Sheaf-Laplacian Obstruction and Projection Hardness for Cross-Modal Compatibility on a Modality-Independent Site

We develop a unified framework for analyzing cross-modal compatibility in learned representations. The core object is a modality-independent neighborhood site on sample indices, equipped with a cellular sheaf of finite-dimensional real inner-product spaces. For a directed modality pair $(a\to b)$, we formalize two complementary incompatibility mechanisms: projection hardness, the minimal complexity within a nested Lipschitz-controlled projection family needed for a single global map to align whitened embeddings; and sheaf-Laplacian obstruction, the minimal spatial variation required by a locally fit field of projection parameters to achieve a target alignment error. The obstruction invariant is implemented via a projection-parameter sheaf whose 0-Laplacian energy exactly matches the smoothness penalty used in sheaf-regularized regression, making the theory directly operational. This separates two distinct failure modes: hardness failure, where no low-complexity global projection exists, and obstruction failure, where local projections exist but cannot be made globally consistent over the semantic neighborhood graph without large parameter variation. We link the sheaf spectral gap to stability of global alignment, derive bounds relating obstruction energy to excess global-map error under mild Lipschitz assumptions, and give explicit constructions showing that compatibility is generally non-transitive. We further define bridging via composed projection families and show, in a concrete ReLU setting, that an intermediate modality can strictly reduce effective hardness even when direct alignment remains infeasible.

Guarded Query Routing for Large Language Models

Query routing, the task to route user queries to different large language model (LLM) endpoints, can be considered as a text classification problem. However, out-of-distribution queries must be handled properly, as those could be questions about unrelated domains, queries in other languages, or even contain unsafe text. Here, we thus study a \emph{guarded} query routing problem, for which we first introduce the Guarded Query Routing Benchmark (GQR-Bench), which covers three exemplary target domains (law, finance, and healthcare), and seven datasets to test robustness against out-of-distribution queries. We then use GQR-Bench to contrast the effectiveness and efficiency of LLM-based routing mechanisms (GPT-4o-mini, Llama-3.2-3B, and Llama-3.1-8B), standard LLM-based guardrail approaches (LlamaGuard and NVIDIA NeMo Guardrails), continuous bag-of-words classifiers (WideMLP, fastText), and traditional machine learning models (SVM, XGBoost). Our results show that WideMLP, enhanced with out-of-domain detection capabilities, yields the best trade-off between accuracy (88\%) and speed (<4ms). The embedding-based fastText excels at speed (<1ms) with acceptable accuracy (80\%), whereas LLMs yield the highest accuracy (91\%) but are comparatively slow (62ms for local Llama-3.1:8B and 669ms for remote GPT-4o-mini calls). Our findings challenge the automatic reliance on LLMs for (guarded) query routing and provide concrete recommendations for practical applications. GQR-Bench will be released as a Python package -- \texttt{gqr}.

Editable Stain Transformation Of Histological Images Using Unpaired GANs

Double staining in histopathology, particularly for metaplastic breast cancer, typically employs H&E and P63 dyes. However, P63's tissue damage and high cost necessitate alternative methods. This study introduces xAI-CycleGAN, an advanced architecture combining Mask CycleGAN with explainability features and structure-preserving capabilities for transforming H&E stained breast tissue images into P63-like images. The architecture allows for output editing, enhancing resemblance to actual images and enabling further model refinement. We showcase xAI-CycleGAN's efficacy in maintaining structural integrity and generating high-quality images. Additionally, a histopathologist survey indicates the generated images' realism is often comparable to actual images, validating our model's high-quality output.

xAI-CycleGAN, a Cycle-Consistent Generative Assistive Network

In the domain of unsupervised image-to-image transformation using generative transformative models, CycleGAN has become the architecture of choice. One of the primary downsides of this architecture is its relatively slow rate of convergence. In this work, we use discriminator-driven explainability to speed up the convergence rate of the generative model by using saliency maps from the discriminator that mask the gradients of the generator during backpropagation, based on the work of Nagisetty et al., and also introducing the saliency map on input, added onto a Gaussian noise mask, by using an interpretable latent variable based on Wang M.'s Mask CycleGAN. This allows for an explainability fusion in both directions, and utilizing the noise-added saliency map on input as evidence-based counterfactual filtering. This new architecture has much higher rate of convergence than a baseline CycleGAN architecture while preserving the image quality.