TMAC: Triple-Mapping Adaptive Coupling

• Triple-Mapping Adaptive Coupling (TMAC) is a spatial refinement mechanism that enhances neural network feature discriminability for dense biomedical instance detection.
• It splits the feature map into two branches to compute idiosyncratic and consensus spatial attention maps, which are adaptively fused with minimal computational overhead.
• Integrated within the CellMamba framework, TMAC significantly improves cell detection accuracy by preserving fine local details while enforcing global spatial consistency.

Triple-Mapping Adaptive Coupling (TMAC) is a spatial refinement mechanism designed to enhance discriminability in neural network backbones for dense biomedical instance detection. Introduced in the context of the CellMamba one-stage cell detection framework, TMAC is inserted after sequence attention layers (either NC-Mamba or Multi-Head Self-Attention) within each CellMamba Block, providing adaptive channel-wise spatial attention that preserves local sensitivity while enforcing global consistency (Liu et al., 25 Dec 2025).

1. Conceptual Overview

TMAC operates on the post-attention feature map $X\in \mathbb{R}^{B\times H\times W\times C}$, where $B$ is the batch size, $H\times W$ is the spatial grid, and $C$ indicates channel count. The module splits the channel dimension into two sub-paths, computes two idiosyncratic spatial attention maps (one per sub-path) and a consensus attention map (jointly from both sub-paths), and adaptively fuses them. This process enables the network to respond both to fine-grained, branch-specific cues and to shared, spatially consistent object signals, addressing challenges in pathological image analysis such as densely packed cell regions and ambiguous boundaries.

2. Architectural Structure

A CellMamba Block incorporating TMAC follows this ordered sequence:

• Sequence Attention (NC-Mamba or MSA)
• TMAC (spatial refinement)
• Layer Normalization
• Feed-Forward Network (FFN)
• Residual Addition

Within TMAC, the feature map is split, attention maps are built and adaptively fused, and the processed features are then passed on for further normalization and transformation. The module introduces negligible computational overhead, as all attention computations use lightweight 2D convolutions with shared parameters.

Table 1 summarizes the main stages within TMAC:

Stage	Operation	Output Shape
Channel Split	Flatten & split	$X_1, X_2: B\times L\times C/2$
Spatial Reshape	Reshape branches	$F_m^{idi}: B\times H\times W\times C/2$
Idiosyncratic Attention	Mean/max pool + Conv	$A_m^{idi}: H\times W\times 1$
Consensus Attention	Sum + pool + Conv	$A^{cons}: H\times W\times 1$
Feature Merge	Refine, concat	$\hat{X}: B\times L\times C$

3. Mathematical Formulation

3.1 Channel Splitting

The input $X$ is reshaped and split along channels: $$X_{\mathrm{flat}} = \mathrm{reshape}(X) \in \mathbb{R}^{B\times L\times C}$$

$$[X_1, X_2] = [X_{\mathrm{flat}}[:,:,1:\tfrac{C}{2}], X_{\mathrm{flat}}[:,:,\,\tfrac{C}{2}+1:C]]$$

Each $X_m$ is reshaped back to $$F_m^{idi} \in \mathbb{R}^{B\times H\times W\times C/2}$$.

3.2 Idiosyncratic Attention Maps

For each branch $m$, feature averaging and max-pooling are performed across channels, the results concatenated and processed by a shared lightweight convolution followed by sigmoid activation: $$A_m^{idi} = \sigma\bigl(\mathrm{Conv}\left([\mathrm{mean}_m, \mathrm{max}_m]\right)\bigr)$$ where

$$\mathrm{mean}_m(i,j) = \frac{1}{C/2} \sum_{k=1}^{C/2} F_m^{idi}(i,j,k),\quad \mathrm{max}_m(i,j) = \max_{k=1..\frac{C}{2}} F_m^{idi}(i,j,k)$$

3.3 Consensus Attention Map

The two branches are summed to produce a consensus feature: $F^{cons} = F_1^{idi} + F_2^{idi}$ Mean and max pooling across channels, shared-weight convolution, and sigmoid activation yield: $$A^{cons} = \sigma\bigl(\mathrm{Conv}\left([\mathrm{mean}_{cons}, \mathrm{max}_{cons}]\right)\bigr)$$

3.4 Adaptive Coupling

A binary mask determines when to apply the consensus map: $$\alpha = \begin{cases} 0, & \text{epoch} < N\ 1, & \text{epoch} \geq N\ \end{cases} \quad \widetilde A^{cons} = \alpha A^{cons} + (1-\alpha)\mathbf{1}$$ The final attention map for each branch is

$A_m = A_m^{idi}\odot \widetilde A^{cons}$

3.5 Feature Refinement and Merge

Each $A_m$ is broadcast across channels and multiplied: $F_m^{final}(i,j,k) = A_m(i,j)\,F_m^{idi}(i,j,k)$ Flatten and concatenate both branches to recover the original feature shape: $$\hat{X} = \mathrm{concat}\left(\mathrm{flatten}(F_1^{final}),\,\mathrm{flatten}(F_2^{final})\right)$$

4. Analysis of Local Sensitivity and Global Consistency

TMAC enforces a dual mechanism: the idiosyncratic attention maps $A_m^{idi}$ allow each branch to specialize in detecting localized or diverse cues, such as unique textures or edge boundaries, thus preserving fine spatial detail. The consensus map $A^{cons}$, computed over the sum of both branches, responds to shared spatial signals and encourages both branches to align with globally relevant regions.

During early training ($\alpha=0$), the consensus path is omitted, letting each branch develop its own discriminative criteria. After a predefined epoch threshold ($N=35$), the consensus map is incorporated multiplicatively, ensuring local cues are filtered by global context: $A_m = A_m^{idi} \cdot A^{cons}$ This mechanism formally gates the forward pass and its gradients, so feature propagation is weighted by both branch-specific and spatially consistent criteria. This scheme was empirically found optimal on datasets such as CoNSeP and CytoDArk0 (Liu et al., 25 Dec 2025).

5. Implementation Details and Hyperparameters

TMAC uses only lightweight operators to minimize overhead:

• Convolutions are $1\times1$ (or optionally $3\times3$), parameters are shared across all attention branches.
• No additional parameters are introduced beyond the two shared convolutional layers per TMAC module.
• TMAC is inserted after every sequence-attention layer in the four-stage backbone ($[2,2,8,4]$ blocks).
• Layer normalization follows TMAC, before each FFN.
• Training uses SGD (initial learning rate $1\text{e}{-3}$, weight decay $1\text{e}{-4}$), with a LinearLR warmup and MultiStepLR schedule.
• The dynamic coupling threshold is fixed at $N=35$ epochs.
• Sigmoid activation bounds all attention maps to $[0,1]$.

6. Integration and Pseudocode

The TMAC module fits seamlessly into any backbone using token or spatial sequence attention. For each block:

Y = SequenceAttention(Input) Y_prime = TMAC_Block(Y, current_epoch) Z = LayerNorm(Y_prime) Out = FFN(Z) + Y # residual

Within TMAC:

def TMAC_Block(X, epoch): B,H,W,C = X.shape L = H*W X_flat = reshape(X, [B, L, C]) X1 = X_flat[:,:, :C//2] X2 = X_flat[:,:, C//2:] F1_idi = reshape(X1, [B, H, W, C//2]) F2_idi = reshape(X2, [B, H, W, C//2]) A1_idi = compute_map(F1_idi) A2_idi = compute_map(F2_idi) F_cons = F1_idi + F2_idi A_cons = compute_map(F_cons) if epoch < N: A_cons_eff = ones([H,W,1]) else: A_cons_eff = A_cons A1 = A1_idi * A_cons_eff A2 = A2_idi * A_cons_eff F1_final = F1_idi * broadcast(A1, channel=C//2) F2_final = F2_idi * broadcast(A2, channel=C//2) out = concat(reshape(F1_final, [B, L, C//2]), reshape(F2_final, [B, L, C//2]), axis=2) return out

Function compute_map(F) performs channel-wise mean and max pooling, concatenation, lightweight convolution, and sigmoid activation.

7. Empirical Performance and Role in CellMamba

Within the CellMamba architecture, TMAC contributed to significant performance improvements on high-resolution cell detection tasks, yielding superior accuracy over CNN-, Transformer-, and Mamba-based baselines while reducing both model size and inference latency. TMAC’s channel splitting and triple-attention design are credited for preserving both fine detail and global cell context, which are essential for robust instance recognition in biomedical imaging (Liu et al., 25 Dec 2025).