Bidirectional Progressive Feature Interactor (BPFI)

• BPFI is a cross-scale interaction mechanism within the GMBI module of GMBINet that enables bidirectional and progressive feature refinement using forward guidance and backward enhancement.
• It integrates grouped multiscale extraction with a parameter-free EWMS rule to maintain scale-invariant complexity and a lightweight computational profile.
• Empirical results confirm that BPFI improves defect detection performance in real time, delivering enhanced feature communication with minimal added latency.

Bidirectional Progressive Feature Interactor (BPFI) is the cross-scale interaction mechanism introduced inside the Group Multiscale Bidirectional Interactive (GMBI) module of GMBINet, a lightweight architecture for real-time steel surface defect detection. Within that framework, BPFI is designed to convert multiscale extraction from a set of largely isolated grouped branches into an interactive process that operates both during and after scale-specific feature extraction. Its defining elements are a forward guidance path, a backward enhancement path, and a parameter-free Element-Wise Multiplication-Summation (EWMS) interaction rule. In the reported GMBINet instantiation, this design is integrated into a five-stage encoder-decoder network and contributes to a model reported at 0.19 M parameters, 0.39 G FLOPs, 1048 FPS on GPU, and 16.53 FPS on CPU at 512 resolution (Zhang et al., 22 Aug 2025).

1. Architectural identity and location

Within GMBINet, BPFI is not a standalone head or auxiliary refinement block. It is the central interaction component of the GMBI module, which serves as the backbone’s basic building block. GMBI is described as having four parts: group multiscale feature extraction, bidirectional progressive feature interactor (BPFI), element-wise multiplication-summation (EWMS), and multiscale feature fusion. The first three are identified as the core of the module (Zhang et al., 22 Aug 2025).

The input to a GMBI block is a feature tensor

$F_{in} \in \mathbb{R}^{c \times w \times h}.$

This tensor is evenly split along channels into $n$ groups,

$$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$

with each group corresponding to one scale. BPFI operates directly on these grouped feature subsets $\{x_1,\dots,x_n\}$, producing refined multiscale outputs $\{y_1^{en},\dots,y_n^{en}\}$. These are subsequently concatenated and fused through a pointwise convolution with a residual shortcut to obtain

$$F_{out} = F_{in} + f_{pw}(cat(y^{en}_{1}, y^{en}_{2}, \ldots, y^{en}_{n})).$$

At network scale, the encoder is built by stacking GMBI modules. The architecture is described as a five-stage encoder-decoder, with the encoder following a ResNet-like depth pattern of 3, 4, 6, and 3 GMBI modules in stages 2–5. BPFI is therefore repeatedly instantiated throughout the encoder rather than applied once at a terminal fusion point. This repeated use is central to its claimed cumulative effect on multiscale representation quality (Zhang et al., 22 Aug 2025).

2. Design rationale and problem setting

BPFI is introduced in response to a specific critique of prior lightweight multiscale architectures. Recent DSConv-based multibranch methods are described as improving scale awareness by constructing several branches with different receptive fields, but each branch often processes the full input tensor. The paper argues that this produces linearly growing computation, memory, and latency as the number of scales increases. It also characterizes those branches as largely independent until late fusion, resulting in weak cross-scale interaction, information isolation between branches, computational redundancy, and post-hoc fusion that cannot guide feature extraction itself (Zhang et al., 22 Aug 2025).

The paper makes a related criticism of MINet’s MI module. Although that design introduces interaction after multiscale extraction, it is still presented as inheriting the linear complexity growth of multibranch architectures, and its interaction remains too late in the pipeline. The stated concern is that “post-hoc feature interaction fails to effectively guide the multiscale feature extraction process.” BPFI is proposed precisely to shift cross-scale communication into the extraction process while maintaining a lightweight computation profile.

The architectural response has two parts. First, grouped multiscale extraction assigns only $c/n$ channels to each scale rather than exposing all $c$ channels to every scale branch. Second, BPFI enables communication between those grouped scales in two directions. The mechanism is called bidirectional because information flows in opposite directions across scale groups, and progressive because interaction is organized sequentially between adjacent scales rather than through a global all-to-all fusion pattern. The paper explicitly relates this to a neurocognitive framing combining bottom-up integration and top-down modulation (Zhang et al., 22 Aug 2025).

3. Mechanism: forward guidance, backward enhancement, and EWMS

The forward stage of BPFI is the forward guidance path, in which smaller-scale features guide larger-scale feature extraction. Groups are processed in order from $i=1$ to $i=n$. The first group is processed independently, while each later group first interacts with the previous group’s output and only then passes through a scale-specific DSConv:

$n$0

Here, $n$1 is a $n$2 DSConv with dilation rate $n$3, and $n$4 denotes the multiscale interaction operation. Because $n$5 depends on $n$6 rather than only on $n$7, the process is explicitly progressive. The authors interpret this as allowing smaller-scale information to provide hierarchical priors for larger-scale groups and to progressively enlarge the effective receptive field (Zhang et al., 22 Aug 2025).

After forward-guided extraction, BPFI applies a reverse-direction backward enhancement stage intended to let larger-scale, more semantic features refine neighboring lower-scale features. The paper gives

$n$8

The paper’s notation is explicitly somewhat inconsistent at this point. Its prose states that “higher-level and larger-scale features provide modulation signals to refine adjacent lower-level and smaller-scale features,” while the indexing in the displayed equation is not elaborated further. The most faithful reading is that the backward stage still operates through adjacent-scale refinement, but now in the reverse semantic direction. Stronger claims about exact loop order are not fully supported by the printed exposition and therefore should be treated cautiously (Zhang et al., 22 Aug 2025).

The interaction operator $n$9 is implemented through EWMS, which is parameter-free. For the forward path, the paper gives the interaction explicitly:

$$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$0

where $$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$1 is sigmoid. The previous-scale feature is thus transformed into an attention-like coefficient map, multiplied element-wise with the current feature, and then combined with a residual addition of the original $$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$2. The paper further states that a similar process is applied in the backward path, but it does not provide a separate printed equation for that reverse-direction case.

Several properties follow directly from this formulation. The multiplicative term acts as parameter-free modulation; the residual addition preserves the original signal and mitigates information loss; and the interaction introduces neither extra convolution nor concatenation-based channel expansion. BPFI therefore defines the topology and directionality of interaction, while EWMS specifies the actual feature-mixing rule (Zhang et al., 22 Aug 2025).

After bidirectional refinement, the refined group outputs are concatenated and passed through a pointwise convolution. This restores global channel mixing after grouped processing and is followed by residual addition with $$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$3. The paper does not specify further normalization or nonlinearity details for the DSConv internals, and it does not mention interpolation or downsampling inside BPFI itself. All groups retain the same spatial resolution $$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$4, so the interaction is between adjacent scale groups at identical feature-map size (Zhang et al., 22 Aug 2025).

4. Computational formulation and implementation profile

A major claim attached to BPFI is that it preserves the lightweight character of grouped multiscale extraction. The computational argument begins with the grouped extractor. The cost of GMBI is derived as

$$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$5

which simplifies to

$$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$6

This is the same complexity form reported for a standard DSConv:

$$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$7

On that basis, the paper characterizes GMBI as scale-invariant in complexity: increasing the number of scales does not induce the same linear growth in FLOPs and parameters that conventional multibranch designs incur, because the total processed channel budget remains fixed (Zhang et al., 22 Aug 2025).

The paper contrasts this with a conventional DSConv multibranch module of $$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$8 branches, whose cost is written as

$$x_i \in \mathbb{R}^{\frac{c}{n} \times w \times h}, \quad i \in \{1,2,\dots,n\},$$9

and with the MI module of MINet, whose cost is written as

$\{x_1,\dots,x_n\}$0

Against those baselines, GMBI with BPFI is presented as achieving multiscale extraction and cross-scale interaction at complexity equivalent in form to a single DSConv block.

BPFI’s own contribution to efficiency is attributed to EWMS. Because EWMS consists only of sigmoid, element-wise multiplication, and element-wise addition, the paper repeatedly emphasizes that BPFI introduces no additional parameters or convolutional overhead for cross-scale interaction. In that sense, the module’s claim is not merely that it is lightweight relative to attention-heavy fusion, but that its inter-scale interaction is nearly cost-free relative to the grouped extraction around it (Zhang et al., 22 Aug 2025).

Implementation details are tightly specified. The grouped extractor uses $\{x_1,\dots,x_n\}$1 evenly split channel groups, each processed with a $\{x_1,\dots,x_n\}$2 depthwise separable convolution whose dilation rate is drawn from $\{x_1,\dots,x_n\}$3. Experiments examine $\{x_1,\dots,x_n\}$4, and the chosen default is $\{x_1,\dots,x_n\}$5. Figure 1(c), as described in the text, corresponds to $\{x_1,\dots,x_n\}$6. The paper does not mention weight sharing across scales; because $\{x_1,\dots,x_n\}$7 is indexed by $\{x_1,\dots,x_n\}$8 and uses different dilation rates, a natural reading is that each scale uses its own DSConv configuration rather than shared parameters (Zhang et al., 22 Aug 2025).

5. Empirical evidence and observed effects

The clearest isolation of BPFI’s contribution appears in the ablation study on SD-Saliency-900. Four interaction variants are compared: w/o Interaction, w/ FG, w/ BE, and Ours. All four use the same model budget: Param = 0.19 M and FLOPs = 0.39 G. The reported results are as follows (Zhang et al., 22 Aug 2025).

Variant	Metrics	Speed
w/o Interaction	MAE 0.0150; WF 0.9095; OR 0.8342; SM 0.9202; PFOM 0.8534; IoU 0.8491	1098 FPS
w/ FG	MAE 0.0135; WF 0.9125; OR 0.8436; SM 0.9224; PFOM 0.8751; IoU 0.8629	1074 FPS
w/ BE	MAE 0.0141; WF 0.9138; OR 0.8395; SM 0.9238; PFOM 0.8813; IoU 0.8605	1085 FPS
Ours	MAE 0.0126; WF 0.9273; OR 0.8653; SM 0.9334; PFOM 0.9077; IoU 0.8728	1048 FPS

These numbers support three explicit conclusions drawn by the paper. Either direction alone improves over the no-interaction case; the two directions are complementary, since using both outperforms either alone; and the gain is achieved without increasing parameter count or FLOPs, at the cost of only a slight speed reduction. The authors summarize this by stating that forward guidance and backward enhancement “are complementary and effectively facilitate communication between multiscale feature maps.”

The paper also isolates EWMS as BPFI’s internal interaction rule. Replacing EWMS with alternative operators yields: w/ Sum: 0.19 M, 0.39 G, 1072 FPS, IoU 0.8668; w/ Multiply: 0.19 M, 0.39 G, 1067 FPS, IoU 0.8587; w/ Concat: 0.53 M, 0.89 G, 932 FPS, IoU 0.8698; Ours (EWMS): 0.19 M, 0.39 G, 1048 FPS, IoU 0.8728. The reported interpretation is that EWMS gives the best overall performance while preserving the lightweight budget of sum and multiply and remaining much cheaper than concatenation (Zhang et al., 22 Aug 2025).

Qualitative evidence is described in Figure 2, which visualizes feature maps from the last GMBI module in the second stage. The text states that with BPFI, salient target regions are more strongly highlighted, indicated by warmer attention values. The authors further attribute improved structural integrity relative to MINet on SD-Saliency-900, and reduced over-segmentation relative to CSNet and MINet on NRSD-MN, primarily to BPFI’s ability to enhance target-region perception and expand the receptive field through scale-aware interaction. At full network level, GMBINet is reported to achieve 1048 FPS on GPU, 16.53 FPS on CPU, 0.19 M parameters, and 0.39 G FLOPs on SD-Saliency-900, with additional evaluation on the NEU-CLS defect classification dataset used to support broader generalization beyond surface defect detection (Zhang et al., 22 Aug 2025).

6. Terminological scope and relation to adjacent research

The exact acronym BPFI is tied, in the supplied literature, to GMBINet’s multiscale grouped interaction mechanism. Related papers use substantially similar descriptors—bidirectional and progressive—but they do not define the same module. In "BiPVL-Seg: Bidirectional Progressive Vision-Language Fusion with Global-Local Alignment for Medical Image Segmentation" (Sultan et al., 30 Mar 2025), the corresponding component is BiFusion: Bidirectional Progressive Fusion, inserted between a 4-stage vision encoder and a stage-divided 4-stage BERT encoder. There, bidirectionality refers to two-way exchange between visual and textual streams, and progressiveness refers to repeated stage-wise fusion across encoder depth. The interaction operator is cross-attention with LayerNorm, self-attention, MLP, and residual addition, rather than grouped DSConv plus EWMS.

In "Bidirectional Progressive Transformer for Interaction Intention Anticipation" (Zhang et al., 2024), the closest analogue is the Bidirectional Progressive Enhancement Module inside BOT. That mechanism alternates refinement between a hand-trajectory branch and an interaction-hotspot branch over future time steps. Here the progressive axis is primarily temporal rather than multiscale spatial grouping, and the interactor is implemented with cross-attention blocks rather than parameter-free element-wise modulation.

In "RevBiFPN: The Fully Reversible Bidirectional Feature Pyramid Network" (Chiley et al., 2022), the relevant analogue is RevSilo, a reversible bidirectional multi-scale fusion module stacked to form RevBiFPN. RevSilo also performs structured top-down and bottom-up inter-scale exchange, but its defining contribution is exact invertibility through additive coupling and activation recomputation, not parameter-free adjacent-scale guidance inside grouped DSConv branches.

A common misconception would be to treat all such modules as interchangeable instances of a single generic BPFI pattern. The supplied papers do not support that equivalence. What they do support is a broader family resemblance: each replaces purely late or one-way fusion with repeated interaction embedded into representation formation itself. Within that family, BPFI’s distinctive identity is narrower and more specific. It is a cross-scale, adjacent-group, bidirectional, progressive, and parameter-free-interaction mechanism embedded in the grouped multiscale extractor of GMBINet. A plausible implication is that its main contribution is not merely bidirectionality as such, but the particular combination of in-process multiscale communication and scale-invariant lightweight computation that the GMBINet paper makes central to real-time industrial deployment (Zhang et al., 22 Aug 2025).