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Despite prolific work on evaluating generative models, little research has been done on the quality evaluation of an individual generated sample. To address this problem, a lightweight generated sample quality evaluation (LGSQE) method is proposed in this work. In the training stage of LGSQE, a binary classifier is trained on real and synthetic samples, where real and synthetic data are labeled by 0 and 1, respectively. In the inference stage, the classifier assign soft labels (ranging from 0 to 1) to each generated sample. The value of soft label indicates the quality level; namely,the quality is better if its soft label is closer to 0. LGSQE can serve as a post-processing module for quality control. Furthermore, LGSQE can be used to evaluate the performance of generative models, such as accuracy, AUC, precision and recall, by aggregating sample-level quality. Experiments are conducted on CIFAR-10 and MNIST to demonstrate that LGSQE can preserve the same performance rank order as that predicted by the Frechet Inception Distance (FID) but with significantly lower complexity.

Fig. 1 shows the pipeline of the proposed method. The LGSQE method consists of three cascaded modules:

Module 1: Representation Learning. effective local and global representations of images are learned based upon PixelHop framework.

Module 2: Discriminant Feature Test (DFT). Use DFT to choose powerful features from large numbers of representations obtained from Module 1 against a particular task.

Module 3: Binary Classification for Evaluation. We partition the real/generated data into training and testing sets. A binary classifier is trained on the union of real and generated training samples, which are labeled with “0” and “1”, respectively. The classifier assigns a soft score, to each testing sample as the sample quality index.

Fig. 2 shows the evaluation of generated [...]

Hong-Shuo Chen studied Johann Georg Büsch, the mathematician in MCL genealogy, and shared his study with MCL members in the pre-seminar sharing on November 14, 2022. Johann Georg Büsch was born on January 3, 1728, at Alten-Weding in Hanover and died on August 5, 1800, in Hamburg. He is a German mathematics teacher and writer on statistics and commerce. He is the 14th ancestor of Professor Kuo.

When he was three years old, he came to Hamburg with his parents. He studied at the Georg-August-University of Gottingen and the Martin Luther University of Halle Wittenberg. After he graduates, he becomes a mathematics professor in the Hamburg gymnasium. He wrote a lot of books related to commerce and political economy.  As a math teacher, he mentored and helped the young Johann Elert Bode, who later became a famous astronomer. Johann Elert Bode calculated the orbit of Uranus and recommended the planet’s name.

Johann Georg Büsch married Margarete Augusta Schwalb in 1759, and they had 5 sons and 5 daughters. Two sons became the merchant. He also owned a library of 3200 math books and some scientific instruments. Besides his contribution to math, he established an association for the promotion of art and industry and the foundation of a school of trade. Both of them became one of the most noted establishments of their class in the world under his direction. Before his death, Büsch was almost totally blind. However, he was still working effortlessly until the last day of his life.

References: https://en.wikipedia.org/wiki/Johann_Georg_B%C3%BCsch

The Keller Colloquium is a distinguished lecture series for the CMS (Computing and Mathematical Sciences) department at the California Institute of Technology (Caltech). The CMS department includes Applied Math, Control, and Computer Science programs. A committee of students and faculty chooses the speakers across these areas. Professor Kuo was invited to lecture during the Fall Quarter of the 2022-23 academic year.

Professor Kuo visited Caltech on October 31 (Monday). He met Professor P. P. Vaidyanathan and Professor Thomas Yizhao Hou before his seminar at 4 pm. The title of his lecture was “Green Learning: Methodology, Examples, and Outlook,” with the following abstract:

“The rapid advances in artificial intelligence in the last decade are primarily attributed to the wide applications of deep learning (DL). Yet, the high carbon footprint yielded by larger DL networks is a concern to sustainability. Green learning (GL) has been proposed as an alternative to address this concern. GL is characterized by low carbon footprints, small model sizes, low computational complexity, and mathematical transparency.  It offers energy-effective solutions in cloud centers and mobile/edge devices.  It has three main modules: 1) unsupervised representation learning, 2) supervised feature learning, and 3) decision learning. GL has been successfully applied to a few applications. This talk provides an overview of the GL solution, its demonstrated examples, and its technical outlook. The connection between GL and DL will also be discussed.”

The Lecture was well attended. People showed interest in this new machine-learning paradigm.

Knowledge graphs (KGs) store human knowledge in a graph-structured format, where nodes and edges denote entities and relations, respectively. Most KGs, such as wikidata [1], suffer from the incompleteness problem; namely, a large number of factual triples are missing, leading to performance degradation in downstream applications. Thus, there is growing interest in developing KG completion (KGC) methods to solve the incompleteness problem by inferring undiscovered factual triples based on existing ones.

Prior KGC work focuses on learning embeddings for entities and relations through a simple score function. Yet, a higher-dimensional embedding space is usually required for a better reasoning capability, which leads to larger model size and hinders applicability to real-world problems (e.g., large-scale KGs or mobile/edge computing). A lightweight modularized KGC solution, called GreenKGC, is proposed to address this issue. GreenKGC consists of three modules: representation learning, feature pruning, and decision learning, to extract discriminant KG features and make accurate predictions on missing relationships using classifiers and negative sampling. The overview of the model is shown in Fig. 1.

Experimental results demonstrate several advantages of GreenKGC. First, it only requires a low-dimensional space (e.g. d = 8) to achieve achieve competitive or even better performance against high-dimensional models with much smaller model sizes. Second, as compared with other classification-based methods, it requires a shorter inference time and provides better performance. Third, the feature pruning module is 20x faster than knowledge distillation methods in training powerful low-dimensional features. A comparison of GreenKGC and other KGC models under different dimensions is given in Fig. 2.

-By Yun Cheng Wang

Reference:

[1] Vrandečić, Denny, and Markus Krötzsch. “Wikidata: a free collaborative knowledgebase.” Communications of the ACM 57.10 (2014): 78-85.

Xuejing Lei studied on Nicolaus Copernicus, the first mathematician in MCL genealogy, and shared her study with MCL members in the pre-seminar sharing on September 12, 2022. Nicolaus Copernicus was born in 1473 in Toruń, Royal Prussia, Poland and died in 1543 aged 70. He was a Renaissance polymath, who made contributions in a wide variety of fields including astronomy, canon law, economics, mathematics, etc. He is best known for Heliocentrism, Quantity theory of money and Gresham–Copernicus law.

Nicolaus Copernicus was born in a powerful family. His father was a well-to-do merchant who dealt in copper, and died about 1483. His mother was the daughter of a wealthy Toruń patrician and city councilor, deceased after 1495. After his father’s death, his maternal uncle, Lucas Watzenrode the Younger, took the little boy under his wing and saw to his education and career. Lucas formed close relations with three successive Polish monarchs Watzenrode and many rulers. He came to be considered the most powerful man in Warmia, and his wealth, connections and influence allowed him to secure Copernicus’s education and career as a canon at Frombork Cathedral.

Nicolaus Copernicus’s study in University of Kraków (now Jagiellonian University) gave him a thorough grounding in the mathematical astronomy and initiated his analysis of logical contradictions in the two “official” systems of astronomy — Aristotle’s theory of homocentric spheres, and Ptolemy’s mechanism of eccentrics and epicycles. He then went to Italy and studied in University of Bologna for 4 years and University of Padua for 2 years, and obtained his Doctoral degree of Canon Law in University of Ferrara in 1503.

Although Nicolaus Copernicus was best known to his contemporaries as a doctor and the Canon of Frauenburg Cathedral, he is best [...]