A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via graphical diagrams with virtual crossings. Virtual knot theory studies non-planar Gauss…
Paper reinterprets majorizing measure theorem in terms of coding theory.
Topological theory for qLDPC codes enables non-Clifford gates and magic state injection.
We use matricial free energy to regularize autoencoders, producing Gaussian-like codes.
Germs of Goursat distributions can be classified according to a geometric coding called an RVT code. Jean (1996) and Mormul (2004) have shown that this coding carries precisely the same data as the small growth vector. Montgomery and Zhitomirskii (2010) have shown that such germs correspond to finite jets of Legendrian…
Study on reducing forgetting in neural networks using compression theory.
In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan, et al. We present the set of PD-codes as a stand alone object and discuss its relationship with link diagrams. We give an explicit …
Paper develops a decoder for sparse codes without encoder matrix, achieving optimal recovery.
Constructs manifolds from quantum codes with novel geometric properties.
New method calculates knot and link properties using state codes.
Quantum codes linked to abelian varieties, providing mathematical rigor.
Coding theory is a central discipline underpinning wireline and wireless modems that are the workhorses of the information age. Progress in coding theory is largely driven by individual human ingenuity with sporadic breakthroughs over the past century. In this paper we study whether it is possible to automate the disco…
PredNet, a deep predictive coding network developed by Lotter et al., combines a biologically inspired architecture based on the propagation of prediction error with self-supervised representation learning in video. While the architecture has drawn a lot of attention and various extensions of the model exist, there is …
Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing solutions, both in the applicable range of parameters and in the complexity of the invol…
The design of codes for communicating reliably over a statistically well defined channel is an important endeavor involving deep mathematical research and wide-ranging practical applications. In this work, we present the first family of codes obtained via deep learning, which significantly beats state-of-the-art codes …
A new model for sequential memory using temporal predictive coding.
In this paper we study output coding for multi-label prediction. For a multi-label output coding to be discriminative, it is important that codewords for different label vectors are significantly different from each other. In the meantime, unlike in traditional coding theory, codewords in output coding are to be predic…
New fault-tolerant quantum gates for homological LDPC codes with constant or almost-constant rate.
A new predictive coding algorithm improves machine learning performance.
This paper generalizes the Maurer--Pontil framework of finite-dimensional lossy coding schemes to the setting where a high-dimensional random vector is mapped to an element of a compact set of latent representations in a lower-dimensional Euclidean space, and the reconstruction map belongs to a given class of nonlinear…
Paper proves method for calculating NML code length works for continuous models.
Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that 97% of proteins are, however, classified as unknots when intra-chain interaction…
New model reveals balance crucial for robust neural coding.
New algorithm for active learning from feedback coding.
For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall short in the finite bit-length regime, as it requires non-trivial tuning of hand-…
Text classification is a challenging problem which aims to identify the category of texts. In the process of training, word embeddings occupy a large part of parameters. Under the limitation of limited computing resources, it indirectly limits the ability of subsequent network designs. In order to reduce the number of …
New theory shows predictive coding makes learning landscape easier to navigate.
The paper relaxes constraints on predictive coding models, making them more biologically plausible.
Bayesian Predictive Coding improves deep learning uncertainty quantification.
A new algorithm reduces regret in multi-player bandits without collision info.
Paper proposes IABF to improve NECST robustness.
Source coding is the canonical problem of data compression in information theory. In a locally encodable source coding, each compressed bit depends on only few bits of the input. In this paper, we show that a recently popular model of semi-supervised clustering is equivalent to locally encodable source coding. In this …
Unified theory explains housing cycle across metros, showing credit expansion impacts.
Poisson variational autoencoders introduce a metabolic cost term that penalizes high baseline activity.
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the …
A method to improve image synthesis diversity using mutual information.
New analysis tightens memory capacity of Hopfield models using spherical codes.
Paper encodes textile structures and classifies them up to complexity five.
A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrari…
Study on list learning with noisy data, showing limits and some learnable cases.
LoRA-One uses one-step full gradient to align adapters for efficient large model fine-tuning.
Unlike traditional programs (such as operating systems or word processors) which have large amounts of code, machine learning tasks use programs with relatively small amounts of code (written in machine learning libraries), but voluminous amounts of data. Just like developers of traditional programs debug errors in the…
Study of manifolds with prime cyclic group actions and curvature properties.
Machine learning model predicts DFT total energy to complete basis set limit.
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead, we build a statistical surrogate for the input-output relationship with a modest …
Develops a method to optimize tax codes with practical constraints.
We introduce a new cohomology-theoretic method for classifying generic immersed curves in closed compact surfaces by using Gauss codes. This subsumes a result of J.S. Carter on classifying immersed curves in oriented compact surfaces, and provides a criterion for when an immersion is two-colorable. We note an applicati…