Related papers: Heraclitean Dialectical Concept Space
Concept-based interpretability for Convolutional Neural Networks (CNNs) aims to align internal model representations with high-level semantic concepts, but existing approaches largely overlook the semantic roles of individual filters and…
Speech and audio systems operate in inherently non-stationary environments, yet continual learning (CL) research in this domain, especially in the foundation model era, remains fragmented that fail to account for the coupled,…
Neural-symbolic approaches to machine learning incorporate the advantages from both connectionist and symbolic methods. Typically, these models employ a first module based on a neural architecture to extract features from complex data.…
Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…
Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
Continual learning (CL) aims to enable learning systems to acquire new knowledge constantly without forgetting previously learned information. CL faces the challenge of mitigating catastrophic forgetting while maintaining interpretability…
Cattani-Sassone's notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher…
We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…
Concept discovery is one of the open problems in the interpretability literature that is important for bridging the gap between non-deep learning experts and model end-users. Among current formulations, concepts defines them by as a…
Enabling generative models to decompose visual concepts from a single image is a complex and challenging problem. In this paper, we study a new and challenging task, customized concept decomposition, wherein the objective is to leverage…
After learning a concept, humans are also able to continually generalize their learned concepts to new domains by observing only a few labeled instances without any interference with the past learned knowledge. In contrast, learning…
Learning concepts from natural high-dimensional data (e.g., images) holds potential in building human-aligned and interpretable machine learning models. Despite its encouraging prospect, formalization and theoretical insights into this…
Hyperbolic geometry has been successfully applied in modeling brain cortical and subcortical surfaces with general topological structures. However such approaches, similar to other surface based brain morphology analysis methods, usually…
Large Language Models (LLMs) offer vast potential for creative ideation; however, their standard interaction paradigm often produces unstructured textual outputs that lead users to prematurely converge on sub-optimal ideas-a phenomenon…
Recent applications in computer vision have come to heavily rely on superpixel over-segmentation as a pre-processing step for higher level vision tasks, such as object recognition, image labelling or image segmentation. Here we present a…
The evolution of organismal populations is not typically thought of in terms of classical mechanics. However, many of the conceptual models used to approximate evolutionary trajectories have implicit parallels to dynamic physical systems.…
Topological neural networks have emerged as powerful successors of graph neural networks. However, they typically involve higher-order message passing, which incurs significant computational expense. We circumvent this issue with a novel…
Concept formation in transformer language models is depth-extended, not a single-layer event: concepts emerge gradually across a contiguous region of the residual stream. Mechanistic interpretability methods identify the single layer of…