Brian Summa

Yu Qin, Brittany Terese Fasy, Carola Wenk et al.

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights real-world examples of this approach visualizing the important topological features in graph, 3D shape, and medical image data.

Fangzheng Wu, Brian Summa

Attention sinks -- tokens that receive disproportionate attention mass -- are assumed to be functionally important in autoregressive language models, but their role in diffusion transformers remains unclear. We present a causal analysis in text-to-image diffusion, dynamically identifying dominant attention recipients per timestep and suppressing them via paired, training-free interventions on the score and value paths. Across 553 GenEval prompts on Stable Diffusion~3 (with SDXL corroboration), removing these sinks does not degrade text-image alignment (CLIP-T) or preference proxies (ImageReward, HPS-v2) at $k{=}1$; only under stronger interventions ($k\!\geq\!10$) does HPS-v2 exhibit a metric-dependent boundary, while CLIP-T remains robust throughout. The perceptual shifts induced by suppression are nonetheless \emph{sink-specific} -- $\sim\!6\times$ larger than equal-budget random masking -- revealing an empirical dissociation between trajectory-level perturbation and \emph{semantic alignment} in diffusion transformers. \footnote{Code available at https://github.com/wfz666/ICML26-attention-sink.}

Syed Fahim Ahmed, Gnanesh Rasineni, Florian Koehler et al.

Whole-slide image (WSI) classification in computational pathology is commonly formulated as slide-level Multiple Instance Learning (MIL) with a single global bag representation. However, slide-level MIL is fundamentally underconstrained: optimizing only global labels encourages models to aggregate features without learning anatomically meaningful localization. This creates a mismatch between the scale of supervision and the scale of clinical reasoning. Clinicians assess tumor burden, focal lesions, and architectural patterns within millimeter-scale regions, whereas standard MIL is trained only to predict whether "somewhere in the slide there is cancer." As a result, the model's inductive bias effectively erases anatomical structure. We propose Progressive-Context MIL (PC-MIL), a framework that treats the spatial extent of supervision as a first-class design dimension. Rather than altering magnification, patch size, or introducing pixel-level segmentation, we decouple feature resolution from supervision scale. Using fixed 20x features, we vary MIL bag extent in millimeter units and anchor supervision at a clinically motivated 2mm scale to preserve comparable tumor burden and avoid confounding scale with lesion density. PC-MIL progressively mixes slide- and region-level supervision in controlled proportions, enabling explicit train-context x test-context analysis. On 1,476 prostate WSIs from five public datasets for binary cancer detection, we show that anatomical context is an independent axis of generalization in MIL, orthogonal to feature resolution: modest regional supervision improves cross-context performance, and balanced multi-context training stabilizes accuracy across slide and regional evaluation without sacrificing global performance. These results demonstrate that supervision extent shapes MIL inductive bias and support anatomically grounded WSI generalization.

Fangzheng Wu, Brian Summa

We present a model-centric diagnostic framework that treats training state as a latent variable and unifies a family of internal readouts -- head-gradient norms, confidence, entropy, margin, and related signals -- as anchor-relative projections of that state. A preliminary version of this work introduced a head-gradient probe for checkpoint selection. In this version, we focus on the unifying perspective and structural diagnostics; full algorithmic details, theoretical analysis, and experimental validation will appear in a forthcoming paper. We outline the conceptual scaffold: any prediction head induces a local loss landscape whose geometry (gradient magnitude, curvature, sharpness) reflects how well the upstream features are aligned with the task. Different readout choices -- gradient norms, softmax entropy, predictive margin -- correspond to different projections of this geometry, each with complementary strengths. The framework suggests that checkpoint selection, early stopping, and lightweight architecture pre-screening can all be viewed as querying the same underlying state through different lenses. Illustrative experiments on ImageNet classification and COCO detection/segmentation hint at the practical potential; rigorous benchmarks and ablations are deferred to the full paper.

Fangzheng Wu, Brian Summa

We introduce SteeringDiffusion, a bottlenecked activation-level control interface for diffusion models that exposes a smooth, monotonic, and runtime-adjustable control surface over the content--style trade-off. Our method keeps the U-Net backbone frozen and learns a small, prompt-conditioned latent code projected to FiLM/AdaGN-style modulation parameters. A zero-initialized design guarantees exact equivalence to the base model at zero scale, while timestep-aware gating restricts modulation to later denoising stages. A single scalar at inference continuously traverses the control surface without retraining. Across experiments on Stable Diffusion~1.5 and SDXL covering multiple artistic styles, we show that SteeringDiffusion produces smooth and monotonic content--style trade-offs. Under matched parameter budgets, it outperforms LoRA in controllability and stability, while ControlNet and rank-1 adapters do not expose a comparable control surface. We further introduce an inversion-stability diagnostic based on DDIM inversion, used as a post-hoc trajectory probe, which reveals strong correlations with intervention magnitude. These results position \emph{Steering Bottlenecked Explicit Control (S-BEC)} as a practical, general-purpose control interface for frozen diffusion backbones.

Yu Qin, Brittany Terese Fasy, Carola Wenk et al.

Merge trees are a valuable tool in the scientific visualization of scalar fields; however, current methods for merge tree comparisons are computationally expensive, primarily due to the exhaustive matching between tree nodes. To address this challenge, we introduce the Merge Tree Neural Network (MTNN), a learned neural network model designed for merge tree comparison. The MTNN enables rapid and high-quality similarity computation. We first demonstrate how to train graph neural networks, which emerged as effective encoders for graphs, in order to produce embeddings of merge trees in vector spaces for efficient similarity comparison. Next, we formulate the novel MTNN model that further improves the similarity comparisons by integrating the tree and node embeddings with a new topological attention mechanism. We demonstrate the effectiveness of our model on real-world data in different domains and examine our model's generalizability across various datasets. Our experimental analysis demonstrates our approach's superiority in accuracy and efficiency. In particular, we speed up the prior state-of-the-art by more than $100\times$ on the benchmark datasets while maintaining an error rate below $0.1\%$.

Yu Qin, Brittany Terese Fasy, Carola Wenk et al.

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances has been challenging due to the computational cost. In this paper, we propose a persistence diagram hashing framework that learns a binary code representation of persistence diagrams, which allows for fast computation of distances. This framework is built upon a generative adversarial network (GAN) with a diagram distance loss function to steer the learning process. Instead of using standard representations, we hash diagrams into binary codes, which have natural advantages in large-scale tasks. The training of this model is domain-oblivious in that it can be computed purely from synthetic, randomly created diagrams. As a consequence, our proposed method is directly applicable to various datasets without the need for retraining the model. These binary codes, when compared using fast Hamming distance, better maintain topological similarity properties between datasets than other vectorized representations. To evaluate this method, we apply our framework to the problem of diagram clustering and we compare the quality and performance of our approach to the state-of-the-art. In addition, we show the scalability of our approach on a dataset with 10k persistence diagrams, which is not possible with current techniques. Moreover, our experimental results demonstrate that our method is significantly faster with the potential of less memory usage, while retaining comparable or better quality comparisons.

Guillaume Favelier, Noura Faraj, Brian Summa et al.

This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framework, called Persistence Atlas, enables the visualization of the dominant spatial patterns of critical points, along with statistics regarding their occurrence in the ensemble. The persistence atlas represents in the geometrical domain each dominant pattern in the form of a confidence map for the appearance of critical points. As a by-product, our method also provides 2-dimensional layouts of the entire ensemble, highlighting the main trends at a global level. Our approach is based on the new notion of Persistence Map, a measure of the geometrical density in critical points which leverages the robustness to noise of topological persistence to better emphasize salient features. We show how to leverage spectral embedding to represent the ensemble members as points in a low-dimensional Euclidean space, where distances between points measure the dissimilarities between critical point layouts and where statistical tasks, such as clustering, can be easily carried out. Further, we show how the notion of mandatory critical point can be leveraged to evaluate for each cluster confidence regions for the appearance of critical points. Most of the steps of this framework can be trivially parallelized and we show how to efficiently implement them. Extensive experiments demonstrate the relevance of our approach. The accuracy of the confidence regions provided by the persistence atlas is quantitatively evaluated and compared to a baseline strategy using an off-the-shelf clustering approach. We illustrate the importance of the persistence atlas in a variety of real-life datasets, where clear trends in feature layouts are identified and analyzed.