Ka Chun Lam

Florian P. Mahner, Ka Chun Lam, Francisco Pereira et al.

The study of representations is widespread across fields, including neuroscience, psychology, and artificial intelligence. While representations are often studied and compared through similarities between stimuli, current methods provide only limited access to the dimensions that shape these representations and are often limited in interpretability. To overcome these challenges, here we introduce Similarity-Based Representation Factorization (SRF), a general computational method for recovering low-dimensional, non-negative, interpretable embeddings from similarity matrices derived from measured data. Across simulations and many neural, behavioral, and computational datasets, SRF recovers interpretable dimensions from diverse forms of representational data, even for very sparsely sampled, incomplete data. The dimensions derived from these datasets match those obtained by task-specific models, predict independent behavioral properties, improve exploratory analysis, and offer higher power for confirmatory hypothesis testing than comparing similarity matrices. Together, these results establish SRF as a general-purpose method with broad applications for uncovering, understanding, and leveraging the dimensions underlying representations.

Florian P. Mahner, Johannes Roth, Ka Chun Lam et al.

Deep neural networks trained with different architectures, objectives, and datasets have been reported to converge on similar visual representations. However, what remains unknown is which visual properties models actually converge on and which factors may underlie this convergence. To address this, we decompose the object similarity structure of 162 diverse vision models into a small set of non-negative dimensions. To determine universal versus model-specific dimensions, we then estimate how often each dimension reappears across models. In contrast to model-specific dimensions, universal dimensions are more interpretable and more strongly driven by conceptual image properties, indicating the relevance of interpretability and semantic content as implicit factors driving universality across models. Differences in architecture, objective function, training data, model size, and model performance do not explain the emergence of universal dimensions. However, models with more universal dimensions also better predict macaque IT activity and human similarity judgments, suggesting that universality reflects representations relevant to biological vision. These findings have important implications for understanding the emergent representations underlying deep neural network models and their alignment with biological vision.

Ka Chun Lam, Bridget W Mahony, Armin Raznahan et al.

Psychiatry research seeks to understand the manifestations of psychopathology in behavior, as measured in questionnaire data, by identifying a small number of latent factors that explain them. While factor analysis is the traditional tool for this purpose, the resulting factors may not be interpretable, and may also be subject to confounding variables. Moreover, missing data are common, and explicit imputation is often required. To overcome these limitations, we introduce interpretability constrained questionnaire factorization (ICQF), a non-negative matrix factorization method with regularization tailored for questionnaire data. Our method aims to promote factor interpretability and solution stability. We provide an optimization procedure with theoretical convergence guarantees, and an automated procedure to detect latent dimensionality accurately. We validate these procedures using realistic synthetic data. We demonstrate the effectiveness of our method in a widely used general-purpose questionnaire, in two independent datasets (the Healthy Brain Network and Adolescent Brain Cognitive Development studies). Specifically, we show that ICQF improves interpretability, as defined by domain experts, while preserving diagnostic information across a range of disorders, and outperforms competing methods for smaller dataset sizes. This suggests that the regularization in our method matches domain characteristics. The python implementation for ICQF is available at \url{https://github.com/jefferykclam/ICQF}.

Ho Law, Gary P. T. Choi, Ka Chun Lam et al.

Image registration has been widely studied over the past several decades, with numerous applications in science, engineering and medicine. Most of the conventional mathematical models for large deformation image registration rely on prescribed landmarks, which usually require tedious manual labeling and are prone to error. In recent years, there has been a surge of interest in the use of machine learning for image registration. In this paper, we develop a novel method for large deformation image registration by a fusion of quasiconformal theory and convolutional neural network (CNN). More specifically, we propose a quasiconformal energy model with a novel fidelity term that incorporates the features extracted using a pre-trained CNN, thereby allowing us to obtain meaningful registration results without any guidance of prescribed landmarks. Moreover, unlike many prior image registration methods, the bijectivity of our method is guaranteed by quasiconformal theory. Experimental results are presented to demonstrate the effectiveness of the proposed method. More broadly, our work sheds light on how rigorous mathematical theories and practical machine learning approaches can be integrated for developing computational methods with improved performance.

Ka Chun Lam, Francisco Pereira, Maryam Vaziri-Pashkam et al.

In order to interact with objects in our environment, humans rely on an understanding of the actions that can be performed on them, as well as their properties. When considering concrete motor actions, this knowledge has been called the object affordance. Can this notion be generalized to any type of interaction that one can have with an object? In this paper we introduce a method to represent objects in a space where each dimension corresponds to a broad mode of interaction, based on verb selectional preferences in text corpora. This object embedding makes it possible to predict human judgments of verb applicability to objects better than a variety of alternative approaches. Furthermore, we show that the dimensions in this space can be used to predict categorical and functional dimensions in a state-of-the-art mental representation of objects, derived solely from human judgements of object similarity. These results suggest that interaction knowledge accounts for a large part of mental representations of objects.

Patrick McClure, Dustin Moraczewski, Ka Chun Lam et al.

Deep neural networks (DNNs) are being increasingly used to make predictions from functional magnetic resonance imaging (fMRI) data. However, they are widely seen as uninterpretable "black boxes", as it can be difficult to discover what input information is used by the DNN in the process, something important in both cognitive neuroscience and clinical applications. A saliency map is a common approach for producing interpretable visualizations of the relative importance of input features for a prediction. However, methods for creating maps often fail due to DNNs being sensitive to input noise, or by focusing too much on the input and too little on the model. It is also challenging to evaluate how well saliency maps correspond to the truly relevant input information, as ground truth is not always available. In this paper, we review a variety of methods for producing gradient-based saliency maps, and present a new adversarial training method we developed to make DNNs robust to input noise, with the goal of improving interpretability. We introduce two quantitative evaluation procedures for saliency map methods in fMRI, applicable whenever a DNN or linear model is being trained to decode some information from imaging data. We evaluate the procedures using a synthetic dataset where the complex activation structure is known, and on saliency maps produced for DNN and linear models for task decoding in the Human Connectome Project (HCP) dataset. Our key finding is that saliency maps produced with different methods vary widely in interpretability, in both in synthetic and HCP fMRI data. Strikingly, even when DNN and linear models decode at comparable levels of performance, DNN saliency maps score higher on interpretability than linear model saliency maps (derived via weights or gradient). Finally, saliency maps produced with our adversarial training method outperform those from other methods.

Thomas Y. Hou, De Huang, Ka Chun Lam et al.

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition components by integrating the multiresolution framework into the Implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm.

Lok Ming Lui, Ka Chun Lam, Tsz Wai Wong et al.

Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenience in data transmission and data storage. To tackle this problem, we propose an effective algorithm for compressing surface homeomorphisms using Fourier approximation of the Beltrami representation. The Beltrami representation is a complex-valued function defined on triangular faces of the surface mesh with supreme norm strictly less than 1. Under suitable normalization, there is a 1-1 correspondence between the set of surface homeomorphisms and the set of Beltrami representations. Hence, every bijective surface map is associated with a unique Beltrami representation. Conversely, given a Beltrami representation, the corresponding bijective surface map can be exactly reconstructed using the Linear Beltrami Solver introduced in this paper. Using the Beltrami representation, the surface homeomorphism can be easily compressed by Fourier approximation, without distorting the bijectivity of the map. The storage memory can be effectively reduced, which is useful for many practical problems in computer graphics and imaging. In this paper, we proposed to apply the algorithm to texture map compression and video compression. With our proposed algorithm, the storage requirement for the texture properties of a textured surface can be significantly reduced. Our algorithm can further be applied to compressing motion vector fields for video compression, which effectively improve the compression ratio.