ConvDarts: a fast and exact convolutional algorithm selector for deep learning frameworks

We study the planar maximum coverage location problem (MCLP) with rectilinear distance and rectangular demand zones in the case where “partial coverage” is allowed in its true sense, i.e., when covering part of a demand zone is allowed and the coverage accrued as a result of this is proportional to the demand of the covered part only. We pose the problem in a slightly more general form by allowing service zones to be rectangular instead of squares, thereby addressing applications in camera view-frame selection as well. More specifically, our problem, referred to as PMCLP-PCR (planar MCLP with partial coverage and rectangular demand and service zones), is to position a given number of rectangular service zones (SZs) on the two-dimensional plane to (partially) cover a set of existing (possibly overlapping) rectangular demand zones (DZs) such that the total covered demand is maximized. Previous studies on (planar) MCLP have assumed binary coverage, even when nonpoint objects such as lines or polygons have been used to represent demand. Under the binary coverage assumption, the problem can be readily formulated and solved as a binary linear program; whereas, partial coverage, although much more realistic, cannot be efficiently handled by binary linear programming, making PMCLP-PCR much more challenging to solve. In this paper, we first prove that PMCLP-PCR is NP-hard if the number of SZs is part of the input. We then present an improved algorithm for the single-SZ PMCLP-PCR, which is at least two times faster than the existing exact plateau vertex traversal algorithm. Next, we study multi-SZ PMCLP-PCR for the first time and prove theoretical properties that significantly reduce the search space for solving this problem, and we present a customized branch-and-bound exact algorithm to solve it. Our computational experiments show that this algorithm can solve relatively large instances of multi-SZ PMCLP-PCR in a short time. We also propose a fast polynomial time heuristic algorithm. Having optimal solutions from our exact algorithm, we benchmark the quality of solutions obtained from our heuristic algorithm. Our results show that for all the random instances solved to optimality by our exact algorithm, our heuristic algorithm finds a solution in a fraction of a second, where its objective value is at least 91% of the optimal objective in 90% of the instances (and at least 69% of the optimal objective in all the instances).

A comprehensive empirical study on bug characteristics of deep learning frameworks

Deep learning (DL) frameworks serve as the backbone for a wide range of artificial intelligence applications. However, bugs within DL frameworks can cascade into critical issues in higher-level applications, jeopardizing reliability and security. While numerous techniques have been proposed to detect bugs in DL frameworks, research exploring common API patterns across frameworks and the potential risks they entail remains limited. Notably, many DL frameworks expose similar APIs with overlapping input parameters and functionalities, rendering them vulnerable to shared bugs, where a flaw in one API may extend to analogous APIs in other frameworks. To address this challenge, we propose MirrorFuzz, an automated API fuzzing solution to discover shared bugs in DL frameworks. MirrorFuzz operates in three stages: First, MirrorFuzz collects historical bug data for each API within a DL framework to identify potentially buggy APIs. Second, it matches each buggy API in a specific framework with similar APIs within and across other DL frameworks. Third, it employs large language models (LLMs) to synthesize code for the API under test, leveraging the historical bug data of similar APIs to trigger analogous bugs across APIs. We implement MirrorFuzz and evaluate it on four popular DL frameworks (TensorFlow, PyTorch, OneFlow, and Jittor). Extensive evaluation demonstrates that MirrorFuzz improves code coverage by 39.92% and 98.20% compared to state-of-the-art methods on TensorFlow and PyTorch, respectively. Moreover, MirrorFuzz discovers 315 bugs, 262 of which are newly found, and 80 bugs are fixed, with 52 of these bugs assigned CNVD IDs.

Exact and fast algorithm for two-dimensional image wavelet moments via the projection transform

Accurate prediction and confirmation of mechanical properties are critical for the reliable design and deployment of sustainable aluminum–agro-waste composites (AWCs). This study presents a confirmatory analytical–experimental–deep machine learning (DML) framework for the identification of true material properties under multi-response conditions. Experimental characterization yielded mean tensile strength of 190.61 MPa, compressive strength of 287.16 MPa, flexural strength of 243.94 MPa, wear rate of 5.46 × 10⁻⁶ mm³ /N·m, coefficient of friction of 0.34, and fatigue life of 5.86 × 10⁵ cycles, with low variability observed in strength-related properties and higher dispersion in tribological and fatigue responses. Isolated analytical predictions produced comparable estimates for tensile (189.60 MPa), compressive (296.42 MPa), flexural (255.75 MPa), and fatigue properties (5.97 × 10⁵ cycles), but failed to reliably capture tribological behavior, yielding a non-physical negative wear rate (− 4.06 mm³/N·m) and an overestimated coefficient of friction (0.45). Consolidated analytical modeling improved agreement for tensile (187.60 MPa), compressive (285.63 MPa), flexural (244.88 MPa), and fatigue life (5.86 × 10⁵ cycles), yet significantly deviated in tribological predictions, producing unrealistically high wear rate (0.20 mm³/N·m) and coefficient of friction (2.84). To resolve these discrepancies, DML models—implemented via a deep convolutional neural network (ID-CNN) and a hybrid residual CNN guided by a residual-based loss function—were employed to reconcile analytical (isolated/consolidated) predictions with experimental data. The DML framework successfully minimized analytical–experimental residuals and confirmed true predictive reliability for compressive strength, flexural strength, coefficient of friction, and fatigue life, while consistently identifying wear rate as falsely predicted across analytical frameworks. These findings establish DML as both a predictive and diagnostic tool, enabling discrimination between truly confirmed and analytically unstable properties. The proposed framework offers a scalable, data-informed pathway for optimized composite design, process refinement, and industrial adoption, with potential extension to multi-scale modeling and real-time process monitoring. Residual-based DML loss quantifies and minimizes analytical–experimental prediction errors. • Residual-based DML loss quantifies and minimizes analytical–experimental prediction errors. • Integrated analytical–DML modeling confirms strength, fatigue, and friction properties. • Bulk properties converge, while wear rate shows persistent tribological uncertainty. • The framework supports reliable certification and sustainable composite design.

Deep reinforcement learning for transportation network combinatorial optimization: A survey

As the device shapes keep shrinking, the designs are more sensitive to manufacturing processes. In order to improve performance predictability and yield, mask-layout uniformity/evenness is highly desired, and it is usually measured by the feature densities within defined feasible ranges determined by the manufacturing-process design rules. To address the density-control problem, one fundamental problem is how to calculate density accurately and efficiently. In this paper, we propose a fast exact algorithm to identify the maximum/minimum density for a given layout. Compared with the existing exact algorithms, our algorithm reduces the running time from days/long hours to a few minutes/seconds. Moreover, it is even faster than the existing approximate algorithms in the literature.

We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in O/spl tilde/(n/sup 2+/spl mu//) time, where /spl mu/ satisfies the equation /spl omega/(1,/spl mu/,1)=1+2/spl mu/ and /spl omega/(1,/spl mu/,1) is the exponent of the multiplication of an n/spl times/n/sup /spl mu// matrix by an n/sup /spl mu///spl times/n matrix. The currently best available bounds on /spl omega/(1,/spl mu/,1), obtained by Coppersmith and Winograd, and by Huang and Pan, imply that /spl mu/ 0 is an error parameter and W is the largest edge weight in the graph, after the edge weights are scaled so that the smallest non-zero edge weight in the graph is 1. It returns estimates of all the distances in the graph with a stretch of at most 1+/spl epsiv/. Corresponding paths can also be found efficiently.

Gaussian stochastic process (GaSP) has been widely used as a prior over functions due to its flexibility and tractability in modeling. However, the computational cost in evaluating the likelihood is , where n is the number of observed points in the process, as it requires to invert the covariance matrix. This bottleneck prevents GaSP being widely used in large-scale data. We propose a general class of nonseparable GaSP models for multiple functional observations with a fast and exact algorithm, in which the computation is linear (O(n)) and exact, requiring no approximation to compute the likelihood. We show that the commonly used linear regression and separable models are special cases of the proposed nonseparable GaSP model. Through the study of an epigenetic application, the proposed nonseparable GaSP model can accurately predict the genome-wide DNA methylation levels and compares favorably to alternative methods, such as linear regression, random forest, and localized Kriging method. The supplementary materials of this article are online and the algorithm for fast computation is implemented in the FastGaSP R package on CRAN. Supplemental materials for this article are available online.

A fast computer algorithm, the pebble game, has been used successfully to analyze the rigidity of two-dimensional (2D) elastic networks, as well as of a special class of 3D networks, the bond-bending networks, and enabled significant progress in studies of rigidity percolation on such networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on bcc and fcc lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first-order rigidity percolation transition, which is in contrast to the second-order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed previously for Bethe lattices and networks with "chemical order," here it is in a regular randomly diluted network. In the case of site dilution, the transition is also first order for bcc lattices, but results for fcc lattices suggest a second-order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent nonuniversality, make this phase transition highly unusual.

Deep learning (DL) frameworks are essential to DL-based software systems, and framework bugs may lead to substantial disasters, thus requiring effective testing. Researchers adopt DL models or single interfaces as test inputs and analyze their execution results to detect bugs. However, floating-point errors, inherent randomness, and the complexity of test inputs make it challenging to analyze execution results effectively, leading to existing methods suffering from a lack of suitable test oracles. Some researchers utilize metamorphic testing to tackle this challenge. They design Metamorphic Relations (MRs) based on input data and parameter settings of a single framework interface to generate equivalent test inputs, ensuring consistent execution results between original and generated test inputs. Despite their promising effectiveness, they still face certain limitations. (1) Existing MRs overlook structural complexity, limiting test input diversity. (2) Existing MRs focus on limited interfaces, which limits generalization and necessitates additional adaptations. (3) Their detected bugs are related to the result consistency of single interfaces and far from those exposed in multi-interface combinations and runtime metrics (e.g., resource usage). To address these limitations, we propose ModelMeta, a model-level metamorphic testing method for DL frameworks with four MRs focused on the structure characteristics of DL models. ModelMeta augments seed models with diverse interface combinations to generate test inputs with consistent outputs, guided by the QR-DQN strategy. It then detects bugs through fine-grained analysis of training loss/gradients, memory/GPU usage, and execution time. We evaluate the effectiveness of ModelMeta on three popular DL frameworks (i.e., MindSpore, PyTorch, and ONNX) with 17 DL models from ten real-world tasks ranging from image classification to object detection. Results demonstrate that ModelMeta outperforms state-of-the-art baselines from the perspective of test coverage and diversity of generated test inputs. Regarding bug detection, ModelMeta has identified 31 new bugs, of which 27 have been confirmed, and 11 have been fixed. Among them, seven bugs existing methods cannot detect, i.e., five wrong resource usage bugs and two low-efficiency bugs. These results demonstrate the practicality of our method.

Objective: To design a deep transfer learning framework for modeling fluence map predictions for stereotactic body radiation therapy (SBRT) of adrenal cancer and similar sites that usually have a small number of cases. Approach: We developed a transfer learning framework for adrenal SBRT planning that leverages knowledge in a pancreas SBRT planning model. Treatment plans from the two sites had different dose prescriptions and beam settings but both prioritized gastrointestinal sparing. A base framework was first trained with 100 pancreas cases. This framework consists of two convolutional neural networks (CNN), which predict individual beam doses (BD-CNN) and fluence maps (FM-CNN) sequentially for 9-beam intensity-modulated radiation therapy (IMRT) plans. Forty-five adrenal plans were split into training/validation/test sets with the ratio of 20/10/15. The base BD-CNN was re-trained with transfer learning using 5/10/15/20 adrenal training cases to produce multiple candidate adrenal BD-CNN models. The base FM-CNN was directly used for adrenal cases. The deep learning (DL) plans were evaluated by several clinically relevant dosimetric endpoints, producing a percentage score relative to the clinical plans. Main results: Transfer learning significantly reduced the number of training cases and training time needed to train such a DL framework. The adrenal transfer learning model trained with 5/10/15/20 cases achieved validation plan scores of 85.4/91.2/90.7/89.4, suggesting that model performance saturated with 10 training cases. Meanwhile, a model using all 20 adrenal training cases without transfer learning only scored 80.5. For the final test set, the 5/10/15/20-case models achieved scores of 73.5/75.3/78.9/83.3. Significance: It is feasible to use deep transfer learning to train an IMRT fluence prediction framework. This technique could adapt to different dose prescriptions and beam configurations. This framework potentially enables DL modeling for clinical sites that have a limited dataset, either due to few cases or due to rapid technology evolution.

A new ansatz is proposed to implement finite size scaling analysis of the dielectric breakdown model. Calculations on very small cells already allow to obtain good qualitative determinations of the fractal dimensions d in a wide range of dimensionalities and model parameters. Exact enumerations or high accuracy Monte Carlo calculations on larger cells (SI2 x 12) in d =2 show a remarkable degree of convergence towards values known from large scale simulations for d, and, to a lesser extent, for the multifractal dimension D(q) with qa-I. General difficulties inherent to Monte Carlo determinations of D(q) for negative q are also pointed out. For calculating the electrostatic potential inside these cells we use a new exact and fast algorithm, explained in detail in the appendix

This dissertation focuses on the problem of assigning the modules of a program to the processors in a distributed system with the goal of minimizing the overall cost of running the program. The cost depends on the execution times of the modules on the processors and on the cost of communication between modules. This module allocation problem arises in a variety of situations where one is interested in making optimum use of available computer resources. The general module allocation problem is intractable; however it becomes polynomially-solvable when the communication graph is restricted. In this dissertation, we restrict our attention to k-trees. As the first problem, we study parametric module allocation on partial k-trees. We allow the costs, both execution and communication, to vary linearly as functions of a real parameter t. We show that if the number of processors is fixed, the sequence of optimum assignments that are obtained, as t varies from zero to infinity, can be constructed in polynomial time. As an auxiliary result, we develop a linear-time algorithm to find a separator in a k-tree. We discuss the implications of our results for parametric versions of the weighted vertex cover, independent set, and 0-1 quadratic programming problems on partial k-trees. Next, we consider two variants of the assignment problem. The first problem is to find a minimum-cost assignment when one of the processors has a limited memory. The second is to find an assignment that minimizes the maximum processor load. We present exact dynamic programming algorithms for both problems, which lead to approximation schemes for the case where the communication graph is a partial k-tree. Faster algorithms are presented for trees with uniform costs. In contrast to these results, we show that, for arbitrary graphs, no fully polynomial time approximation schemes exist unless P = NP. Both dynamic programming algorithms have been implemented. The implementation details and our experimental results are presented.

Image-based 3D reconstruction and permeability modelling of rock using enhanced interpretable deep residual learning