Intermediate Fusion Strategy

Updated 5 December 2025

Intermediate fusion is a strategy that combines modality-specific encoded features at intermediate network layers, capturing rich cross-modal interactions.
It provides a balanced trade-off between semantic fidelity and computational efficiency, outperforming early and late fusion approaches in diverse applications.
The approach employs operations like concatenation, attention, and calibration, with implementations in biomedical analytics, vision-language systems, autonomous vehicles, and distributed computing.

Intermediate fusion is a strategy for combining multiple streams or modalities of information at the level of learned feature representations within a deep architecture, rather than at the raw input (early fusion) or final output (late fusion) stages. This approach enables modality-specific encoders to first extract semantically rich features, which are then fused at one or more intermediate layers to capture cross-modal or cross-module interactions. Intermediate fusion has become central in multimodal deep learning, collaborative perception systems, code optimization, and model merging, as it affords a trade-off between information fidelity, computational efficiency, and communication overhead. Properly designed, intermediate fusion architectures can outperform both early and late fusion baselines across diverse domains including biomedical analytics, natural language-vision models, automatic driving, distributed computation, and neural model merging (Guarrasi et al., 2 Aug 2024, Zhang et al., 24 Nov 2024, Oladunni et al., 6 Aug 2025, Willis et al., 26 Nov 2025, Wang et al., 2023, Yazgan et al., 24 Apr 2024, Bodaghi et al., 12 Mar 2024, Aksu et al., 21 Jan 2025, Yadav et al., 26 Jun 2024, Luenam et al., 18 Jun 2025).

1. Formal Characterization and Contrast with Other Fusion Strategies

Intermediate fusion is formally characterized by a sequence of operations:

Each modality $x_i$ is first encoded by a modality-specific encoder $f_i$ to yield hidden features $h_i = f_i(x_i)$ .
These features are merged by a fusion operation $\mathcal{F}$ at an intermediate network depth: $h = \mathcal{F}(h_1, h_2, ...)$ .
The joint feature $h$ is fed to subsequent multimodal layers $g$ , leading to output $y = g(h)$ .

This is distinct from:

Early fusion: $x = \mathcal{F}(x_1, x_2, ...)$ at the raw data level, $y = f(x)$ ;
Late fusion: modals are processed separately $y_i = f_i(x_i)$ and then $y = \mathcal{F}(y_1, y_2, ...)$ at the output level;
Intermediate fusion fuses at feature level, preserving and then combining abstraction from each stream (Guarrasi et al., 2 Aug 2024, Willis et al., 26 Nov 2025, Oladunni et al., 6 Aug 2025).

2. Architectural Taxonomy and Fusion Operations

Intermediate fusion architectures can be classified by:

When fusion occurs (depth and scheduling)
- Single fusion (all features fused at one intermediate layer)
- Multiple fusion (fusion at several depths)
- Gradual fusion (hierarchical or step-wise merging)
- Multi-flow fusion (multiple parallel fusion streams merged)
What is fused
- Features from different modalities or modules
- Representations of different abstraction level (e.g., shallow vs. deep)
How the fusion is computed
- Concatenation ( $\oplus$ )
- Elementwise or tensor operations ( $\odot$ )
- (Self- or cross-) attention mechanisms ( $\otimes$ )
- Squeeze-and-excitation recalibration ( $\circ$ )
- Knowledge-sharing via contrastive or regularized representation alignment ( $\star$ )

The majority of biomedical and multimodal systems employ concatenation for single fusion points, but sophisticated tensor, attention, or calibration blocks prevail in multi-stage and high-performing systems (Guarrasi et al., 2 Aug 2024).

3. Mathematical Formulation and Learning Algorithms

Intermediate fusion layers are systematically formulated:

For a fusion at position $i$ involving representations $\alpha_j, \alpha_k, ...$ , processed through $l$ layers, denote: $h = \mathcal{F}(N^{[l]}(\alpha_j), N^{[m]}(\alpha_k), ...)$ .

Common fusion operators:

Concatenation: $[h_1 \Vert h_2 ...]$ ;
Hadamard product: $h_1 \odot h_2$ ;
Cross-attention: $A = \text{softmax}((W_Q h_1)(W_K h_2)^T/\sqrt{d})$ , $h = A(W_V h_2)$ ;
Calibration: $h'_i = s \odot h_i$ with $s = \sigma(W_2\delta(W_1[h_1 \oplus h_2]))$ .

In neural architecture search-based approaches such as OptFusion, both the fusion graph (which layers/components to fuse) and the fusion operators themselves are learned jointly. In this paradigm (Zhang et al., 24 Nov 2024):

The architecture is parameterized using connection strengths $\alpha_{ij}$ (for edge i→j) and operator weights $\beta_j^o$ (selecting fusion operator $o$ at each node $j$ ).
A one-shot optimization minimizes the network’s task loss jointly over model and fusion parameters, with architectural choices finalized after the search phase.

In model fusion scenarios, e.g., “neuron interpolation” (Luenam et al., 18 Jun 2025), intermediate fusion operates by aligning and interpolating activations at hidden layers between parent networks, guided by neuron-importance scores and clustering/matching strategies to optimize a representation-matching cost.

4. Domain-Specific Implementations and Applications

Intermediate fusion occurs across a spectrum of applications:

a) Multimodal Biomedical Models:

Multi-stage intermediate fusion, as in PET/CT cancer subtype classification, employs repeated voxelwise attention blocks coupling streams at each abstraction level ( $L$ stages), yielding statistically significant accuracy and AUC improvements over early and late fusion, or single-stage intermediate fusion. Performance improvements attributed to maintaining both spatial and abstraction-level complementarities (Aksu et al., 21 Jan 2025, Guarrasi et al., 2 Aug 2024).

b) Multimodal Vision-Language Systems:

Intermediate fusion enables cross-modal feature interaction at multiple feature-hierarchy depths. For example, fusing BERT and vision backbone features (at multiple layers, via concatenation and attention submodules) provides a trade-off between accuracy and latency—the approach is especially useful in resource-constrained, low-latency inference contexts (Willis et al., 26 Nov 2025).

c) Collaborative Perception in Autonomous Systems:

Intermediate-feature sharing is the mainstay of collaborative perception, e.g., exchange and graph-attentive aggregation of BEV feature maps among vehicles, with recent work focusing on transmission-efficient compression and attention-based spatial/channel weighting. This paradigm achieves a compromise between bandwidth (reduced to 1–5% of early fusion protocols) and detection accuracy, while being resilient to real-world degradation such as pose noise and communication failures (Wang et al., 2023, Yazgan et al., 24 Apr 2024, Ahmed et al., 2023, Hao et al., 30 Apr 2025).

d) Distributed Computation and Code Optimization:

In scientific computing, intermediate fusion refers to the transformation of loop nests and kernel invocations into an optimized, fused kernel that eliminates temporaries, increases data locality, and improves vectorization. HFAV uses a formal fusion of iteration-nest DAGs based on algebraic constraints for dataflow and memory reuse (Sewall et al., 2017).

e) Cross-Domain Model Fusion:

Intermediate-layer neuron-alignment methods for fusing entire neural networks enable the construction of zero-shot, non-IID capable fused models from non-aligned parents. The learning objective couples clustering of parent-unit activations with approximation by the fused model’s units (Luenam et al., 18 Jun 2025).

5. Performance Analysis and Comparative Metrics

Empirical studies consistently show that intermediate fusion outperforms unimodal, early fusion, and late fusion approaches in a broad range of metrics and application areas:

In biomedical applications, intermediate fusion improves AUC by 2–7% over early and late baselines, with statistical significance validated in cross-validation studies (Guarrasi et al., 2 Aug 2024).
On large-scale CTR prediction, automated intermediate fusion search (OptFusion) exceeds state-of-the-art by up to +0.0036 AUC and achieves lower log-loss, while also reducing training time compared to NAS-based methods (Zhang et al., 24 Nov 2024).
In collaborative autonomous driving and UAV perception, intermediate fusion achieves up to 97% early-fusion accuracy at 1–2% of the communication cost, or near-early-fusion mAP at orders-of-magnitude bandwidth reduction (Hao et al., 30 Apr 2025, Yazgan et al., 24 Apr 2024).
In distributed runtimes, code-level intermediate-task fusion can yield 2–10x speedups over unfused task streams, with minimal added compile-time cost (Yadav et al., 26 Jun 2024, Sewall et al., 2017).
In multimodal stress detection, intermediate fusion with manifold reduction boosts classification accuracy to 96% (LOSO-CV), surpassing early/late fusion and unimodal baselines (Bodaghi et al., 12 Mar 2024).
Model-fusion via intermediate-layer alignment closes most of the gap to ensemble performance, outperforming both naive parameter and logit-level approaches in zero-shot settings (Luenam et al., 18 Jun 2025).

6. Open Challenges and Future Research Directions

Despite its demonstrated benefits, intermediate fusion faces several persistent challenges (Guarrasi et al., 2 Aug 2024, Yazgan et al., 24 Apr 2024):

Missing modalities and input heterogeneity: Most current architectures fail when modalities are missing at inference; few employ permutation-invariant pooling or attention masking to accommodate such cases.
Benchmarks and standardization: The absence of large, open multimodal datasets and uniform evaluation metrics hampers comparative research.
Fusion operation simplicity: Most systems default to naive concatenation. Advanced operations (multi-head attention, squeeze-and-excitation) are underutilized but consistently improve performance in ablation studies.
Hyperparameter tuning: Optimal selection of fusion depth, modality representation size, and operator choice remains empirical; information-theoretic and data-driven criteria are proposed as remedies.
Explainability and transparency: Few works offer detailed interpretability or feature-attribution analyses in intermediate-fusion pipelines, a critical gap in high-stakes domains such as medicine.
Evaluation rigor: Inadequate cross-validation practices, lack of ablation studies, and insufficient code sharing present reproducibility barriers.

Recommended best practices include progressive or multi-flow fusion for complex modality interactions, modality-aware representation sizing (e.g. via autoencoder bottlenecks), integration of advanced fusion operations, explainability at all layers, and rigorous comparative evaluation. The consensus is that robust, scalable intermediate fusion systems require modular, adaptive design, and must be able to contend with adversarial conditions, domain shifts, and missing inputs (Guarrasi et al., 2 Aug 2024, Yazgan et al., 24 Apr 2024, Willis et al., 26 Nov 2025, Aksu et al., 21 Jan 2025).

7. Representative Implementations and Notation Table

Application Domain	Representative Design	Fusion Operator(s)
CTR Prediction (Zhang et al., 24 Nov 2024)	Graph search + NAS (OptFusion)	ADD, PROD, CONCAT, ATT
Vision-Language (Willis et al., 26 Nov 2025)	Layer-wise concat + attention	Linear, Multi-head Attn
Biomedical (Guarrasi et al., 2 Aug 2024, Aksu et al., 21 Jan 2025)	Multi-stage 3D-CNN, cross-attn	Concat, Hadamard, Attn
Collaborative Perception (Wang et al., 2023, Ahmed et al., 2023)	BEV features, GAT, channel/spatial attn	Attention
Distributed Computing (Sewall et al., 2017, Yadav et al., 26 Jun 2024)	DAG merging, JIT fusion	Task, kernel fusion
Stress Detection (Bodaghi et al., 12 Mar 2024)	Per-branch CNN + MDS + concat	Manifold reduction, Conv1D
Model Merging (Luenam et al., 18 Jun 2025)	Neuron-interpolation, KD	Clustering, matching

Each domain adopts variant implementations, but nearly all combine dedicated unimodal representation learners, at least one intermediate feature-level fusion operation (often attention or tensor-based), and a downstream multimodal processing block.

References: (Guarrasi et al., 2 Aug 2024, Zhang et al., 24 Nov 2024, Oladunni et al., 6 Aug 2025, Willis et al., 26 Nov 2025, Wang et al., 2023, Yazgan et al., 24 Apr 2024, Bodaghi et al., 12 Mar 2024, Aksu et al., 21 Jan 2025, Yadav et al., 26 Jun 2024, Luenam et al., 18 Jun 2025, Sewall et al., 2017, Ahmed et al., 2023, Hao et al., 30 Apr 2025).