arXiv subjects

Jarek Duda

Publications and source records attributed to Jarek Duda.

At least 19 recordsLinked to original sources

arXiv2026

Higher order PCA-like rotation-invariant features for detailed shape descriptors modulo rotation

PCA can be used for rotation invariant features, describing a shape with its $p_{ab}=E[(x_i-E[x_a])(x_b-E[x_b])]$ covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real shapes are usually much more complicated, hence there is proposed its extension to e.g. $p_{abc}=E[(x_a-E[x_a])(x_b-E[x_b])(x_c-E[x_c])]$ order-3 or higher tensors describing central moments, or polynomial times Gaussian allowing decodable shape descriptors of arbitrarily high accuracy, and their analogous rotation invariants. Its practical applications could be rotation-invariant features to include shape modulo rotation e.g. for molecular shape descriptors, or for up to rotation object recognition in 2D images/3D scans maybe also for 3D scene understanding, or shape similarity metric allowing inexpensive comparison of objects modulo rotation avoiding costly optimization over rotations.

cs.CV↗

arXiv2025

Experimental estimation of Asymmetry of Radiation for Wheeler-Feynman theory for gravitational waves

Maxwell equations mathematically allow both retarded and advanced solutions, also their convex combinations. While Wheeler-Feynman absorber theory assumed their symmetric contributions (1/2-1/2), e.g. inspiraling show Asymmetry of Radiation instead, and currently there dominates unquestioned assumption of 1-0 only retarded. As it should depend on the boundary conditions, like absorber/emitter imbalance - which is essential but not necessarily perfect, we propose to finally verify this assumption experimentally, trying to distinguish it from e.g. 0.99-0.01 contributions. Experimental estimation of such Asymmetry of Radiation is currently difficult for EM waves due to receiver-emitter asymmetry. However, e.g. LIGO just measures lengths, which are invariant to T/CPT symmetry, making available gravitational wave observations appropriate for such estimation, and there are already observed suggestions for advanced waves. For example gravitational observations of e.g. neutron star merger, with required but clearly missing (retarded) EM counterpart, would leave possibility of being advanced wave. Also there are observed events happening too early according to current knowledge e.g. mergers of black holes in the Mass Gap, or insufficient number of retarded sources e.g. for "vibrations of the Universe" observed by Pulsar Timing Arrays.

physics.gen-ph↗

arXiv2025

Comparing BFGS and OGR for Second-Order Optimization

Estimating the Hessian matrix, especially for neural network training, is a challenging problem due to high dimensionality and cost. In this work, we compare the classical Sherman-Morrison update used in the popular BFGS method (Broy-den-Fletcher-Goldfarb-Shanno), which maintains a positive definite Hessian approximation under a convexity assumption, with a novel approach called Online Gradient Regression (OGR). OGR performs regression of gradients against positions using an exponential moving average to estimate second derivatives online, without requiring Hessian inversion. Unlike BFGS, OGR allows estimation of a general (not necessarily positive definite) Hessian and can thus handle non-convex structures. We evaluate both methods across standard test functions and demonstrate that OGR achieves faster convergence and improved loss, particularly in non-convex settings.

cs.LG↗

arXiv2025

Linear cost mutual information estimation and independence test of similar performance as HSIC

Evaluation of statistical dependencies between two data samples is a basic problem of data science/machine learning, and HSIC (Hilbert-Schmidt Information Criterion)~\cite{HSIC} is considered the state-of-art method. However, for size $n$ data sample it requires multiplication of $n\times n$ matrices, what currently needs $\sim O(n^{2.37})$ computational complexity~\cite{mult}, making it impractical for large data samples. We discuss HCR (Hierarchical Correlation Reconstruction) as its linear cost practical alternative, in tests of even higher sensitivity to dependencies, and additionally providing actual joint distribution model for chosen significance level, by description of dependencies through features being mixed moments, starting with correlation and homoscedasticity. Also allowing to approximate mutual information as just sum of squares of such nontrivial mixed moments between two data samples. Such single dependence describing feature is calculated in $O(n)$ linear time. Their number to test varies with dimension $d$ - requiring $O(d^2)$ for pairwise dependencies, $O(d^3)$ if wanting to also consider more subtle triplewise, and so on.

cs.LG↗

arXiv2025

Improving KAN with CDF normalization to quantiles

Data normalization is crucial in machine learning, usually performed by subtracting the mean and dividing by standard deviation, or by rescaling to a fixed range. In copula theory, popular in finance, there is used normalization to approximately quantiles by transforming x to CDF(x) with estimated CDF (cumulative distribution function) to nearly uniform distribution in [0,1], allowing for simpler representations which are less likely to overfit. It seems nearly unknown in machine learning, therefore, we would like to present some its advantages on example of recently popular Kolmogorov-Arnold Networks (KANs), improving predictions from Legendre-KAN by just switching rescaling to CDF normalization. Additionally, in HCR interpretation, weights of such neurons are mixed moments providing local joint distribution models, allow to propagate also probability distributions, and change propagation direction.

cs.LG↗

arXiv2025

Adaptive stable distribution and Hurst exponent by method of moments moving estimator for nonstationary time series

Nonstationarity of real-life time series requires model adaptation. In classical approaches like ARMA-ARCH there is assumed some arbitrarily chosen dependence type. To avoid their bias, we will focus on novel more agnostic approach: moving estimator, which estimates parameters separately for every time $t$: optimizing $F_t=\sum_{\tau<t} (1-\eta)^{t-\tau} \ln(\rho_\theta (x_\tau))$ local log-likelihood with exponentially weakening weights of the old values. In practice such moving estimates can be found by EMA (exponential moving average) of some parameters, like $m_p=E[|x-\mu|^p]$ absolute central moments, updated by $m_{p,t+1} = m_{p,t} + \eta (|x_t-\mu_t|^p-m_{p,t})$. We will focus here on its applications for alpha-Stable distribution, which also influences Hurst exponent, hence can be used for its adaptive estimation. Its application will be shown on financial data as DJIA time series - beside standard estimation of evolution of center $\mu$ and scale parameter $\sigma$, there is also estimated evolution of $\alpha$ parameter allowing to continuously evaluate market stability - tails having $\rho(x) \sim 1/|x|^{\alpha+1}$ behavior, controlling probability of potentially dangerous extreme events.

stat.ME↗

arXiv2025

Time crystal $\phi^4$ kinks by curvature coupling as toy model for mechanism of oscillations propelled by mass, like observed for electron and neutrinos

Dirac equation requires $E=mc^2$ energy of resting particle, leading to some $\exp(-iEt/\hbar)$ its evolution - periodic process of $\omega=mc^2/\hbar$ frequency, literally propelled by mass of particle, confirmed experimentally e.g. for quantum phase of electron as de Broglie clock/Zitterbewegung (and its angular momentum), or flavor oscillations of neutrinos for 3 masses. Entities having energetically preferred periodic process already in the lowest energy state are recently searched for as time crystals. To understand such mechanism of clock propulsion by mass itself, it would be valuable to recreate something analogous in simple models like wobbling kinks. There is proposed such toy model as 1+1D $(\phi,\psi)$ Lorentz invariant two-component scalar field theory, extending popular $\phi^4$ model by second component $\psi$ corresponding to such periodically evolving degree of freedom, which is coupled through powers of curvature $R=\partial_0 \phi\, \partial_1 \psi-\partial_1 \phi \,\partial_0 \psi$, as suggested by earlier 3+1D model~\cite{my}. This way kink spatial structure $\partial_x \phi\neq 0$ brings energetic preference for nonzero $\partial_t \psi$ time derivative, by energy minimization leading to periodic process of $0<\omega<\infty$ frequency, as required for time crystals.

physics.gen-ph↗

arXiv2024

Testing stimulated emission photon directions

While naively laser only causes excitation of external target, e.g. Rabi cycle, STED microscopy or ASE/SASE/SSA demonstrate it can also stimulate its deexitation, however, under uncommon condition of being prepared as excited. These two causalities are governed by absorption-stimulated emission pair of equations, and swap places in perspective of T/CPT symmetry, however, it means photon direction of stimulated emission should be opposite to usually assumed, allowing for negative radiation pressure $\vec{p}=\langle \vec{E}\times \vec{H}\rangle/c$. This article discusses various arguments and proposes simple direct tests to experimentally verify existence of such backward photon trajectories, complementing consequent forward textbook trajectories. Depending on the results, it could lead to many proposed applications like medical, astronomical or 2WQC more symmetric quantum computers. Alternatively, if unsuccessful, it would require macroscopic violation of CPT symmetry, so far tested probably only in microscopic settings.

physics.gen-ph↗

arXiv2024

3-SAT solver for two-way quantum computers

While quantum computers assume existence of state preparation process $|0\rangle$, CPT symmetry of physics says that performing such process in CPT symmetry perspective, e.g. reversing used EM impulses ($V(t)\to V(-t)$), we should get its symmetric analog $\langle 0|$, referred here as state postparation - which should provide results as postselection, but with higher success rate. Two-way quantum computers (2WQC) assume having both $|0\rangle$ and $\langle 0|$ pre and postparation. In theory they allow to solve NP problems, however, basic approach would be more difficult than Shor algorithm, which is now far from being practical. This article discusses approach to make practical 2WQC 3-SAT solver, requiring exponential reduction of error rate, what should be achievable through linear increase of the numbers of gates. 2WQC also provides additional error correction capabilities, like more stable Grover algorithm, or mid-circuit enforcement of syndrome to zero, like proposed equalizer enforcing qubit equality.

physics.gen-ph↗

arXiv2024

No-cloning theorem for 2WQC and postselection

Two-way quantum computers (2WQC) are proposed extension of standard 1WQC: adding conjugated state preparation operation $\langle 0|$ similar to postselection $|0\ra \langle 0|$, by performing a process which from perspective of CPT symmetry is the original state preparation process, for example by reversing EM impulses used for state preparation. As there were concerns that this extension might violate no-cloning theorem for example for attacks on quantum cryptographic protocols like BB84, here we extend the original proof to show this theorem still holds for 2WQC and postselection.

quant-ph↗

arXiv2024

Biology-inspired joint distribution neurons based on Hierarchical Correlation Reconstruction allowing for multidirectional propagation of values and densities

Recently a million of biological neurons (BNN) has turned out better from modern RL methods in playing Pong~\cite{RL}, reminding they are still qualitatively superior e.g. in learning, flexibility and robustness - suggesting to try to improve current artificial e.g. MLP/KAN for better agreement with biological. There is proposed extension of KAN approach to neurons containing model of local joint distribution: $\rho(\mathbf{x})=\sum_{\mathbf{j}\in B} a_\mathbf{j} f_\mathbf{j}(\mathbf{x})$ for $\mathbf{x} \in [0,1]^d$, adding interpretation and information flow control to KAN, and allowing to gradually add missing 3 basic properties of biological: 1) biological axons propagate in both directions~\cite{axon}, while current artificial are focused on unidirectional propagation - joint distribution neurons can repair by substituting some variables to get conditional values/distributions for the remaining. 2) Animals show risk avoidance~\cite{risk} requiring to process variance, and generally real world rather needs probabilistic models - the proposed can predict and propagate also distributions as vectors of moments: (expected value, variance) or higher. 3) biological neurons require local training, and beside backpropagation, the proposed allows many additional ways, like direct training, through tensor decomposition, or finally local and promising: information bottleneck. Proposed approach is very general, can be also used as extension of softmax in embeddings of e.g. transformer, JEPA, Mamba, suggesting interpretation that features are mixed moments of joint density of real-world properties.

cs.LG↗

arXiv2024

Simple inexpensive vertex and edge invariants distinguishing dataset strongly regular graphs

While standard Weisfeiler-Leman vertex labels are not able to distinguish even vertices of regular graphs, there is proposed and tested family of inexpensive polynomial time vertex and edge invariants, distinguishing much more difficult SRGs (strongly regular graphs), also often their vertices. Among 43717 SRGs from dataset by Edward Spence, proposed vertex invariants alone were able to distinguish all but 4 pairs of graphs, which were easily distinguished by further application of proposed edge invariants. Specifically, proposed vertex invariants are traces or sorted diagonals of $(A|_{N_a})^p$ adjacency matrix $A$ restricted to $N_a$ neighborhood of vertex $a$, already for $p=3$ distinguishing all SRGs from 6 out of 13 sets in this dataset, 8 if adding $p=4$. Proposed edge invariants are analogously traces or diagonals of powers of $\bar{A}_{ab,cd}=A_{ab} A_{ac} A_{bd}$, nonzero for $(a,b)$ being edges. As SRGs are considered the most difficult cases for graph isomorphism problem, such algebraic-combinatorial invariants bring hope that this problem is polynomial time.

cs.CC↗

arXiv2024

Phase space maximal entropy random walk: Langevin-like ensembles of physical trajectories

As written by statistician George Box "All models are wrong, but some are useful", standard diffusion derivation or Feynman path ensembles use nonphysical infinite velocity/kinetic energy nowhere differentiable trajectories - what seems wrong, might be only our approximation to simplify mathematics. This article introduces some basic tools to investigate this issue. To consider ensembles of more physical finite velocity trajectories, we can work in $(x,v)$ phase space like in Langevin equation with velocity controlling spatial steps, here also controlled with spatial potential $V(x)$. There are derived and compared 4 approaches to predict stationary probability distributions: using Boltzmann ensemble of steps/points in space (GRW - generic random walk) or in phase space (psGRW), and analogously Boltzmann ensemble of paths in space (MERW - maximal entropy random walk) and in phase space (psMERW), also generalized to L{\'e}vy flights. Path ensembles generally have much stronger Anderson-like localization, MERW has stationary distribution exactly as quantum ground state. Proposed novel MERW in phase space has some slight differences, which might be distinguished experimentally. For example for 1D infinite potential well: $\rho=1$ stationary distribution for step ensemble, $\rho\sim \sin^2$ for path ensemble (as in QM), and $\rho\sim \sin$ for proposed smooth path ensembles - more frequently approaching the barriers due to randomly gained velocity.

cond-mat.stat-mech↗

arXiv2023

Extracting individual variable information for their decoupling, direct mutual information and multi-feature Granger causality

Working with multiple variables they usually contain difficult to control complex dependencies. This article proposes extraction of their individual information, e.g. $\overline{X|Y}$ as random variable containing information from $X$, but with removed information about $Y$, by using $(x,y) \leftrightarrow (\bar{x}=\textrm{CDF}_{X|Y=y}(x),y)$ reversible normalization. One application can be decoupling of individual information of variables: reversibly transform $(X_1,\ldots,X_n)\leftrightarrow(\tilde{X}_1,\ldots \tilde{X}_n)$ together containing the same information, but being independent: $\forall_{i\neq j} \tilde{X}_i\perp \tilde{X}_j, \tilde{X}_i\perp X_j$. It requires detailed models of complex conditional probability distributions - it is generally a difficult task, but here can be done through multiple dependency reducing iterations, using imperfect methods (here HCR: Hierarchical Correlation Reconstruction). It could be also used for direct mutual information - evaluating direct information transfer: without use of intermediate variables. For causality direction there is discussed multi-feature Granger causality, e.g. to trace various types of individual information transfers between such decoupled variables, including propagation time (delay).

stat.ML↗

arXiv2023

Two-way quantum computers adding CPT analog of state preparation

Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce a chosen initial state, however, for the final state measurement chooses a random value instead. As e.g. pull/push, negative/positive pressure, stimulated emission/absorption causing deexcitation/excitation are CPT analogs, and one can be used for state preparation, the second should allow for its CPT analog, referred here as CPT(state preparation) - allowing for additional chosen enforcement of the final state, its more active treatment than measurement. It should act similarly to postselection, but through applied physical constraints (instead of running multiple times). Like pumped to $|1\rangle$ prepared state vs its "unpumped" $\langle 0|$ CPT analog, hopefully allowing to construct two-way quantum computers (2WQC) e.g. hydrodynamical, and hopefully photonic: seen as $\langle Φ_{\textrm{final}}|U_{\textrm{quantum gates}}|Φ_{\textrm{initial}}\rangle$ like for scattering matrix, with influenced both initial and final states. If possible, for example for an instance of 3-SAT problem on $n$ variables, we could prepare ensemble of $2^n$ inputs with Hadamard gates, calculate 3-SAT alternatives for them, and use CPT(state preparation) to enforce outcomes of all these alternatives to '1'. This way hopefully restricting this ensemble to satisfying given 3-SAT problem: $\sum_{a:\textrm{SAT}(a)} |a\rangle$, in theory allowing to attack NP problems by simultaneously pushing and pulling information through the system for better control.

physics.gen-ph↗

arXiv2023

Four-dimensional understanding of quantum mechanics and Bell violation

While our natural intuition suggests us that we live in 3D space evolving in time, modern physics presents fundamentally different picture: 4D spacetime, Einstein's block universe, in which we travel in thermodynamically emphasized direction: arrow of time. Arguments for such nonintuitive and nonlocal living in kind of "4D jello" come among others from: Lagrangian mechanics we use from QFT to GR saying that history between fixed past and future situation is the one optimizing action, special relativity saying that different velocity observers have different own time directions, general relativity deforming shape of the entire spacetime up to switching time and space below the black hole event horizon, or the CPT theorem concluding fundamental symmetry between past and future for example in the Feynman-Stueckelberg interpretation of antiparticles as propagating back in time. Accepting this nonintuitive living in 4D spacetime: with present moment being in equilibrium between past and future - minimizing tension as action of Lagrangian, leads to crucial surprising differences from intuitive "evolving 3D" picture - allowing to conclude Bell inequalities, violated by the real physics. Specifically, particle in spacetime becomes own trajectory: 1D submanifold of 4D, making that statistical physics should consider ensembles like Boltzmann distribution among entire paths (like in Ising model), what leads to quantum behavior as we know from Feynman's Euclidean path integrals or similar Maximal Entropy Random Walk (MERW).

physics.gen-ph↗

arXiv2023

Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals

Electroencephalography (EEG) signals are resultants of extremely complex brain activity. Some details of this hidden dynamics might be accessible through e.g. joint distributions $ρ_{Δt}$ of signals of pairs of electrodes shifted by various time delays (lag $Δt$). A standard approach is monitoring a single evaluation of such joint distributions, like Pearson correlation (or mutual information), which turns out relatively uninteresting - as expected, there is usually a small peak for zero delay and nearly symmetric drop with delay. In contrast, such a complex signal might be composed of multiple types of statistical dependencies - this article proposes approach to automatically decompose and extract them. Specifically, we model such joint distributions as polynomials, estimated separately for all considered lag dependencies, then with PCA dimensionality reduction we find the dominant joint density distortion directions $f_v$. This way we get a few lag dependent features $a_i(Δt)$ describing separate dominating statistical dependencies of known contributions: $ρ_{Δt}(y,z)\approx \sum_{i=1}^r a_i(Δt)\, f_{v_i}(y,z)$. Such features complement Pearson correlation, extracting hidden more complex behavior, e.g. with asymmetry which might be related with direction of information transfer, extrema suggesting characteristic delays, or oscillatory behavior suggesting some periodicity. There is also discussed extension of Granger causality to such multi-feature joint density analysis, suggesting e.g. two separate causality waves. While this early article is initial fundamental research, in future it might help e.g. with understanding of cortex hidden dynamics, diagnosis of pathologies like epilepsy, determination of precise electrode position, or building brain-computer interface.

eess.SP↗

arXiv2023

Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series

The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid their bias, we will focus on recently proposed agnostic philosophy of moving estimator: in time $t$ finding parameters optimizing e.g. $F_t=\sum_{\tau<t} (1-\eta)^{t-\tau} \ln(\rho_\theta (x_\tau))$ moving log-likelihood, evolving in time. It allows for example to estimate parameters using inexpensive exponential moving averages (EMA), like absolute central moments $m_p=E[|x-\mu|^p]$ evolving for one or multiple powers $p\in\mathbb{R}^+$ using $m_{p,t+1} = m_{p,t} + \eta (|x_t-\mu_t|^p-m_{p,t})$. Application of such general adaptive methods of moments will be presented on Student's t-distribution, popular especially in economical applications, here applied to log-returns of DJIA companies. While standard ARMA-ARCH approaches provide evolution of $\mu$ and $\sigma$, here we also get evolution of $\nu$ describing $\rho(x)\sim |x|^{-\nu-1}$ tail shape, probability of extreme events - which might turn out catastrophic, destabilizing the market.

stat.ME↗