The central insight behind ANNE is that two very different mathematical tools can do complementary jobs inside a single U-shaped encoder-decoder. In the encoder, the authors deploy Mamba, a selective state-space model that has attracted wide attention since its introduction as a linear-time alternative to transformer attention. Instead of building a quadratic attention matrix over every pair of pixels, Mamba propagates information along a flattened sequence of the feature map through input-dependent state parameters, allowing long-range context to flow through the network at a cost that scales linearly with image size. This is what lets ANNE reason about broad spatial relationships without the memory burden that typically accompanies global modeling.

The second ingredient, and the paper’s main methodological novelty, is a module the authors call Adaptive Progressive Expansion Neurons, or A-PEN. The idea builds on a line of prior work known as progressively expanded neuron models, which increase the nonlinear expressiveness of a network by computing polynomial terms of the input features, such as squared and cubed activations, and combining them with learned weights. In earlier designs, however, the set of expansion terms and the activation applied afterward were fixed in advance. A-PEN makes both adaptive: a bank of candidate polynomial branches is weighted by normalized gates derived from trainable logits through a softmax function, and the post-expansion nonlinearity is a parametric PReLU whose negative slope is learned during training.

The authors are notably careful about how these gates should be interpreted. Because each normalized gate multiplies an unconstrained trainable coefficient, the effective contribution of a polynomial branch is the product of the two, meaning different gate-coefficient combinations can produce identical outputs. The gates therefore form a coupled parameterization that modulates the relative scaling of candidate branches during optimization, not a uniquely identifiable measure of how important each polynomial order is. The team also draws a precise boundary around its use of Remez approximation: the classical minimax theory of best polynomial approximation motivates the idea that compact polynomial bases can represent complex nonlinear mappings, but ANNE never executes the Remez exchange algorithm and claims no minimax guarantee. The polynomial coefficients are simply learned end to end from the segmentation loss.

Architecturally, ANNE follows the familiar U-shaped template that has defined biomedical segmentation since U-Net. Convolutional stem layers preserve local spatial structure at the input, Mamba blocks then model long-range dependencies at progressively coarser resolutions, and A-PEN blocks refine nonlinear feature interactions at the bottleneck and in the decoder before upsampling. Skip connections carry fine-grained encoder information to matching decoder stages, and the decoder employs multi-scale depth-wise convolutions with kernel sizes of one, three, and five. A final projection produces a binary segmentation map, with the whole pipeline trained using a weighted combination of binary cross-entropy and soft Dice loss.

The evaluation is unusually transparent about how comparisons were made. The authors tested ANNE on eight public 2D datasets spanning three clinical domains: dermoscopic lesion segmentation on ISIC 2016, ISIC 2017, ISIC 2018, and PH2; colonoscopic polyp segmentation on Kvasir-SEG and CVC-ClinicDB; and retinal-vessel segmentation on DRIVE and CHASE_DB1. Crucially, the results tables distinguish controlled reproductions, where competing methods were retrained under an identical protocol with the same splits, preprocessing, loss, and five fixed random seeds, from literature-reported values, which may reflect different experimental conditions. Statistical claims are restricted to the controlled comparisons, while literature numbers are described only as context.

Within that framework, ANNE delivers a strong and consistent showing. On ISIC 2018 and PH2 it achieved the strongest tabulated values among the compared methods, and on ISIC 2017 it recorded the lowest 95th-percentile Hausdorff distance, a boundary-sensitive metric, even though another method reported higher overlap scores. In polyp segmentation it topped the tables on Kvasir-SEG across Dice, IoU, and boundary distance, and placed second on CVC-ClinicDB with the best boundary accuracy. For retinal vessels, where thin, branching structures test a model’s ability to preserve fine detail, ANNE achieved the best tabulated IoU and boundary distance on DRIVE and swept all three metrics on CHASE_DB1.

Ablation experiments illuminate why the design works. Comparing a compact U-Net-like baseline against versions augmented with only A-PEN, only Mamba, or both, the authors found that A-PEN consistently improved boundary-sensitive performance while Mamba tended to boost overlap where broad context matters. The full model achieved the best Dice score in every ablation row, supporting the claim that the two modules are complementary rather than interchangeable. A separate resolution analysis showed that accuracy improved as input size rose from 128 by 128 to 256 by 256 pixels, but saturated beyond that point even as computational cost continued to climb roughly quadratically, making 256 by 256 the identified sweet spot for lesion and polyp tasks.

The authors are candid about the limits of their evidence. All experiments used public 2D benchmarks, so nothing is established about 3D volumes, video, or prospective clinical workflows. The evaluation is in-distribution, with no external cohorts from different scanners, institutions, or populations, and several benchmarks are small enough that uncertainty remains despite repeated runs. Efficiency was measured on an NVIDIA A100 GPU, which characterizes relative cost but says nothing about real-time performance on edge devices or hospital hardware. The team also notes that segmentation accuracy alone is insufficient for clinical deployment, which would additionally demand uncertainty estimation, failure detection, calibration, fairness analysis, and workflow integration.

Even with those caveats, ANNE represents a compelling data point in the ongoing effort to shrink medical AI without shrinking its competence. By pairing a linear-time state-space encoder with learnable polynomial feature expansion, the architecture shows that competitive overlap and boundary accuracy across dermoscopy, colonoscopy, and fundus imaging can be achieved with a parameter budget far below that of transformer-heavy rivals. The code, dataset split manifests, and configuration files have been released in a public repository, and the authors point toward volumetric extensions, external-domain validation, and deployment-oriented profiling on resource-constrained hardware as the next frontiers. For clinics and research labs where compute is scarce but precision is not, that combination of transparency, efficiency, and measured performance may prove just as influential as the architecture itself.

Subject of Research: A parameter-efficient deep learning architecture combining Mamba state-space blocks and adaptive polynomial neuron expansion for 2D medical image segmentation

Article Title: ANNE: adaptive neuron network expansion for 2D medical image segmentation

Article References: Reyes-Angulo, A. A., & Paheding, S. (2026). ANNE: adaptive neuron network expansion for 2D medical image segmentation. Applied Intelligence, 56(15), Article 464. https://doi.org/10.1007/s10489-026-07503-8

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07503-8

Keywords: medical image segmentation, Mamba, state-space models, polynomial expansion, neural architecture, dermoscopy, polyp segmentation, retinal vessels, parameter efficiency, deep learning, U-Net, computer vision