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

Rong Fu; Ziming Wang; Shuo Yin; Kun Liu; Xianda Li; Simon Fong

cs.MMFeb 18, 2026

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

Authors: Rong Fu, Ziming Wang, Shuo Yin, Kun Liu, Xianda Li, Simon Fong

Organizations: Independent Researcher

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.

Figures & tables

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 $\approx 3.8^{\circ}$ ).

Figure 6: Single-factor hyperparameter scans showing Acc2 versus the swept factor. The default operating point is marked.

Figure 7: Heatmap of Acc2 as a function of curvature ratio and orthogonality penalty, revealing a stable plateau.

Figure 8: Training curve under 8 random seeds (shaded area = min/max envelope). The small envelope confirms stable convergence.

Figure 9: Two test samples with the highest geometric-asymmetry score $s_{\mathrm{asym}}$ . Input modalities, EC-Net prediction, ground-truth label. Large $s_{\mathrm{asym}}$ correlates with sentiment mismatch, illustrating the cue’s decision boundary.

Figure 10: Poincaré-disk scatter of randomly sampled emotion embeddings (1,000 points) colored by label; superimposed geodesics illustrate geometric separation.

Figure 11: Mirror-space t-SNE: left original $h_{E}$ , right mapped $f_{\psi}(g_{\phi}(h_{E}))$ ; gray lines connect corresponding points. Small cycle distances indicate good involution behaviour.

Figure 12: Corruption robustness: bars show performance under clean, light and heavy corruption conditions for several methods.

Figure 13: Peak GPU memory vs. Acc2 Pareto plot across batch sizes. EC-Net occupies a favourable memory-accuracy region.

Figure 14: Training curve with mean and 95% confidence band from three seeds. Low variance indicates stable training dynamics.

Method	CMU-MOSI					CMU-MOSEI
Method	Acc7	Acc2	F1	MAE $\downarrow$	Corr	Acc7	Acc2	F1	MAE $\downarrow$	Corr
HyCon [ 3 ]	46.6	85.2	85.1	0.741	0.779	52.8	85.4	85.6	0.554	0.751
UniMSE [ 34 ]	48.7	86.9	86.4	0.691	0.809	54.4	87.5	87.5	0.523	0.773
ConFEDE [ 35 ]	42.3	85.5	85.5	0.742	0.782	54.9	85.8	85.8	0.522	0.780
MGCL [ 36 ]	49.3	86.7	86.7	0.685	0.707	53.9	86.4	86.4	0.535	0.772
HyDiscGAN [ 37 ]	43.2	86.7	86.3	0.749	0.782	54.4	86.3	86.2	0.533	0.761

Table 1: CMU-MOSI [ 31 ] and CMU-MOSEI [ 32 ] full-modality comparison. Metrics: Acc7 (%), Acc2 (%), F1 (%), MAE (lower better), Corr. Best entries are bold . Mean

\pm

std over 3 runs.

Model	WA (%) $\uparrow$	UA (%) $\uparrow$
TwoStageFT [ 42 ]	74.9	76.1
AdaptiveMixup [ 43 ]	75.4	76.0
EmoAug [ 44 ]	72.7	73.8
MoMKE [ 45 ]	77.9	77.1
APIN [ 46 ]	77.8	78.2
IAM [ 47 ]	74.8	75.6

Table 2: IEMOCAP [ 33 ] full-modality comparison. WA: weighted accuracy; UA: unweighted accuracy. Best entries are bold . Mean

\pm

std over 3 runs.

Available	GCNet [ 50 ]	IMDer [ 51 ]	MoMKE [ 45 ]	LNLN [ 52 ]	EUAR [ 53 ]	CIDer [ 54 ]	EC-Net (ours)
{t}	83.7/83.6/42.3	84.8/84.7/44.8	86.2/86.1/38.1	84.9/84.7/45.1	86.0/86.0/46.1	83.7/83.6/41.3	90.0/90.0/50.0
{v}	56.1/55.7/16.9	61.3/60.8/22.2	54.1/53.7/17.0	52.2/58.9/18.8	64.9/64.9/23.6	57.8/42.3/15.5	68.5/68.5/24.5
{a}	56.1/54.5/16.6	62.0/62.2/22.0	59.3/59.0/18.4	52.2/58.9/18.0	63.0/62.3/23.2	57.8/43.2/15.2	69.0/69.0/25.0
{t,v}	84.3/84.2/43.4	85.5/85.4/45.3	86.5/86.4/37.5	84.3/84.6/44.6	86.2/86.2/45.5	83.8/83.8/42.1	91.0/91.0/51.5
{t,a}	84.3/84.2/43.4	85.4/85.3/45.0	86.5/86.4/38.6	84.9/85.2/45.1	86.1/86.1/44.7	83.8/83.8/41.7	91.5/91.5/52.0
{v,a}	62.0/61.9/17.2	63.6/63.4/23.8	59.6/59.6/20.1	52.2/58.9/18.8	66.1/65.8/24.2	57.8/44.0/15.5	70.5/70.5/26.0

Table 3: Fixed missing-modality results on CMU-MOSI [ 31 ] . Each cell reports Acc2 / F1 / Acc7. Column ‘Available’ indicates which modalities are available (t: text, a: audio, v: visual). Best results are bold . Mean

\pm

std over 3 runs.

Missing rate $\eta$	GCNet [ 50 ]	IMDer [ 51 ]	MoMKE [ 45 ]	LNLN [ 52 ]	EUAR [ 53 ]	CIDer [ 54 ]	EC-Net (ours)
0.1	82.4/82.2/41.9	83.3/83.2/43.0	83.6/83.6/35.5	81.1/82.0/42.0	84.1/84.1/43.8	81.1/79.6/39.4	90.0/90.0/48.5
0.2	79.6/79.3/38.9	80.9/80.8/40.7	80.7/80.7/33.7	78.0/79.5/39.5	81.9/81.9/41.5	78.5/75.6/36.7	87.5/87.5/46.5
0.3	76.7/76.5/35.9	78.5/78.4/38.4	77.8/77.7/31.9	74.8/77.0/36.9	79.8/79.7/39.2	76.0/71.6/34.0	85.5/85.5/44.5
0.4	73.6/73.2/33.0	76.0/75.9/36.0	74.7/74.6/29.8	71.6/74.4/34.3	77.4/77.3/36.9	73.4/67.4/31.2	83.0/83.0/41.5
0.5	70.4/69.9/30.1	73.5/73.4/33.6	71.6/71.4/27.8	68.4/71.8/31.7	75.1/74.9/34.7	70.8/63.3/28.5	80.5/80.5/38.8
0.6	67.3/66.7/27.2	71.0/70.9/31.2	68.5/68.3/25.8	65.2/69.2/29.0	72.8/72.6/32.5	68.2/59.1/25.8	78.0/78.0/36.5

Table 4: Varying global missing rate

\eta

on CMU-MOSI [ 31 ] . Each cell reports Acc2 / F1 / Acc7. Best results are bold . Mean

\pm

std over 3 runs.

Variant	FIX (Acc2 / F1 / Acc7)	MR (Acc2 / F1 / Acc7)
w/o property embedding pathway	76.5 / 76.3 / 33.0	79.2 / 79.0 / 37.8
w/o reconstruction module	77.7 / 77.5 / 34.8	80.4 / 80.3 / 39.1
w/o mirror involution	78.0 / 77.8 / 35.1	80.6 / 80.5 / 39.3
w/o fusion module	79.1 / 79.0 / 36.3	81.5 / 81.4 / 40.4
w/o property pathway + reconstruction	75.4 / 75.2 / 32.2	78.1 / 77.9 / 36.1
w/o all modules	73.6 / 73.4 / 30.5	76.3 / 76.1 / 33.0

Table 5: Ablation study of EC-Net on CMU-MOSI [ 31 ] . Each entry reports Acc2 / F1 / Acc7 for FIX and MR regimes. Best results are bold .

Condition	FIX	MR
With corruption	79.4 / 79.4 / 37.4	80.7 / 80.7 / 39.7
Clean (no corruption)	80.1 / 80.1 / 38.3	81.4 / 81.4 / 40.6

Table 6: Robustness to synthetic corruption on CMU-MOSI [ 31 ] (Acc2 / F1 / Acc7). Best results are bold .

Hyperparameter	Range	Acc2 (%)	Default	Significance
Curvature ratio ( $c_{E}/c_{A}$ )	[0.5, 2.0]	80.0–80.2	0.8	$p<0.01$
Orthogonal penalty ( $\lambda_{\mathrm{orth}}$ )	[0.05, 0.2]	79.8–80.3	0.1	$p<0.01$
Mask rate schedule	fixed vs anneal	$-1.3\%$	anneal	$p<0.01$
EWMA decay	[0.95, 0.999]	79.9–80.2	0.99	$p<0.01$
Gradient clip norm	[1.0, 5.0]	80.0–80.1	1.0	$p<0.01$
Mirror layer depth	[1, 3]	79.7–80.2	2	$p<0.01$

Table 7: Hyperparameter sensitivity analysis of EC-Net on CMU-MOSI. Each parameter is varied while keeping others at default values. Best results are bold .

Test Condition	$\Delta$ Acc2	Peak Memory (GB)	Notes
Batch size 128 $\rightarrow$ 64	$-0.4\%$	18 $\rightarrow$ 13.2	Minor performance change together with large memory reduction
Curvature ratio = 10	$-6.2\%$	—	Gradient explosion observed, motivates ratio clipping in practice
$\lambda_{\mathrm{orth}}=0.5$	$-0.7\%$	—	Excessive orthogonality harms representational capacity

Table 8: Extreme stress testing summary for EC-Net. Peak memory is reported where applicable.

Method	Spearman $\rho$	$p$ -value	Sample size	Detection accuracy (%)
Random baseline	0.00	$>0.05$	2560	50.2
Logistic regression baseline	0.18	$<0.05$	2560	58.7
MGCL	0.35	$<0.01$	2560	63.4
IMDer	0.38	$<0.01$	2560	65.1
EC-Net ( $s_{\mathrm{asym}}$ )	0.44	$<0.001$	2560	68.9

Table 9: Analysis of asymmetry deception cue

s_{\mathrm{asym}}

correlation with human deception labels. Best results are bold .

Metric	Value
Trainable Parameters	27.6M (8.9M MLPs, 18.7M SetTransformer)
FLOPs per Forward Pass	2.3 GFLOPs (all modalities), 1.8 GFLOPs (30% masking)
Inference Throughput	312 FPS (batch=1), 389 FPS (batch=64)
Latency per Sample	$<$ 2.6 ms (batch=64)
Peak Memory Footprint	22.1 GB (batch=128), 13.2 GB (batch=64)
Training Time	3.2 min per epoch (CMU-MOSI), $\approx$ 2.7 hours for 50 epochs

Table 10: Complexity Analysis of EC-Net on RTX-3090

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GeoMER: A Joint Euclidean-Hyperbolic Geometry Framework for Multimodal Emotion Recognition

Ting Zhu, Huizhi Liang, Boguslaw Obara, Shufei Duan+1

Newcastle University, Newcastle upon Tyne, United Kingdom · Taiyuan University of Technology, Shanxi, China

Multimodal Emotion Recognition Multimodal Fusion Geometric Representation Learning Hierarchical Representation Learning Hyperbolic Representation Learning

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Multimodal Emotion Recognition (MER) aims to understand human emotions by integrating information from multiple modalities such as speech and text. Psychological studies suggest that emotions exhibit latent hierarchical structured relationships in their semantic representations. However, most MER approaches rely on Euclidean representations, which capture fine-grained cross-modal interactions but do not explicitly provide a geometric prior for organizing hierarchical emotional structures. To mitigate this gap, we propose GeoMER, a joint Euclidean-Hyperbolic modeling framework that introduces hyperbolic emotion-core routing to capture higher-level, abstract emotional representations for MER. The proposed framework jointly models token-level cross-modal semantic interactions and latent emotion representations in two complementary geometric spaces. Specifically, GeoMER consists of a Euclidean Multimodal Fusion Module (EuclFusion) for multimodal representation fusion and a Hyperbolic Geometric Core Routing (HypGeoRoute) module that performs geometry-aware core assignment and aggregation in a hyperbolic manifold to capture more abstract feature representations. The HypGeoRoute module complements the Euclidean token-level modeling. We experiment on the IEMOCAP multimodal MER benchmark and demonstrate that the proposed method achieves the best performance, with 83.54% weighted accuracy and 83.35% unweighted accuracy, outperforming Euclidean baselines, including MemoCMT.

Abstract

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