Related papers: The Representational Geometry of Number

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Foundation models learn highly transferable representations through large-scale pretraining on diverse data. An increasing body of research indicates that these representations exhibit a remarkable degree of similarity across architectures…

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the…

While neural representations are central to modern deep learning, the conditions governing their geometry and their roles in downstream adaptability remain poorly understood. We develop a framework clearly separating the underlying world,…

The internal representations learned by deep networks are often sensitive to architecture-specific choices, raising questions about the stability, alignment, and transferability of learned structure across models. In this paper, we…

Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In…

Different encodings of datapoints in the latent space of latent-vector generative models may result in more or less effective and disentangled characterizations of the different explanatory factors of variation behind the data. Many works…

Prior work has shown that large language models (LLMs) often converge to accurate input embedding for numbers, based on sinusoidal representations. In this work, we quantify that these representations are in fact strikingly systematic, to…

Recent work exhibited that distributed word representations are good at capturing linguistic regularities in language. This allows vector-oriented reasoning based on simple linear algebra between words. Since many different methods have…

High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory, and lexical information for many tasks related to human-generated data. Human language makes use of a large and…

Textual representations based on pre-trained language models are key, especially in few-shot learning scenarios. What makes a representation good for text classification? Is it due to the geometric properties of the space or because it is…

Compositional representations are thought to enable humans to generalize across combinatorially vast state spaces. Models with learnable object slots, which encode information about objects in separate latent codes, have shown promise for…

Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. Yet it remains unclear to what extent LLMs linearly organize representations related to semantic…

To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…

This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…

Representation learning, and interpreting learned representations, are key areas of focus in machine learning and neuroscience. Both fields generally use representations as a means to understand or improve a system's computations. In this…

Representation learning is a widely adopted framework for learning in data-scarce environments, aiming to extract common features from related tasks. While centralized approaches have been extensively studied, decentralized methods remain…

Neural networks are powerful tools for cognitive modeling due to their flexibility and emergent properties. However, interpreting their learned representations remains challenging due to their sub-symbolic semantics. In this work, we…

The integration of structured hierarchical embeddings into transformer-based architectures introduces a refined approach to lexical representation, ensuring that multi-scale semantic relationships are preserved without compromising…

Although behavioral studies have documented numerical reasoning errors in large language models (LLMs), the underlying representational mechanisms remain unclear. We hypothesize that numerical attributes occupy shared latent subspaces and…