Towards an Explainable Comparison and Alignment of Feature Embeddings

While several feature embedding models have been developed in the literature, comparisons of these embeddings have largely focused on their numerical performance in classification-related downstream applications. However, an interpretable comparison of different embeddings requires identifying and analyzing mismatches between sample groups clustered within the embedding spaces. In this work, we propose the \emph{Spectral Pairwise Embedding Comparison (SPEC)} framework to compare embeddings and identify their differences in clustering a reference dataset. Our approach examines the kernel matrices derived from two embeddings and leverages the eigendecomposition of the difference kernel matrix to detect sample clusters that are captured differently by the two embeddings. We present a scalable implementation of this kernel-based approach, with computational complexity that grows linearly with the sample size. Furthermore, we introduce an optimization problem using this framework to align two embeddings, ensuring that clusters identified in one embedding are also captured in the other model. We provide numerical results demonstrating the SPEC's application to compare and align embeddings on large-scale datasets such as ImageNet and MS-COCO. The code is available at [https://github.com/mjalali/embedding-comparison](github.com/mjalali/embedding-comparison).

PromptWise: Online Learning for Cost-Aware Prompt Assignment in Generative Models

The rapid advancement of generative AI models has provided users with numerous options to address their prompts. When selecting a generative AI model for a given prompt, users should consider not only the performance of the chosen model but also its associated service cost. The principle guiding such consideration is to select the least expensive model among the available satisfactory options. However, existing model-selection approaches typically prioritize performance, overlooking pricing differences between models. In this paper, we introduce PromptWise, an online learning framework designed to assign a sequence of prompts to a group of large language models (LLMs) in a cost-effective manner. PromptWise strategically queries cheaper models first, progressing to more expensive options only if the lower-cost models fail to adequately address a given prompt. Through numerical experiments, we demonstrate PromptWise's effectiveness across various tasks, including puzzles of varying complexity and code generation/translation tasks. The results highlight that PromptWise consistently outperforms cost-unaware baseline methods, emphasizing that directly assigning prompts to the most expensive models can lead to higher costs and potentially lower average performance.

DiffPattern-Flex: Efficient Layout Pattern Generation via Discrete Diffusion

Recent advancements in layout pattern generation have been dominated by deep generative models. However, relying solely on neural networks for legality guarantees raises concerns in many practical applications. In this paper, we present \tool{DiffPattern}-Flex, a novel approach designed to generate reliable layout patterns efficiently. \tool{DiffPattern}-Flex incorporates a new method for generating diverse topologies using a discrete diffusion model while maintaining a lossless and compute-efficient layout representation. To ensure legal pattern generation, we employ {an} optimization-based, white-box pattern assessment process based on specific design rules. Furthermore, fast sampling and efficient legalization technologies are employed to accelerate the generation process. Experimental results across various benchmarks demonstrate that \tool{DiffPattern}-Flex significantly outperforms existing methods and excels at producing reliable layout patterns.

pFedFair: Towards Optimal Group Fairness-Accuracy Trade-off in Heterogeneous Federated Learning

Federated learning (FL) algorithms commonly aim to maximize clients' accuracy by training a model on their collective data. However, in several FL applications, the model's decisions should meet a group fairness constraint to be independent of sensitive attributes such as gender or race. While such group fairness constraints can be incorporated into the objective function of the FL optimization problem, in this work, we show that such an approach would lead to suboptimal classification accuracy in an FL setting with heterogeneous client distributions. To achieve an optimal accuracy-group fairness trade-off, we propose the Personalized Federated Learning for Client-Level Group Fairness (pFedFair) framework, where clients locally impose their fairness constraints over the distributed training process. Leveraging the image embedding models, we extend the application of pFedFair to computer vision settings, where we numerically show that pFedFair achieves an optimal group fairness-accuracy trade-off in heterogeneous FL settings. We present the results of several numerical experiments on benchmark and synthetic datasets, which highlight the suboptimality of non-personalized FL algorithms and the improvements made by the pFedFair method.

Dissecting CLIP: Decomposition with a Schur Complement-based Approach

The use of CLIP embeddings to assess the alignment of samples produced by text-to-image generative models has been extensively explored in the literature. While the widely adopted CLIPScore, derived from the cosine similarity of text and image embeddings, effectively measures the relevance of a generated image, it does not quantify the diversity of images generated by a text-to-image model. In this work, we extend the application of CLIP embeddings to quantify and interpret the intrinsic diversity of text-to-image models, which is responsible for generating diverse images from similar text prompts. To achieve this, we propose a decomposition of the CLIP-based kernel covariance matrix of image data into text-based and non-text-based components. Using the Schur complement of the joint image-text kernel covariance matrix, we perform this decomposition and define the matrix-based entropy of the decomposed component as the \textit{Schur Complement Entropy (SCE)} score, a measure of the intrinsic diversity of a text-to-image model based on data collected with varying text prompts. Additionally, we demonstrate the use of the Schur complement-based decomposition to nullify the influence of a given prompt in the CLIP embedding of an image, enabling focus or defocus of embeddings on specific objects or properties for downstream tasks. We present several numerical results that apply our Schur complement-based approach to evaluate text-to-image models and modify CLIP image embeddings. The codebase is available at https://github.com/aziksh-ospanov/CLIP-DISSECTION

Be More Diverse than the Most Diverse: Online Selection of Diverse Mixtures of Generative Models

The availability of multiple training algorithms and architectures for generative models requires a selection mechanism to form a single model over a group of well-trained generation models. The selection task is commonly addressed by identifying the model that maximizes an evaluation score based on the diversity and quality of the generated data. However, such a best-model identification approach overlooks the possibility that a mixture of available models can outperform each individual model. In this work, we explore the selection of a mixture of multiple generative models and formulate a quadratic optimization problem to find an optimal mixture model achieving the maximum of kernel-based evaluation scores including kernel inception distance (KID) and R\'{e}nyi kernel entropy (RKE). To identify the optimal mixture of the models using the fewest possible sample queries, we propose an online learning approach called Mixture Upper Confidence Bound (Mixture-UCB). Specifically, our proposed online learning method can be extended to every convex quadratic function of the mixture weights, for which we prove a concentration bound to enable the application of the UCB approach. We prove a regret bound for the proposed Mixture-UCB algorithm and perform several numerical experiments to show the success of the proposed Mixture-UCB method in finding the optimal mixture of text-based and image-based generative models. The codebase is available at https://github.com/Rezaei-Parham/Mixture-UCB .

A Super-pixel-based Approach to the Stable Interpretation of Neural Networks

Saliency maps are widely used in the computer vision community for interpreting neural network classifiers. However, due to the randomness of training samples and optimization algorithms, the resulting saliency maps suffer from a significant level of stochasticity, making it difficult for domain experts to capture the intrinsic factors that influence the neural network's decision. In this work, we propose a novel pixel partitioning strategy to boost the stability and generalizability of gradient-based saliency maps. Through both theoretical analysis and numerical experiments, we demonstrate that the grouping of pixels reduces the variance of the saliency map and improves the generalization behavior of the interpretation method. Furthermore, we propose a sensible grouping strategy based on super-pixels which cluster pixels into groups that align well with the semantic meaning of the images. We perform several numerical experiments on CIFAR-10 and ImageNet. Our empirical results suggest that the super-pixel-based interpretation maps consistently improve the stability and quality over the pixel-based saliency maps.

Conditional Vendi Score: An Information-Theoretic Approach to Diversity Evaluation of Prompt-based Generative Models

Text-conditioned generation models are commonly evaluated based on the quality of the generated data and its alignment with the input text prompt. On the other hand, several applications of prompt-based generative models require sufficient diversity in the generated data to ensure the models' capability of generating image and video samples possessing a variety of features. However, most existing diversity metrics are designed for unconditional generative models, and thus cannot distinguish the diversity arising from variations in text prompts and that contributed by the generative model itself. In this work, our goal is to quantify the prompt-induced and model-induced diversity in samples generated by prompt-based models. We propose an information-theoretic approach for internal diversity quantification, where we decompose the kernel-based entropy $H(X)$ of the generated data $X$ into the sum of the conditional entropy $H(X|T)$, given text variable $T$, and the mutual information $I(X; T)$ between the text and data variables. We introduce the \emph{Conditional-Vendi} score based on $H(X|T)$ to quantify the internal diversity of the model and the \emph{Information-Vendi} score based on $I(X; T)$ to measure the statistical relevance between the generated data and text prompts. We provide theoretical results to statistically interpret these scores and relate them to the unconditional Vendi score. We conduct several numerical experiments to show the correlation between the Conditional-Vendi score and the internal diversity of text-conditioned generative models. The codebase is available at \href{https://github.com/mjalali/conditional-vendi}{https://github.com/mjalali/conditional-vendi}.

On the Statistical Complexity of Estimating VENDI Scores from Empirical Data

Reference-free evaluation metrics for generative models have recently been studied in the machine learning community. As a reference-free metric, the VENDI score quantifies the diversity of generative models using matrix-based entropy from information theory. The VENDI score is usually computed through the eigendecomposition of an $n \times n$ kernel matrix for $n$ generated samples. However, due to the high computational cost of eigendecomposition for large $n$, the score is often computed on sample sizes limited to a few tens of thousands. In this paper, we explore the statistical convergence of the VENDI score and demonstrate that for kernel functions with an infinite feature map dimension, the evaluated score for a limited sample size may not converge to the matrix-based entropy statistic. We introduce an alternative statistic called the $t$-truncated VENDI statistic. We show that the existing Nystr\"om method and the FKEA approximation method for the VENDI score will both converge to the defined truncated VENDI statistic given a moderate sample size. We perform several numerical experiments to illustrate the concentration of the empirical VENDI score around the truncated VENDI statistic and discuss how this statistic correlates with the visual diversity of image data.

Robust Model Evaluation over Large-scale Federated Networks

In this paper, we address the challenge of certifying the performance of a machine learning model on an unseen target network, using measurements from an available source network. We focus on a scenario where heterogeneous datasets are distributed across a source network of clients, all connected to a central server. Specifically, consider a source network "A" composed of $K$ clients, each holding private data from unique and heterogeneous distributions, which are assumed to be independent samples from a broader meta-distribution $\mu$. Our goal is to provide certified guarantees for the model's performance on a different, unseen target network "B," governed by another meta-distribution $\mu'$, assuming the deviation between $\mu$ and $\mu'$ is bounded by either the Wasserstein distance or an $f$-divergence. We derive theoretical guarantees for the model's empirical average loss and provide uniform bounds on the risk CDF, where the latter correspond to novel and adversarially robust versions of the Glivenko-Cantelli theorem and the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality. Our bounds are computable in polynomial time with a polynomial number of queries to the $K$ clients, preserving client privacy by querying only the model's (potentially adversarial) loss on private data. We also establish non-asymptotic generalization bounds that consistently converge to zero as both $K$ and the minimum client sample size grow. Extensive empirical evaluations validate the robustness and practicality of our bounds across real-world tasks.