Pseudo-random number generators (PRNG) are a fundamental element of many security algorithms. We introduce a novel approach to their implementation, by proposing the use of generative adversarial networks (GAN) to train a neural network to behave as a PRNG. Furthermore, we showcase a number of interesting modifications…
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48 results for “pseudo-random numbers”
Transformers can predict pseudo-random sequences from LCGs with unseen parameters and moduli.
problem Learning pseudo-random number sequences from linear congruential generators with unknown parameters and moduli.
method Investigated the ability of Transformers to learn LCG sequences with varying complexity and moduli. Analyzed embedding layers and attention patterns.
result Transformers can predict pseudo-random sequences from LCGs with unseen parameters and moduli, up to , using a two-step strategy.
Measurements of cosmic microwave background (CMB) anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. Using the direct bou…
On the effects of biased quantum random numbers on the initialization of artificial neural networksquant-ph
Study finds no significant difference in neural network weights with quantum random numbers.
problem Effects of biased quantum random numbers on neural network initialization.
method Empirical study using quantum hardware and classical pseudo-random numbers.
result No statistically significant difference found between quantum random numbers and other types.
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In many problems in finance to which Monte Carlo simulation is applied, many random n…
Paper presents quantum algorithms for pricing financial derivatives using complex models.
problem Implementing complex financial models like local volatility on quantum computers.
method Developed two quantum circuit implementations for local volatility model.
result Demonstrated reduced qubit requirements for local volatility model.
We formulate statistical watermarking as hypothesis testing and establish near-optimal bounds.
problem Statistical watermarking in the context of hypothesis testing.
method Formulated as a hypothesis testing problem, using coupling of output tokens and rejection regions.
result Established nearly matching upper and lower bounds on the number of i.i.d. tokens required for small Type I and Type II errors.
Quantum computers outperform classical methods in density modeling.
problem Density modeling with quantum computers.
method Quantum-classical separation for density modeling.
result Quantum computers offer a super-polynomial advantage over classical algorithms for density modeling.
Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which usually causes subsampling bias, inflates generalization errors and jeopardizes the r…
The Levy-Levy-Solomon model (A microscopic model of the stock market: cycles, booms, and crashes, Economic Letters 45 (1))is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang (Some new results on the Levy, L…
Compressive Sensing (CS) theory asserts that sparse signal reconstruction is possible from a small number of linear measurements. Although CS enables low-cost linear sampling, it requires non-linear and costly reconstruction. Recent literature works show that compressive image classification is possible in CS domain wi…
Study tests financial market efficiency using random number generator tests.
problem Check for informational efficiencies in financial markets.
method Analysed binary daily returns as random number generators, split analysis by annual and company levels, investigated longer-term efficiency over Nasdaq-listed companies.
result Information efficiency varies across years and reflects large-scale market impacts.
Bayesian Neural Networks (BNNs) have been proposed to address the problem of model uncertainty in training and inference. By introducing weights associated with conditioned probability distributions, BNNs are capable of resolving the overfitting issue commonly seen in conventional neural networks and allow for small-da…
Energy-efficient sampling for machine learning using magnetic tunnel junctions.
problem Costly and inefficient random sampling in machine learning.
method Energy-efficient algorithm using stochastic magnetic tunnel junctions for uniform Float16 sampling.
result Higher energy efficiency than state-of-the-art algorithms, with a minimum factor of 9721.
Generative moment matching networks (GMMNs) are introduced for generating quasi-random samples from multivariate models with any underlying copula in order to compute estimates under variance reduction. So far, quasi-random sampling for multivariate distributions required a careful design, exploiting specific propertie…
In our recent work (Bubeck, Price, Razenshteyn, arXiv:1805.10204) we argued that adversarial examples in machine learning might be due to an inherent computational hardness of the problem. More precisely, we constructed a binary classification task for which (i) a robust classifier exists; yet no non-trivial accuracy c…
Improved neural network training in low-dimensional random bases.
problem Inefficient optimization in large-scale neural networks.
method Re-draw random subspace at each training step, apply independent projections to different network parts.
result Significantly better optimization performance and efficiency.
AGMMNs improve learning of copula models by adaptively selecting kernels.
problem Learning dependence structures in copula models.
method Adaptive bandwidth selection for MMD in GMMNs, increasing kernels based on validation loss.
result AGMMNs significantly improve training performance over GMMNs and parametric models.
Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate modelsstat.CO
The paper develops methods to analyze sensitivity in stochastic models using surrogate models.
problem Quantifying the impact of input variability on stochastic simulators with randomness.
method The authors propose using generalized lambda models to emulate response distributions of stochastic simulators and estimate sensitivity indices.
result The proposed method can estimate sensitivity indices even with strong heteroskedasticity and small signal-to-noise ratio.
Unified framework for online LLM watermark detection using e-processes.
problem Detecting AI-generated text from human-written content in online settings.
method Unified framework based on e-processes for anytime-valid hypothesis testing on independence.
result Proposed methods achieve competitive performance in watermark detection.
This study examines how financial tick data becomes more random with time aggregation.
problem Investigating the randomness of financial tick data over time.
method Applied statistical randomness tests from NIST and TestU01 batteries to ultra-high frequency financial data.
result Financial tick data becomes increasingly random as the aggregation level of transaction time increases.
Likelihood-free inference involves inferring parameter values given observed data and a simulator model. The simulator is computer code which takes parameters, performs stochastic calculations, and outputs simulated data. In this work, we view the simulator as a function whose inputs are (1) the parameters and (2) a ve…
New lower bounds show learning intersections of halfspaces is hard even for a few halfspaces.
problem Learning intersections of halfspaces in polynomial time under standard assumptions.
method Unified connection to parallel pancakes distribution for proving hardness.
result Learning halfspaces in dimension requires super-polynomial time under standard assumptions.
New DGA detection models use side info to improve robustness.
problem Adversaries craft domain names to evade DGA detection.
method Train deep learning and RF classifiers using domain name and side info.
result Models using both domain name and side info are more robust.
Readouts for Echo-state Networks Built using Locally Regularized Orthogonal Forward Regressionstat.ML
Echo state network (ESN) is viewed as a temporal non-orthogonal expansion with pseudo-random parameters. Such expansions naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the variance of the tea…
We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior of diagrammatic bridge numbers under the connected sum operation. For each notion of diagrammatic bridge number considered, we find crossing …
Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
problem Understanding the relationship between unknotting numbers and crossing numbers of spatial embeddings of planar graphs.
method Analyzing specific examples of planar graphs and their spatial embeddings to find counterexamples.
result There exist planar graphs and their spatial embeddings where the unknotting number is greater than half the crossing number.
The unknotting number of a knot is the minimum number of crossings one must change to turn that knot into the unknot. The algebraic unknotting number is the minimum number of crossing changes needed to transform a knot into an Alexander polynomial-one knot. We work with a generalization of unknotting number due to Math…
The paper bounds the handle number of sutured manifolds using Morse-Novikov numbers and tunnel numbers.
problem Bounding the handle number of sutured manifolds.
method Developed bounds on the Morse-Novikov number of a link in terms of its tunnel number, and used these to bound the handle number of Heegaard splittings.
result The handle number function is bounded, constant on rays from the origin, and locally maximal.
New measure shows how links can be untangled as twists increase.
problem Understanding how links can be simplified through repeated twists.
method Introduced the stable unknotting number to analyze links in a twist family.
result The stable unknotting number depends only on the winding number of the link, not the wrapping number.
New number bounds knot complexity, including unknotting and crosscap numbers.
problem Bounding knot complexity and understanding knot types.
method Introducing an unknotting-type number to estimate crosscap number.
result Determines set of knots with crosscap number at most two.
We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation…
Paper shows that for torus knots, the pinch number equals the unoriented band unknotting number.
problem Determining the minimum number of band surgeries to unknot torus knots.
method Used the torsion order of unoriented knot Floer homology.
result Pinch number and unoriented band unknotting number coincide for torus knots.
Delta-unlinking number measures how to unlink algebraically split links.
problem Measuring unlinking complexity of algebraically split links.
method Defining delta-unlinking number as minimum delta-moves to unlink, proving bounds and calculating specific values.
result Precise delta-unlinking numbers for algebraically split prime links up to 9 crossings, and 4-genus values for most.
Study on knot properties, showing relation between unknotting and crossing numbers.
problem Relations between unknotting and crossing numbers of spatial embeddings.
method Analyzes handcuff-graphs and theta curves, extends known results to handlebody-knots.
result Characterizes handlebody-knots satisfying the equality between unknotting and crossing numbers.
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
problem Analyzing crossing and rotation numbers of cycles in plane immersions of graphs.
method Generic immersions and Legendrian embeddings of graphs, focusing on cycles of specific lengths.
result Sum of rotation numbers of all 5-cycles is even, and sum of crossing numbers is odd.
Study computability of real numbers from group properties.
problem Computability of real numbers from group properties.
method Analyzing -Betti numbers and -torsion of groups.
result Real numbers as -Betti numbers or -torsion are computable.
We define the basket number, the flat plumbing number and the flat plumbing basket number of a link. Then we provide some upperbounds for these plumbing numbers by using Seifert's algorithm. We study the relation between these plumbing numbers and the genera of links.
The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical crossings. All previously known estimates for virtual crossing number were principally no more than linear in the number of classic…
This paper calculates stick numbers for rail arcs and knot classes.
problem Calculating the minimum number of sticks needed for rail arcs and knot classes.
method Rail isotopies, ambient isotopies, winding number invariant, and lattice stick number.
result Calculates stick numbers for rail arcs and knot classes with crossing number at most 9.
The (ordinary) unknotting-number of 1-dimensional knots, which is defined by using the crossing-change, is a very basic and important invariant. It is very natural to consider the `unknotting-number' associated with other local-moves on n-dimensional knots, where n is a natural number. In this paper we prove the follow…
In this paper we investigate the unlinking numbers of 10-crossing links. We make use of various link invariants and explore their behaviour when crossings are changed. The methods we describe have been used previously to compute unlinking numbers of links with crossing number at most 9. Ultimately, we find the unlinkin…
The clock number of a knotmath.GT
This paper is about the clock number of a knot. First we define the clock number by using states of a knot defined by Kauffman. Next we show that if K is a prime knot, its clock number is greater than or equal to its crossing number. Finally we prove that its clock number is equal to its crossing number if and only if …
We study three knot invariants related to smoothly immersed disks in the four-ball. These are the four-ball crossing number, which is the minimal number of normal double points of such a disk bounded by a given knot; the slicing number, which is the minimal number of crossing changes to a slice knot; and the concordanc…
For a knot the cube number is a knot invariant defined to be the smallest for which there is a cube diagram of size for . There is also a Legendrian version of this invariant called the \emph{Legendrian cube number}. We will show that the Legendrian cube number distinguishes the Legendrian left hand toru…
Straight knotsmath.GT
Jablan and Radović originally defined two invariants called the Meander number and OGC number of knots for certain classes of knots. We generalize these definitions to all knots and name the straight number and contained straight number of a knot, respectively, and prove they are well defined. We answer two questions a…
New insights into knot fusion numbers via cabling.
problem Understanding fusion numbers of ribbon knots and their behavior under cabling.
method Utilizing knot Floer homology and cabling formulas to analyze fusion numbers.
result The fusion number and strong homotopy fusion number of (p,1)-cable knots are preserved.