Neural representations learned by neural networks encode task-relevant information, but their behavior under communication constraints is still poorly understood. We propose an information-theoretic framework for the comparison of classical compression and quantum-inspired amplitude encoding for the transfer of representations under controlled dimensional constraints. We analyze frozen intermediate features extracted from a pretrained ResNet-50 on the ImageNet-1K validation set at different depths in the network. The classical pipeline performs rate-controlled dimensionality reduction and uniform quantization, while the quantum-inspired pipeline does amplitude encoding and computational-basis probability decoding without variational circuits or trainable quantum parameters. Quality of representation was evaluated using differential entropy and a decoder-based lower bound on mutual information. Classical compression achieves higher decoder-based mutual information lower bounds at moderate and high communication budgets. However, the quantum-inspired pipeline retained a larger fraction of decoder-extractable task-relevant information under severe dimensional compression, with resource-normalized information efficiency providing a complementary perspective to the substantially higher absolute decoder-based mutual information lower bounds of the classical pipeline. Robustness analyses with qubit reduction and physically motivated noise models showed predictable degradation. Ablation and SHAP analyses indicate that task-relevant information is structured within representational subspaces. These findings support quantum-inspired representation transfer as a framework for studying communication-efficient neural representation transfer under low-bandwidth constraints.
This paper investigates the spatial analyticity of solutions to the Korteweg–de Vries equation and exploits this property to improve the efficiency of numerical modeling and to solve inverse problems. It is theoretically proven that the solutions of the Korteweg–de Vries equation belong to Gevrey spaces, and an estimate for the analyticity radius σ(t) is derived, showing that it decays at an algebraic rate governed by σ(t)≥σ0/(1+Cσ0t). This property ensures that the Fourier coefficients decay exponentially, which is leveraged to design an efficient spectral numerical scheme with exponentially small truncation error. A detailed convergence analysis demonstrates that the spectral method achieves exponential accuracy, significantly outperforming conventional finite-difference approaches. Furthermore, a reconstruction algorithm is developed to recover the full wave field from limited sensor data, achieving an L2 error below 10−3 using only 10% of the spatial domain data. Extensive numerical experiments, including sensitivity analysis with respect to the estimated analyticity radius and comparison with finite-difference methods, confirm the theoretical predictions and demonstrate the robustness of the proposed approach. The results establish that spatial analyticity provides a powerful and practical framework for both forward modeling and data reconstruction in dispersive partial differential equations.
This paper introduces the Slash Q-Lindley (SQL) distribution, a new heavy-tailed model for positive data obtained as the ratio of a Q-Lindley variable to an independent power-distributed variable. The SQL inherits the flexibility of the baseline Q-Lindley while adding a tail parameter that controls polynomial decay. Its hazard rate tends to zero and, numerically, is decreasing or unimodal. Explicit expressions for the PDF, CDF, and hazard functions are derived using incomplete gamma and confluent hypergeometric functions. Key properties (moments, order statistics, stochastic ordering, entropy, and stress–strength reliability) are investigated. Parameter estimation is performed via maximum likelihood, Anderson–Darling, Cramér–von Mises, maximum product of spacings, ordinary and weighted least squares, and Bayesian MCMC methods. A simulation study evaluates finite-sample behavior, showing that the Bayesian estimator has the smallest overall rank, followed closely by the maximum product of spacings estimator, with maximum likelihood third. The practical advantage of the SQL is demonstrated on two real heavy-tailed datasets (flood discharges and coastal island areas), where it provides superior fits compared to several competing models based on multiple criteria (Akaike Information Criterion, Bayesian Information Criterion, Kolmogorov–Smirnov statistic, Anderson–Darling statistic, Cramér–von Mises statistic). The SQL offers a tractable and flexible alternative for modeling positive data with extreme values.
This study provides a unified theoretical and empirical examination of the Generalized Hyperbolic (GH) distribution family. The special and limiting relationships among the GH distribution and its important subclasses are reviewed. The empirical analysis considers daily returns on the SPDR S&P 500 ETF Trust (SPY) from 4 January 2010 to 22 July 2024. The unrestricted GH distribution and its subclasses—Variance Gamma (VG), Normal Inverse Gaussian (NIG), Normal Reciprocal Inverse Gaussian (NRIG), Hyperbolic (H), Reciprocal Hyperbolic (RH) and Hyperbola (HA)—are estimated via the maximum likelihood method. Overall, the results demonstrate that the GH family provides a flexible and effective alternative to the Gaussian benchmark, although the preferred subclass depends on whether predictive adequacy or model parsimony is emphasized.
Many animal species have unique patterns on their body that allow for individual identification, and these patterns often have a genetic basis. This individual-level pattern variation can be leveraged in ecological applications in a number of ways, such as facilitating the identification of individuals in mark-recapture study systems, and informing conservation efforts by identifying the source populations of animals trafficked in the wildlife trade, for example. We tested four convolutional neural network architectures that researchers with access to training data can use to extract features for clustering individuals into a known number of biologically relevant groups in species with unique individual patterns. We used a common freshwater turtle species, the painted turtle (Chrysemys picta), which has intricate individual-level variation in plastron pattern. We compared the ability of our neural network approaches, traditional geometric morphometric methods, and software for identifying individuals to group individuals by clutch and population using two clustering methods. We found that no methods reliably recovered clutch membership (i.e., half or full siblings) from plastron patterns (Adjusted Rand indices < 0.266). However, individuals could be sorted into source populations with high agreement using both methods, with the convolutional autoencoder resulting in the best clustering (Adjusted Rand index = 0.858). Most of our neural network approaches outperformed (had higher Adjusted Rand indices than) the geometric morphometric methods in both cases, and both of these approaches outperformed the similarity scores calculated by the individual identification software. These results demonstrate that neural-network-derived image features can provide an effective approach for evaluating whether uniquely identifiable individuals cluster into biologically relevant groups.
