Router-Gated Cross-Modal Feature Fusion

• Router-gated cross-modal feature fusion is a technique that adaptively controls the integration of diverse modalities using data-dependent gates and routing coefficients.
• It selectively injects, suppresses, or blends cross-modal signals to handle noise, modality dominance, and missing inputs in tasks like sentiment analysis and speech recognition.
• Empirical studies indicate that dynamic routing improves accuracy and efficiency over uniform fusion, enhancing performance across tracking, vision-language, and retrieval systems.

Router-gated cross-modal feature fusion denotes a family of multimodal architectures in which cross-modal interaction is not passed forward uniformly, but is modulated by data-dependent gates, routing coefficients, or reliability scores that determine how much information from one modality should enter another or a joint representation. In the literature, this pattern appears in multimodal sentiment analysis, audio-visual speech recognition, tracking, object detection, e-commerce retrieval, vision-LLMs, remote sensing, medical imaging, and depth-conditioned humanoid locomotion, with implementations ranging from sigmoid forget gates and token-wise reliability gates to capsule routing and per-channel convex mixing (Jiang et al., 2022, Lim et al., 26 Aug 2025, Liu et al., 2024, Kim et al., 17 Apr 2026).

1. Core idea and formal structure

A recurrent design principle is to separate cross-modal interaction from cross-modal admission control. Cross-attention, cross-correlation, or part-whole routing first computes candidate signals that encode complementary evidence; a gate or router then determines whether those signals should be injected, suppressed, or blended with the unimodal pathway. In "Cross-Modality Gated Attention Fusion for Multimodal Sentiment Analysis" (Jiang et al., 2022), this appears as a pairwise forget vector

$$f_{(i,j)} = \sigma( [a_{(i,j)} \oplus z_j] W^f + b^f )$$

and a residual-gated fusion rule

$$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$

where the residual term preserves the original modality signal while the gate filters noisy or redundant cross-modal content. In "Improving Noise Robust Audio-Visual Speech Recognition via Router-Gated Cross-Modal Feature Fusion" (Lim et al., 26 Aug 2025), the same logic is pushed to token granularity:

$$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$

In "Information Router for Mitigating Modality Dominance in Vision-LLMs" (Kim et al., 17 Apr 2026), routing acts directly on selected channels:

$$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$

for $d \in \mathcal{D}_{\text{less}}^A$. In "Part-Whole Relational Fusion Towards Multi-Modal Scene Understanding" (Liu et al., 2024), routing coefficients from capsule routing serve as modality-aware gates that yield both modal-shared semantics and modal-specific semantics.

This suggests that router-gated fusion is better understood as a family of conditional computation mechanisms than as a single module class. Some variants gate attention outputs, some gate feature channels, some gate dense connections across fusion units, and some route information between part-level and whole-level capsules; what they share is selective information flow conditioned on multimodal evidence.

2. Architectural realizations and routing granularity

Architectural differences are largely differences of routing granularity and placement. Some systems route utterance-level vectors, some route decoder tokens, some route feature-map pixels or channels, and some route experts or capsules. The following representative systems illustrate this design space (Jiang et al., 2022, Lim et al., 26 Aug 2025, Lu et al., 2024, Kim et al., 17 Apr 2026, Liu et al., 2024, Liang et al., 19 Aug 2025).

System	Task domain	Routing granularity
CMGA	Multimodal sentiment analysis	Pairwise utterance-level forget gate
Router-gated AVSR	Audio-visual speech recognition	Token-level local gate plus layer-wise global gate
AFter	RGBT tracking	Soft per-unit router over fusion structures
MoIR	Vision-LLMs	Per-channel routing on selected low-information channels
PWRF	Multi-modal scene understanding	Capsule routing coefficients from part to whole
UniECS	E-commerce retrieval	Per-token, per-feature sigmoid gate

At the compact end of the spectrum, CMGA summarizes text, visual, and audio streams into utterance-level vectors and computes cross-attention over vectors rather than full sequences. Each modality is projected to a shared $d_k = 128$, so each cross-attention is $O(d_k)$ per pair, and the fusion self-attention over three pairwise tokens is negligible at $O(3^2 d_h)$ (Jiang et al., 2022). At the opposite end, the AVSR model inserts a Gated Cross-Attention block into each of six Transformer decoder layers, with a frozen router that produces token-level acoustic corruption scores and a local gate aligned to decoder length $N$ (Lim et al., 26 Aug 2025).

Other systems move routing into the structure of the fusion network itself. AFter constructs a three-layer Hierarchical Attention Network with four fusion units per layer—SEU, CEU, CMEU$_{r2t}$, and CMEU$$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$0—and equips every unit with a router

$$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$1

that predicts soft combination weights for dense inter-layer connections (Lu et al., 2024). PACGNet uses bidirectional spatial and channel gates at each pyramid level and then a progressive hierarchical gate $$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$2 derived from level $$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$3 to preserve fine-grained detail through the pyramid (Gu et al., 20 Dec 2025). MultiModNet places a Gated Fusion Unit early in the secondary modality stream, where the primary modality’s PAF output computes a per-pixel, per-channel gate

$$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$4

before late fusion (Liu et al., 2021).

The same pattern appears in sequence models and retrieval models under different names. UniECS uses modality-specific cross-attention followed by a per-token, per-feature gate

$$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$5

to retain unimodal strength when the partner modality is absent or unhelpful (Liang et al., 19 Aug 2025). WQ-Fusion integrates the gate into attention itself by projecting $$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$6 jointly and using $$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$7, so routing occurs at the per-token, per-dimension level inside a single-layer Gated Transformer (Lin et al., 25 Jun 2026). AR-CNN, by contrast, performs routing only after region-level alignment, where reliability scores derived from per-modality foreground and background probabilities gate the fused aligned RoI feature (Zhang et al., 2022).

3. Representative systems across domains

In multimodal sentiment analysis, router-gated fusion is used to regulate semantic, acoustic, and visual interaction rather than merely concatenate modality features. CMGA uses text, visual, and audio modalities on MOSI and MOSEI, with a pairwise cross-modality attention stage, a forget gate, and a transformer-style fusion layer over three pairwise outputs. On MOSI it reports MAE 0.790, corr 0.759, F1 82.3, Acc-2 82.7, and Acc-7 43.3; on MOSEI it reports MAE 0.545, corr 0.762, F1 85.0, Acc-2 85.3, and Acc-7 53.0 (Jiang et al., 2022). AGFN extends the idea by combining an Information Entropy Gate and a Modality Importance Gate after cross-modal interaction. On CMU-MOSI it reports Acc-2 82.75, F1 82.68, Acc-7 48.69, and MAE 71.02; on CMU-MOSEI it reports Acc-2 84.01, F1 84.11, Acc-7 54.30, and MAE 53.57 (Wu et al., 2 Oct 2025).

In audio-visual speech recognition, the central issue is not only cross-modal complementarity but fine-grained reliability estimation under corruption. The router-gated AVSR framework computes token-level acoustic reliability without noise labels and injects the resulting local gate into every Gated Cross-Attention block in the decoder. On LRS3, it reports an 16.51-42.67% relative reduction in word error rate compared to AV-HuBERT, with average WER 13.43% to 7.70% under clean fine-tuning and 8.60% to 7.18% under noise fine-tuning (Lim et al., 26 Aug 2025).

Tracking and detection papers push routing toward spatial and structural adaptivity. AFter addresses RGBT tracking with a dynamic routing algorithm over a fusion structure space, reporting PR=91.6% and SR=78.5% on GTOT, PR=87.6% and SR=63.5% on RGBT210, PR=90.1% and SR=66.7% on RGBT234, PR=70.3%, NPR=65.8%, and SR=55.1% on LasHeR, and PR=84.9% and SR=72.5% on VTUAV (Lu et al., 2024). PACGNet performs deep backbone fusion for RGB-IR detection through Symmetrical Cross-Gating and Pyramidal Feature-aware Multimodal Gating, reaching mAP@50 = 81.7% on DroneVehicle and 82.1% on VEDAI (Gu et al., 20 Dec 2025). AR-CNN addresses weakly aligned RGB-T and RGB-D detection by predicting per-RoI shifts and then reweighting modalities according to confidence and disagreement, achieving MR 24.3, 18.1, and 22.0 on CVC-14 day, night, and all, and mAP 66.3 on SL-RGBD 2D detection (Zhang et al., 2022).

Retrieval and vision-language systems use router-gated fusion primarily to mitigate modality dominance and to handle missing inputs. UniECS introduces a gated multimodal encoder for image, text, and multimodal retrieval; on M-BEER it reports text-to-image R@10 = 0.85 versus 0.57 for GME-Qwen2VL, image-to-text R@10 = 0.87 versus 0.60, and multimodal-to-multimodal R@10 = 0.99 versus 0.98, while using 0.2B parameters compared to 2B and 8B baselines. In deployment on the e-commerce search platform of Kuaishou Inc., it reports Click-Through Rate (+2.74\%) and Revenue (+8.33\%) (Liang et al., 19 Aug 2025). MoIR addresses modality dominance in VLMs by routing complementary information into low-information channels before decoder fusion. On VizWiz with LLaVA-1.5-7B and LoRA on Attn, it reports Acc 28.22 to 32.47, MDI 81.70 to 73.16, and AEI 10.97 to 10.43 (Kim et al., 17 Apr 2026).

Several additional domains show that router-gated fusion is not tied to recognition benchmarks alone. CReF couples proprioception-queried attention, gated residual fusion, and a highway-style output gate for depth-conditioned humanoid locomotion, reaching 97.85% on hard stairs, 44.70% on OOD 80 cm gap, and 84.35% on OOD 43 cm platform, with 20/20 on real stairs 15/30 cm and 18/20 on real 80 cm gap (Hao et al., 31 Mar 2026). CFCI-Net uses selective complementary feature fusion and a modal feature compression interaction transformer for brain tumor segmentation, reporting Avg Dice 84.35 on BraTS2019 and 84.79 on BraTS2020 (Chen et al., 20 Mar 2025). MultiModNet combines Pyramid Attention Fusion and a Gated Fusion Unit for land-cover mapping, reporting OA 0.913 and mF1 0.907 on Vaihingen and mIoU 0.482 on Agriculture-Vision (Liu et al., 2021). PWRF uses capsule routing to convert part-level modalities into a fused whole-level modality, reporting validation mIoU 66.47% on DELIVER, test mIoU 54.29%, and S=93.27 with MAE=0.23 on VDT-2048 (Liu et al., 2024).

4. Training objectives and supervision regimes

Router-gated fusion does not imply a single training regime. Some routers are learned purely from downstream supervision, some are directly supervised, and some are pretrained through self-supervision and then frozen. CMGA is trained as a regression model with Mean Squared Error, uses Adam with initial learning rate $$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$8, and reports no additional regularizers (Jiang et al., 2022). AFter is trained end-to-end with SGD on classification and regression losses inherited from ToMP, with HAN parameters using learning rate $$h_{(i,j)} = \mathrm{ReLU}\!\left( z_i + ( a_{(i,j)} W^m + b^m ) \odot f_{(i,j)} \right),$$9 and fixed iteration number of 50 (Lu et al., 2024). PACGNet retains YOLOv8’s classification and objectness formulation, replaces box regression with Wise-IoU v3, and trains with SGD for 300 epochs using batch size 128, $$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$0, $$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$1, momentum 0.937, and weight decay 0.0005 (Gu et al., 20 Dec 2025).

A distinct regime appears when the router estimates reliability. In the AVSR model, the AVFF router is pretrained on LRS3 with

$$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$2

using $$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$3, $$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$4, and $$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$5, and is then frozen while the AV-HuBERT encoder, decoder, GCA blocks, and gating parameters are fine-tuned end-to-end with sequence-to-sequence cross-entropy (Lim et al., 26 Aug 2025). MAFNet uses explicit frame-level supervision for its scalar router:

$$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$6

and optimizes

$$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$7

where $$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$8 is a binary cross-entropy over dominant modality states in CMOTB (Liu et al., 2023).

Retrieval and VLM systems often combine router-gated fusion with multi-objective optimization. UniECS jointly optimizes Cross-Modal Alignment Loss, Cohesive Local Alignment Loss, and Intra-Modal Contrastive Loss,

$$\lambda_{\text{local}} = \tanh(\mathrm{Interpolate}(1-s_v)) \in (0,1), \qquad r^k = z^{k-1} + (\lambda_{\text{global}} \cdot \lambda_{\text{local}}) \odot A^k.$$9

and updates loss-group weights online by normalized gradient magnitudes with $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$0 (Liang et al., 19 Aug 2025). MoIR uses parameter-efficient fine-tuning via LoRA with AdamW, learning rate $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$1, batch size 8, rank $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$2, scaling $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$3, dropout 0.05, and default exchange ratio $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$4 (Kim et al., 17 Apr 2026). AGFN adds Virtual Adversarial Training to L1 sentiment regression:

$$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$5

with VAT weight $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$6 (Wu et al., 2 Oct 2025).

Across these systems, a consistent distinction emerges between gating as an architectural operation and gating as an explicitly supervised variable. In many papers the gate is only indirectly trained through task loss; in others, such as AVSR, MAFNet, and MoIR, the router or reliability estimate is given a more direct training signal or a dedicated pretraining stage.

5. Empirical properties, robustness, and ablation evidence

Ablation studies consistently show that the router or gate is not a cosmetic addition. In CMGA, removing cross-attention degrades MOSI to MAE 0.845 and Acc-7 41.55, while removing the forget gate degrades it further to MAE 0.856 and Acc-7 41.47; on MOSEI, removing the forget gate yields MAE 0.594 and Acc-7 51.55, compared with MAE 0.545 and Acc-7 53.0 for the full model (Jiang et al., 2022). In the AVSR model, on LRS3 30h with MUSAN-corrupted evaluation, the baseline averages 7.77% WER, the full router + cosine similarity + GCA model reaches 6.67%, replacing $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$7 with $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$8 gives 7.17%, using L2 distance gives 7.25%, and removing GCA gives 7.24% (Lim et al., 26 Aug 2025). In AFter, removing routers reduces RGBT234 from 90.1%/66.7% PR/SR to 86.0%/63.3% and LasHeR from 70.3%/55.1% to 68.7%/54.1% (Lu et al., 2024).

The same pattern appears in retrieval and modality-dominance settings. UniECS reports that removing the gating mechanism drops $$\bar{F}^A[:,:,d] = \alpha_d^A \cdot F^B[:,:,d] + (1-\alpha_d^A)\cdot F^A[:,:,d],$$9 R@1 from 0.63 to 0.12 and $d \in \mathcal{D}_{\text{less}}^A$0 R@1 from 0.38 to 0.15, while text-to-text is largely unaffected, indicating that ungated fusion permits text dominance (Liang et al., 19 Aug 2025). MoIR’s noise-replacement analysis on VizWiz shows unchanged prediction rate dropping from 62.13% to 29.63% for all questions, from 57.80% to 25.20% for vision-dependent questions, and from 69.33% to 37.00% for vision-irrelevant questions, which the paper interprets as reduced reliance on textual shortcuts and increased sensitivity to visual evidence (Kim et al., 17 Apr 2026).

Several papers also show that robustness depends on the kind of routing. In AR-CNN, adding the confidence-aware fusion module reduces MR$d \in \mathcal{D}_{\text{less}}^A$1 at origin by $d \in \mathcal{D}_{\text{less}}^A$2, while RFA and RoI jitter contribute most of the robustness to controlled shift patterns (Zhang et al., 2022). In CReF, the full model attains overall 90.45% success rate excluding MuJoCo OOD, whereas w/o Cross-Attn reaches 78.56%, w/o GRF 83.78%, and w/o Highway Gate 83.29%; on OOD 80 cm gap the contrast is 44.70% versus 8.60%, 29.95%, and 17.20% respectively (Hao et al., 31 Mar 2026). In MultiModNet, missing DSM only reduces mF1 to 0.903, random noise DSM to 0.900, and fully interfered DSM to 0.896, compared with 0.907 for the full IRRG+DSM setting, indicating that the GFU+PAF combination remains robust when the supplementary modality is absent or noisy (Liu et al., 2021).

A plausible implication is that empirical gains arise less from cross-modal interaction alone than from regulated cross-modal interaction. Across sentiment, AVSR, tracking, detection, retrieval, and control, the benefit is strongest when the architecture can decide that some cross-modal information should be attenuated, delayed, or bypassed.

6. Misconceptions, limitations, and open directions

A common misconception is that router-gated fusion is equivalent to mixture-of-experts routing. Several papers explicitly separate these notions. CMGA states that its gates are lightweight, fully differentiable, and directly attached to attention outputs, whereas a dedicated router network with expert indices or top-$d \in \mathcal{D}_{\text{less}}^A$3 routing would add auxiliary load-balancing losses, routing latency, and potential instability (Jiang et al., 2022). WQ-Fusion likewise performs routing through per-token, per-dimension gating inside attention rather than through a separate global router head (Lin et al., 25 Jun 2026). Conversely, AFter and PWRF show that more explicit routing can be useful when the fusion structure itself must change dynamically or when part-whole relations are central (Lu et al., 2024, Liu et al., 2024).

Another misconception is that attention alone solves modality imbalance. The AVSR paper argues that static cross-attention remains overly audio-driven without reliability signals (Lim et al., 26 Aug 2025), and MoIR argues that attention only determines where the model focuses and cannot enrich information that is missing or ambiguous (Kim et al., 17 Apr 2026). UniECS reaches a related conclusion from retrieval: without gating, the text stream dominates fusion and image-driven tasks collapse (Liang et al., 19 Aug 2025). These results frame router-gated fusion as a response not only to feature complementarity but also to modality dominance, signal-to-noise imbalance, and missing-modality conditions.

Current limitations are likewise recurrent. CMGA is sensitive to pair order when reversing pairs involving text and compresses each modality to a single utterance-level vector, which may miss fine-grained temporal interactions (Jiang et al., 2022). The AVSR model assumes clean, synchronized video; occlusions, motion blur, or lip-video desynchronization can mislead the router, and out-of-domain gains on LRS2 under noise fine-tuning are modest at RERR 3.15% (Lim et al., 26 Aug 2025). AFter increases parameters and computation through embedded routers and still fails under extreme occlusion and distractor scenarios (Lu et al., 2024). PACGNet remains dependent on modality quality, and visually ambiguous categories such as van versus car and freight car versus truck remain difficult (Gu et al., 20 Dec 2025). CReF notes that active depth sensing remains sensitive to illumination and reflective surfaces, and its numerical hyperparameters $d \in \mathcal{D}_{\text{less}}^A$4, $d \in \mathcal{D}_{\text{less}}^A$5, and $d \in \mathcal{D}_{\text{less}}^A$6 are not disclosed in the text (Hao et al., 31 Mar 2026). CFCI-Net identifies the tension between complementary fusion and redundancy explosion, motivating feature compression before interaction (Chen et al., 20 Mar 2025).

Future directions proposed in the literature are relatively consistent: explicit routers or MoE-style sparse gating for larger modality sets or long sequences; additional reliability signals, such as visual quality or ASR uncertainty; alignment-aware interpolation; stronger handling of missing modalities; and better calibration of gate distributions (Jiang et al., 2022, Lim et al., 26 Aug 2025, Liang et al., 19 Aug 2025, Kim et al., 17 Apr 2026). This suggests that the field is converging on a broader view of multimodal fusion as adaptive information routing, where the crucial question is not merely how to connect modalities, but how to regulate the strength, location, and granularity of those connections.