Reza Rastegar

Reza Rastegar

Softmax-routed mixture-of-experts models approach hard routing as the temperature tends to zero, but this limit is singular near routing ties. This paper studies that singularity at the population level for squared-loss MoE regression. The central object is the \emph{boundary mass}, namely the probability that the top two router scores are separated by only a small margin. Under smoothness and transversality assumptions on the router and input law, we prove coarea/tube estimates showing that this mass is linear in the slab width, with leading constant given by a surface integral over the routing interface in the binary case. These estimates yield quantitative soft-to-hard risk bounds and, under compactness and uniform margin control, $Γ$-convergence of the soft objectives to the hard-routing objective. The main conclusion is that the zero-temperature limit is controlled by a thin geometric layer around routing interfaces, not by the full input space. We then use this geometric core in two more model-dependent directions. In a teacher--student setting, we prove a conditional landscape-transfer principle showing that, when the profiled hard-routing problem has favorable identifiability and curvature and the relevant derivatives transfer at boundary-layer scale, small-temperature soft routing inherits approximate teacher recovery and strict-saddle behavior away from teacher-equivalent partitions. We also give a reduced two-expert Gaussian calculation that illustrates a local symmetry-breaking mechanism aligned with the teacher separator.

Ahmad Mustafa, Reza Rastegar, Ghassan AlRegib

Prostate gland segmentation from T2-weighted MRI is a critical yet challenging task in clinical prostate cancer assessment. While deep learning-based methods have significantly advanced automated segmentation, most conventional approaches-particularly 2D convolutional neural networks (CNNs)-fail to leverage inter-slice anatomical continuity, limiting their accuracy and robustness. Fully 3D models offer improved spatial coherence but require large amounts of annotated data, which is often impractical in clinical settings. To address these limitations, we propose a hybrid architecture that models MRI sequences as spatiotemporal data. Our method uses a deep, pretrained DeepLabV3 backbone to extract high-level semantic features from each MRI slice and a recurrent convolutional head, built with ConvLSTM layers, to integrate information across slices while preserving spatial structure. This combination enables context-aware segmentation with improved consistency, particularly in data-limited and noisy imaging conditions. We evaluate our method on the PROMISE12 benchmark under both clean and contrast-degraded test settings. Compared to state-of-the-art 2D and 3D segmentation models, our approach demonstrates superior performance in terms of precision, recall, Intersection over Union (IoU), and Dice Similarity Coefficient (DSC), highlighting its potential for robust clinical deployment.