MDRC: Multi Dilated Residual Convolution Block

• Multi Dilated Residual Convolution (MDRC) is a modular block that combines parallel dilated convolutions with residual connections for multi-scale feature extraction.
• It employs two parallel branches with dilation rates of 2 and 3 to capture both fine local details and broader spatial context without sacrificing resolution.
• Empirical results show that using MDRC in convolution layers significantly improves metrics like mAP50 and IoU over conventional YOLOv5 configurations.

Searching arXiv for papers on Multi Dilated Residual Convolution and closely related architectures. Multi Dilated Residual Convolution (MDRC) denotes a family of convolutional modules that combine multiple dilation scales with residual feature propagation in order to enlarge receptive fields while preserving trainability and, in many formulations, spatial resolution. In the strict sense represented by recent satellite-imagery detectors, MDRC is a compact multi-branch block in which parallel dilated convolutions with different dilation rates are fused and then combined with a skip connection (Mostafa et al., 29 Jul 2025). In a broader architectural sense, the term also connects to earlier dilated residual and mixed-scale designs that used serial dilation schedules, dense aggregation, or residual denoising objectives rather than a formally named MDRC block (Zhang et al., 2017).

1. Definition and scope

MDRC is used explicitly in recent object-localization architectures for satellite imagery, where it denotes a backbone feature-extraction block designed to capture multi-scale patterns without reducing spatial resolution (Mostafa et al., 29 Jul 2025). In that usage, the “multi” component refers to multiple dilation rates, the “dilated” component refers to receptive-field expansion through atrous convolution, and the “residual” component refers to skip-based feature preservation and gradient support. The core motivation is that a fixed receptive field is a poor fit when targets vary strongly in scale, shape, and spatial extent, or when they are embedded in clutter and noise (Mostafa et al., 29 Jul 2025).

Two closely related but not identical named forms appear in the literature. “Multi Dilated Residual Convolution (MDRC)” is the terminology used in YOLO-DCAT for gravity-wave localization, whereas “Multi-scale Dilated Residual Convolution (MDRC)” is used in YOLO-DCAP for gravity waves, mesospheric bores, and ocean eddies (Mostafa et al., 29 Jul 2025). Both papers describe a backbone replacement for standard YOLOv5 convolution layers, and both define MDRC as a residual multi-scale dilated module rather than as a generic network-wide principle (Mostafa et al., 8 May 2025).

The term should, however, be delimited carefully. Several earlier papers are often relevant to MDRC discussions but do not define MDRC as a named module. “Learning a Dilated Residual Network for SAR Image Despeckling” presents a single-stream 7-layer dilated residual CNN with two additive skip connections, not a reusable multi-branch MDRC block (Zhang et al., 2017). “Dilated Residual Networks” develops high-resolution residual backbones by removing late downsampling and compensating with dilation, again without introducing a module named MDRC (Yu et al., 2017). This suggests that MDRC is best understood both as a specific module class and as a later crystallization of broader design ideas around dilation, multi-scale context, and residual propagation.

2. Canonical block structure

In the most explicit formulation, MDRC is a two-branch dilated residual block. For an input feature map

$x \in \mathbb{R}^{H \times W \times C},$

the module applies two parallel dilated convolutions with dilation rates

$d_1 = 2,\quad d_2 = 3.$

Each branch produces

$y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$

after which the branch outputs are concatenated along the channel dimension: $F_{concat} = \text{Concat}(y_1, y_2).$ If each branch outputs $C$ channels, then

$F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$

A $1\times1$ convolution then reduces channels back to the original count, followed by batch normalization and ReLU: $$F_{reduced} = \text{ReLU}(\text{BN}(F_{concat} \ast W_{1 \times 1})).$$ Finally, residual output is formed by

$y_{MDRC} = x + F_{reduced}.$

This is the complete mathematical MDRC definition given in the gravity-wave localization paper (Mostafa et al., 29 Jul 2025).

A closely aligned definition appears in YOLO-DCAP. There, MDRC consists of parallel dilated convolution branches applied to the same input feature map, branch outputs concatenated along the channel dimension, a $1\times1$ convolution for fusion and channel reduction, and a residual connection activated when input and output channels match: $d_1 = 2,\quad d_2 = 3.$0 with residual form

$d_1 = 2,\quad d_2 = 3.$1

The operative dilation configuration in the main model is two branches with rates $d_1 = 2,\quad d_2 = 3.$2 (Mostafa et al., 8 May 2025).

The following table summarizes the canonical MDRC structure as explicitly described in those two papers.

Component	YOLO-DCAT MDRC	YOLO-DCAP MDRC
Branch count	2 parallel branches	2 parallel branches in the operative configuration
Dilation rates	$d_1 = 2,\quad d_2 = 3.$3	typically $d_1 = 2,\quad d_2 = 3.$4
Fusion	Concatenation $d_1 = 2,\quad d_2 = 3.$5 conv $d_1 = 2,\quad d_2 = 3.$6 BN $d_1 = 2,\quad d_2 = 3.$7 ReLU	Concatenation $d_1 = 2,\quad d_2 = 3.$8 conv
Residual path	Add input $d_1 = 2,\quad d_2 = 3.$9 after fused transform	Add input when $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$0

This compact two-branch design distinguishes MDRC from larger atrous pyramids. The gravity-wave paper states explicitly that it is not an ASPP-like large pyramid with many rates, but a compact 2-branch multi-dilated residual block (Mostafa et al., 29 Jul 2025).

3. Functional principles

The central functional claim of MDRC is that it provides simultaneous access to multiple effective receptive fields. In the gravity-wave localization setting, the $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$1 branch is intended to preserve more local or fine-grained structure, while the $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$2 branch captures broader spatial context. The paper repeatedly characterizes this as capturing both “fine-grained local patterns” and “broader spatial contexts” (Mostafa et al., 29 Jul 2025). In the satellite object-localization setting, the same logic is extended to targets whose visible extent, pattern, and shape differ substantially across datasets (Mostafa et al., 8 May 2025).

This multi-scale behavior is especially relevant when the target is weak, diffuse, or embedded in interference. The satellite-localization papers motivate MDRC by emphasizing that ordinary convolutions use a fixed receptive field, which can impede detection when objects appear at different scales or when broader contextual evidence is required to disambiguate signal from clutter (Mostafa et al., 8 May 2025). The gravity-wave localization paper is more specific: VIIRS night-band targets may be mixed with clouds, city lights, and instrumental noise in a single-band image, so a single fixed receptive field is a poor fit (Mostafa et al., 29 Jul 2025).

Residual learning supplies the second major principle. In these MDRC formulations, the skip connection is not auxiliary; it is the mechanism that preserves original information and improves gradient flow while the transform path learns multi-scale context. The gravity-wave paper explicitly states that the residual connection helps the model learn these multi-scale transformations while preserving the original signal and improving gradient flow (Mostafa et al., 29 Jul 2025). The YOLO-DCAP paper likewise frames residual connections as preserving important information from earlier layers and improving gradient flow during training (Mostafa et al., 8 May 2025).

A broader theoretical context is provided by work on residual and mixed-scale sparse coding. “Towards Understanding Residual and Dilated Dense Neural Networks via Convolutional Sparse Coding” interprets shortcut propagation as a nonzero initialization effect in a sparse-coding update and explains mixed-scale dense learning through a dictionary of the form

$y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$3

where the identity term preserves previous features and the dilated operator changes receptive-field structure (Zhang et al., 2019). This suggests that MDRC-like modules can be interpreted as combining identity-preserving refinement with multi-scale transformed features, although that paper does not define a module named MDRC.

4. Architectural placement and empirical behavior

In both explicit MDRC papers, placement is a decisive architectural variable. The gravity-wave localization paper states that MDRC is inserted in the backbone and that the modified backbone replaces YOLOv5 convolution layers with MDRC followed by SSCA (Mostafa et al., 29 Jul 2025). It also reports a placement ablation: baseline YOLOv5 achieves mAP50 $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$4, IoU $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$5; MDRC in C3 layers $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$6 gives mAP50 $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$7, IoU $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$8; and MDRC in Conv layers $y_i = x \ast W_i^{(d_i)}, \quad i \in \{1, 2\},$9 gives mAP50 $F_{concat} = \text{Concat}(y_1, y_2).$0, IoU $F_{concat} = \text{Concat}(y_1, y_2).$1 (Mostafa et al., 29 Jul 2025). The same paper concludes that the module is beneficial specifically when placed in standard convolution layers, not inside YOLOv5’s C3 structure.

YOLO-DCAP reports the same qualitative placement conclusion across three satellite datasets. It states that MDRC blocks replace all conventional convolutional layers in the YOLOv5 backbone, while ablations show that using MDRC in Conv layers improves over baseline but using it in C3 layers degrades performance substantially (Mostafa et al., 8 May 2025). For Gravity Wave, Bore, and Ocean Eddy, the Conv-layer placement yields better mAP50 and IoU than baseline, whereas the C3-layer placement is worse than baseline in all three cases (Mostafa et al., 8 May 2025).

Empirical tuning of dilation rates is equally important. The gravity-wave paper compares single rates and pairs, reporting: $F_{concat} = \text{Concat}(y_1, y_2).$2: mAP50 $F_{concat} = \text{Concat}(y_1, y_2).$3, IoU $F_{concat} = \text{Concat}(y_1, y_2).$4; $F_{concat} = \text{Concat}(y_1, y_2).$5: mAP50 $F_{concat} = \text{Concat}(y_1, y_2).$6, IoU $F_{concat} = \text{Concat}(y_1, y_2).$7; $F_{concat} = \text{Concat}(y_1, y_2).$8: mAP50 $F_{concat} = \text{Concat}(y_1, y_2).$9, IoU $C$0; $C$1: mAP50 $C$2, IoU $C$3; $C$4: mAP50 $C$5, IoU $C$6; $C$7: mAP50 $C$8, IoU $C$9 (Mostafa et al., 29 Jul 2025). The paper interprets the superiority of $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$0 as a better balance between local and broader context, while larger dilation such as $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$1 may introduce spatial artifacts or irrelevant contextual information.

YOLO-DCAP provides cross-dataset evidence that multi-scale dilation outperforms a single dilation rate. For Gravity Wave, mAP50/IoU improves from $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$2 with single $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$3 to $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$4 with multi-scale $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$5; for Bore, from $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$6 to $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$7; and for Ocean Eddy, from $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$8 to $F_{concat} \in \mathbb{R}^{H \times W \times 2C}.$9 (Mostafa et al., 8 May 2025). This supports the claim that the “multi” in MDRC is not merely terminological.

A compact summary of the most explicit ablations follows.

Study	Setting	Reported outcome
Dilation-rate ablation	$1\times1$0 vs single or larger rates	$1\times1$1 is best among tested options (Mostafa et al., 29 Jul 2025)
Placement ablation	Conv layers vs C3 layers	Conv-layer insertion helps; C3 insertion hurts (Mostafa et al., 29 Jul 2025)
Single vs multi-scale	$1\times1$2 vs $1\times1$3	Multi-scale improves all three datasets (Mostafa et al., 8 May 2025)

These results also delimit a common misconception. MDRC is not presented as universally beneficial “everywhere” in a backbone. The available evidence instead indicates placement sensitivity and dilation-rate sensitivity.

5. Precursors, adjacent architectures, and non-equivalent uses

Several earlier architectures are MDRC-related without being formal MDRC implementations. “Learning a Dilated Residual Network for SAR Image Despeckling” is especially close in spirit. Its SAR-DRN contains seven dilated convolution layers and two skip connections, with dilation schedule

$1\times1$4

ReLU after layers 1–6, no ReLU after the final layer, skip additions from layer 1 to layer 3 and from layer 4 to layer 7, and no batch normalization (Zhang et al., 2017). The paper describes the benefits of dilation, skip connections, and residual learning in terms strongly aligned with later MDRC motivations, but its design is serial across depth rather than multi-branch within a reusable block.

“Dilated Residual Networks” provides another important precursor. Rather than defining a multi-branch module, it converts ResNet into a high-resolution residual architecture by removing stride from $1\times1$5 and $1\times1$6, then using dilation $1\times1$7 and $1\times1$8 in later groups to preserve receptive field while changing output stride from 32 to 8 (Yu et al., 2017). It also studies gridding artifacts and introduces “degridding” via additional lower-dilation stages, eventually removing residual connections from the final added blocks to suppress artifact propagation (Yu et al., 2017). This is directly relevant to MDRC because it shows that residual identity paths can preserve undesirable high-frequency artifacts under dilation.

Other architectures are even closer to modular MDRC in structure. “Res-CR-Net” uses CONV RES BLOCKs with three parallel branches of separable atrous convolutions with different dilation rates, fused by concatenation or addition before shortcut fusion, with concatenation reported as producing the best result (Abdallah et al., 2020). “Compressed Sensing MRI via a Multi-scale Dilated Residual Convolution Network” does not use the acronym MDRC, but its MDN block combines alternating dilation factors $1\times1$9 and $$F_{reduced} = \text{ReLU}(\text{BN}(F_{concat} \ast W_{1 \times 1})).$$0, local and global residual learning, and concatenation-based multi-scale fusion (Dai et al., 2019). “Densely connected multidilated convolutional networks for dense prediction tasks” proposes multidilated convolution inside DenseNet-style connectivity, where the dilation factor depends on the skip-source group rather than on a ResNet-like residual block (Takahashi et al., 2020). These designs show that the conceptual space around MDRC includes residual, dense, concatenative, and hybrid reuse patterns.

The boundary of the term is therefore important. A true MDRC block, in the narrow modern sense, requires explicit multi-dilated processing inside a compact residual module, usually with parallel branches and explicit fusion. Serial single-stream dilated residual CNNs, high-resolution dilated ResNets, and dense multidilated architectures are best described as MDRC-related rather than as canonical MDRC implementations (Zhang et al., 2017).

6. Limitations, ambiguities, and broader significance

The most immediate limitation is terminological instability. MDRC is explicitly named only in a subset of the literature, whereas many architecturally related modules appear under other names such as SAR-DRN, DRN, MDN, CONV RES BLOCK, or multidilated convolution (Zhang et al., 2017). This makes literature retrieval nontrivial: some of the most relevant antecedents do not contain the term MDRC at all.

A second limitation is specification variability. In YOLO-DCAT, the branch kernel size in the MDRC subsection is not formally confirmed in prose or equations, although the figure and wording imply standard convolution branches (Mostafa et al., 29 Jul 2025). In YOLO-DCAP, several implementation details are not explicitly stated, including branch kernel size, stride, padding, internal normalization, activation inside MDRC, branch-wise channel allocation, and exact skip-path projection behavior when $$F_{reduced} = \text{ReLU}(\text{BN}(F_{concat} \ast W_{1 \times 1})).$$1 (Mostafa et al., 8 May 2025). A plausible implication is that MDRC is often easier to reproduce conceptually than to reproduce exactly from manuscript text alone.

A third issue concerns empirical reporting. The gravity-wave localization paper contains an inconsistency between the IoU reported for “$$F_{reduced} = \text{ReLU}(\text{BN}(F_{concat} \ast W_{1 \times 1})).$$2” in one table and the much larger IoU reported in the Conv-layer placement ablation; the manuscript does not explicitly reconcile those values (Mostafa et al., 29 Jul 2025). The robust conclusion is therefore directional rather than exact: MDRC improves performance, especially recall and mAP50, and works best in Conv layers with dilation pair $$F_{reduced} = \text{ReLU}(\text{BN}(F_{concat} \ast W_{1 \times 1})).$$3.

From a broader architectural perspective, MDRC sits at the intersection of three repeatedly validated ideas: receptive-field enlargement through dilation, preservation and optimization support through residual or skip connections, and explicit handling of scale variation through multi-branch or multi-rate processing. Earlier work on despeckling, denoising, segmentation, classification, and dense prediction repeatedly argues for larger contextual fields without loss of resolution or dramatic parameter growth (Yu et al., 2017). Later MDRC formulations can be read as a compact operationalization of those principles for detectors that must localize diffuse, variable-scale targets in noisy imagery (Mostafa et al., 8 May 2025).

This suggests a precise encyclopedic characterization. MDRC is best regarded not as a single immutable block but as a module family centered on residual multi-dilated feature extraction. Its canonical contemporary form is a compact multi-branch residual unit with parallel dilated convolutions, concatenative fusion, $$F_{reduced} = \text{ReLU}(\text{BN}(F_{concat} \ast W_{1 \times 1})).$$4 projection, and skip addition (Mostafa et al., 29 Jul 2025). Its deeper significance lies in how it consolidates a longer line of work on dilated residual computation, multi-scale context aggregation, and information-preserving feature reuse into a reusable convolutional primitive.