Character Identity in AI and Mathematics

• Character identity is a multidimensional concept that defines distinct, persistent traits via fixed latent embeddings and algebraic formulations.
• It integrates practical generative approaches—such as disentanglement and self-supervised re-identification—with formal mathematical constructs to ensure fidelity.
• Applications span computer vision, role-playing systems, and mathematical physics, enabling consistent, character-specific outputs and improved re-identification techniques.

Character identity is a multidimensional concept central to the representation, preservation, and manipulation of individual or agent-specific properties in computer vision, language modeling, role-playing systems, generative models, animation, and mathematical physics. It encompasses both formal algebraic constructions (e.g., character identities in group theory and vertex operator algebras), and practical algorithmic techniques for maintaining consistent character representations across tasks such as video generation, role-playing dialogue, or re-identification in comics and documents.

1. Formal Definitions and Representations

Character identity, across modalities, refers to the stable, unique set of properties or embeddings that define a character as distinct from others. In generative frameworks (e.g., FairyGen (Zheng et al., 26 Jun 2025), CharCom (Wang et al., 11 Oct 2025), IdentityStory (Zhou et al., 29 Dec 2025)), identity is typically encoded as a fixed vector in a latent embedding space—e.g., $z_\text{id}\in\mathbb{R}^d$ parameterizing facial shape, color, and style. In language modeling, identity may be stratified into parametric and attributive layers: Parametric identity refers to character-specific knowledge resident in model weights, while attributive identity comprises explicit persona prompts (traits, values, background) provided in a structured schema (e.g., a 38-field JSON profile in Jun et al. (Jun et al., 8 Jan 2026)).

Mathematically, character identity in representation theory is instantiated via character functions $\chi_\lambda$, which encode traces of representations; their combinatorial and algebraic identities (e.g., Giambelli, Kac–Weyl) articulate deep structure among classes of modules, fusion rules, or conformal field theory vacuum sectors (Matsuno et al., 2016, Baker et al., 2024, Adamović et al., 25 Nov 2025, Bantay, 2016).

2. Disentanglement and Identity Control in Generative Models

Recent generative systems separate identity modeling from context or motion to enforce persistent character fidelity across scenes and time. In FairyGen, character identity is disentangled via:

• A style-propagation adapter, learning the child's unique artistic style (brushstroke, palette, line thickness) from masked tokens and transferring it to synthetic backgrounds through masked LoRA updates:

$y = W x + PA(x \odot m)$

• A two-stage motion customization adapter, freezing identity parameters after shuffling frame order, and injecting motion dynamics via separate LoRA modules trained on unshuffled sequences:

$$y = W x + A_\text{id}(B_\text{id} x) + A_\text{motion}(B_\text{motion} x)$$

In CharCom, identity is maintained via modular per-character LoRA adapters composed by relevance-weighted prompt-aware networks, achieving robust multi-character consistency without backbone retraining:

$W_Q^\star = W_Q^0 + \sum_{c\in S} w_c\,B_c A_c$

In multi-character video (EverybodyDance (Ling et al., 18 Dec 2025)), identity correspondence (IC) is formalized via a bipartite matching graph optimizing for maximal affinity between ground-truth reference and generated nodes through Mask-Query Attention operations:

$$\mathcal{C} = \frac{\sum_{(r_i,g_j)\in\mathcal{M}^*} w(r_i,g_j)} {\sum_{(r_i,g_j)\in E} w(r_i,g_j)}$$

and a matching loss $-\frac{1}{N}\sum_\ell \mathcal{C}^{(\ell)}$ combined with the standard diffusion objective.

3. Identity Drift, Self-Supervision, and Quantitative Metrics

Identity drift denotes the tendency of autoregressive or temporally extended generative models to lose fidelity to initial character appearance over time, especially in video or audio-driven animation. Lookahead Anchoring (Seo et al., 27 Oct 2025) mitigates this by conditioning each generated segment not on a static keyframe at its boundary, but on a lookahead anchor lying in the future window, typically the reference image itself. The temporal lookahead hyperparameter $D$ directly controls the trade-off between expressivity and strict identity adherence.

Self-supervised learning schemes for character re-identification (e.g., in comics (Soykan et al., 2023) or OCR (Mothes et al., 2019)) leverage paired modalities (face and body crops), contrastive identity-aware losses, and bootstrapping with pseudo-labels to build parameter-efficient encoders that robustly extract character embeddings:

• Identity-aware SSL loss:

$$\mathcal{L}_{SSL} = \sum_{i<j}(L^f_{ij} + L^b_{ij} + L^{id}_{ij})$$

• Semi-supervised metric learning with Triplet-Margin and Multi-Similarity miners.

Quantitative assessment of identity preservation utilizes:

• CLIP-L2/ArcFace/DINO similarity scores for style and face alignment.
• Motion and subject consistency (VBench, ICE-bench) for temporal coherence.

4. Hierarchical and Modular Identity Composition in LLMs

In LLM-based role-playing agents, identity is not monolithic but hierarchically composable (e.g., HIRPF (Sun et al., 2024)). Agent identity comprises multiple levels (personality traits, professions, etc.), each represented by isolated LoRA modules:

$$W_j = W_0 + \sum_{k=1}^{K_{\ell(j)}} w_{jk} (B_{i_k} A_{i_k})$$

Gating and hard-masking ensure precise activation and isolation across levels. Explicit multi-dimensional profiles afford fine-grained control, enabling dynamic simulation of social, occupational, and trait-driven behaviors.

Model performance in simulating identity-level role coherence is evaluated using scale scores (e.g., BFI-1003 for Big-Five traits, field annotation accuracy), open-situation tests with human/LLM judges, and consistency metrics:

$$S_{\text{id}} = \frac{1}{|\mathcal Q|}\sum_{q\in\mathcal Q} \mathbf{1}(\text{agent response matches identity})$$

5. Algebraic Character Identities and Their Mathematical Impact

In mathematical physics and representation theory, character identities encapsulate fundamental structural relations among modules:

• The Giambelli identity expresses the Schur character of any Young diagram as a determinant over hook characters (Matsuno et al., 2016):

$$s_{(a_1,\dots,a_r|l_1,\dots,l_r)}(x) = \det_{1\leq i,j\leq r} s_{(a_i|l_j)}(x)$$

This determinant structure holds upon matrix integration in Chern-Simons models (supermatrix averages, fractional brane backgrounds).

• Fusion identities (Kac–Weyl (Baker et al., 2024)) relate sums of shifted characters to fusion coefficients:

$$\sum_{r\in\Omega_{\mu}}\chi_{r+\nu}(k,\tau,u) = \sum_{\iota} N_{\mu\nu}^{\iota} \chi_{\iota}(k,\tau,u)$$

• Vertex operator algebra (VOA) identities match affine and Virasoro module characters under explicit substitutions, inducing correspondences between fusion rings, Schur indices, and categorically Galois conjugate representation categories (Adamović et al., 25 Nov 2025):

$$\chi_{L_{-2+q/p}(\mathfrak{sl}_2),\mu_{r,s}}(q^{-1/2},q^3) = \chi_{L_\mathrm{Vir}(c_{q,3p},h_{r+1,3s+1}^{q,3p})}(q)$$

These identities underlie core results in modular tensor categories, conformal field theory, and the Langlands program (Hochs et al., 2017, Peng, 22 Jun 2025).

6. Applications, Limitations, and Multidisciplinary Significance

Character identity is fundamental in diverse applications:

• Story illustration and animation (CharCom, FairyGen, Character Mixing, EverybodyDance).
• Document OCR for identity recognition (ID bootstrapping).
• Role-playing in conversational AI/LLMs (HIRPF, Jun et al.).
• Physics (representation theory, fusion rules).
• Game design as a conduit for transcendent value models (Seaborn, 2023).

Persistent bottlenecks include cross-character interference in crowded scenes, attention bottlenecks for peripheral identities, and inability of LLMs to maintain non-default personality or morality traits unless foregrounded in prompts. Theoretical developments (e.g., prompt-aware adapter composition, explicit graph-based objective functions) continue to improve both scalabilities and fidelity.

7. Tables and Quantitative Metrics for Character Identity Evaluation

Model/System	Main Identity Metric(s)	Best Score(s)	Reference
FairyGen	CLIP-L2 style distance, motion smoothness	0.6580 (style), 0.987/0.955 (motion)	(Zheng et al., 26 Jun 2025)
CharCom	Identity Score (IS), ICS, T-ICSₑₘb	4.63 (IS), 0.8742 (T-ICSₑₘb)	(Wang et al., 11 Oct 2025)
IdentityStory	ArcFace Face-Sim, CLIP-T	55.5% (Face-Sim), 35.4% (CLIP-T)	(Zhou et al., 29 Dec 2025)
EverybodyDance	IC consistency $\mathcal{C}$, SSIM, FVD	0.654 (SSIM), 225 (FVD)	(Ling et al., 18 Dec 2025)
HIRPF	$S_\mathrm{id}$, $C_\mathrm{role}$	60.59%–27.60% across traits/profs.	(Sun et al., 2024)
Comic re-id (SSL)	Top-1 accuracy (face+body, aligned)	97%	(Soykan et al., 2023)

Quantitative and qualitative evaluation protocols, explicit identity-recording schemes, and adaptive architectures underpin both advances and measurement standards for character identity fidelity.

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In summary, character identity is a rigorously defined, algebraically and algorithmically controlled property central to consistent agent behavior, person re-identification, role simulation, and structure-preserving generative modeling—anchored in both abstract mathematical identities and high-performing neural architectures.