Explicit Factorization
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Explicit Factorization of $x^{p+1}-1$ over $\mathbb{Z}_{p^e}$: A Structural Approach via Dickson Polynomials
arXiv:2604.19038v2 Announce Type: replace Abstract: Let $p$ be an odd prime. The factorization of the polynomial $x^{p+1}-1$ over the integer residue ring $\mathbb{Z}_{p^e}$ is pivotal for constructing cyclic codes with Hermitian symmetry, a critical resource for Linear Complementary Dual (LCD) codes and Entanglement-Assisted Quantum Error-Correcting Codes (EAQECC). Traditionally, lifting factorizations relies on the generic Hensel's Lemma, masking the underlying algebraic structure.
SkelDPO: A Skeleton-Guided Direct Preference Optimization Framework for Efficient Code Generation
arXiv:2606.06826v1 Announce Type: new Abstract: With the remarkable progress of Code Large Language Models (Code LLMs) in achieving semantic correctness, execution efficiency has become an increasingly important dimension for evaluating their practical utility. However, existing approaches typically treat full programs as a single optimization target during training, without explicitly modeling the structural factors that influence efficiency. As a result, although these models can generate...
Is Memorization Helpful or Harmful? Prior Information Sets the Threshold
arXiv:2602.09405v2 Announce Type: replace-cross Abstract: We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to the prior distribution $\pi$, giving explicit conditions under which optimal generalization necessitates that the training error be (i) near interpolating relative to the noise size (i.e.,...
ForecastCompass: Guiding Agentic Forecasting with Adaptive Factor Memory
Announce Type: new Abstract: Agentic forecasting is important for decision-making in dynamic environments, but it remains challenging because agents must reason from incomplete, time-limited evidence and produce calibrated probabilities before outcomes are resolved. Memory provides a natural mechanism for transferring experience from resolved forecasts to future prediction tasks. However, existing agent-memory methods are not tailored to forecasting, as they typically store past...
PathAR: Structure-First Autoregressive Synthesis of Multimodal Pathology Images
arXiv:2606.01543v1 Announce Type: new Abstract: Data scarcity in multimodal pathology motivates unified generative models that synthesize modality-specific appearance while preserving anatomically coherent structure. Although modalities differ in appearance statistics, morphological structures such as cellular topology and tissue boundaries are largely preserved across acquisition protocols. However, existing methods often model these factors within a homogeneous token stream, implicitly...
MS-DKC: A Dataset Knowledge Card Framework for Designing and Adapting Medical Image Segmentation Models
arXiv:2606.06103v1 Announce Type: new Abstract: Medical image segmentation is often framed as a search for stronger architectures, but this can obscure a more fundamental question: what does the dataset require from the model? In medical imaging, this requirement is shaped by foreground occupancy, morphology, boundary ambiguity, topology sensitivity, annotation quality, acquisition variation, and operating point. This paper introduces the Medical Segmentation Dataset Knowledge Card (MS-DKC),...
Motion-Guided Causal Disentanglement for Robust Multi-View Cine Cardiac MRI Diagnosis
Announce Type: new Abstract: Multi-view cardiac magnetic resonance (CMR) imaging provides complementary anatomical information and is widely used for noninvasive disease assessment. Recent transformer-based models have demonstrated strong representation learning capabilities for CMR analysis; however, they typically learn unified latent embeddings that entangle view-specific anatomical variations with disease-related features. Such entanglement biases classifiers toward structural attributes...
Relaxation Kernel, Spectral Dissipation, and Global Convergence of Blahut--Arimoto Dynamics
arXiv:2604.25106v3 Announce Type: replace Abstract: We develop a spectral theory for continuous- and discrete-time Blahut--Arimoto (BA) dynamics, centered on the relaxation kernel $ \G = \E_p[K^*_X \otimes K^*_X] $. Five main results are established. Along the continuous-time BA flow, the free energy satisfies the exact $ \chi^2 $-dissipation identity $ \dot F_\beta = -\D(q) $, where $ \D(q)=\chi^2(\T q \| q) $ is the Pearson $ \chi^2 $-divergence.
Efficient and Accurate Model Order Reduction for Integral Electromagnetic Formulations in Fusion Device Transient Analysis Toward AI-Enabled Modeling
arXiv:2605.28648v2 Announce Type: replace Abstract: The numerical simulation of electromagnetic transients in fusion devices is essential for analyzing plasma stability and disruptive events. However, it remains computationally demanding due to the large-scale dense systems arising from integral formulations. This work proposes a model order reduction (MOR) strategy for transient electromagnetic problems based on integral formulations.
Beyond Absolute Scores: Relative Edit-induced Difference for Generalizable Image Aesthetic Assessment
Announce Type: new Abstract: Traditional Image Aesthetic Assessment (IAA) methods mainly rely on regressing absolute Mean Opinion Scores (MOS). However, such a paradigm overlooks the inherently dynamic nature of human aesthetic perception, which relies on subconscious comparison against implicit visual references. Consequently, the lack of causal reasoning regarding aesthetic differences prevents models from learning generalizable aesthetic principles, thus limiting their generalization...