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A Geometric Unification of Concept Learning with Concept Cones

arXiv:2512.07355v2 Announce Type: replace Abstract: Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge. While CBMs use supervision to align activations with human-labeled concepts, SAEs rely on sparse coding to uncover emergent ones. We show that both paradigms instantiate the same geometric structure: each...

arXiv CS 1d ago

A Geometric View for Understanding Concept Learning and Neuron Interpretation in Sparse Autoencoders

Announce Type: new Abstract: We propose a unified mathematical framework for a geometric understanding of concept learning and neuron interpretation in sparse autoencoders (SAEs). While SAEs improve interpretability of neural networks by learning sparse feature representations, a principled definition of ''concept'' and ''learning'' remains unclear. We formalize concepts as sets of data points and cast concept learning as a set-alignment problem between human-defined and model-induced concepts.

arXiv CS 2d ago

Formal Concept Lattices are Good Semantic Scaffolds for Concept-Based Learning

arXiv:2606.05471v1 Announce Type: new Abstract: Learning semantics is essential for deep learning models to be interpretable and better aligned with human reasoning. Concept-based models approach this by representing classes through meaningful semantic abstractions, but typically treat all concepts as a flat, unstructured set learned at a single neural network layer. This overlooks a fundamental property of human semantic understanding: concepts being organized hierarchically, from general...

arXiv CS 5d ago

Polaris: Coupled Orbital Polar Embeddings for Hierarchical Concept Learning

Announce Type: replace Abstract: Real-world knowledge is often organized as hierarchies such as product taxonomies, medical ontologies, and label trees, yet learning hierarchical representations is challenging due to asymmetric structure and noisy semantics. We introduce Polaris, a polar hyperspherical embedding framework that separates semanticity from hierarchy using angular geometry and radius, enabling the learning of meaning and structure without interference. To map latent...

arXiv CS 9d ago

Learning Concepts, Not Tokens: Self-Supervised Semantic Alignment for Language Models

arXiv:2603.29123v3 Announce Type: replace Abstract: The next-token prediction (NTP) objective trains language models to predict a single token at each step, even though many continuations can express the same meaning. For example, in the sentence ``this sticker can be placed here'', positioned, attached, or put are all plausible alternatives. While standard NTP training treats these alternatives as mutually exclusive targets, we explore a self-supervised framework that encourages models to...

arXiv CS 7d ago

Crafting Your Evolving Dreams: Concept-Incremental Versatile Customization

Announce Type: new Abstract: Custom diffusion models (CDMs) have garnered significant interest owing to their remarkable capacity for generating personalized concepts. However, the majority of CDMs unrealistically presume that the user's collection of personalized concepts is static and incapable of incremental growth over time. Furthermore, they exhibit significant catastrophic forgetting and concept neglect of previously learned concepts when incrementally learning a sequence of new ones.

arXiv CS 6d ago

From Tokens to Concepts: Leveraging SAE for SPLADE

Announce Type: replace Abstract: Learned Sparse IR models, such as SPLADE, offer an excellent efficiency-effectiveness tradeoff. However, they rely on the underlying backbone vocabulary, which might hinder performance (polysemicity and synonymy) and pose a challenge for multi-lingual and multi-modal usages. To solve this limitation, we propose to replace the backbone vocabulary with a latent space of semantic concepts learned using Sparse Auto-Encoders (SAE).

arXiv CS 8d ago

Disentanglement-Based Equivariant Learning for Compositional VQA

new Abstract: Compositional visual question answering (VQA) represents a challenging yet fundamental task that requires models to comprehend novel combinations of previously learned concepts. The current methods often overlook the disentanglement of underlying concepts and are restricted in terms of their ability to effectively capture the compositional variation mechanism. Moreover, the state-of-the-art techniques depend on additional clues for training, which is not feasible in real-world...

arXiv CS 8d ago

Equilibrated Diffusion: Frequency-aware Textual Embedding for Equilibrated Image Customization

arXiv:2606.02129v1 Announce Type: new Abstract: Image customization learns target subjects from reference concept images and generates conditioned images per text prompts, mainly modifying styles or backgrounds. Prevailing methods adopt fine-tuning to pack diverse concept attributes into a unified latent embedding, yet entangled attributes hinder elimination of irrelevant disturbances from style and background. To address this issue, we propose Equilibrated Diffusion, a frequency-driven...

arXiv CS 8d ago

Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer

arXiv:2408.11266v5 Announce Type: replace Abstract: Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations.

arXiv CS 8d ago