MM-Spectrum: Multimodal Multi-spectral Molecular Structural Elucidation with a Stable MoE Framework

Hai-tao Yu; Nan Min; Zheng Fang; Hongyu Zhan; Yusen Tan; Yuhan Wang; Jun Xia

cs.LGAug 27, 2026

MM-Spectrum: Multimodal Multi-spectral Molecular Structural Elucidation with a Stable MoE Framework

Authors: Hai-tao Yu, Nan Min, Zheng Fang, Hongyu Zhan, Yusen Tan, Yuhan Wang, Jun Xia

Organizations: The Hong Kong University of Science and Technology (Guangzhou) · Southeast University · The Hong Kong University of Science and Technology · Fudan University

Abstract

Inferring molecular structures from multimodal spectroscopic measurements requires integrating complementary yet highly heterogeneous signals. However, the common paradigm of directly concatenating multispectral sequences can exhibit anomalous performance degradation, primarily due to pronounced heterogeneity and the resulting multimodal imbalance across modalities. As a remedy, we propose MM-Spectrum, a sparse Mixture-of-Experts framework tailored for multimodal multispectral spectra-to-structure elucidation. To better match the information characteristics under multispectral imbalance, MM-Spectrum introduces an explicit modality-aware routing mechanism that exposes spectral identity to the router in addition to token content representations. Moreover, it incorporates shared and interaction experts, together with heterogeneous expert capacities, to extract multispectral modality-unique and cross-modal synergistic information while suppressing noise-induced interference. Across full-modality, bimodal, and missing-modality settings on molecular structural elucidation, MM-Spectrum achieves consistent and substantial improvements, supported by ablation studies and interpretability analyses.

Figures & tables

Panel of Figure 1 — Figure 1: The Challenge of Multispectral Elucidation: Mechanism and Consequence. In contrast, MM-Spectrum resolves this imbalance, effectively utilizing all modalities to achieve state-of-the-art performance.

Figure 2: MM-Spectrum overview: PID-guided information decoupling with structured MoE and curriculum scheduling. We formulate multimodal spectra-to-structure generation as an end-to-end encoder–decoder task, where each modality is tokenized with explicit Modality Tags . The encoder block follows LayerNorm $\rightarrow$ MHSA $\rightarrow$ Structured MoE $\rightarrow$ LayerNorm, where an interaction-aware gating mechanism leverages modality tags to route tokens into a structured expert assembly .

Figure 3: Decomposition of multimodal spectral information. The diagram enumerates modality subsets (single, pairwise, and all-modal combinations) and associates them with the dominant information type (unique vs. synergistic vs. redundant).

Figure 4: Channelized modality-aware routing aligned with redundancy/unique/synergy pathways. A modality-aware gating network consumes modality-conditioned representations (e.g., NMR/IR/MS embeddings) and produces routing distributions.

Figure 5: Computation-aware regularization with heterogeneous experts: allocating expensive capacity to high-utility tokens. MM-Spectrum instantiates an explicit cost–utility principle in conditional computation. This mechanism prevents long, low-density modalities from monopolizing compute, while preserving the ability to allocate high-capacity processing to decision-critical evidence, improving both stability and full-modality performance.

Single-modality
Modality Setting	Top-K Accuracy (%)
Modality Setting	Top-1%	Top-2%	Top-3%	Top-4%	Top-5%	Top-6%	Top-7%	Top-8%	Top-9%	Top-10%
NMR (1H + 13C)	69.83 $\pm$ 0.24	77.88 $\pm$ 0.16	80.86 $\pm$ 0.11	82.38 $\pm$ 0.38	83.35 $\pm$ 0.29	84.03 $\pm$ 0.34	84.52 $\pm$ 0.26	84.89 $\pm$ 0.32	85.08 $\pm$ 0.46	85.18 $\pm$ 0.12
MS (all MS spectra)	17.35 $\pm$ 0.30	23.82 $\pm$ 0.22	27.80 $\pm$ 0.41	30.08 $\pm$ 0.29	31.73 $\pm$ 0.15	32.90 $\pm$ 0.18	33.81 $\pm$ 0.40	34.52 $\pm$ 0.46	35.04 $\pm$ 0.17	35.31 $\pm$ 0.35
IR (binned spectrum)	23.22 $\pm$ 0.47	30.90 $\pm$ 0.42	35.01 $\pm$ 0.17	37.65 $\pm$ 0.14	39.44 $\pm$ 0.27	40.72 $\pm$ 0.21	41.73 $\pm$ 0.22	42.44 $\pm$ 0.29	42.88 $\pm$ 0.21	43.07 $\pm$ 0.19
Dual-modality

Table 1: Modality-combination study. Top-

K

SMILES elucidation accuracy (%) under single-modality, bimodal, and full-modality.

Setting	Missing ratio			Baseline			MM-Spectrum			Improvement
Setting	NMR	MS	IR	Top-1%	Top-5%	Top-10%	Top-1%	Top-5%	Top-10%	Top-1%	Top-5%	Top-10%
S0	0.0	0.0	0.0	44.29 $\pm$ 0.50	59.39 $\pm$ 0.17	62.04 $\pm$ 0.44	76.04 $\pm$ 0.18	87.83 $\pm$ 0.28	90.26 $\pm$ 0.16	31.75 $\pm$ 0.49	28.44 $\pm$ 0.34	28.22 $\pm$ 0.41
S1	0.1	0.1	0.1	33.42 $\pm$ 0.45	44.79 $\pm$ 0.47	46.80 $\pm$ 0.49	65.01 $\pm$ 0.47	75.11 $\pm$ 0.37	76.43 $\pm$ 0.19	31.59 $\pm$ 0.30	30.33 $\pm$ 0.37	29.63 $\pm$ 0.17
S2	0.3	0.3	0.3	17.29 $\pm$ 0.12	23.24 $\pm$ 0.10	24.31 $\pm$ 0.37	45.91 $\pm$ 0.26	54.21 $\pm$ 0.17	55.40 $\pm$ 0.19	28.62 $\pm$ 0.33	30.97 $\pm$ 0.16	31.09 $\pm$ 0.44
S3	0.6	0.6	0.6	4.28 $\pm$ 0.14	5.77 $\pm$ 0.24	6.05 $\pm$ 0.48	21.38 $\pm$ 0.41	26.20 $\pm$ 0.42	27.04 $\pm$ 0.46	17.10 $\pm$ 0.32	20.42 $\pm$ 0.47	21.00 $\pm$ 0.34
S4	0.6	0.1	0.1	14.88 $\pm$ 0.46	20.02 $\pm$ 0.17	20.94 $\pm$ 0.17	28.96 $\pm$ 0.47	33.47 $\pm$ 0.21	34.02 $\pm$ 0.29	14.09 $\pm$ 0.40	13.44 $\pm$ 0.47	13.09 $\pm$ 0.28

Table 2: Missing-modality robustness. Top-

K

accuracy (%) under test-time missing-modality settings (S0–S6).

Bucket	HAC range	#Samples	Baseline			MM-Spectrum			Improvement
Bucket	HAC range	#Samples	Top-1%	Top-5%	Top-10%	Top-1%	Top-5%	Top-10%	Top-1%	Top-5%	Top-10%
HAC_S (Small)	$\leq 15$	14821	63.46 $\pm$ 0.22	78.48 $\pm$ 0.37	81.44 $\pm$ 0.28	82.28 $\pm$ 0.42	91.30 $\pm$ 0.35	92.45 $\pm$ 0.32	18.82 $\pm$ 0.30	12.82 $\pm$ 0.38	11.01 $\pm$ 0.12
HAC_M (Medium)	16–25	35985	46.89 $\pm$ 0.29	63.16 $\pm$ 0.16	66.04 $\pm$ 0.39	77.52 $\pm$ 0.32	88.03 $\pm$ 0.37	89.19 $\pm$ 0.44	30.63 $\pm$ 0.34	24.87 $\pm$ 0.25	23.15 $\pm$ 0.32
HAC_L (Large)	$\geq 26$	28635	29.93 $\pm$ 0.35	43.56 $\pm$ 0.35	46.48 $\pm$ 0.45	69.44 $\pm$ 0.29	81.50 $\pm$ 0.23	82.86 $\pm$ 0.38	39.51 $\pm$ 0.31	37.94 $\pm$ 0.33	36.38 $\pm$ 0.16

Table 3: Stratified evaluation by molecular complexity. Top-

K

accuracy (%) across Heavy Atom Count (HAC) bins. MM-Spectrum yields larger relative improvements on more complex molecules.

Protocol	Setting	Top-K Accuracy (%)
Protocol	Setting	Top-1%	Top-5%	Top-10%
Scratch	NMR	18.15 $\pm$ 0.31	31.74 $\pm$ 0.25	33.69 $\pm$ 0.42
	MS	5.38 $\pm$ 0.18	11.07 $\pm$ 0.22	13.92 $\pm$ 0.15
	IR	13.21 $\pm$ 0.29	25.48 $\pm$ 0.34	26.61 $\pm$ 0.27
	Baseline (Full)	14.10 $\pm$ 0.33	27.13 $\pm$ 0.41	31.53 $\pm$ 0.38
	Ours (Full)	26.67 $\pm$ 0.24	38.91 $\pm$ 0.19	47.37 $\pm$ 0.26

Table 4: Generalization to real-world experimental spectra. Top-

K

SMILES elucidation accuracy (%) on the SDBS database under from-scratch and pre-training & fine-tuning (FT) protocols.

Figure 6: Representation evolution over training. Dense concatenation (top row) vs. MM-Spectrum (bottom row) at multiple training steps. MM-Spectrum exhibits more coherent and stable structure in the learned representation space, consistent with reduced cross-modal interference.

Figure 7: Layer-wise expert utilization. 100% stacked bar charts of Top- $1$ expert fractions per layer. Different layers display distinct utilization profiles, indicating layer-dependent specialization rather than trivial collapse or uniform routing.

Figure 8: Routing dynamics (Layer $\times$ Expert heatmaps). Top- $1$ expert occupancy across layers at multiple training steps. The routing pattern transitions from early exploration to structured specialization and stabilizes at later stages, providing direct evidence of emergent expert division of labor.

Router-aware	Tag-routing	Top-K Accuracy (%)
Router-aware	Tag-routing	Top-1%	Top-5%	Top-10%
$\boldsymbol{\checkmark}$	$\boldsymbol{\checkmark}$	76.04 $\pm$ 0.20	87.83 $\pm$ 0.39	90.26 $\pm$ 0.13
$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	72.57 $\pm$ 0.26	86.39 $\pm$ 0.48	88.93 $\pm$ 0.39
$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	71.23 $\pm$ 0.25	86.06 $\pm$ 0.16	88.83 $\pm$ 0.15
$\boldsymbol{\times}$	$\boldsymbol{\times}$	70.11 $\pm$ 0.30	84.43 $\pm$ 0.31	86.06 $\pm$ 0.34

Table 5: Ablation: routing signals. Impact of Router-aware signals and Tag routing on Top-

K

accuracy (%).

Shared	Interaction	Dynamic	Top-K Accuracy (%)
Shared	Interaction	Dynamic	Top-1%	Top-5%	Top-10%
$\boldsymbol{\checkmark}$	$\boldsymbol{\checkmark}$	$\boldsymbol{\checkmark}$	76.04 $\pm$ 0.15	87.83 $\pm$ 0.32	90.26 $\pm$ 0.21
$\boldsymbol{\checkmark}$	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	74.41 $\pm$ 0.28	86.54 $\pm$ 0.41	88.83 $\pm$ 0.19
$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	74.39 $\pm$ 0.35	86.34 $\pm$ 0.22	88.63 $\pm$ 0.45
$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	$\boldsymbol{\checkmark}$	75.01 $\pm$ 0.12	86.90 $\pm$ 0.33	89.20 $\pm$ 0.27
$\boldsymbol{\times}$	$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	72.70 $\pm$ 0.40	84.65 $\pm$ 0.18	87.05 $\pm$ 0.36

Table 6: Ablation: expert subspaces and dynamic activation. Effects of Shared experts, Interaction experts, and Dynamic activation on Top-

K

accuracy (%).

Hetero.	Regularizer	Top-K Accuracy (%)
Hetero.	Regularizer	Top-1%	Top-5%	Top-10%
$\boldsymbol{\checkmark}$	$\boldsymbol{\checkmark}$	76.04 $\pm$ 0.14	87.83 $\pm$ 0.29	90.26 $\pm$ 0.18
$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	74.81 $\pm$ 0.35	86.61 $\pm$ 0.22	89.21 $\pm$ 0.41
$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	74.07 $\pm$ 0.19	85.93 $\pm$ 0.38	88.65 $\pm$ 0.26
$\boldsymbol{\times}$	$\boldsymbol{\times}$	74.24 $\pm$ 0.44	86.08 $\pm$ 0.15	88.65 $\pm$ 0.32

Table 7: Ablation: heterogeneous experts and regularization. Effects of heterogeneous capacities (Hetero) and computation-aware regularization on Top-

K

accuracy (%).

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 9: Visualizing the mechanism of failure versus the mechanism of synergy. (a) The Pathology of Naive Concatenation: Treating heterogeneous signals (NMR/IR/MS) as a uniform sequence leads to Modality Collapse . The shared parameter space succumbs to gradient conflicts (visualized as “Internal Chaos”), where high-redundancy modalities overwhelm high-density constraints, resulting in entangled representations and distorted molecular predictions. (b) The Solution via MM-Spectrum: We resolve this by introducing a Structured MoE Encoder . Through a modality-aware gating mechanism $G(x)$ , the model dynamically disentangles information flows by routing tokens to functionally specialized modules—allocating Heavy Experts for complex topology inference and Light Experts for noise filtering—thereby restoring optimization stability and generation precision.

Modality	Token type	Compression $\phi_{m}$	Max length
NMR ( 1 H/ 13 C)	symbolic / constraint-rich	identity / conservative parsing	$L_{\max}^{\mathrm{NMR}}$
IR	dense / autocorrelated	local binning / aggregation	$L_{\max}^{\mathrm{IR}}$
MS	sparse peaks + noise tail	top- $k$ peak filtering	$L_{\max}^{\mathrm{MS}}$

Appendix

Table 8: Modality preprocessing and sequence configuration (illustrative). Operators are chosen to reduce redundancy while preserving chemically critical evidence.

Hyperparameter	Value
#experts $E$	8
Top- $k$	2
Capacity factor $C$	1.25
Aux losses	$\mathcal{L}_{\mathrm{bal}},\mathcal{L}_{\mathrm{ent}},\mathcal{L}_{\mathrm{cost}}$
Schedules	$\lambda(t)$ (cosine), $\tau(t)$ (exp or cosine)
Expert families	shared / modality-specific / interaction

Appendix

Table 9: Key MoE hyperparameters.

Panel of Figure 10 — Figure 10: Routing Evolution Dashboard. The top panel shows routing Uniformity (Entropy $H$ ), while the bottom panel shows Imbalance (Max/Mean load). Observation: A clear phase transition is visible at the end of the warmup. Imbalance drops initially (Coverage Phase) and then stabilizes at a non-zero level, indicating that the router has moved from ”random exploration” to ”structured specialization” rather than collapsing to a trivial solution.

Category	Parameter	Value
Backbone	Model Architecture	Transformer Encoder-Decoder
	Layers ( $L$ )	6 (Encoder) / 6 (Decoder)
	Hidden Dimension ( $d_{\text{model}}$ )	512
	Attention Heads ( $H$ )	8
	Feed-Forward Dimension	2048 (in non-MoE layers)
MM-Spectrum MoE	Total Experts ( $E$ )	8 (Partitioned: 2 Shared, 2 NMR, 2 IR/MS, 2 Interact)

Appendix

Table 10: Complete Hyperparameter Configuration. The settings cover model architecture, the specific MM-Spectrum MoE design, data preprocessing constraints, and optimization details.

Method	Top-1%	Top-5%	Top-10%
Dense Concatenation ( Alberts et al., 2024 )	44.29 $\pm$ 0.35	59.39 $\pm$ 0.31	62.04 $\pm$ 0.47
Cross-Attention Fusion	42.15 $\pm$ 0.41	56.45 $\pm$ 0.38	61.91 $\pm$ 0.52
Contrastive Alignment ( Liang et al., 2024 )	39.01 $\pm$ 0.28	52.74 $\pm$ 0.44	57.06 $\pm$ 0.39
OGM-GE ( Wu et al., 2022 )	44.87 $\pm$ 0.30	60.93 $\pm$ 0.27	63.32 $\pm$ 0.41
PCGrad ( Yu et al., 2020 )	44.73 $\pm$ 0.34	61.24 $\pm$ 0.49	64.92 $\pm$ 0.36
Gradient Blending ( Wang et al., 2020 )	46.78 $\pm$ 0.25	63.45 $\pm$ 0.33	67.82 $\pm$ 0.45

Appendix

Table 11: Comparison with alternative fusion baselines. Evaluation of Top-

K

SMILES elucidation accuracy (%) under full tri-modality inputs on the canonical benchmark dataset.

Modality Configuration	Method	Top-1%	Top-5%	Top-10%
NMR-only ( 1 H + 13 C)	Dense Baseline	79.41 $\pm$ 0.16	89.45 $\pm$ 0.22	94.71 $\pm$ 0.11
MS-only	Dense Baseline	25.13 $\pm$ 0.42	28.42 $\pm$ 0.35	31.28 $\pm$ 0.51
IR-only	Dense Baseline	19.35 $\pm$ 0.38	23.60 $\pm$ 0.29	27.04 $\pm$ 0.34
Full-Modality Concatenation	Dense Baseline	65.71 $\pm$ 0.50	85.07 $\pm$ 0.34	89.02 $\pm$ 0.46
Full-Modality (Ours)	MM-Spectrum	87.35 $\pm$ 0.19	95.87 $\pm$ 0.14	98.72 $\pm$ 0.12

Appendix

Table 12: SMILES elucidation performance on the large-scale MMST dataset. All models are trained from scratch directly on the simulated data splits.

Omitted Modality Channel	Method	Top-1%	Top-5%	Top-10%
Mass Spectrometry (MS) Removed	Dense Baseline	25.71 $\pm$ 0.49	28.52 $\pm$ 0.36	30.84 $\pm$ 0.41
Mass Spectrometry (MS) Removed	MM-Spectrum	73.94 $\pm$ 0.22	86.12 $\pm$ 0.15	88.47 $\pm$ 0.18
Infrared (IR) Removed	Dense Baseline	31.52 $\pm$ 0.38	35.78 $\pm$ 0.42	37.79 $\pm$ 0.35
Infrared (IR) Removed	MM-Spectrum	74.81 $\pm$ 0.17	86.79 $\pm$ 0.20	89.05 $\pm$ 0.24
Nuclear Magnetic Resonance (NMR) Removed	Dense Baseline	18.65 $\pm$ 0.52	20.46 $\pm$ 0.47	23.17 $\pm$ 0.55
Nuclear Magnetic Resonance (NMR) Removed	MM-Spectrum	39.24 $\pm$ 0.31	59.36 $\pm$ 0.28	63.41 $\pm$ 0.39

Appendix

Table 13: Inference evaluation under the complete absence of a single modality. Models are optimized on full modalities and evaluated with one modality entirely omitted at test time.

$E$	Top-1 $\uparrow$	Top-3 $\uparrow$	Top-5 $\uparrow$	Top-10 $\uparrow$	Latency $\downarrow$	Throughput $\uparrow$
2	73.15	85.02	87.10	89.05	19.8 ms	50.2 s/sample
4	74.82	86.95	88.45	90.12	20.1 ms	49.5 s/sample
8	76.04	87.83	90.26	91.80	21.3 ms	46.8 s/sample
16	75.88	87.60	90.15	91.75	24.5 ms	40.5 s/sample

Appendix

Table 14: Sensitivity to the number of experts

E

(Top-

k=2

). We fix Top-

k=2

and vary the expert pool size. Best values are bold. The results show a consistent improvement from small

E

to a moderate regime, with performance saturating (or slightly degrading) when

E

becomes too large due to routing dilution. This supports our choice of

E=8

as the default setting.

Top- $k$	Top-1 $\uparrow$	Top-3 $\uparrow$	Top-5 $\uparrow$	Top-10 $\uparrow$	Latency $\downarrow$	Throughput $\uparrow$	Activated Cost $\downarrow$
1	73.50	85.20	87.35	89.20	13.5 ms	74.0 s/sample	1.0 $\times$
2	76.04	87.83	90.26	91.80	21.3 ms	46.8 s/sample	2.0 $\times$
4	76.12	87.85	90.30	91.85	38.6 ms	25.8 s/sample	4.0 $\times$

Appendix

Table 15: Sensitivity to Top-

k

routing (fix

E=8

). We fix

E=8

and vary Top-

k

. Best trade-off is achieved at Top-

k=2

. Top-

k=1

limits expert composition capacity, while larger

k

increases compute and routing congestion without commensurate accuracy gains.

Model	Top-1 $\uparrow$	Top-10 $\uparrow$	#Params $\downarrow$	#Active Params $\downarrow$	Throughput $\uparrow$	Peak Mem. $\downarrow$	Latency $\downarrow$
Dense (Concat)	44.29	62.04	110M	110M	4,850 tok/s	16.5 GB	18.2 ms
MM-Spectrum (MoE, Top- $k$ =2)	76.04	90.26	450M	135M	4,210 tok/s	22.4 GB	21.3 ms

Appendix

Table 16: Resource consumption and efficiency comparison. MM-Spectrum achieves significantly better accuracy while maintaining a favorable compute/memory profile compared to the Dense concatenation baseline. Note that while Total Parameters increase due to the expert pool, the Active Parameters (computational cost) remain comparable.

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