Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Emotion Collider: Dual Hyperbolic Mirror Manifolds for Sentiment Recovery via Anti Emotion Reflection

Rong Fu, Ziming Wang, Shuo Yin, Wenxin Zhang, Haiyun Wei, Kun Liu, Xianda Li, Zeli Su, Simon Fong

TL;DR

Results indicate that explicit hierarchical geometry combined with hypergraph fusion is effective for resilient multimodal affect understanding, particularly when modalities are partially available or contaminated by noise.

Abstract

Emotional expression underpins natural communication and effective human-computer interaction. We present Emotion Collider (EC-Net), a hyperbolic hypergraph framework for multimodal emotion and sentiment modeling. EC-Net represents modality hierarchies using Poincare-ball embeddings and performs fusion through a hypergraph mechanism that passes messages bidirectionally between nodes and hyperedges. To sharpen class separation, contrastive learning is formulated in hyperbolic space with decoupled radial and angular objectives. High-order semantic relations across time steps and modalities are preserved via adaptive hyperedge construction. Empirical results on standard multimodal emotion benchmarks show that EC-Net produces robust, semantically coherent representations and consistently improves accuracy, particularly when modalities are partially available or contaminated by noise. These findings indicate that explicit hierarchical geometry combined with hypergraph fusion is effective for resilient multimodal affect understanding.

Emotion Collider: Dual Hyperbolic Mirror Manifolds for Sentiment Recovery via Anti Emotion Reflection

TL;DR

Results indicate that explicit hierarchical geometry combined with hypergraph fusion is effective for resilient multimodal affect understanding, particularly when modalities are partially available or contaminated by noise.

Abstract

Emotional expression underpins natural communication and effective human-computer interaction. We present Emotion Collider (EC-Net), a hyperbolic hypergraph framework for multimodal emotion and sentiment modeling. EC-Net represents modality hierarchies using Poincare-ball embeddings and performs fusion through a hypergraph mechanism that passes messages bidirectionally between nodes and hyperedges. To sharpen class separation, contrastive learning is formulated in hyperbolic space with decoupled radial and angular objectives. High-order semantic relations across time steps and modalities are preserved via adaptive hyperedge construction. Empirical results on standard multimodal emotion benchmarks show that EC-Net produces robust, semantically coherent representations and consistently improves accuracy, particularly when modalities are partially available or contaminated by noise. These findings indicate that explicit hierarchical geometry combined with hypergraph fusion is effective for resilient multimodal affect understanding.
Paper Structure (43 sections, 1 theorem, 55 equations, 14 figures, 10 tables, 1 algorithm)

This paper contains 43 sections, 1 theorem, 55 equations, 14 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Hyperbolic representations for emotion and sentiment
  4. Multimodal fusion and learning with missing modalities
  5. Contrastive and representation learning in multimodal affective tasks
  6. Geometric and manifold-based methods
  7. Robustness, corruption and deception-related cues
  8. Theoretical advances and disentanglement
  9. EC-Net position
  10. Methodology
  11. Notation and manifold assumptions
  12. inter-curvature diffeomorphism
  13. Numerical safeguards for exponential map and clipping statistics
  14. Paired hyperbolic embeddings
  15. Differentiable Mirror Layer implemented as a learnable involution
  16. ...and 28 more sections

Key Result

Theorem A.1

Let $\mathcal{F}=\{x\mapsto d_{\mathrm{P}}(h_{E},f_{\psi}(g_{\phi}(h_{E}))) \mid \phi,\psi\in\Theta\}$ be the asymmetry-score hypothesis class defined on the Poincaré ball $\mathbb{B}_{c}^{n}$ of radius $1/\sqrt{c}$. Assume the following conditions hold. The learnable residuals are uniformly bounded and suppose $\gamma<1/\sqrt{c}$. Then for any i.i.d. sample $S$ of size $N\ge n$ and any $\delta\in

Figures (14)

  • Figure 1: Overview of the Emotion Collider (EC-Net) architecture for sentiment recovery. The framework projects multimodal features ($x^L, x^A, x^V$) into paired hyperbolic embeddings across the Emotion Manifold ($\mathcal{M}_E$) and the Anti-Emotion Manifold ($\mathcal{M}_A$), both modeled as Poincaré balls. A Differentiable Mirror Layer, realized as a learnable involution ($g_\phi, f_\psi$), facilitates bidirectional mapping between the dual manifolds while enforcing geometric consistency through Riemannian importance re-weighting. For recovery of missing modalities, the system utilizes mirror-space implicit score matching ($s_\theta$) to reconstruct the emotion vector field $\widehat{V}$ in the tangent space. Available and recovered embeddings are integrated via a SetTransformer-based fusion network to produce the final prediction $\hat{y}$. Additionally, the geometric discrepancy between the paired manifolds is captured as an asymmetry deception cue ($s_{\mathrm{asym}}$) for auxiliary task enhancement.
  • Figure 2: Radar summary across six missing patterns and three metrics (Acc2 / F1 / MAE). EC-Net shows consistent advantage.
  • Figure 3: Training trajectories for principal losses (mean across three seeds). Task loss, reconstruction loss, property-alignment loss and involution loss all decline stably.
  • Figure 4: Stacked bar plot showing Acc2 drops for each ablation across FIX and MR regimes.
  • Figure 5: Histogram of principal angles $\theta(\Sigma,\mu)$ after training (50 bins). The distribution concentrates near small angles (mean $\approx 3.8^\circ$).
  • ...and 9 more figures

Theorems & Definitions (2)

  • Theorem A.1
  • proof