Mohammad S. Jalali

Azim Ospanov, Jingwei Zhang, Mohammad Jalali et al.

While standard evaluation scores for generative models are mostly reference-based, a reference-dependent assessment of generative models could be generally difficult due to the unavailability of applicable reference datasets. Recently, the reference-free entropy scores, VENDI and RKE, have been proposed to evaluate the diversity of generated data. However, estimating these scores from data leads to significant computational costs for large-scale generative models. In this work, we leverage the random Fourier features framework to reduce the computational price and propose the Fourier-based Kernel Entropy Approximation (FKEA) method. We utilize FKEA's approximated eigenspectrum of the kernel matrix to efficiently estimate the mentioned entropy scores. Furthermore, we show the application of FKEA's proxy eigenvectors to reveal the method's identified modes in evaluating the diversity of produced samples. We provide a stochastic implementation of the FKEA assessment algorithm with a complexity $O(n)$ linearly growing with sample size $n$. We extensively evaluate FKEA's numerical performance in application to standard image, text, and video datasets. Our empirical results indicate the method's scalability and interpretability applied to large-scale generative models. The codebase is available at https://github.com/aziksh-ospanov/FKEA.

Jingwei Zhang, Mohammad Jalali, Cheuk Ting Li et al.

A fine-grained comparison of generative models requires the identification of sample types generated differently by each of the involved models. While quantitative scores have been proposed in the literature to rank different generative models, score-based evaluation and ranking do not reveal the nuanced differences between the generative models in producing different sample types. In this work, we propose solving a differential clustering problem to detect sample types generated differently by two generative models. To solve the differential clustering problem, we develop a spectral method called Fourier-based Identification of Novel Clusters (FINC) to identify modes produced by a generative model with a higher frequency in comparison to a reference distribution. FINC provides a scalable algorithm based on random Fourier features to estimate the eigenspace of kernel covariance matrices of two generative models and utilize the principal eigendirections to detect the sample types present more dominantly in each model. We demonstrate the application of the FINC method to large-scale computer vision datasets and generative modeling frameworks. Our numerical results suggest the scalability of the developed Fourier-based method in highlighting the sample types produced with different frequencies by generative models. The project code is available at https://github.com/buyeah1109/FINC.

Mohammad Jalali, Azim Ospanov, Amin Gohari et al.

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}.

Azim Ospanov, Mohammad Jalali, Farzan Farnia

The use of CLIP embeddings to assess the fidelity 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 alignment 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 are responsible for generating diverse images from similar text prompts, which we refer to as prompt-aware diversity. 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 Schur Complement ENtopy DIversity (Scendi) score, as a measure of the prompt-aware diversity for prompt-guided generative models. Additionally, we discuss the application of the Schur complement-based decomposition to nullify the influence of a given prompt on the CLIP embedding of an image, enabling focus or defocus of the embedded vectors on specific objects. We present several numerical results that apply our proposed Scendi score to evaluate text-to-image and LLM (text-to-text) models. Our numerical results indicate the success of the Scendi score in capturing the intrinsic diversity of prompt-guided generative models. The codebase is available at https://github.com/aziksh-ospanov/scendi-score.

Ning-Yuan Georgia Liu, Flower Yang, Mohammad S. Jalali

Causal graphs are commonly used to understand and model complex systems. Researchers often construct these graphs from different perspectives, leading to significant variations for the same problem. Comparing causal graphs is, therefore, essential for evaluating assumptions, integrating insights, and resolving disagreements. The rise of AI tools has further amplified this need, as they are increasingly used to generate hypothesized causal graphs by synthesizing information from various sources such as prior research and community inputs, providing the potential for automating and scaling causal modeling for complex systems. Similar to humans, these tools also produce inconsistent results across platforms, versions, and iterations. Despite its importance, research on causal graph comparison remains scarce. Existing methods often focus solely on structural similarities, assuming identical variable names, and fail to capture nuanced semantic relationships, which is essential for causal graph comparison. We address these gaps by investigating methods for comparing causal graphs from both semantic and structural perspectives. First, we reviewed over 40 existing metrics and, based on predefined criteria, selected nine for evaluation from two threads of machine learning: four semantic similarity metrics and five learning graph kernels. We discuss the usability of these metrics in simple examples to illustrate their strengths and limitations. We then generated a synthetic dataset of 2,000 causal graphs using generative AI based on a reference diagram. Our findings reveal that each metric captures a different aspect of similarity, highlighting the need to use multiple metrics.

M. S. Jalali

We developed a simulation game to study the effectiveness of decision-makers in overcoming two complexities in building cybersecurity capabilities: potential delays in capability development; and uncertainties in predicting cyber incidents. Analyzing 1,479 simulation runs, we compared the performances of a group of experienced professionals with those of an inexperienced control group. Experienced subjects did not understand the mechanisms of delays any better than inexperienced subjects; however, experienced subjects were better able to learn the need for proactive decision-making through an iterative process. Both groups exhibited similar errors when dealing with the uncertainty of cyber incidents. Our findings highlight the importance of training for decision-makers with a focus on systems thinking skills, and lay the groundwork for future research on uncovering mental biases about the complexities of cybersecurity.