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Qualcomm AI Research 展示了将 Combinatorial Multigrid 图粗化作为热启动与 Particle Polynomial Relaxation 非凸连续重构相结合，能在计算受限条件下更有效地逃离 MAX-CUT 的局部最优，在 Biq Mac 和 G-set 基准上取得接近最优的结果并大幅降低内存占用。
This arXiv paper introduces the Edge-Conditioned Spectral Operator (ESO), a spectral neural operator that uses local edge-wise variations to adapt global spectral mixing, improving performance on physics-sensitive PDE benchmarks.
This paper introduces DFSC, a PyTorch environment built around a Mittag-Leffler Spectral Layer (MLSL) that enables error-controlled, differentiable fractional propagation in hybrid neural models. It separates known fractional dynamics from data-driven corrections, supports batched/dense/sparse operator paths, and provides certified error bounds in certain regimes.
Proposes FRAME, a mixture-of-experts adapter that uses learnable fractional-Fourier orders to interpolate between spatial and spectral domains, improving parameter-efficient fine-tuning performance on LLMs across multiple benchmarks.
This paper theoretically demonstrates that two-layer neural networks trained on group composition tasks learn spectral representations, with neurons converging to irreducible representations and achieving rotational rank-one alignment, providing a representation-theoretic account of feature learning.
DeepMDMD combines deep learning with algebraic constraints to learn compact, dynamically coherent Koopman operator representations that enforce the product rule as an exact constraint. The method outperforms geometric approaches on high-dimensional chaotic and fluid dynamics problems, reducing spectral pollution and enabling stable long-term forecasting.
This paper proposes Energy-Gated Attention (EGA) and Morlet Positional Encoding (MoPE) to address missing inductive biases in transformer attention: token salience and scale-adaptive locality. Experiments on TinyShakespeare show superadditive gains when combined, highlighting complementarity.
This paper proposes DG-Hard, a post-hoc spectral repair method that recovers capabilities damaged by fine-tuning without retraining, using only the pretrained and fine-tuned checkpoints. It applies Donoho-Gavish hard singular-value thresholding to weight updates to remove noise and restore degraded performance.
Spectral Tempering (SpecTemp) proposes a learning-free method for embedding compression in dense passage retrieval that adaptively determines optimal spectral scaling based on signal-to-noise ratio analysis, outperforming fixed hyperparameter approaches like PCA and whitening.