Barbara Toniella Corradini

Paolo Andreini, Alessandra Bernardi, Monica Bianchini et al.

Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, which reproduces the Strassen algorithm for $2\times 2$ multiplication. Across many independent runs the network always converges to a rank-$7$ tensor, thus numerically recovering Strassen's optimal algorithm. We then train the same architecture on $3\times 3$ multiplication with rank $r\in\{19,\dots,23\}$. Our experiments reveal a clear numerical threshold: models with $r=23$ attain significantly lower validation error than those with $r\le 22$, suggesting that $r=23$ could actually be the smallest effective rank of the matrix multiplication tensor $3\times 3$. We also sketch an extension of the method to border-rank decompositions via an $\varepsilon$--parametrisation and report preliminary results consistent with the known bounds for the border rank of the $3\times 3$ matrix--multiplication tensor.

Barbara Toniella Corradini, Mustafa Shukor, Paul Couairon et al.

Foundation models have exhibited unprecedented capabilities in tackling many domains and tasks. Models such as CLIP are currently widely used to bridge cross-modal representations, and text-to-image diffusion models are arguably the leading models in terms of realistic image generation. Image generative models are trained on massive datasets that provide them with powerful internal spatial representations. In this work, we explore the potential benefits of such representations, beyond image generation, in particular, for dense visual prediction tasks. We focus on the task of image segmentation, which is traditionally solved by training models on closed-vocabulary datasets, with pixel-level annotations. To avoid the annotation cost or training large diffusion models, we constraint our setup to be zero-shot and training-free. In a nutshell, our pipeline leverages different and relatively small-sized, open-source foundation models for zero-shot open-vocabulary segmentation. The pipeline is as follows: the image is passed to both a captioner model (i.e. BLIP) and a diffusion model (i.e., Stable Diffusion Model) to generate a text description and visual representation, respectively. The features are clustered and binarized to obtain class agnostic masks for each object. These masks are then mapped to a textual class, using the CLIP model to support open-vocabulary. Finally, we add a refinement step that allows to obtain a more precise segmentation mask. Our approach (dubbed FreeSeg-Diff), which does not rely on any training, outperforms many training-based approaches on both Pascal VOC and COCO datasets. In addition, we show very competitive results compared to the recent weakly-supervised segmentation approaches. We provide comprehensive experiments showing the superiority of diffusion model features compared to other pretrained models. Project page: https://bcorrad.github.io/freesegdiff/

Simone Bonechi, Paolo Andreini, Barbara Toniella Corradini

The rapid progress of generative diffusion models has enabled the creation of synthetic images that are increasingly difficult to distinguish from real ones, raising concerns about authenticity, copyright, and misinformation. Existing supervised detectors often struggle to generalize across unseen generators, requiring extensive labeled data and frequent retraining. We introduce FRIDA (Fake-image Recognition and source Identification via Diffusion-features Analysis), a lightweight framework that leverages internal activations from a pre-trained diffusion model for deepfake detection and source generator attribution. A k-nearest-neighbor classifier applied to diffusion features achieves state-of-the-art cross-generator performance without fine-tuning, while a compact neural model enables accurate source attribution. These results show that diffusion representations inherently encode generator-specific patterns, providing a simple and interpretable foundation for synthetic image forensics.

Caterina Gallegati, Monica Bianchini, Franco Scarselli et al.

As generative models achieve unprecedented visual quality, the gold standard for image evaluation remains traditional feature-distribution metrics (e.g., FID). However, these metrics are provably hindered by the closed-vocabulary bottleneck of outdated features and the assumptive bias of rigid parametric formulations. Recent alternatives exploit modern backbones to solve the feature bottleneck, yet continue to suffer from parametric limitations. To close this gap, we introduce APEX (Assumption-free Projection-based Embedding eXamination), a novel evaluation framework leveraging the Sliced Wasserstein Distance as a mathematically grounded, assumption-free similarity measure. APEX inherits effective scalability to high-dimensional spaces, as we prove with theoretical and empirical evidences. Moreover, APEX is embedding-agnostic and uses two open-vocabulary foundation models, CLIP and DINOv2, as feature extractors. Benchmarking APEX against established baselines reveals superior robustness to visual degradations. Additionally, we show that APEX metrics exhibit intra- and cross-dataset stability, ensuring highly stable evaluations on out-of-domain datasets.