Related papers: TokenBlowUp: Resolving Representational Singularit…

The application of large language models (LLMs) to chemistry is frequently hampered by a "tokenization bottleneck", where tokenizers tuned on general-domain text tend to fragment chemical representations such as SMILES into semantically…

Multimodal large language models (MLLMs) have made significant advancements in vision understanding and reasoning. However, the autoregressive Transformer architecture used by MLLMs requries tokenization on input images, which limits their…

Token uniformity is commonly observed in transformer-based models, in which different tokens share a large proportion of similar information after going through stacked multiple self-attention layers in a transformer. In this paper, we…

Scaling large multimodal models (LMMs) to 3D understanding poses unique challenges: point cloud data is sparse and irregular, existing models rely on fragmented architectures with modality-specific encoders, and training pipelines often…

Geometric problem solving constitutes a critical branch of mathematical reasoning, requiring precise analysis of shapes and spatial relationships. Current evaluations of geometric reasoning in vision-language models (VLMs) face limitations,…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Geometric analyses of large language model (LLM) representations reveal structured variation across depth but remain fundamentally correlational with respect to token prediction formation. Meanwhile, causal interventions expose…

We construct a functor from the category of manifolds with generalized corners to the category of complexes of toric monoids, and for every `refinement' of the complex associated to a manifold, we show there is a unique `blow-up', i.e., a…

We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution $u(x,t)$, the graph…

The rapid advancement of large language models (LLMs) has intensified the need for effective mechanisms to transform continuous multimodal data into discrete representations suitable for language-based processing. Discrete tokenization,…

Classic AI planning problems have been revisited in the Large Language Model (LLM) era, with a focus of recent benchmarks on success rates rather than plan efficiency. We examine the degree to which frontier models reason optimally versus…

Autoregressive (AR) models, long dominant in language generation, are increasingly applied to image synthesis but are often considered less competitive than Diffusion-based models. A primary limitation is the substantial number of image…

We present a rigorous analysis of the slow passage through a Turing bifurcation in the Swift-Hohenberg equation using a novel approach based on geometric blow-up. We show that the formally derived multiple scales ansatz which is known from…

We study the exchange of stability in scalar reaction-diffusion equations which feature a slow passage through transcritical and pitchfork type singularities in the reaction term, using a novel adaptation of the geometric blow-up method.…

We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic blow-up point at the origin, and a blow-up surface which is…

We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the…

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains…

We consider molecule generation in 3D space using language models (LMs), which requires discrete tokenization of 3D molecular geometries. Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. Here,…

Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…

The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…