fft

一篇技术评论文章，批评 OpenAI 在数学论文集中声称的更快快速傅里叶变换（FFT）算法，指出其改进微乎其微，更像是利用理论模型在硬件上并不实际可行的“恶意利用”，而非真正的突破。

A team claims to halve optimizer-state VRAM by transforming AdamW gradient states into the frequency domain with an FFT, dropping low-energy frequencies instead of using quantization, trading extra compute per step for near-zero OOM risk. They're sharing their Colab environment and baseline weights and asking whether others are exploring non-quantization VRAM-reduction methods.

An independent researcher's paper ablates filter properties (DC/Nyquist suppression, bandwidth, centre frequency, multi-scale coverage) for FourierQK frequency-collapse attention, finding that admissible bandpass filters like the Mexican Hat DOG yield gains over dot-product attention in bidirectional settings, while causal autoregressive use requires a Morlet-based variant. Part of a seven-paper series on spectral inductive biases for transformer attention.

This paper proposes a zero-shot time-series anomaly detection framework that enhances LLM inputs with frequency-domain evidence from FFT to better capture structural anomalies.

The paper presents a new method for inverting polyphase filter banks using a circulant formalism and FFT-based algorithm, enabling high-resolution spectral analysis in radio astronomy with effective quantization noise mitigation.

A beginner-friendly walkthrough of the Fast Fourier Transform using R, explaining how to interpret the fft function output, amplitude, phase, and the Nyquist limit.

A solo researcher introduces Wave Field attention, replacing standard O(N²) dot-product attention with FFT wave convolution, achieving O(N log N) training and O(1) inference per token. Claimed 80+ tok/s on CPU with 128K context and better zero-shot performance than GPT-2 124M.

This paper introduces CDLinear, a block-circulant neural network layer that reduces parameter count and improves Hessian conditioning via FFT diagonalization, validated on MNIST with theoretical proofs.

This article provides a detailed mathematical derivation of the Cooley-Tukey Fast Fourier Transform algorithm, explaining how it reduces the complexity of the Discrete Fourier Transform.

Interactive deep-dive explaining how Shazam uses FFT-derived spectrograms and audio fingerprinting to identify songs in seconds.