#01Jul 23, 2026
hep-ph
Neural solutions of coupled ghost and gluon Dyson--Schwinger equations in Landau gauge
Rodrigo Carmo Terin
The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.
#02Jul 23, 2026
cs.LG
Context-weighted Discrete Flow Matching
Daniil Cherniavskii, Daniel Severo, Karen Ullrich
Discrete flow matching provides a flexible framework for generative modeling on discrete structures. However, the standard factorized training objective exposes the model to targets of varying difficulty, mixing well-conditioned, predictable tokens with ambiguous, high-entropy ones. We empirically demonstrate that the uncertainty over the value of each token is closely related to the density of available context in its neighborhood. Motivated by this observation, we propose a simple modification to the underlying continuous-time Markov chain (CTMC) that incorporates local context information. Our context-weighted sampler improves generation quality with negligible computational overhead, while our scaled cross-entropy loss function reweights the training signal from different tokens and reduces generative perplexity by up to 63% on OpenWebText. Moreover, our approach matches a strong semi-autoregressive block diffusion baseline in quality while retaining the ability to perform generation in any order. These results highlight the role of local context as an important factor in discrete generative modeling and show that simple context-aware modifications can significantly improve both sampling and training efficiency.
#03Jul 23, 2026
cs.LG
KroQuant: Kronecker-Structured Block Transforms for Efficient Post-Training Quantization of Diffusion Transformers
Yann Bouquet, Alireza Khodamoradi, Kristof Denolf and 1 more
Post-training quantization (PTQ) of diffusion transformers (DiTs) to W4A4 severely degrades output quality, because activations entering each linear layer contain outliers that 4-bit formats cannot represent. The standard fix applies an invertible linear transform to the activations and its inverse to the weights before quantizing both. Normalization layers between blocks force this transform to run online at every denoising step, making its inference computation cost the binding design constraint. Existing options trade quantization quality for inference cost: per-channel scaling (SmoothQuant) is computationally cheap but impacts the magnitude of the channels, which can harm quantization accuracy; fixed Hadamard transforms yield better quantization accuracy but require large block sizes that incur a high online cost; learned full-$d$ invertible transforms calibrate best but entail a prohibitive dense $d \times d$ matrix multiplication (GEMM) per layer per step. We propose KroQuant, a PTQ method that applies a learned Kronecker-structured invertible transform to each 32-element block of the activation, storing less than half the parameters of per-channel scaling. The block-local structure runs as small tensor-core GEMMs, and on an MI350 GPU the KroQuant quantizer kernel is up to $14\%$ faster than the SmoothQuant kernel. Offline LoRaQ weight calibration then absorbs the residual per-weight quantization error. On PixArt-$Σ$, SANA, and FLUX.1-schnell at W4A4 (MXFP4e2), KroQuant produces outputs closer to the FP reference than SVDQuant and LoRaQ on MJHQ-30K and SDCI, while preserving or improving image quality.
#04Jul 23, 2026
math.OC
Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$
Dawei Li, Xiaotian Jiang, Mingyi Hong
Barzilai--Borwein (BB) method has shown strong practical performance in continuous optimization, yet its convergence dynamics remains poorly understood. In particular, a central unresolved question is whether BB converges superlinearly for almost every strictly convex quadratic problem and initialization. We provide a negative answer to this question. Specifically, for every finite dimension $n\geq4$, we construct a nonempty open, hence positive-Lebesgue-measure, family of strictly convex quadratic problems and initial points for which the long Barzilai--Borwein method (BB1) converges but cannot converge root-superlinearly. More precisely, with the explicit constants $ρ_{\min}=10^{-6},ρ_{\max}=0.61$, every spectral component of the gradient is bounded above and below by the corresponding geometric sequence. Consequently, the gradient norm and the energy norm of the error satisfy two-sided geometric estimates with the same rates, while the objective gap satisfies the corresponding estimates with squared rates. In particular, all three quantities are bounded below by geometric sequences, ruling out superlinear convergence. The construction is highly nontrivial, based on a computer-assisted proof of a nonresonant, attracting seven-cycle of the projectivized BB dynamics in dimension four.
#05Jul 23, 2026
cs.CV
Synthetic data generation framework for quality control automation in gravure printing
Korota Arsène Coulibaly, Mohamed Hamlich, Khalid Hmali and 1 more
Quality control in printing, particularly in rotogravure printing, still depends on slow, costly, and subjective manual inspection. Automated surface defect detection is critical for maintaining high-quality standards in rotogravure printing. Deep learning models give prospects for automation. However, training robust deep learning models, such as YOLO or Vision Transformers, is heavily hindered by the extreme scarcity of real-world industrial defects images. To overcome this limitation, this paper introduces a novel synthetic data generation framework tailored for rotogravure printing quality control. The proposed pipeline automatically generates high-fidelity images of specific printing defects (creases, streaks, misregistration, etc.) and outputs corresponding bounding boxes and annotations. To validate the framework, a synthetic dataset of 7533 images was generated and used to train the state-of-the-art object-detection model RFDETR. Experimental results demonstrate that the model trained on our synthetic data achieves a Mean Average Precision (mAP) of 80.9\% on real industrial testing samples. This framework provides a zero-cost, rapid-deployment solution for automating defect inspection in printing lines without requiring massive manual data collection.