In semi-supervised segmentation, capturing meaningful semantic structures from unlabeled data is essential. This is particularly challenging in histopathology image analysis, where objects are densely distributed. To address this issue, we propose a semi-supervised segmentation framework designed to robustly identify and preserve relevant topological features. Our method leverages multiple perturbed predictions obtained through stochastic dropouts and temporal training snapshots, enforcing topological consistency across these varied outputs. This consistency mechanism helps distinguish biologically meaningful structures from transient and noisy artifacts. A key challenge in this process is to accurately match the corresponding topological features across the predictions in the absence of ground truth. To overcome this, we introduce a novel matching strategy that integrates spatial overlap with global structural alignment, minimizing discrepancies among predictions. Extensive experiments demonstrate that our approach effectively reduces topological errors, resulting in more robust and accurate segmentations essential for reliable downstream analysis. Code is available at https://github.com/MelonXu/MATCH.

AAblation Study1 We conduct ablation studies to evaluate three key design choices in PosterAgent: (1) the binary-tree2 layout strategy for layout planning; (2) the inclusion of a commenter module as a visual critic; and3 (3) the use of in-context examples to enhance the visual perception capabilities of the commenter.4 We define the following variants:5 Direct: replacing the binary-tree layout with direct layout generation by an LLM;6 Tree: using the binary-tree layout strategy but removing the commenter module;7 Tree + Commenter: including the commenter module but without in-context examples;8 Tree + Commenter + IC: the full system, with both the commenter and in-context examples.9 All ablation variants are implemented using PosterAgent-4o, keeping all other components un-10 changed to isolate the effect of each factor. We visualize and compare results across five randomly11 selected papers from Paper2Poster, as shown in Figures 1 to 5.12 When prompting the LLM to directly generate poster layouts (Direct), the results are often structurally13 compromised (e.g., Figures 1a-3a), or resemble blog-style layouts that lack visual hierarchy and14 appeal (Figures 4a,5a). Fine-grained layout components, such as text boxes and figures, are especially15 challenging to synthesize in this setting: for instance, Figures1a-4a exhibit missing text boxes that16 leave noticeable blank areas, and Figure 4a fails to preserve the correct aspect ratio of figures.17

We investigate whether the training protocol can induce spatial locality in the early layers of a Vision Transformer (ViT) trained from scratch, without large-scale pretraining. Keeping the architecture and optimization procedure fixed, we compare a Baseline protocol with a Modern protocol (AutoAugment/ColorJitter, CutMix, and Label Smoothing) on CIFAR-10, CIFAR-100, and Tiny-ImageNet, characterizing each attention head via Mean Attention Distance (MAD) and normalized entropy. Across all three datasets, the Modern protocol produces more local and more concentrated attention in early layers; on CIFAR-100, the minimum MAD drops from 0.316 (Baseline) to 0.008 (Modern). To identify the source of this effect, we conduct an ablation study on CIFAR-100 by adding or removing each component individually. The results identify CutMix as the determining component within our experiments: all conditions with CutMix exhibit MAD 0.024, while all conditions without CutMix remain at MAD 0.210. AutoAugment and Label Smoothing show no independent effect on locality. Taken together, these findings suggest that the pressure to classify from partial image regions, induced by CutMix, can promote the emergence of local attention in Vision Transformers.

This supplementary material begins with a comprehensive visualization of the datasets central to our study. The specifics of our experimental settings are subsequently outlined in Section 1.2. Section 1.1 features an expanded analysis, including results from ablation studies. A key highlight of this section is the visual interpretation of the CLIP image features facilitated by t-SNE [6]. Concurrently, a comparative analysis is conducted, comparing the efficacy of interpolation-based strategies with our learning-based methods(i.e.

Overall dataset-specific architecture: The overall architecture equipped with all our datasetspecific modules is shown in Figure 1. We design the dataset-specific modules to be light-weight, which allows us to save on memory costs.

S1.1 Step-by-step derivation of min-max optimization in Section 2.2.1 By substituting Eq. 2 into Eq. 1 in the main manuscript, we can obtain the objective function of subscript z (we temporarily drop ifor clarity): J(z) = max Since z might be in high dimensional space, solving such a large system of linear equations under the constraint |z| 1is oftentimes computationally challenging. In order to find a practical solution for z that satisfies the constrained minimization problem in Eq. By setting zl as point of coincidence, we can find a separable majorizer of M(z) by adding the non-negative function (z zl) (βI Gx Gx)(z zl) (S6) 37th Conference on Neural Information Processing Systems (NeurIPS 2023). Note, to unify the format, we use the matrix transpose property in Eq. Then, the next step is to find z RN that minimizes z z 2bz subject to the constraint |z| 1. Let's first consider the simplest case where z is a scalar: argmin If b 1, then the solution is z = b.

This section presents more comprehensive experimental results. A.1 Comparison with post-hoc methods We also compare the performance of our textual outlier method with post-hoc approaches, which are another prominent approach in OoD detection. We conducted comparisons with six widely used and recently proposed methods known for their detection performance (MSP [4], ODIN [8], Mahalanobis [7], Energy [10], ReAct [14], KNN [15]). All advanced baseline methods follow the original paper's settings. Among these methods, our textual outlier approach demonstrate the best performance, further emphasizing its effectiveness as demonstrated in Table 6.

This document contains additional details and experiments that did not fit in the main text due to space constraints. For animations and additional results please also check the included videos. We use a similar optimization strategy with DreamFusion, so unless otherwise noted the hyperparameters remain the same. For example, we use the Distributed Shampoo optimizer [2]. Similarly with DreamFusion we also train on a TPUv4 machine with 4 chips.