Related papers: Fiber Bundle Morphisms as a Framework for Modeling…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of…
Foundation Models (FMs) are models trained on large corpora of data that, at very large scale, can generalize to new tasks without any task-specific finetuning. As these models continue to grow in size, innovations continue to push the…
We train one multilingual model for dependency parsing and use it to parse sentences in several languages. The parsing model uses (i) multilingual word clusters and embeddings; (ii) token-level language information; and (iii)…
Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…
Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…
Predicting multiple real-world tasks in a single model often requires a particularly diverse feature space. Multimodal (MM) models aim to extract the synergistic predictive potential of multiple data types to create a shared feature space…
Perceptual learning enables humans to recognize and represent stimuli invariant to various transformations and build a consistent representation of the self and physical world. Such representations preserve the invariant physical relations…
Three-dimensional Morphable Models (3DMMs) are powerful statistical tools for representing the 3D surfaces of an object class. In this context, we identify an interesting question that has previously not received research attention: is it…
Multiphonics, the presence of multiple pitches within the sound, can be produced in several ways. In wind instruments, they can appear at low blowing pressure when complex fingerings are used. Such multiphonics can be modeled by the Impulse…
Diffusion magnetic resonance imaging, a non-invasive tool to infer white matter fiber connections, produces a large number of streamlines containing a wealth of information on structural connectivity. The size of these tractography outputs…
Manifolds and fiber bundles, while superficially different, have strong parallels; in particular, they are both defined in terms of equivalence classes of atlases or in terms of maximal atlases, with the atlases treated as mere adjuncts.…
Language exhibits structure at different scales, ranging from subwords to words, sentences, paragraphs, and documents. To what extent do deep models capture information at these scales, and can we force them to better capture structure…
We apply the equal load-sharing fiber bundle model of fracture failure in composite materials to model the traffic failure in a system of parallel road network in a city. For some special distributions of traffic handling capacities…
Training machine learning models requires feeding input data for models to ingest. Input pipelines for machine learning jobs are often challenging to implement efficiently as they require reading large volumes of data, applying complex…
One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions.…
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between…
Foundation models for vision and language are the basis of AI applications across numerous sectors of society. The success of these models stems from their ability to mimic human capabilities, namely visual perception in vision models, and…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
With the wide adoption of functional magnetic resonance imaging (fMRI) by cognitive neuroscience researchers, large volumes of brain imaging data have been accumulated in recent years. Aggregating these data to derive scientific insights…