Language Models Trained to do Arithmetic Predict Human Risky and Intertemporal Choice
Authors: Jian-Qiao Zhu
Haijiang Yan
Thomas L. Griffiths
Venue: ICLR 2025 Poster (2025)
Keywords: cognitive model
language model
computational models of cognition
rationality
economics
Primary area: applications to neuroscience & cognitive science
TL;DR: Pre-training a small language model on ecologically valid arithmetic datasets effectively captures human risky and intertemporal choices.

Abstract: The observed similarities in the behavior of humans and Large Language Models (LLMs) have prompted researchers to consider the potential of using LLMs as models of human cognition. However, several significant challenges must be addressed before LLMs can be legitimately regarded as cognitive models. For instance, LLMs are trained on far more data than humans typically encounter, and may have been directly trained on human data in specific cognitive tasks or aligned with human preferences. Consequently, the origins of these behavioral similarities are not well understood. In this paper, we propose a novel way to enhance the utility of language models as cognitive models. This approach involves (i) leveraging computationally equivalent tasks that both a language model and a rational agent need to master for solving a cognitive problem and (ii) examining the specific task distributions required for a language model to exhibit human-like behaviors. We apply this approach to decision-making -- specifically risky and intertemporal choice -- where the key computationally equivalent task is the arithmetic of expected value calculations. We show that a small language model pretrained on an ecologically valid arithmetic dataset, which we call Arithmetic-GPT, predicts human behavior better than many traditional cognitive models. Pretraining language models on ecologically valid arithmetic datasets is sufficient to produce a strong correspondence between these models and human decision-making. Our results also suggest that language models used as cognitive models should be carefully investigated via ablation studies of the pretraining data.

Published as a conference paper at ICLR 2025
LANGUAGE MODELS TRAINED TO DO ARITHMETIC PREDICT HUMAN RISKY AND INTERTEMPORAL
CHOICE
Jian-Qiao Zhu
Haijiang Yan
Department of Computer Science Princeton University jz52040pr nceton. edu
Department of Psychology University Warwick
Thomas L. Griffiths
Department of Psychology and Computer Science Princeton University
ABSTRACT
The observed similarities in the behavior of humans and Large Language Mod- els (LLMs) have prompted researchers to consider the potential of using LLMs models of human cognition. However, several significant challenges must be addressed before LLMS can be legitimately regarded as cognitive models. For in- stance, LLMs are trained far more data than humans typically encounter, and may have been directly trained on human data in specific cognitive tasks or aligned with human preferences. Consequently, the origins of these behavioral similarities are not well understood. In this paper, we propose a novel way to enhance the util- ity of language models as cogmitive models. This approach involves (i) leveraging computationally equivalent tasks that both language model and rational agent need to master for solving a cognitive problem and (ii) examining the specific task distributions required for a language model to exhibit human-like behaviors. We apply this approach to decision- makiinn - -pecificalll risky and intertemporal choice where the key computationally equivalent task is the arithmetic of ex- pected value calculations. We show that a small language model pretrained on an ecologically valid arithmetic dataset, which call Arithmetic-GPP man behavior better than many traditional cognitive models. Pretraining language models on ecologically valid arithmetic datasets is sufficient to produce a strong correspondence between these models and human decision-making Our results also suggest that language models used as cognitive models should be carefully investigated via ablation studies of the pretraining data.
predicts hu-
INTRODUCTION
Scientists studying the behavior of Large Language Models (LLMs) cognitive tasks typically per- formed by humans have found substantial evidence that LLMs produce performance similar to that
of human participants (Binz & Schulz 2023b; Horton 2023 Zhu & Griffiths 2024 Dasgupta et al.)
2022
Frank 2023b Marjich al. 2023 Webb al. 2023 Coda-Form et al. 2024 Like hu-
mans. LLMs often make judgments and decisions that deviate from rational norms (Binz& & Schulz,
2023b Horton 2023 Zhu & Griffiths/ 2024| Coda-Forno et al. 2024). For instance, GPT-3 demon-
strates human-like biases in risky choice, such as risk aversion and loss aversion (Binz & Schulz, 2023b), and the statistical properties of probability judgments generated by L.MSs align qualitatively with those of humans (Zhu & Griffiths, 2024). LLMs also make errors in other related settings; for example, when trained on the task of predicting the next token in sequences involving arithmetic
LLLMs can also display significant deviations from human hehavior (e.g., Chen et al.
2023 Hagendorff
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A Synthetic dataset
B
Ecological distributtions
20"0.224"0.8--2
Arthmetic-
umbeddings
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0.872-10.64
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Risky choice problems
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Please select option or
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Underlinng Probebd
A: $16 with certainty
16-110, 6.600-00.
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P(yalue) x valuee -0.045
B: $1 with probability 0.6
choice datas
$40 with probabilty 0.4
Intertemporal choice problams
Please select option A or A: $5 today
sty calcclation
5-10AD, D. SO
B: $10 in 4 days
Figure 1: (A) Pre-training and evaluation pipelines. We began by generating synthetic dataset comprised of mathematical equations including addition, subtraction, multiplication, and exponen- tiation. Arithmetic-GPT was pretrained on this synthetic dataset. After training, we froze model weights and extracted embeddings from the pretrained model, which then processes stylized choice tasks as input. These embeddings were subsequently compared with human choice data to evaluate their correspondence. (B) Ecological distributions of probabilities and values. In the top panel, English ceeaabiliyydescribbii phrases (black bars) can be modeled using a Beta(0.27, 0.27) distri- bution. In the bottom panel, the value distribution of debits from UK bank accounts (scatterpoints) follows power-law distribution. Figures adapted from Zhu et al. 2020) and Stewart et al. (2006).
operations, they fail to learn precise arithmetic operands and instead approximate the correct results up to certain input range (Nogueira et al. 2021 Lee et al. 2023).
In this paper, we focus on risky and intertemporal choice as exemplar domains for comparing the be- havior of language models and humans (see Figure [. Central to both domains is the computational challenge of calculating expectations. To assess the benefits of engaging in a gamble, an intelligent system must be able calculate the expected value (EV) of the gamble, typically represented
EV(A) = Σ ps X Zz
(I)
EEA
where each outcome of gamble A is associated with a payoff x, and probability pt, with the constraint that Σ3 P: = 1. Similarly, in considering an intertemporal choice the computation of the present value (PV) of future outcomes in A is crucial:
(A = Σ x 22
(2)
EEA
where the value x, realized time and discounted by a factor of d, reflecting the time prefer- ence of the
maker. Note that a risk-neutral and time-consistent agent should always select the option that maximizes EV and PV. However, extensive research in economies and psychology demonstrates that people systematically deviate from this maximizer model (Kahneman & Tversky 2013 Gigerenzer & Gaissmaier 2011 Laibson 1997 Zhu al., 2020).
Pretrained, off-the-shele LLMss, such as the GPT and L.LaMA series, have demonstrated behavioral similarities to humans in tasks involving risky and intertemporal choices (Horton) 2023 Binz & Schulz, 2023b; Manning al., (0244.. However, the embeddings generated by these LLMs are not by default able to account for human data. For example, embeddings from the LLaMA- 1.AMA-1-663 1-65B model, when not finetuned on human risky choices, poorly predict those choices (Binz & Schulz 2023a). Therefore, understanding what enables LLMs to exhibit human- decision decision-making be- havior remains an unresolved challenge.
We propose a hypothesis about how human-like decision patterns might be produced in language models for risky and intertemporal choice: such human-like behaviors might arise from lan-
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guage model trained ecologically valid caleulations of expectations. This suggests that human- like biases could result from the training task and numerical reasoning, independent of natural language supervision. As a corollary, this hypothesis also implies that deviations from rational choice in humans could be primarily explained by computational errors during the EV or PV calculations. To test this hypothesis, we generate series of synthetic datasets that contain pected value computations: examples include O. 5+100=+50 O. 8+1+0 000+++0.-21000000 22+10=+7 2, and 30x0. 19-261+0.. 8. 83- 199. 93. Subsequently, we train small, randomly-initialized language model (approximately 10M parameters) on these datasets. After training, we extract embeddings from the now pretrained language model and analyze how well they can account for human choices.
We conduct carefully ablated experiments on different aspects of the synthetic data to isolate the factors that result in embeddings that better predict human choice patterns. Our findings reveal that when the synthetic dataset reflects the ecological distributions of probabilities and values-mirroring real-world frequencies-the the resulting embeddings best predict human choices. With this pretraining, models based on the derived embeddings outperform many existing behavioral models of risky and intertemporal choice.
BACKGROUND
The question of whether language models can serve as models of human cognition has sparked in- tense debate within the fields of machine learning and cognitive science (Frank) 2023b Messeri & Crockett 2024 Griffiths et al. 2023 Horton 2023 Although there are behavioral similarities be- tween off-the-shelff LLMs and humans. these do not inherently qualify LLMs as effective cognitive models (c.f. the Clever Hans effect) (Shiftrin & Mitchell 2023). There compelling reasons why current LLMs may not be suitable as cognitive models. First, LLMs are trained on datasets vastly larger than those available to human learners (Frank (023a). Second, LLMS may have already been trained on the test questions, particularly if the training data is undisclosed and poorly controlled Jiang al. 2024). Third, the inclusion of value alignment steps, such Reinforcement Learning from Human Feedback (Ziegler et al. 2019) and Direct Preference Optimization (Rafailov et al., 2024]. may artificially enhance human-like behaviors in leading LLMs. Finally, the immense size of deep neural networks and the proprietary nature of leading LLMs hinder detailed investigation into their internal representations.
Researchers have taken steps to address some of the concerns associated with using L.MSs as cogni- tive models. One branch of research looks at the potential benefits of fine-tuning off-the-shelf L.MSs to better understand human cognition. For instance, fine-tuning the LLa.A-116658 model (Tourron cct al. 2023) on datasets of human choices results in a model that can predict human data more accu- rately than traditional cognitive models (Binz& & Schulz, 2023a). Although the specific mechanisms underlying the finetuned LLM's ability to replicate human choices remain unclear, this work serves as proof-of-concepp and suggests that the embeddings learned from extensive pretraining on Inter- net text and/or from the value alignment process may offer valuable insights into human cognitive processes that complement those provided by traditional cognitive models.
Another line of research emphasizes the importance of the composition of synthetic datasets, which are critical for enhancing certain capabilities of LLMs (Lee et al. (023). These studies typically assess LLMS based on their problem-solving abilities rather than their human-likeness. For exam- ple, it has been found that larger language models tend perform arithmetic tasks, such as addition and multiplication, better than their smaller counterparts Yuuan et al., 2023). Moreover, the order of input and the inclusion of intermediate information about task decomposition have been shown to fa- cilitate chain-of thhougghttt reasoning, which significantly helps smaller language models in mastering arithmetic tasks [Lee et al.) 2023).
Finally, there is precedent for the idea that pretraining machine learning models on synthetic datasets can improve performance in predicting human decisions. [Bourgin et al. (2019) showed that a model pretrained on choice data generated from psychological theory could perform ex- tremely well in predicting human decisions when fine-tuned with a small amount of human data. Our approach builds on this idea, but reduces it to the most primitive components rather than pre- training on data generated from psychological theory. we pretrain on a task that captures the basic computations required to make rational decisions.
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3 ARITHMETIC-GPT: A SMALL LANGUAGE MODEL TRAINED TO PERFORM ARITHMETIC
In this paper, confront the challenges of making language models cognitive models head-on. First, we define a data generation algorithm to produce synthetic datasets, thereby gaining complete control over the training data for language models and addressing issues related to data gaps and contamination. Second, we have direct access to the neural activation patterns that are crucial for Deeision-making processes. This approach allows us to more thoroughly evaluate and understand the capabilities and limitations of language models.
3.1
MODEL DETAILS
Our small language model employs a standard architecture for a Generative Pretrained Transformer (GPT) model (Vaswani al. 2017 Radford et al., 2019). Detailed specifications of the model architecture are provided in Table
Table Arithmetic- GPT 10M: a small language model pretrained to do arithmetic
Pre-training hyperparameters
Value
Hidden size
320
Layers
8
Heads
8
Context length
Vocabulary size
320
Attention variant
Causal self attention
Dropout
0.2
Biases
None
Tokenizer. To handle domain-specific vocabulary dedicated for arithmetic equations, built a custom tokenizer on the sub-word level. The vocabulary size is 320, containing special tokens (e.g., <AMB>, , <PAD>), arithmetic operators (e.g., +,
-). and all the integers from 0 to 300 which are designed to split numbers into individual digits. The vocabulary can cover most EV calculations in risky choice and PV calculations in intertemporal choice tasks.
Positional embedding, Absolute positional embedding was learned during training through an embedding layer. Each position had a corresponding 320 dimensional embedding vector.
Attention Mask. To ensure that attention is only applied to the left in the input sequence, we incorporated causal mask prevent attending to future tokens when predicting the next one.
3.2 SYNTHETIC DATASETS
At the heart of the EV and PV computations lies the multiplication of two real numbers. Typically, each outcome appears in the computation as either a probability multiplied by a value, or a discount factor multiplied by value. Probabilities are real numbers ranging from to represented with precision of up to two decimal places. Similarly, values are real numbers that range from 0 to 300, also with a maximum of decimal places. We selected these ranges align with the numerical scope of human experimental studies. A single training example involves either the addition or subtraction of two simulated outcomes, which together constitute the left-hand side of an equation. We then compute the corresponding result and place it on the right-hand side of the equation. In total, we randomly simulated IM such equations.
In our experiment, evaluate four variants of the data generation algorithm by manipulating the frequency probabilities and values (see Table 3). The Uniform synthetic data generates proba- bilities and values with maximum uncertainty; probabilities are uniformly distributed between 0 and (i.e., U0, 1)). and values range from 0 to 300 (i.e., U0, 300].. Conversely. the Ecological syn- thetic data generates probabilities following Beta distribution Beta(0.27. 0.27) (Zhu et al.) 2020) and values according to a plwer-law distribution with an exponent -0.945 for the same range (Stewart et al. 2006). These distributions are chosen because they have been shown to closely match
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the natural frequencies of probabilities and values in real-world scenarios (Stewart al. 2006 Zhu
eet al., 2020 (see Figure B for details). For both uniform and ecological synthetic datasets, we also created matching dataset where the answers the right-hand side are generated with a 50% chance of displaying the incorrect sign (i.e., the ablated variants Table 3) In each of the four synthetic datasets, randomly masked 10% of the probability values using special <AMB> token to denote unknown probabilities.
3.3 PRETRAINING DETAILS
We trained our Arithmetic- GPT models from scratch with a context length of 26. Batch size was set to 2048 lines of mathematical equations, randomly sampled from the synthetic datasets, and the learning rate was 10-3 To optionally terminate the training process, we designated 90% of the synthetic dataset the training set, reserving the remaining 10% for validation. We used cross- entropy loss to measure the discrepancy between the predicted and target sequences. Training was stopped when the validation loss plateaued, with validation loss evaluated every 100 epochs (see Figure A1 in Appendix C for an example learning curve). The Adam W optimizer was used.
3.4 HUMAN TARGETS
To investigate whether Arithmetic- GPT contains information pertinent to explaining human decision-making, reanalyzed recent experiments in which people were asked make risky and
intertemporal choices (Peterson et al. 2021 Frev et al. 2017 Gershman & Bhui 2020 Agrawal et al., 2023). The primary reason for examining these particular types of human choices is that calculations of expected value are integral to making rational decisions (see Equations | [ndd In
other words, they are computationally equivalent tasks under the assumption of rationality.
As summarized in Table we sampled four existing datasets from the literature, which included two large-scale experiments (Peterson al. [02T Agrawal al., 2023). experiments involving risky choices (Peterson et al., Erev et al. (011]) 7, participants were often presented with two options, each fully describing the details of a gamble (see Figure [TA risky choices). In cases involving ambiguous gambles where probabilities are unknown, we used the special token <AMB> to denote trials, as these would
gambles with unknown probabilities. We excluded secision-witt-feeddiee require additional assumptions about how individuals respond to feedback (but see Table A2 of Appendix B for a comparison based on the entire choices 3k dataset). intertemporal choice tasks (Gershman & Bhui 2020 Chávez et al. 2017: Agrawal al. 2023), participants were also presented with two options, typically offering a choice between a smaller, sooner payoff and a larger, later payoff (see Figure DAA intertemporal choices). Without loss of generality, we fixed the annual discount factor at dyear 0.85 throughout the paper. This also corresponds to a monthly discount factor of dmonth 0.98 and daily discount factor of dany 0.99. We rescaled the values in both options by the same factor to fit within the specified range.
Table 2: Overview of human experiments and data sources
Paper
Dataset
Domain
No. Participants No. Problems
Peterson et al. (2021)
choicesl 13k
Risky choices
15,153
13,006
Erev et al. 2017)
epc18 8
Risky choices
446
270
Gershman & Bhui (2020)
gershman20
Intertemporal choices 221
4,794
Agrawal et al. (2023)
agrawal22 123
Intertemporal choices 12,906
9,853
Note. In our analysis of the choicesll 3k and cpc1 8 datasets, we excluded trials involving risky choices made with feedback. Modeling how individuals respond to feedback requires additional
cognitive mechanisms beyond the scope of this work.
4
OTHER MODELS
We also conduct model comparison on human data, evaluating the following approaches: (i) clas- sical behavioral models such as prospect theory (Kahneman & Tversky] (0033) and the hyperbolic discounting model (Laibson 1997); (ii) neural network directly trained the human datasets; (iii)
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an untrained Arithmetic-GP7 model; and (iv) an off-the- open- open-weight LLM, LLaMA-3-70B. Instruct
Classical behavioral models. To explain human risky choices, prospect theory proposes an S- shaped utility function that is concave for gains, convex for losses, and steeper for losses than for gains (reflecting loss aversion). The utility function is represented mathematically as:
x
if 2 if <
U(z) = -xx
(3)
where x denotes the value, while the shape parameters a and 3 define the curvature of the utility function. The parameter À 2 reflects loss aversion. The theory further suggests that individuals possess a distorted perception of probabilitics, modeled as follows:
pd
w(() +1 p)
(4)
where p is the objective probability, and ry is a parameter controlling the curvature of the weighting function. Consequently, the utility of gamble is formally expressed as:
U(A) = Σ w(ps) x (x:))
TEA
Contrary to the consistent risk preferences implied by Equation orr other monotonic transformations of value, prospect theory suggests that risk preferences are inconsistent across different values and probabilities. This inconsistency results in incoherent choices when individuals are faced with risky decisions (versky & Kahneman 1992).
To capture human time preferences, particularly the impact of present bias, the hyperbolic discount- ing model suggests that future values should be discounted as follows:
PV
(6)
1+ kt
where Te is the value to be received at future time t, and ls is the discount factor that quantifies the degree of time preference. In contrast to the consistent time preferences implied by Equation [ the hyperbolic discounting model suggests that time preferences inconsistent across different time horizons, leading to stronger preference to immediate over future rewards (Laibson) 1997).
MLPs directly trained on human choices. We also implemented Multilayer Perceptrons (MLPs) with a single hidden layer containing 320 neurons and using the sigmoid activation function. These MLPs were directly trained on each of the four human datasets, using the stimuli features as input to predict choice rates. These MLPs potentially capture an upper bound of the explainable vari- ance within human data (Agrawal et al., (2200) However, they may have overlooked significant constraints from the original psychological experiments, as these models use task features as input rather than the actual stimuli presented in texts or the stylized representations required for rational agents, in our Arithmetic-GPT.
Choice probabilities and embeddings from ween-weight LLMs. To further investigate the impact of different input formats and compare with off-the-shelf LLMs, we evaluated the performance of the LLaMA3 model not
LLaMA-3-4 3-----77--nsttt only excels in arithmetic tasks but also comprehends and generates human-lii like text. This capability results from its training on extensive text data and a significantly larger number of model parameters. In short, LLaMA3 is more versatile and powerful model, also based on the transformer architecture and trained autoregressively.
on human choice data. Unlike Arithmetic-
Given these features of LLaMA3, we presented each choice problem in two different formats: text- based and arithmetic equation-based. The text format converts each choice problem into descrip- tive narrative, simulating the stimuli presented to human participants (see Appendix A detailed description of the text prompts). We instructed the model to report its selection between the two options, using the log probability of the chosen option determine the model's predicted choice rates for the corresponding option. In contrast, the arithmetic-equatin problems as a series of arithmetic computations required by a rational agent. Note that this format is identical to the input used for Arithmetic-GPT We obtained the embeddings from LLaMA3 for each choice problem represented in the arithmetic-equation format.
format presents the choice
https: / amaa met.a.... com/11ama3]

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Table 3: Proportion of the variance of human choices explained (R²) by embeddings from the pretrained Arithmetic-GPT model compared other computational models. Bold numbers indicate the best models within each group.
Risky choices
Intertemporal choices
Model
Training data
choicesi 3k cpc18
gershman20 agrawa,
Arith.-GPT
Synthetic (unif.)
69.3%
63.2%
64.0%
96.1% %
Arith-GPPT
Synthetic (unif. abl.)
57.5%
37.9%
59.8%
81.1%
Arith--GPT
Synthetic (eco.)
70.8%
65.5%
67.8%
95.5%
Arith.-GPT
Synthetic (eco. abl.)d
61 .1.4%
33.8%
60.7%
80.1%
Arith--GPT
None
21.0%
28.4%
10.8%
21.1%
LLaMA3 (txt.)
Undisclosed
14.2%
8.3%
4.0%
3.0%
LLaMA3 (txt emb.)
Undisclosed
66.2%
55.7%
66.5%
98.0% %
LLaMA3 (arith.)'
Undisclosed
63.6%
34.8%
69.3%
96.0%
Prospect theory
Human choices
51.5%
54.2%
N/A
N/A
Hyperbolic/
Human choices
N/A
N/A
53.4%
36.1%
Expected value
None
31.6%
43.9%
41.7%
26.1%
MLP
Human choices
82.7%
97.8%
60.6%
94.0%
Note. UUniform synthetic datasets. 'The same uniform synthetic datasets but with the answers the right-hand side of the equations removed and the signs randomized between positive and negative. 'Ecological synthetic datasets. "The same ecological synthetic datasets but with the answers on the right-hand side of the equations removed and the signs randomized between positive and negative. "Embeddings from an untrained Arithmetic-GPP model with randomly initialized weights. 'Log probabilities of LLaMA3 elicited from text descriptions of choice problems. 9The training data not publicly available, but Meta has disclosed some summary statistics of the training corpus. "Embeddings of LLaMA3 elicited from text descriptions of choice problems. 'Embeddings of LLaMA3 elicited from arithmetic equations of choice problems. 'The hyperbolic discounting model for intertemporal choices. *Logistic regression results when applied to the expected value difference between the two choice options.
5
EXPERIMENTAL RESULTS
5.1 MODEL COMPARISONS
In this section, we present the experimental results from our model comparisons. We first obtained embeddings from Arithmetic-Gi GPT and LLaMA3 models, evaluating versions of the model that were pretrained on each of our four distinct synthetic datasets as well as version without any training. Specifically, we extracted embeddings for the expected values of the two options, denoted as ea and ep. Additionally, е사-B- All embeddings were derived from the representation in the final layer before the autoregres- sive prediction. We then performed logistic regression using CA, en, and CA-B independent variables, with human choice probabilities as the dependent variable. Adjusted R² values were used for all logistic regressions, including those for Arithmetic-GPrT LLaMA3, and EV results. All other R2 values were reported as the squared Pearson's r between model predictions and human data. These results indicate that the embeddings from the Arithmetic-GPT model pretrained on ecologi- cally valid synthetic datasets most accurately capture human choices. This model also outperforms the embeddings obtained from the LLaMA3 model (the 7th row of Table 33) suggesting that pre- training on synthetic datasets is sufficient to create a strong correspondence between LIMS and human makiin. However, the LLaMA3 model performs comparably to Arithmetic-GPP in predicting intertemporal choices. The log probabilities from the same LLaMA3 model perform poorly in comparison to human data (the 6th row of Table (3), replicating previous findings using choice rates reported from LLaMA1 (Binz& & Schulz 2023a). The R² values between Arithmetic- GPT pretrained on uniform and ecological synthetic datasets are small yet consistent. This may be due to the limited range tested in the human datasets.
obtained embeddings for the difference in expected values. denoted as
To benchmark the performance of Arithmetic- GPT models in explaining human data, we directly fit behavioral models and ML.ss each of the human choice datasets. Prospect theory and the

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A
11
Emboiddnge
Embreddince
+00
6.2010
Bu30020 0.09133
Probabiities
Values
Disocunttactorr
Figure 2: Embeddings from ecologically pretrained Arithmetic-GPT for inputs including (A) prob- abilities, (B) values, and (C) discount factors. Inputs are shown along the horizontal axes and em- beddings are shown on the vertical axes. The embeddings. shown black dots, were reduced to 1D using multidimensional scaling. Embeddings for probabilities and discount factors are normalized between 0 and 1 (see Appendix D for details). The red curves represent the best-fitting behavioral economic models: (A) the probability weighting functiin from with best-fitting ? = 0.58, (B) the utility function from PT with best-fitting 0.42, B 0.45, 1.4, and (C) the hyperbolic discount function with best-fitting k = 0.08.
hyperbolic discounting model are leading behavioral models in risky and intertemporal choices, re- spectively (Kahneman & Tversky 2013 Laibson (997). The behavioral models have interpretable mechanisms and contain few free parameters. However, they do not explain human data as well as the embeddings from both LLaMA3 and Arithmetic-GP7 although they still outperform a simple choice model based on EV difference. Moreover, prospect theory and the hyperbolic discounting model do not generalize both risky and intertemporal choices, resulting in N/A values in their respective rows of Table
In contrast, fitting an MLP directly on human data potentially reveals the ceiling performance of any model in explaining the data (Agrawal al. 2020; Peterson et al. (021). Except for the intertem- poral choice tasks, MLPs outperform all other models. is important to note that MLP training was based task features rather than text descriptions that simulated participants' experiences or arithmetic equations that mimic a rational agent's 's computations. Consequently, these differences in input formats could also lead to diverging performance. The arithmetic format of intertemporal choice may provide a better fit for human data. Indeed, there is increasing evidence from experimen- tal economies suggesting that the complexity of discounting values, even in the absence of actual payoff delays, influences intertemporal choices (Enke et al. 2023 We include a robustness check using 10-fold cross-validation in Appendix B
5.2 IMPLICIT FUNCTIONS OF PROBABILITIES, VALUES, AND DISCOUNT FACTORS
To understand why Arithmetic-GPP pretrained to calculate expected values with ecological distri- butions of probabilities and values, can capture human choices, we examined the implicit functions of probabilities, values, and times derived from the model embeddings. We extracted embeddings for probabilities ranging from 0.0 to 1.0, values ranging from -300 to +3000, and discount factors ranging from 0.99 to 0.9930, These high-dimensional embeddings were then reduced to a single dimension using multidimensional scaling with Euclidean distance. Additionally, for probabilities and discount factors, we normalized the embeddings to a range between and 1.
We find that the embeddings from ecologically pretrained Arithmetic-GPP replicate classical find- ings from behavioral economics, including value and probability weighting functions from the prospect theory (Tversky & Kahneman) 1992) and the hyperbolic discounting function (Laibson, 1997p. Specifically, probabilities close to 0.5 are more similar to each other than to probabilities close to either 0 or 1 (see Figure Z and Equation 4). Embeddings for values illustrate concavity for positive values, convexity for negative values, and a steeper slope for negative values than for positive values (see Figure 2B and Equation 3). These features reflect risk aversion for gains, risk secking for losses, and loss aversion (Kahneman & Tversky 2013) Tversky & Kahneman 1992). Moreover, embeddings for the discount factor demonstrate that distant times more similar (see
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and Equation 6). enabling present- present-bias (Meier & Sprenger 2010). However, embed- dings from Arithmetic-Gi GPT pretrained on non-ecological datasets (i.e.. ablated ecological, uniform, and ablated uniform) and those from LLaMA3 exhibit fewer human-like distortions in their implicit functions (see Appendix
Figure 2C
F for details).
For the probability weighting function, the curvature parameter (+) of human participants was found to be 0.61 for gains and 0.69 for losses (Tversky & Kahneman, 1992). Follow-up replications by (Wu & Gonzalez, 1996) found Y values around 0.7. Moreover, the utility curvature parameters (a and B) typically range between 0,5 and 0.9, while the loss aversion parameter (A) is approximately 2.25 (Tversky Kahneman 1992). Regarding human intertemporal choices, typical & values range between 0.01 and 0.1 for small magnitude studies (Odum 20IT). Comparing to these best- best-fitting parameters from human experiments, we observe that the implicit functions derived from the embed- dings of Arithmetic-GPT also quantitatively match those observed in humans (see Figure (). The implicit functions, however, exhibit discontinuities, suggesting that the smooth functions derived from human theories may not be directly applicable to explain the embeddings of Arithmetic-GPT.
6 DISCUSSION
We introduced an approach to transforming language models into cognitive models by pretraining them on tasks that mirror the computational process performed by a rational agent. Specifically, we pretrained Arithmetic-GPTT to calculate expected values using ecologically distributed probabilities and values. This pretraining allows the model to better capture human risky and intertemporal choices compared to classical behavioral models and, in some cases, even surpass the performance of the in LLMs may stem from the training task, architecture, and numerical reasoning abilities, without requiring natural language supervision. These results have implications for a number of questions in cognitive science and machine learning, although we also note the limitations of our current work.
LLaMA3 model. These results suggest that the observed cognitive biases
Language Models as Cognitive Models. There a growing research effort focused on exploring LLMs scientific tools for understanding the human mind (Binz & Schulz, 2023a Frank] 2023b]
Horton 2023). Despite the challenges outlined in Section 2. LLMs offer unique opportunities for investigating cognitive processes in ways that are not feasible with human participants. Recent studies have even demonstrated that fine-tuning LLaMA model on human data allows the model to outperform classical models in explaining this data (Binz & Schulz] 2023a). While the LLaMA series' model architecture and weights are publicly available, researchers lack access to the training data, which makes crucial scientific inference practically impossible. In contrast, we explicitly manipulate the training data for our Arithmetic-GPP thereby uncovering a key factor that contributes to the model's ability to explain human choices. This targeted approach, however, comes at the cost of the broader versatility inherent in off-the-shelf LLMs, which are designed to handle a wider range of tasks. Notably, language models, including Arithmetic-GBB GPT, do not directly model human cognitive processes. Instead, our work suggests that these models are better suited for probing the computational problems that human cognition aims to solve.
Bayesian Models of Cognition, Meta-learning, and Pre-training. Bayesian models of cognition have been instrumental in understanding human performance across a variety of cognitive tasks by providing optimal solutions to the inductive inference problem. Recently, has been argued that Bayesian models and neural network models can be viewed as complementary to one another (Grif- fhth et al. 2023). Neural networks that are meta-trained have also been shown to exhibit properties consistent with Bayesian models (Lake & Baroni 2023 McCoy & Griffiths 2023). Moreover, pre- training neural network model for improved performance on downstream tasks can be seen as form of meta-learning or the acquisition of useful inductive biases, similar to Bayesian models (Hsu et al. 2018). Our work makes the implicit priors learned by Arithmetic-GPT more explicit by specifying the synthetic dataset on which it pre-trained.
Computationally Equivalent Tasks for Cognitive Modeling, Modeling human cognition is chal- lenging because the hypothesis space of possible cognitive mechanisms that can explain human data equally well is vast. This makes principles of rationality desirable, as assuming people are rational in some sense greatly constrains the hypothesis space, thereby making scientific inference more effec- tive. However, human rationality has been a subject of debate in economics and psychology for over century (von Neumann & Morgenstern 1944 Kahneman & Tversky 2013 Simon 1997). While

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significant progress has been made in understanding human rationality (e.g.. Lieder & Griffiths 2020 Gershman et al. 2013). the advent of LLMs seems to challenge the need for rational theories. Simply training LLMs predict the next word appears sufficient to produce human-like behaviors, suggesting that we can model human cognition without the constraints imposed by rational theories. However, our experimental results suggest an alternative route enhancing the correspondence be- tween behaviors produced by LLMs and humans: pretraining on computationally equivalent tasks that a rational agent would need to master. Future research should investigate the impact of different assumptions about the nature of rationality on task content and distributions, and explore whether there are more effective assumptions for pre-training models to explain human behavior.
Implications for Theories of Human Risk and Time Preferences. The success of Arithmetic- GPT in explaining human risky and intertemporal choices has significant implications for theoretical work on human risk and time preferences. While the Homo economicus portrayal of human beings as perfectly rational and self-interested agents has been inadequate in describing human choices GGierrnzzrr & Gaissmaier 2011 Kahneman & Tversky 2013), existing behavioral models that deviate from rationality do not generalize well across different task domains. For instance, it is challenging to use prospect theory model time preferences to the hyperbolic discounting model to explain risk preferences. In contrast, Arithmetic- GPT has demonstrated substantial trans- ferability across task domains. The same model, in principle, can be adapted to other judgment and recision-making tasks such as social choice, probability judgment, and belief updating. The key factor enabling language models to generalize across a wide range of tasks the presence of language interface, which underpins significant range of cognitive tasks.
The Importance of Training Data Disclosure. Our results demonstrate that the training data used for LLMs is crucial for understanding their emergent capabilities and the inductive biases they ac- quire during pretraining. Adjusting the distribution of, or ablating, the training data can significantly affect the degree to which LLMs correspond with human behaviors. These findings suggest that existing off-the-shelf L.M,s, whether proprietary or open-weight, including the GPT series (Brown) et al. 2020) and the ILLMAA series (Touvron et al.] 2023). are less effective as models of human cognition. This is primarily because their training data is rarely disclosed, making difficult for scientists to control for data contamination and thereby precisely identify the sources of human-like behaviors in these models.
Limitations and Future Research. While we have made progress in addressing many challenges associated with using language models as cognitive models, some issues remain unresolved. To ad- dress the data gap between L.MMs and human learners, we limited the scope of our synthetic dataset to the arithmetic of expected value calculations. Despite this, LLMs still require a substantial amount of training data perform arithmetic accurately within a limited range of input values. Moreover, it is unrealistic for human learners to process IM randomly generated mathematical equations, as Arithmetic-GPT did, acquire the skill of computing expected values. Further research is needed to continue bridging this data gap (but see Appendix F for an initial attempt).
Additional ablation studies could be performed on model architectures and training objectives. Our work is fundamentally limited to autoregressive training and decoder-only transformer architec- ture. We believe that alternative training mechanisms and model architectures could potentially yield better embeddings from language models. One area for future research is estimating the lower bounds on model size necessary to achieve a certain level of correspondence with human behavior. Another area of future work involves leveraging interpretability techniques to distill novel cognitive mechanisms from Arithmetic-GPi
Conclusion. Large language models have opened new horizons for research on human cognition, but also introduce a new set of challenges based on the volume of training data, the content of those data, the influence of value alignment, and limited access to the training regimes and weights of these models. We have proposed an approach to addressing these challenges, based on training small language models with datasets that are generated based on tasks that are hypothesized to be computationally related to the problem that human minds face. Our results show that this approach extremely effective in predicting human decisions, where training on arithmetic results in repre- sentations that can be used to predict human choices better than both existing psychological models and large language models trained on broader datasets. This approach is easily generalizable to other cognitive tasks that primarily rely on language interface, and can even be used with other kinds of foundation models to study human perception.
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Acknowledgments. This work and related results made possible with the support of the NOMIS Foundation. H. Yan acknowledges the Chancellor's International Scholarship from the University of Warwick for additional support.
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A PROMPTS
EXAMPLE OF A RISKY CHOICE DESCRIBED IN TEXT
You are participating in gambling game where you will shown two options, Gamble A and Gamble в. Your task is to choose between the two. You must select one option.
System:
User: Gamble A offers 10% chance to win $10 and 90% chance to lose $12. Gamble В offers 408 chance to lose $13 and 608 chance to win $22. Please limit your answer to either 'X' or 'B'.
EXAMPLE OF INTERTEMPORAL CHOICE DESCRIBED IN TEXT
System: You are participating in an intertemporal choice experiment. You will be presented with two options, and B, and your task is to choose between them. You must select one option.
User:
Option offers $80 after 30 days. Option offers $13 immediately. Please limit your answer to either 'A' or 'B'.
B ROBUSTNESS CHECK
We supplement our main results with a robustness check using 10-fold cross-validation. Each dataset of human choices was randomly partitioned into 90% training and 10% validation For the gershman2 0 dataset, stratified kuin/validation split was employed due to the certainty equiv- alence design of the experiment (Gershman Bhui 2020), ensuring that choices made within the same problem were grouped together.
Embeddings from Arithmetic-GPt models and regression with LASSO penalty on the training set. MLPs were fitted to task features in the training set. Performance for all models was assessed on the validation set, with S22 calculated as the squared Pearson's s This process was repeated 10 times, each with random train/validation split. The mean and standard error (SE) of Rd are summarized in Table A1 demonstrating a replication of our main results presented in Table 3 Finally, choicesl 3k dataset, including the decision Drcision-ffomm-ii nooo-feedbbck trials (see AA2). We observe that ILaMA3 can outperform MI. the agra ww 123 dataset. While the neural network models use different task formats as inputs, which may contribute to the differences in performance, is also possible that the dataset lacks sufficient statistical power reliably distinguish between the two models.
were fitted using logistic
conducted model comparison using the entire
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Table A1: Cross- validation results. Propotion of the variance in human choices explained (R²) on the validation set for each model. Numbers in parentheses represent standard errors from 10-fold vross-validation.
Risky choices
Intertemporal choices
Model
Training data
choices13k
epc18
gershman20 agr aarawal22 123
56.4%
46.3%
56.7% %
81.5%
Arith.-GPT
Synthetic (unif.)
(0,4%)
(3.1%)
(1.1%)
(0.4%)
38.5%
21.9%
51.1%
54.0%
Arith.-GPT
Synthetic (unif. abl.)
(1.5%)
(4.6%)
(0.7%)
(0.3%)
57.7% %
51.7%
57.1%
83.7% %
Arith.-GPT
Synthetic (eco.)
(0.4%)
(4.9%)
(1.2%)
(0.3%)
38.5%
33.6%
55.3%
68.3%
Arith.-GPT
Synthetic (eco. abl.)
(1.5%)
(5.0%)
(1.2%)
(0.2%)
33.1%
23.5%
15.3%
50.4%
Arith.-GPT
None
(1.5%)
(3.8%)
(1.7%)
(5.1%)
54.0%
35.0%
52.7%
89.9%
LLaMA3 (Ixt emb.)
Undisclosed
(0.8%)
(5.0%)
(1.1%)
(0.1%)
38.6%
20.8%
54.9%
87.6%
LLaMA3 (arith.)
Undisclosed
(1.5%)
(3.0%)
(1.2%)
(0.1%)
62.3%
50.3%
58.7%
84.9%
MI.P
Human choices
(1.2%)
(3.9%)
(1.3%)
(2.4%)
Note. The bold numbers represent the ao-performing variants of the Arithmetic-Gii GPT models, measured by R², In cases where multiple models are highlighted, the differences in Ri² values are not statistically significant the p 0.05 level.
Table A2: Proportion of the variance in human choices explained (R²) on the entire choices dataset for each model. Bold numbers indicate the best models within each group.
Model APT
Training data
Entire choices133
Synthetic (unif.)
64.0%
Arith.-GPT
Synthetic (unif. abl.)
49.2%
Arith.-GPT
Synthetic (eco.)
64.3%
Arith.-GPT
Synthetic (eco. abl.)
52.1% 1%
LLaMA3 (txt.)
Undisclosed
14.6%
LLaMA3 (txt emb.)
Undisclosed
65.6% %
ILaMA3 (arith.)
Undisclosed
60.6%
Prospect theory
Human choices
45.6%
Expected value
None
40.2%
MLP
Human choices
73.8%
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C LEARNING CURVE
B
107
107
12
2000
2006-
ree
Emror
Figure Al: (A) Training loss decreases over the course of training epochs for Arithmetic-GPT trained on ecological synthetic dataset. (B) Histogram displaying the differences between the top-1 responses of the pretrained Arithmetic-GPP GPT model and the actual expected values in the ecological synthetic dataset.
D DIMENSIONALITY REDUCTION DETAILS
We used multidimensional scaling to reduce the dimensionality of embeddings to ID, with Euclidean distance serving as the dissimilarity metric for forming the ID manifolds. Embeddings of proba- bilities and discount factors normalized using max-min normalization to ensure the resultant values fell within the range of [0, 1].
E ADDITIONAL IMPLICIT FUNCTIONS
LLaMA-3-70B-Instruce
Embeddinge
Embetrdings
Embeddings
+000
+300
+200
+300
0.25
0.5
0.75
1.5.
6.9970
0.99"10
0.99/20
0.99-30
Probabilitiss
Values
Discount factors
Figure A2: Visualizations of embeddings from LLA-MAA---77--IIstie
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A
Arithmetic-GPT pretrained on uniform synthetic dataset
Finbedrinng
Emfoedelnne
Embreddings
-300
-200
-100
+200
-300
4M4
0.0
0.25
0.5
0.75
0.90-10
C,00120
0.90-
Probabilties
Values
Disoount factors
B
Arithmetic-GPT pretrained on ablated uniform synthetic dataset
v.a's
Embeoddnge
Embeddiings
Emboddingz
0.22
3.0
0.99920 5.9916
0.99-30
Probuliiities
factors
C
Arithmetic-GPT pretrained on ablated ecological synthetic dataset
Embeddingg
Emboddiine
Embeddinng
0.0
3.25
0.5 0.15
1.0
0.9600
Dupensc
D. sehgo
0.99-30
Probabittiis
Value
Discount factors
Figure A3: Visualizations embeddings from Arithmetic-GPTs pretrained on different synthetic datasets. (A) Uniform synthetic dataset. (B) Ablated uniform synthetic dataset. (C) Ablated ecolog- ical synthetic dataset.
F VARIATIONS IN MODEL SIZES, DATA QUANTITY, AND DATA DISTRIBUTIONS
In this section, explore how adjustments key hyperparameters of ArithmetieGGPT impact the quality of its pretrained embeddings. Specifically, we investigate the effects of reducing the model's hidden size from 320 (as reported in the main text) 104 and 16. Moreover, we examine the in- fluence of decreasing the size of the ecological synthetic dataset, reducing it from 1M mathematical equations (as reported the main text) subsets 100K and 10K equations. Apart from these modifications, adhered to the same pretraining procedure and evaluated the resulting embeddings on the two largest datasets, choices 3k for risky choices (Peterson et al. 2022] and agrawal23 (Agrawal al. 2023) for intertemporal choices, using 10-fold cross- cross-validation..
The results, summarized in Table A3 reveal an intriguing pattern: reducing the size of the ecological synthetic dataset as few 10K equations does significantly impair the ability of the 10M model's 's embeddings to predict human choices. is important to note that Arithmetic-Gr never exposed to human data during pretraining. However, significant reductions in the model
models
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size particularly 30K parameters - lead to a decline in performance, highlighting the critical role of model capacity embedding quality.
Table A3: Variants Arithmetic-GrP models pretrained on ecological synthetic datasets of vary- ing sizes. In each cell, R results (in percentage) are reported agrawa 123 (right of '7). Numbers in parentheses indicate standard errors obtained from 10-fold cross-validation.
(left of '/") and
Model Sizes
TOM
1M
30K
(hidden size=320)
(hidden size=104) (hidden size=16)
IM 57.7 (0.4) / 83.7 (0.3) 54.7 (0.6) / 83,4 (0.3) 30.6 (0.4) / 56.8 (0.4) Data quantity 100K 57.2 (0.6) 83.6 (0.4) 55.5 (0.5) 81.6 (0.4) 31.4 (0.8) 63.4 (0.2)
10K 57.7 (0.5) / 83.6 (0.3) 50.0 (0.5) 84.1 (0.3) 29.1 (0.6) / 63.0 (0.4)
Note. The bold numbers represent the top-performing variants of the Arithmetic-Gii models, measured by R.2. In cases where multiple models are highlighted, the differences in R² values are not statistically significant at the p 0.05 level.
We conducted an exploratory analysis using the original Arithmetic-GPT model architecture and synthetic datasets of IM equations to investigate the effects of varying data distributions. Specif- ically, we independently manipulated the distributions of probabilities and values. For probability distributions, we considered Beta(0.27, 0.27) (ecological), Beta(1, 1) (uniform), and Beta(2, 2). For value distributions, we examined power-law distributions with exponents of 0 (uniform). -0.945 (ecological), and -2. All Arithmetie-GiP models were randomly initialized and trained following the procedure outlined in Section 3.1.
As shown in Table aligning probability distributions with ecological patterns, such as Beta(0.2) 0.27), generally enhances the quality of embeddings for predicting risky choices. Conversely, adopt- ing a power-law distribution for values with an exponent of -2 tends to improve the model's perfor- mance in predicting intertemporal choices.
Table A4: Variants of Arithmetic- GPA models pretrained on different data distributions. In each cell, R² results (in percentage) are reported as choi ces1 3k (left of '/') and agrawal 22 (right of !"). Numbers in parentheses indicate standard errors obtained from 10-fold cross-validation.
Distribution of probabilities Beta(I.1)
Beta(0.27.00277)
Beta(,,2)
0 56.5 (0.5) 82.5 (0.4) 56.4 (0.4) 81.5 (0.4) 56.0 (0.3) 77.5 (0.4)
Distribution of values
-0.945 57.7 (0.4)/ 83.7 (0.3) 56.7 (0.3) 78.4 (0.5) 56.5 (0.3) / 77.6 (0.4)
(exponent of power-law)
-2 55.7 (0.3) / 85.9 (0.3) 56.3 (0.5) / 82.6 (0.4) 55.5 (0.4) / 82.2 (0.4)
Note. The bold numbers represent the oop-peffrrming variants of the Arithmetic- models, as measured by R²
G COMPUTATIONAL ABILITIES OF LANGUAGE MODELS
We evaluate the abilities of 1-O-AA---77B-Inttttue and Arithmetic-Gri in computing expected values using two newly generated test datasets. Both test sets consist of 20K synthetically generated equations involving expected value calculations. In one test set, the probabilities and values in the equations sampled from uniform distribution, while the other test set features probabilities and values derived from ecological distributions, as illustrated in Figure] The train-test relationships for these datasets are summarized in A5
The computational ability of Arithmetic models was assessed by calculating the probability of generating correct expected values (rounded to two decimal places). Formally, the correct prob- ability is computed as P Prodee (true expected values the left-hand side of the equation), using token probabilities. Arithmetic-GPT, when pretrained ecological distributions, demonstrated higher
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Published as a conference paper at ICLR 2025
probabilities of generating correct values across both uniform and ecological test sets. When com- paring performance on the same model across the two test sets, expected values in the ecological test set were found to be casier to predict. One possible explanation for the improved performance of Arithmetic-GPT models pretrained on ecological distributions that these distributions are more "bursty," characterized by multiple occurrences of similar numerical values (cf. Chan et al. 2022). Pretraining on bursty sequences has been shown to facilitate emergent behaviors in LLMs, such as in-context learning (Chan al. 2022).
To evaluate LLaMA3's ability to compute expected values, we directly prompted the model to solve arithmetic equations while setting the temperature 0. The integer part of the expected values was extracted from LLaMA3's responses by filtering out irrelevant tokens. The correct probability was calculated as the relative frequency of correctly predicting the integer part of the true expected values across 20K questions. As shown in Table A5 LLaMA3 performed poorly compared to Arithmetic-GPP achieving only 20.97% and 38. 79% accuracy on the uniform and ecological test sets, respectively.
The model's 's behavioral performance on the ecological test set broadly predicts the ranking of its embeddings in modeling human data. However, directly interpreting language model's perfor- mance on arithmetic tasks in relation to model-fitting results that leverage its embeddings can be challenging. Therefore, further investigation is necessary to establish robust connection between a language model's arithmetic capabilities and the predictive power of its embeddings in predicting human choices.
Table A5:
Evaluation of language models' probabilities of generating correct expected values across different train-test distributions. Numbers in parentheses represent standard errors.
Model Training data
Test data
Correct probability
Arith. Synthetic (unif.)
Uniform
0.8261 (0.0023)
Ecological
0.9336 (0.0014)
Arith.-GPP TTT Synthetic (eco.)
Uniform
0.9388 (0.0013)
Ecological
0.9780 (0.0007)
LLaMA3
Undisclosed
Uniform
0.2097
Ecological
0.3879
H IMPLEMENTATION DETAILS
Here we detail the hyperparameter setup for experiments. All computations for synthetic datasets single Nvidia RTX 3060 GPU, and those for LLaMA3 embeddings are run on single A100 GPU.
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Reviews:
[{"review_id": "Gfak7tIkzG", "reviewer": "Reviewer_2CbN", "summary": "The paper shows that by solely training next token prediction on arithmetic data requiring computations related to real-world decisions (e.g., computing expectations) it's possible to predict with good accuracy human behavior. Results improve (slightly?) when the pretrained computations involve numbers which resemble real-world distributions.", "questions": "- I wonder if the positioning of the paper may be different - something along the lines of \"LLMs were observed to replicate human cognitive biases, here we show a possible explanation, indicating that this may be due to the task, architecture, and numerical reasoning, without requiring any natural language supervision, world knowledge or common sense.\" Does this make sense? If so, I think it would have been easier for me to understand the paper.\n- I wonder what would happen if the LLM was trained on other mathematical tasks, not relating to expectation? Would it still be able to explain human behavior to some extent?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- I found the results of the paper very surprising, I think that the approach is creative, and to the best of my knowledge, may perhaps offer a minimal explanation for why LLMs replicate human behavior in some cognitive biases - namely, something about the next word prediction mechanism and mathematical data? Without the need for any language-related observations at all.", "weaknesses": "I don't have strong concerns, and I'm generally positive about this paper, though I feel like Section 3.4 (Human Targets) contains many preprocessing decisions with some very specific factors (annual discount factor set to 0.85). I didn’t understand the need for these, or whether they affect the results. For example, I don’t understand this part: “In cases involving ambiguous gambles where probabilities are unknown, we used the special token to denote gambles with unknown probabilities.” (Line 237) Can you please elaborate?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "exiWFxsQpF", "reviewer": "Reviewer_EZUX", "summary": "The paper presented a method to enable a model to act as a cognitive model for a cognitive task by training it on 1) computationally similar tasks 2) with similar distribution. The authors demonstrate their method on the task of risky and intertemporal choice, by pre-training on synthetic expected value calculations data of ecological distribution. The paper compares their trained model, Arithmetic-GPT, with Llama-3-70B, and a few traditional cognitive models. Arithmetic-GPT shows a good ability to explain human data.", "questions": "1. There are open models with open data e.g. LLM360 and OLMo, how does this affect your LLMs experiment in the context of the paper experiments?\n2. Is there a way to produce figures like the ones in Figure 2 from LLaMA3 embeddings?\n3. Can a strong model trained on the human data provide a better upper limit and also act as a cognitive model?\n\nComments:\n1. LLaMA3 is a bit better in Intertemporal choices and on par with the Arithmetic-GPT. The text there doesn't reflect that and does not explain it. Also, the top results from LLaMA3 are not in bold.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is clear and well-written.\n2. The method is novel and demonstrates strong results for a small model and relatively small data.\n3. The results showcase the method's ability to create a good cognitive model for the target task.\n4. The deduction of implicit values from ARITHMETIC-GPT is interesting and insightful.", "weaknesses": "1. The paper is a bit lean on the experimental side.\n2. Lack of experimentation with different model sizes that can allow a better understanding of their effect on the model's ability to act as a cognitive model. Similarly, there are no experiments designed to assess the effect of the data quantity that is emphasized as key factors that differentiate humans from LLMs.\n3. The paper claims that their approach is general, but they only train on one type of computational task, e.g. expected value calculations. Another example can enhance the paper, even pointing to other concrete examples can be valuable. For example, does this also hold to more language-oriented tasks? in that case, are smaller dedicated models will also outperform strong LLMs? \n4. Part of your rationale for choosing ecological distribution is that in humans this can lead to computational errors that are the basis for deviating from the rational decision. However, you didn't analyze both LLaMA3 and Arithmetic-GPT computational abilities both in and out of distributions, and examine their effect on the results.\n5. There is no discussion on the trade-off between a general model like LLaMA3 that can act as a cognitive model in a wide array of tasks and a small and dedicated model as you proposed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "exodwrkSlH", "reviewer": "Reviewer_eVJL", "summary": "Humans often deviate from optimal choices in tasks involving expected value or temporal patterns. This behavior is also observed in LLMs, though embeddings do not fully capture this deviation. This study explores how this tendency arises in language models by pre-training a small model (Arithmetic-GPT) on expectation calculation tasks then testing its alignment with human choices. \n\nSynthetic datasets (uniform and ecological, each with perturbed and unperturbed versions) are created for model pre-training and tested on four human datasets related to risky and inter-temporal decisions. Model comparisons included pre-trained Llama (natural language input + log-likelihoods, natural language + text embeddings, arithmetic + embeddings), Arithmetic-GPT variants (four dataset versions and no training), four behavioral models, and MLPs directly trained on task features. Results show that Arithmetic-GPT trained on unperturbed ecological data shows the highest explained variance with human decisions (input: embeddings/log-likelihoods, output: human decisions).", "questions": "- A minor question regarding the experiments: Why not also try training Llama or Arithmetic-GPT on the task features as the MLP?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- **Originality**: \n     - Proposes a new test environment to evaluate the effectiveness of using language models as cognitive models.\n     - The ecological data pre-training approach is a simple approach to model principles with human decision-making patterns.\n\n - **Quality and Clarity**: \n     - Comprehensive benchmarking across multiple models, including classical behavioral and neural models.\n     - Very clear writing, but with minor typos (e.g., line 376, \"fitted\" → \"fit\").", "weaknesses": "Overall, I am uncertain if the proposed task is too simple to make any sophisticated claims on language models as cognitive models. \n\n - Does Arithmetic-GPT’s performance really represent actual human decision processes, or is it not possible that Arithmetic-GPT's \"human-like behavior” could instead be a reflection of general statistical tendencies that happen to deviate from optimal choice, rather than an insight into genuine human cognition?\n- Table 3 shows that Arithmetic-GPT only marginally outperforms the larger Llama model. This suggests that Llama, without specialized pre-training, already captures much of the variance in human choices. I suppose the claim is somewhat valid given the limited capacity of the Arithimetic-GPT backbone, but the authors’ emphasis on Arithmetic-GPT's superiority might be overstated given that its improvement is slight and comes from training on targeted synthetic data.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1UApfBPckf", "reviewer": "Reviewer_27fR", "summary": "The authors explore how language models can serve as cognitive models by investigating their behavior in risky and intertemporal choice tasks. The authors introduce Arithmetic-GPT, a small language model specifically trained on arithmetic tasks that simulate expected value (EV) and present value (PV) calculations essential to decision-making. By training Arithmetic-GPT (A-GPT) on a non-ecologically and ecologically valid datasets, the authors show that A-GPT exhibits decision-making patterns that closely resemble human choices (in particular for the ecologically valid dataset). Moreover, A-GPT outperforms both traditional behavioral models and some large, general-purpose language models in predicting human risk and time preferences. The work porposed by the authors underscores the importance of tailored training datasets for aligning language model behavior with human cognitive processes and provides insights into how synthetic datasets may enhance models' ability to predict human decision patterns.", "questions": "Typo:\n\nThere is an issue with the presentation of Figure A2 which falls under appendix F rather than E.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. This work exemplifies the potential of LLMs to gain insights in human cognitive processing, and as a results showcases the elegance of the auhtors thought process.\n\n2. The auhors compare their model to a relevant suite of other models, and use several datasets to drive their point. This systematic comparison highlights the quality of this work and further amplifies the results obtained with A-GPT.\n\n3. The paper is clear and well structured, allowing for smooth reading. The figures are informative and clearly illustrate the points made in the text.", "weaknesses": "Within the range of what the paper is tackling, I do not see any weaknesses in this work.\n\nI do however believe that the authors could have gained further understanding of human risky and intertemporal choices by generating several other datasets that systematically target specific aspect of EV and PV calculations, i.e., parametrically changing the ablation level of specific EV and PV compononents. \n\nMoreover, it would be interesting to relate the A-GPT results with explainability in order to potentially provide more interpretability to the embeddings.\n\nI will however not discount any points in my rating. I understand the limitations in terms of computation,cost, time and manuscript space.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)