No Comparison Model (NCM) in Social Reward Analysis

• No Comparison Model (NCM) is a computational baseline that models subjective reward valuation using only self-derived signals, completely omitting partner information.
• It utilizes a multilayer mMLDA framework with collapsed Gibbs sampling for inference, achieving a Rand Index of 0.75 in primate reward evaluation experiments.
• The findings highlight the limits of ignoring social signals, emphasizing the importance of partner data for accurate modeling in social reward tasks.

The No Comparison Model (NCM) is a computational baseline used to analyze social comparison mechanisms, particularly in the context of primate reward and decision processing. The NCM explicitly disregards social information from a partner and instead relies exclusively on self-derived and environmental signals in modeling subjective reward valuation. It stands in direct contrast to models that encode or infer social context, such as the Internal Prediction Model (IPM), which estimates partner subjective value, and the External Comparison Model (ECM), which incorporates objective partner rewards. NCM is instrumental in testing the hypothesis that social agents, such as macaques, process rewards without any comparative or inferential computation regarding their conspecifics (Taniuchi et al., 21 Dec 2025).

1. Model Specification and Scope

The NCM utilizes a probabilistic generative framework built using multilayer, multimodal Latent Dirichlet Allocation (mMLDA). The critical distinguishing feature is the omission of any input or latent nodes representing partner-derived modalities. Specifically, NCM includes:

• Self action-intention (licking behavior): Encoded as an independent LDA module.
• Self reward counts: Represented as another standalone modality.
• Stimulus encoding: Derived from high-dimensional codebook counts of stimulus images via VQ-VAE.

No partner action, reward, or inferred subjective value enters any part of the model's graphical structure. All inferences regarding subjective value depend solely on the agent's own reward structure and task cues.

2. Generative Process and Probabilistic Structure

Within NCM, the generative process unfolds across two or more layers:

• Layer 1: Self action-intention and reward modalities are processed independently by their respective LDA modules.
• Layer 2: The self subjective-value node is inferred from these bottom-layer modules in conjunction with the stimulus modality.
• Joint Likelihood: For block $j$, the marginal probability is given by

$$p_j(\{w^m,z^m\}) = \prod_{m \in \{A_S, R_S, S\}} p(\theta^m_j) \prod_i p(z^m_{ij} \mid \theta^m_j) p(w^m_{ij} \mid z^m_{ij}, \phi^m)$$

Partner modalities are omitted, and the latent topic assignment is driven purely by self-referential data streams.

This structure ensures that the posterior over the self subjective-value node ($z^{R_S}$) is unaffected by partner outcomes or behavior.

3. Implementation Details and Inference Procedure

NCM, like the other comparison models, is implemented within the SERKET framework and utilizes a collapsed Gibbs sampler for posterior inference. Topic assignments within each modality are iteratively updated based on posterior count statistics, but the message-passing structure does not incorporate any signals except those pertaining to the self.

• Hyperparameters: Number of latent topics $K^* = 6$ (matching the six experimental conditions); Dirichlet priors ($\alpha^m$, $\beta^m$) are set to 1.0.
• Modality Weights: Bayesian optimization is used to tune modality weights to minimize the Kullback-Leibler divergence between predicted and observed self-licking frequencies, yielding a self-reward/action weight of 200 and stimulus weight of 300.

Each block (document) is updated for 100 iterations per module, with a total of 300 iterations for convergence.

4. Experimental Design and Evaluation Metrics

The comparative analysis of NCM centers on multi-session behavioral recordings from a pair of macaques performing reward-based social tasks:

• Data: 292 consecutive days, six pre-defined experimental conditions varying self and partner reward probabilities, and 40 trials per block.
• Feature Extraction: Stimuli encoded via VQ-VAE, reward vectors as $\{n_\text{rewarded}, n_\text{unrewarded}\}$, and licking as $\{n_\text{lick}, n_\text{no\_lick}\}$ after preprocessing.
• Performance Assessment: Subjective-value classification measured by the Rand Index (RI), where true cluster labels correspond to ground-truth experimental condition assignments.

5. Empirical Results and Comparative Context

Under held-out evaluation, NCM exhibits a Rand Index of 0.75, moderately above the chance level (0.72 for six equally frequent clusters), but below the IPM (0.79) and ECM (0.88). Table:

Model	Rand Index	Remarks
NCM	0.75	Self-only
IPM	0.79	Infers partner
ECM	0.88	Uses partner reward
Chance	0.72	Baseline

Key empirical findings:

• Licking Behavior Prediction: NCM reverses the behavioral trend in partner-variable blocks, indicating failure to capture reward context based on others.
• Topic Usage: NCM typically utilizes only 3/6 possible topics, indicating lower coherence with the experimental conditions compared to ECM and IPM.
• Information Flow: Normalized mutual information analysis demonstrates significantly lower efficiency in NCM for propagating social information to valuation nodes.

6. Significance and Limits of the NCM Approach

The NCM serves as a control, allowing isolation of model performance attributable solely to self-referential mechanisms. Its lower clustering accuracy and inability to replicate partner-sensitive behavioral trends highlight the significance of social information processing in primate reward evaluation. The fact that ECM, which directly incorporates partner reward as an observed modality, significantly surpasses NCM, substantiates the necessity of external comparison rather than purely internal value computation in the tested paradigm (Taniuchi et al., 21 Dec 2025).

It is plausible to infer that NCM—and related self-only generative models—are insufficient for capturing complex social cognitive phenomena where comparative reasoning or inference about others' states materially affects behavior.

7. Contextualization and Application

While the NCM is devised within the domain of social comparison in primate reward tasks, the underlying modeling principle—complete exclusion of external/social signals—can generalize to other domains where one wishes to benchmark the additive impact of social or external variables. In comparative modeling studies, NCM provides a baseline, quantifying the effect size associated with introducing partner- or other-centric modalities or latents.

Its use in the multilayered mMLDA/SERKET framework underscores a modular approach to latent structure construction, providing a pathway to systematically vary the degree of social information integration and empirically dissect model components. In broader cognitive modeling or machine learning applications, NCM-like architectures serve as minimal reference points against which more complex, context-aware models are assessed.