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arXiv research

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.

168,742 papers · 148 categories

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48 results for CSS codes

Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.

problem Improving quantum error correction performance with hyperbolic lattices.
method Unified framework using Hyperbolic Cycle Basis algorithm for CSS codes construction and benchmarking.
result Achieved higher encoding rates and lower qubit overhead in hyperbolic quantum error correction codes.

In this paper we study properties of the area evolute (AE) and the center symmetry set (CSS) of a convex planar curve γγ. The main tool is to define a Minkowski plane where γγ becomes a constant width curve. In this Minkowski plane, the CSS is the evolute of γγ and the AE is an involute of the CSS. We prove that the…

2013-01-27abs ↗pdf ↗

We develop time-uniform confidence spheres for estimating means of random vectors.

problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub-ψψ random vectors.

Topological theory for qLDPC codes enables non-Clifford gates and magic state injection.

problem Fault-tolerant quantum computation in qLDPC codes with non-Clifford gates and magic state resources.
method Developed a topological theory using simplicial or CW complex structures and deformation retraction.
result Achieved non-Clifford gates and magic state injection in qLDPC codes with constant rate and polynomial distance.

RLFA estimates misstated monetary fraction with weighted sampling without replacement.

problem Estimating misstated monetary fraction with given accuracy and confidence.
method Developed new confidence sequences for weighted average of unknown values using randomized weighted sampling and side information.
result Adaptive methods improve accuracy of estimates based on side information's predictive power.

The betting CI outperforms classical methods in constructing confidence intervals for bounded means.

problem Constructing nonasymptotic confidence intervals for bounded means.
method A betting-based approach to define and time-uniform variants of confidence intervals (CSs).
result The betting CI matches the fundamental limits, outperforming existing empirical Bernstein CIs.

New method uses imperfect LLM annotations for valid statistical inference in social science.

problem Inaccurate large language model annotations in social science research.
method Design-based supervised learning (DSL) combining imperfect LLM surrogates with gold-standard labels.
result DSL provides valid statistical inference with comparable predictive accuracy to existing methods.

Study efficient sequential evaluation of large language models using historical data.

problem Sequentially evaluate a new large language model (LLM) on a fixed question set.
method Construct a confidence sequence (CS) and design active querying rules to shrink CS width.
result Simple uniform sampling can sometimes outperform adaptive querying rules.

New methods for private statistical inference under local differential privacy.

problem Private statistical inference for population means with bounded observations.
method Nonparametric, nonasymptotic statistical inference using a generalized randomized response mechanism.
result Private confidence intervals and sequences for population means under LDP constraints.

Recently, the paradigm of unfolding iterative algorithms into finite-length feed-forward neural networks has achieved a great success in the area of sparse recovery. Benefit from available training data, the learned networks have achieved state-of-the-art performance in respect of both speed and accuracy. However, the …

2019-10-11abs ↗pdf ↗

The paper introduces methods to quantify uncertainty in sampling without replacement.

problem Accurately estimating parameters from finite populations sampled without replacement.
method Develops confidence sequences using Bayesian and empirical methods.
result Improved confidence intervals and sequences for sampling without replacement.

Many software analysis methods have come to rely on machine learning approaches. Code segmentation - the process of decomposing source code into meaningful blocks - can augment these methods by featurizing code, reducing noise, and limiting the problem space. Traditionally, code segmentation has been done using syntact…

2019-07-18abs ↗pdf ↗

Contrastive Code Representation Learning improves code summarization and type inference.

problem Code representations are sensitive to edits, hindering downstream semantic understanding tasks.
method ContraCode: a contrastive pre-training task that learns code functionality.
result Contrastive pre-training improves code summarization and type inference accuracy.

Investigates neural codes and their embeddings, proving conjectures and introducing new code types.

problem Analyzing neural codes and their embedding dimensions.
method Combinatorial, topological, and algebraic analysis; proving conjectures; introducing new neural code types.
result Proves conjectures about neural codes and their embeddings, introduces new code types.

Characterization of a patient clinical phenotype is central to biomedical informatics. ICD codes, assigned to inpatient encounters by coders, is important for population health and cohort discovery when clinical information is limited. While ICD codes are assigned to patients by professionals trained and certified in c…

2018-11-28abs ↗pdf ↗

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the m…

2013-11-26abs ↗pdf ↗

Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation (…

2012-05-09abs ↗pdf ↗

We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain probability …

2009-01-15abs ↗pdf ↗

We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the pp-faces of the nn-cube (for n>pn>p) and stabilizer constraints with faces of dimension (p±1)(p\pm1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into $N = 2^…

2019-11-08abs ↗pdf ↗

Code search and comprehension have become more difficult in recent years due to the rapid expansion of available source code. Current tools lack a way to label arbitrary code at scale while maintaining up-to-date representations of new programming languages, libraries, and functionalities. Comprehensive labeling of sou…

2019-06-03abs ↗pdf ↗

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…

2017-07-12abs ↗pdf ↗

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 …

2018-07-02abs ↗pdf ↗

We discuss Gauss codes of virtual diagrams and virtual doodles. The notion of a left canonical Gauss code is introduced and it is shown that oriented virtual doodles are uniquely presented by left canonical Gauss codes.

2018-06-15abs ↗pdf ↗

Sparse codes improve optimal control tasks with correlated inputs.

problem Optimal control tasks with correlated feature inputs.
method Used a sparse code to represent natural images in an optimal control task solved with neuro-dynamic programming.
result An over-complete sparse code increases memory capacity and learning speed beyond a complete code.

We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8πl);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2πl)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.

2013-07-17abs ↗pdf ↗

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 …

2013-09-12abs ↗pdf ↗

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been conside…

2014-09-08abs ↗pdf ↗

Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As per Turing's Halting problem proof, estimating code complexity is mathematically…

2019-11-04abs ↗pdf ↗