We summarize our axioms for higher categories, and describe the blob complex. Fixing an n-category C, the blob complex associates a chain complex B_*(W;C)$ to any n-manifold W. The 0-th homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should …
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31 results for “blobs”
BLoB fine-tunes LLMs with Bayesian methods to improve uncertainty estimation.
problem Overconfidence in LLMs during inference for domain-specific tasks.
method Continuous Bayesian low-rank adaptation during fine-tuning.
result BLoB improves generalization and uncertainty estimation in LLMs.
The blob complexmath.AT
Given an n-manifold M and an n-category C, we define a chain complex (the "blob complex") B_*(M;C). The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, and as a generalization of Hochschild homology to n-categories and n-manifolds. It enjoys a number of nice formal properti…
Computes invariants distinguishing between immersions and embeddings of doodles and blobs on surfaces.
problem Distinguishing between immersions and embeddings of doodles and blobs on surfaces.
method Regular embeddings, bordisms, and exact sequences of abelian groups.
result Exact sequence describing bordisms of immersions and embeddings of doodles on .
New definition of skein lasagna module for specific 4-manifolds.
problem Defining a new homology theory for specific 4-manifolds.
method Elementary definition using diagrams in the 4-manifold.
result Explicit calculations for disk bundles over S^2.
Study how large-scale flows align small-scale vortices in 3D Euler equations.
problem Understanding how large-scale flows align small-scale vortices in 3D Euler equations.
method Constructing a Lagrangian coordinate to identify when the Lie bracket is zero and investigating the locality of the pressure term.
result Clarified conditions under which small-scale vortices are aligned by large-scale flows.
In this report, we review the calculation of entropy-regularised Wasserstein loss introduced by Cuturi and document a practical implementation in PyTorch. Code is available at https://github.com/t-vi/pytorch-tvmisc/blob/master/wasserstein-distance/Pytorch_Wasserstein.ipynb
BLOB combines organic and bandit signals for better user interest estimation.
problem Combining organic and bandit signals for improved user interest estimation.
method Bayesian Latent Organic Bandit (BLOB) model using variational auto-encoders and local re-parametrization.
result BLOB outperforms organic and bandit-based methods in both organic and bandit-rich environments.
Transaction Costs and Speed in the Ethereum Ecosystem: Scalability of the Mainnet and Layer 2sq-fin.TR
Ethereum upgrades increased TPS and lowered fees, with L2s surpassing Solana in 2029.
problem Transaction speed and fees in Ethereum
method Comparing Ethereum Mainnet and Layer 2 networks, Solana, and Polygon
result Ethereum Mainnet and L2 networks surpassed Solana in terms of TPS and lowered fees
Handlebody diagram algebrasmath.QA
The paper explores handlebody versions of various diagram algebras.
problem None explicitly stated, but related to algebraic structures.
method Study of handlebody versions of classical diagram algebras and reformulation of cellular algebras.
result All mentioned algebras are part of the reformulated cellular algebra theory.
New structure for quantum algebra representations.
problem Understanding representations of quantum algebras.
method Constructing a quotient category of annular quantum webs.
result Equivalent to finite dimensional representations of quantum Levi subalgebras.
We define symplectic fractional twists, which generalize Dehn twists, and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with the invariant contact structures that were studied by Lutz and Giroux. We show th…
Machine learning algorithms learn from data and use data from databases that are mutable; therefore, the data and the results of machine learning cannot be fully trusted. Also, the machine learning process is often difficult to automate. A unified analytical framework for trustable machine learning has been presented i…
Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a data set. The estimator is based on binary neighbourhood information about the ob…
The paper extends Thurston's method to new variants of Mather-Thurston theorem.
problem Proving new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
method Generalizing Thurston's technique to prove new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
result The paper answers questions posed by Gelfand-Fuks and Greenberg on PL foliations and Rybicki on contactomorphisms.
The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present explicit solutions of the binormal equation in higher-dimensions that collapse in finite time. The local nature of this phenomenon suggests the appearance of singularity in nearb…
The manifold hypothesis states that many kinds of high-dimensional data are concentrated near a low-dimensional manifold. If the topology of this data manifold is non-trivial, a continuous encoder network cannot embed it in a one-to-one manner without creating holes of low density in the latent space. This is at odds w…
A new method learns discrete representations for images and videos, improving upon previous models.
problem Learning discrete representations for images and videos to improve performance.
method Depthwise application of Vector Quantized Variational Autoencoders (VQVAE) to feature axis.
result 33% improvement in performance compared to previous discrete models.
IVON improves LoRA finetuning with minimal overhead and significant accuracy gains.
problem Improving LoRA finetuning with Bayesian methods.
method IVON, a variational algorithm, with posterior pruning.
result Significant accuracy improvements over AdamW and other Bayesian methods.
Capsule networks improve performance on image classification tasks with fewer parameters.
problem Improving performance of capsule networks with fewer parameters.
method Inverted dot-product attention routing, Layer Normalization, concurrent iterative routing.
result Improves performance on benchmark datasets CIFAR-10 and CIFAR-100, and performs at-par with ResNet-18.
Local Hebbian learning is believed to be inferior in performance to end-to-end training using a backpropagation algorithm. We question this popular belief by designing a local algorithm that can learn convolutional filters at scale on large image datasets. These filters combined with patch normalization and very steep …
GP-ND avoids obstacles in trajectory planning using Gaussian Process regression.
problem Avoiding obstacles in trajectory planning for real-world systems.
method GP-ND models negative data pairs using Gaussian distributions and maximizes their KL divergence from the GP to avoid them.
result GP-ND outperforms traditional GP learning in obstacle-aware trajectory planning.
Preprint proves quantum coideal Schur-Weyl duality and generalizes Jones-Wenzl projectors.
problem Quantum coideal Schur-Weyl duality and Jones-Wenzl projectors in type B/D.
method Combinatorial proofs and functional analytic arguments.
result Explicit proof of quantum coideal Schur-Weyl duality and generalization of Jones-Wenzl projectors.
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial couplin…
Training large deep neural networks on massive datasets is computationally very challenging. There has been recent surge in interest in using large batch stochastic optimization methods to tackle this issue. The most prominent algorithm in this line of research is LARS, which by employing layerwise adaptive learning ra…
Point source detection at low signal-to-noise is challenging for astronomical surveys, particularly in radio interferometry images where the noise is correlated. Machine learning is a promising solution, allowing the development of algorithms tailored to specific telescope arrays and science cases. We present DeepSourc…
A new robust scaling approach improves downstream metabolomics analysis.
problem Challenges in choosing scaling techniques for metabolomics data.
method Introduces a weighted scaling approach robust to outliers.
result The proposed method outperforms traditional scaling techniques in both outlier-free and outlier-present datasets.
In many settings, it is desirable to learn decision-making and control policies through learning or bootstrapping from expert demonstrations. The most common approaches under this Imitation Learning (IL) framework are Behavioural Cloning (BC), and Inverse Reinforcement Learning (IRL). Recent methods for IRL have demons…
Exploiting Epistemic Uncertainty of Anatomy Segmentation for Anomaly Detection in Retinal OCTeess.IV
Diagnosis and treatment guidance are aided by detecting relevant biomarkers in medical images. Although supervised deep learning can perform accurate segmentation of pathological areas, it is limited by requiring a-priori definitions of these regions, large-scale annotations, and a representative patient cohort in the …
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, wa…
Deep nets trained with MSE loss exhibit Neural Collapse, collapsing features and classifiers to class means.
problem Understanding Neural Collapse in MSE-trained deep nets.
method Developed a new MSE loss decomposition and introduced the central path concept.
result Exact dynamics of Neural Collapse along the central path can be predicted.