | 0.7984    | 0.5300      | 0.5508     | 14.2531     | 0.6747      |\n|                     |                        | GPT-4o-mini        | 0.6456    | 0.5085   | 8.0727    | 0.7529    | 0.5200      | 0.5278     | 7.7066      | 0.6975      |\n|                     |                        | GPT-4o             | 0.7300    | 0.6654   | 3.9386    | 0.8423    | 0.5700      | 0.5967     | 5.6261      | 0.7467      |\n|                     |                        | Qwen3              | 0.7400    | 0.6760   | 7.0435    | 0.8033    | 0.5400      | 0.5487     | 9.5013      | 0.7060      |\n|                     |                        | DeepSeek-r1        | 0.7000    | 0.6282   | 3.6154    | 0.8439    | 0.5500      | 0.5392     | 8.8895      | 0.6855      |\n|                     | TextGrad               | gemini-2.0-flash   | 0.5400    | 0.2432   | 1.1934    | 0.4718    | 0.5000      | 0.4511     | 4.1290      | 0.7345      |\n|                     |                        | GPT-4o-mini        | 0.5700    | 0.3111   | 0.9551    | 0.5292    | 0.5000      | 0.4686     | 4.7960      | 0.6460      |\n|                     |                        | GPT-4o             | 0.5600    | 0.3316   | 0.9441    | 0.6256    | 0.5600      | 0.5321     | 2.3468      | 0.6721      |\n|                     |                        | Qwen3              | -         |  -       | -         | -         | -           | -          | -           | -           |\n|                     |                        | DeepSeek-r1        | 0.5800    | 0.3356   | 0.9631    | 0.6344    | 0.4300      | 0.4235     | 3.1080      | 0.5948      |\n|                     | **ATHENA (ours)**      | gemini-2.0-flash   | 0.7850    | 0.7219   | 0.8100    | 0.9063    | 0.6500      | 0.5978     | 0.8305      | 0.7998      |\n|                     |                        | GPT-4o-mini        | 0.7467    | 0.7097   | 1.0849    | 0.8624    | 0.6500      | 0.6079     | 0.8034      | 0.8133      |\n|                     |                        | GPT-4o             | 0.7650    | 0.7121   | 0.8645    | 0.8760    | 0.6700      | 0.6213     | 0.7765      | 0.8279      |\n|                     |                        | Qwen3              | 0.7451    | 0.7158   | 0.8211    | 0.7526    | 0.5929      | 0.5885     | 1.1659      | 0.7777      |\n|                     |                        | DeepSeek-r1        | 0.7450    | 0.6759   | 0.8078    | 0.8461    | 0.6600      | 0.6501     | 0.8115      | 0.8212      |\n| **Utility-Based**   | MNL                    | /                  | 0.6101    | 0.3887   | 0.8353    | 0.7074    | 0.4150      | 0.1955     | 1.0510      | 0.4301      |\n|                     | CLogit                 | /                  | 0.5714    | 0.2424   | 0.8916    | 0.5976    | 0.4150      | 0.1955     | 1.0510      | 0.5000      |\n|                     | Latent Class MNL       | /                  | 0.6101    | 0.3967   | 0.8175    | 0.7182    | 0.1950      | 0.1088     | 1.0986      | 0.5000      |\n| **Machine Learning**| Logistic Regression    | /                  | 0.5620    | 0.5570   | 0.9310    | 0.7460    | 0.6500      | 0.6690     | 0.7630      | 0.8330      |\n|                     | Random Forest          | /                  | 0.7100    | 0.7050   | 0.7380    | 0.8810    | 0.6300      | 0.6470     | 0.7290      | 0.8420      |\n|                     | XGBoost                | /                  | 0.7080    | 0.7050   | 0.7040    | 0.8810    | 0.6300      | 0.6480     | 1.1420      | 0.8150      |\n|                     | **BERT (finetuned)**   | /                  | 0.6960    | 0.4770   | 0.6917    | 0.9121    | 0.6400      | 0.6500     | 0.8091      | 0.8074      |\n|                     | **TabNet**             | /                  | 0.7154    | 0.7301   | 0.6723    | 0.9190    | 0.6400      | 0.6306     | 0.7980      | 0.8707      |\n|                     | **MLP**                | /                  | 0.6077    | 0.5982   | 0.8047    | 0.8097    | 0.6496      | 0.6335     | 0.8328      | 0.8069      |\n\n*Note. Qwen3‑32B TextGrad baseline experiments are still running; we will publish the final numbers and update the table within the next 1–2 days.*\n\nWe evaluate ATHENA against two state-of-the-art open-source models (Qwen3-32b and DeepSeek-R1-Distill-Qwen-32B) and three leading commercial offerings (GPT-4o-mini, GPT-4o, and Gemini-2.0-Flash). Across both tasks, ATHENA achieves superior performance—recording the highest accuracy, F1 score, and AUC of all baselines. To further broaden our comparison, we also include three additional benchmarks: BERT, TabNet, and a multilayer perceptron (MLP).\n\n> **Why GPT-4o-mini & Gemini-Flash were the original choices**\n\n\n1. Practical adaptation cost: Individual-level TextGrad Adaptation requires hundreds of forward passes per person. Inferencing large open-source models like Qwen3 or DeepSeek-r1 locally or stronger models like GPT-4o via API is prohibitively expensive. GPT-4o-mini and Gemini-Flash are smaller, more efficient models that still provide strong reasoning capabilities.\n2. Representative reasoning strength: GPT-4o-mini is explicitly tuned for chain-of-thought tasks, while Gemini-Flash is optimized for low-latency inference. Together they bracket a typical speed-versus-reasoning trade-off faced in practice."}, {"review_id": "pmFXcwuY2N", "reviewer": "Reviewer_zWuZ", "summary": "This work proposed a neural-symbolic approach to personalized decision making. It employs a two-stage procedure:\n\n- Group-level symbolic utility discovery, a procedure that iteratively identifies a symbolic expression for utility prediction. This procedure terminates when a convergence criterion (defined as the best-worst optimality gap) is met.\n- Individual-level semantic adaptation, which iteratively updates the semantic template via a TextGrad-esque procedure to optimize for individual utility losses.\n\nIn sum, the first stage amortizes (or warm-starts) symbolic expressions per group, and then the second stage adapts this expression to individuals. Experimental results show impressive gains over purely LLM-based and predictive model baselines.", "questions": "See weaknesses, and also:\n- I'm not entirely familiar with the Swissmetro and the Vaccine datasets, but the authors have elected for a simplified version of them for budget control. Could the authors discuss whether these simplified variants maintain the core challenge of this problem, and what the normal problem instances would look like?\n- I'd be curious to see the scaling behaviors of this approach. Say you increase the number of iterations for both stages, would you get better results?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "__Strengths__\n- __Quality and Clarity__: The writing is generally in good shape. The authors did a good job to present preliminary concepts, mathematical formalism, and their LLM implementations in detail. I appreciate the ablation study which shows that both components of the authors' approach are integral to the final performance.\n- __Significance__: As LLMs are increasingly embedded into daily usages, it is important to assess their capabilities and limitations. The authors have shown that LLMs are not yet capable as an end-to-end system for personalized decision making, and have proposed means to improve their performance. I believe this is an important area for future research\n- __Originality__: I'm a fan of neural-symbolic approaches wherein an LLM functions as a \"central hub\" to process and reason with textual / symbolic information, while delegating more quantitative operations to specialized packages. The authors have demonstrated a good application of this approach in personalized regression.\n\n__Weaknesses__\n- Extensive usage of LLMs is stated as a limitation to the approach, and it'd be good to report token consumptions (or monetary costs) associated with each run. \n- There are quite a few hyperparameters involved in this approach, such as the optimality gap $\\delta$ and the number of iterations $T, T^\\prime$. I could not find these numbers within the main text nor the appendix. It'd be good for the authors to report them as they're crucial to the understanding of the overall complexity of this approach.\n- The literature review section is overall well-done, but the section on \"LLM-based Decision-Making Models\" could've done a better job at interfacing with works that specifically addresses decision making via LLMs (right now it focuses more on general reasoning and instruction-following capabilities). For example, [1][2] studies decision making under uncertainty with LLMs, and [2][3][4] study their applications in supply chain optimization, personalized medicine, and autonomous driving respectively. \n- A benefit of symbolic regression is their interpretability. It would be good to discuss some of the expressions and explain why it makes sense.\n\n[1] DeLLMa: Decision Making Under Uncertainty with Large Language Models\n\n[2] STRUX: An LLM for Decision-Making with Structured Explanations\n\n[3] Large Language Models for Supply Chain Optimization\n\n[4] Leveraging Large Language Models for Decision Support in Personalized Oncology\n\n[5] A Language Agent for Autonomous Driving", "was_revised": true, "final_justification": "I thank the authors for their detailed response. I have also reviewed their responses to other reviewers and adjusted my score accordingly.", "rebuttal": "We thank you for your time and effort in reviewing our paper! We find your suggestions very helpful and we hereby address your questions:\n\n> **W1: Complexity, inference time, and token / cost footprint**\n\nWe sincerely thank the reviewer for highlighting this point. Here we performed an additional experiment that tracks the number of the token consumed and estimated cost, which is reported below.\n\nAll runs use **GPT-4o-mini** (128 k ctx.; *$0.15 / M input tok., $0.60 / M output tok.*).  \nCosts below list *input → output* fees. Pricing source: OpenAI docs (July 2025).  \n\n### Stage 1 Symbolic search  \n| Dataset | T (iterations) | Total tok. | Wall-time (min) | Cost (USD; input → output) |\n|---------|--------------:|-----------:|----------------:|---------------------------:|\n| Swissmetro | 5  | **19 871** | 3.7  | **$0.003 → $0.012** |\n|        | 15 | **93 256** | 15.9 | **$0.014 → $0.056** |\n|        | 30 | **548 811** | 73.8 | **$0.082 → $0.329** |\n| Vaccine   | 5 | **15 000** | 3.0 | **$0.002 → $0.009** |\n|           | 15| **70 000** | 12.5| **$0.011 → $0.042** |\n|           | 30 | **410 692** | 57.5 | **$0.062 → $0.246** |\n\n### Stage 2 TextGrad refinement  \n| Dataset | T′ (iterations) | Total tok. | Wall-time (min) | Cost (USD; input → output) |\n|---------|---------------:|-----------:|----------------:|---------------------------:|\n| Swissmetro | 1 | **1 197** | 1.39 | **$0.000 → $0.001** |\n|          | 3 | **4 074** | 3.55 | **$0.001 → $0.002** |\n|          | 5 | **6 956** | 5.81 | **$0.001 → $0.004** |\n| Vaccine     | 1 | **962** | 0.22 | **$0.000 → $0.001** |\n|          | 3 | **3 101** | 2.34 | **$0.000 → $0.002** |\n|          | 5 | **5 536** | 4.71 | **$0.001 → $0.003** |\n\n**Take-aways**\n\n* Stage 1 dominates both tokens and time; Stage 2 is negligible (< 7 k tokens, < 6 min).  \n* Even the heaviest configuration (30 + 5 iters) costs **< $0.35/run**, very affordable.  \n* Token growth matches our theoretical $\\mathcal{O}\\bigl((K T + N T′)\\bigr)$ prediction; adding more threads lets us parallel-slice Stage 1 to reduce wall-time.\n* Since LLM outputs are not that stable nad can occasionally drift from instructions (e.g., formatting glitches), we should consider the budget for automatic retries; the table above is just for reference, actual costs fluctuate and are model-dependent.\n\n> **W2: Value range of hyperparameters**\n\n\nThank you for pointing out that several run-time hyper-parameters were not explicitly reported.\nWe have added the following table for clarity:\n\n| Symbol | Description | Value |\n| :--- | :--- | :--- |\n| LLMs Used | The specific large language models utilized for both the symbolic discovery and semantic adaptation stages of ATHENA. | `gpt-40-mini-2024-07-18` and `gemini-2.0-flash` |\n| T | The number of iterations for the group-level symbolic utility discovery process, as shown in the accuracy trajectory analysis. | 30 |\n| $T'$ | The maximum number of iterations for the individual-level semantic adaptation. | 5 |\n| $K$ | The number of candidate symbolic utility functions sampled in each group-level iteration. | 10 |\n| $\\delta$ | The predefined convergence threshold for the group-level discovery process. | / |\n\n\n> **W3: LLM-based Decision-Making Models**\n\nThank you for drawing our attention to the recent work that applies LLMs directly to decision making under uncertainty! We have carefully read the papers you mentioned (e.g., DeLLMa [1], STRUX [2], and the follow-up studies on supply-chain optimization, personalized medicine, and autonomous driving [3–4]) and found them extremely insightful. We will incorporate these contributions into the final version, expanding the “LLM-based Decision-Making Models” subsection to include those works and discuss the complementary design choices each line of work makes. We greatly appreciate the pointer and will keep a close eye on the continued progress of these research groups.\n\n> **W4: Qualitative Analysis for Formulas in Main Text**\n\nThanks for your suggestions to enhance the qualitative analysis of the formulas presented in the main text! We have discussed about some representative examples in the rebuttal section of [Reviewer HnWo](https://openreview.net/forum?id=RDt0crdC7N&noteId=STQUOcL5iO).\n\n> **Q1: Dataset, Subset Selection Concern**\n\nWe thank the reviewer for raising this insightful question.\nWe only down-sampled via stratified sampling; every feature and label stays, so the joint distribution matches the originals.\n\n> **Q2: Scaling Behavior**\n\n**Stage 1 – Group-level symbolic discovery**  \nThe scalability of Stage 1 is shown in **Table2** of our paper: as we extend the symbolic-search loop from 0 → 30 iterations, performance gains steadily increase. But it will reach a threshold where further iterations will not yield significant improvements.\n\n**Stage 2 – Individual-level semantic adaptation**\n\n**Experimental setup.** We selected 5 individuals from each dataset and ran Stage 2 for 1, 5, 10, and 15 iterations. The results are summarized in the tables below.\nAll scaling runs use gpt-4o-mini as base model via OpenAI API (July 2025 release) for Stage 2. For each experiment `T` (Stage 1) is set to 30. \n\n**Swissmetro (5 individuals)**  \n\n| T′ | Accuracy | F1 | AUC |\n|---:|:--------:|:---:|:---:|\n| 1  | 0.90 | 0.3111 | 0.50 |\n| 5  | 0.90 | 0.3111 | 0.50 |\n| 10 | 0.90 | 0.3111 | 0.50 |\n| 15 | **1.00** | **0.3333** | 0.50 |\n\n**Vaccine (5 individuals)**  \n\n| T′ | Accuracy | F1 | AUC |\n|---:|:--------:|:---:|:---:|\n| 1  | 0.40 | 0.2000 | 0.50 |\n| 5  | 0.60 | **0.3111** | 0.50 |\n| 10 | 0.50 | 0.1778 | 0.50 |\n| 15 | **0.60** | 0.2444 | 0.50 |\n\n**Key observations**\n\n1. **Fast saturation.** For Swissmetro, metrics stabilise after 5 iterations, with only a slight bump at 15. Vaccine peaks at 5–15 iterations, with no monotonic gains thereafter.  \n2. **Modest Stage‑2 gain.** The largest improvement over the 1‑iteration baseline is +0.10 accuracy, confirming that Stage 1 contributes the bulk of predictive power.  \n3. **Practical default.** Capping Stage 2 at 5 iterations captures > 95 % of the attainable benefit while keeping extra cost (< 7 k tokens) negligible."}]

Author rebuttal:

Meta-review: The paper tackles the problem of bridging the gap between population-level utility models and individual decision-making through a two-stage framework combining symbolic utility discovery with LLM-powered semantic adaptation (termed ATHENA).

In summary, the reviews suggest that this work hits a sweet spot of methodological innovation and practical relevance. The authors elegantly sidestep the false dichotomy between interpretable-but-rigid utility models and flexible-but-opaque neural approaches. Reviewers specifically comment on several strengths. Among others:
- The quality of writing and presentation
- Strong premise/motivation
- Good performance
- Interpretability
- Originality of the idea

The authors also made a commendable effort in addressing reviewer concerns by adding stronger baselines and cost analysis, the latter of which shows the approach is practically viable even under budget constraints.

There were a few weaknesses noted:
- The reliance on predefined demographic groups is both a strength and limitation. Though this is well-justified theoretically, it does constrain generalizability
- More importantly, the evaluation is limited to two domains with relatively small datasets. The claim of broad applicability would ideally be backed by stronger empirical support across diverse contexts
- The symbolic discovery stage, while novel in its LLM integration, essentially performs a kind of guided search over a constrained space. The innovation lies more in the orchestration than a fundamental algorithmic advance

Overall, my view is that this paper advances an important research direction with a technically sound approach and clear promise for high-stakes applications. The authors have also responded well to many of the raised concerns. I think this is a clear accept.
Decision: Accept (spotlight)