Transformer-Evolution-Paper
  • README
  • 数学符号
  • Act
    • A survey on recently proposed activation functions for Deep Learning
  • Arch
    • Supplementary Material Implementation and Experiments for GAU-based Model
    • MetaFormer is Actually What You Need for Vision
    • Deeper vs Wider A Revisit of Transformer Configuration
    • Perceiver General Perception with Iterative Attention
    • General-purpose, long-context autoregressive modeling with Perceiver AR
    • Hierarchical Transformers Are More Efficient Language Models
    • Branchformer: Parallel MLP-Attention Architectures to Capture Local and Global Context for Speech Recognition and Understanding
    • Generalization through Memorization: Nearest Neighbor Language Models
  • FFN
    • Large Memory Layers with Product Keys
    • Transformer Feed-Forward Layers Are Key-Value Memories
    • GLU Variants Improve Transformer
    • Simple Recurrence Improves Masked Language Models
    • Pay Attention to MLPs
    • S2-MLP Spatial-Shift MLP Architecture for Vision
    • S2-MLPv2 Improved Spatial-Shift MLP Architecture for Vision
    • HyperMixer An MLP-based Green AI Alternative to Transformers
    • DeFINE: DEep Factorized INput Token Embeddings for Neural Sequence Modeling & DeLighT: Deep and Light-weight Transformer
    • When Shift Operation Meets Vision Transformer: An Extremely Simple Alternative to Attention Mechanism
    • Sparse MLP for Image Recognition: Is Self-Attention Really Necessary?
  • Head
    • Multi-Head Attention Collaborate Instead of Concatenate
    • Fast Transformer Decoding: One Write-Head is All You Need
  • Memory
    • Compressive Transformers for Long-Range Sequence Modelling
    • Memformer The Memory-Augmented Transformer
    • Memory Transformer
    • Do Transformers Need Deep Long-Range Memory
    • LaMemo Language Modeling with Look-Ahead Memory
    • GMAT Global Memory Augmentation for Transformers
    • Block-Recurrent Transformers
    • Augmenting Self-attention with Persistent Memory
    • Recurrent Memory Transformer
    • Memorizing Transformers
    • Scaling Transformer to 1M tokens and beyond with RMT
    • Adapting Language Models to Compress Contexts
  • MHA
    • FFT
      • Fourier Neural Operator for Parametric Partial Differential Equations
      • Global Filter Networks for Image Classification
      • Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers
      • FNet: Mixing Tokens with Fourier Transforms
    • LocalGlobal
      • CrossFormer: A Versatile Vision Transformer Hinging on Cross-scale Attention
      • Nested Hierarchical Transformer: Towards Accurate, Data-Efficient and Interpretable Visual Understanding
      • Neighborhood Attention Transformer
      • FMMformer: Efficient and Flexible Transformer via Decomposed Near-field and Far-field Attention
      • Adaptive Attention Span in Transformers
      • CoLT5: Faster Long-Range Transformers with Conditional Computation
    • MatrixMethod
      • Skyformer Remodel Self-Attention with Gaussian Kernel and Nyström Method
      • Is Attention Better Than Matrix Decomposition
    • RightProduct
      • Kronecker Attention Networks
      • An Attention Free Transformer
      • Transformer with Fourier Integral Attentions
      • Linear Complexity Randomized Self-attention Mechanism
      • UFO-ViT: High Performance Linear Vision Transformer without Softmax
      • XCiT: Cross-Covariance Image Transformers
      • SimpleTRON: Simple Transformer with O(N) Complexity
      • A Dot Product Attention Free Transformer
      • On Learning the Transformer Kernel
      • Momentum Transformer: Closing the Performance Gap Between Self-attention and Its Linearization
    • SparseOrLowRank
      • Explicit Sparse Transformer: Concentrated Attention Through Explicit Selection
      • Scatterbrain: Unifying Sparse and Low-rank Attention Approximation
      • Sparse Factorization of Large Square Matrices
      • Blockwise Self-Attention for Long Document Understanding
      • H-Transformer-1D: Fast One-Dimensional Hierarchical Attention for Sequences
      • ChunkFormer: Learning Long Time Series with Multi-stage Chunked Transformer
      • Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting
      • Fast Transformers with Clustered Attention
      • Long-Short Transformer: Efficient Transformers for Language and Vision
      • LongT5: Efficient Text-To-Text Transformer for Long Sequences
      • Luna: Linear Unified Nested Attention
      • Memory-efficient Transformers via Top-k Attention
      • Separable Self-attention for Mobile Vision Transformers
      • Simple Local Attentions Remain Competitive for Long-Context Tasks
      • You Only Sample (Almost) Once: Linear Cost Self-Attention Via Bernoulli Sampling
    • Others
      • Synthesizer: Rethinking Self-Attention in Transformer Models
      • Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kern
      • Combiner Full Attention Transformer with Sparse Computation Cost
      • Ripple Attention for Visual Perception with Sub-quadratic Complexity
      • Sinkformers: Transformers with Doubly Stochastic Attention
      • SOFT: Softmax-free Transformer with Linear Complexity
      • Value-aware Approximate Attention
      • EL-Attention: Memory Efficient Lossless Attention for Generation
      • Flowformer: Linearizing Transformers with Conservation Flows
      • ETSformer: Exponential Smoothing Transformers for Time-series Forecasting
      • IGLOO: Slicing the Features Space to Represent Sequences
      • Swin Transformer V2: Scaling Up Capacity and Resolution
      • Skip-Attention: Improving Vision Transformers by Paying Less Attention
  • Normalize_And_Residual
    • ReZero is All You Need Fast Convergence at Large Depth
    • Batch Normalization Biases Residual Blocks Towards the Identity Function in Deep Networks
    • Improving Deep Transformer with Depth-Scaled Initialization and Merged Attention
    • RealFormer Transformer Likes Residual Attention
    • On Layer Normalizations and Residual Connections in Transformers
    • Transformers without Tears: Improving the Normalization of Self-Attention
    • Query-Key Normalization for Transformers
    • Understanding the difficulty of training transformers
  • Pe
    • A Simple and Effective Positional Encoding for Transformers
    • DeBERTa Decoding-enhanced BERT with Disentangled Attention
    • DecBERT Enhancing the Language Understanding of BERT with Causal Attention Masks
    • Encoding word order in complex embeddings
    • Improve Transformer Models with Better Relative Position Embeddings
    • KERPLE Kernelized Relative Positional Embedding for Length Extrapolation
    • PermuteFormer Efficient Relative Position Encoding for Long Sequences
    • Rethinking Positional Encoding in Language Pre-training
    • Transformer-XL Attentive Language Models Beyond a Fixed-Length Context
    • Translational Equivariance in Kernelizable Attention
    • Transformer Language Models without Positional Encodings Still Learn Positional Information
    • Stable, Fast and Accurate: Kernelized Attention with Relative Positional Encoding
    • Randomized Positional Encodings Boost Length Generalization of Transformers
  • Pretrain
    • XLNet Generalized Autoregressive Pretraining for Language Understanding
    • Transcormer Transformer for Sentence Scoring with Sliding Language Modeling
    • Optimus Organizing Sentences via Pre-trained Modeling of a Latent Space
    • ELECTRA Pre-training Text Encoders as Discriminators Rather Than Generators
    • Cramming: Training a Language Model on a Single GPU in One Day
  • Softmax
    • Transformer with a Mixture of Gaussian Keys
    • Normalized Attention Without Probability Cage
  • Others
    • Accelerating Neural Transformer via an Average Attention Network
    • Do Transformer Modifications Transfer Across Implementations and Applications?
    • Object-Centric Learning with Slot Attention
    • Do Transformer Modifications Transfer Across Implementations and Applications?
    • Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetries
  • LongConv
    • Legendre Memory Units: Continuous-Time Representation in Recurrent Neural Networks
    • Parallelizing Legendre Memory Unit Training
    • Simplified State Space Layers for Sequence Modeling
    • Pretraining Without Attention
    • What Makes Convolutional Models Great on Long Sequence Modeling?
    • Hungry Hungry Hippos: Towards Language Modeling with State Space Models
    • Hyena Hierarchy: Towards Larger Convolutional Language Models
    • RWKV
    • Simple Hardware-Efficient Long Convolutions for Sequence Modeling
    • Time-aware large kernel convolutions
    • Resurrecting Recurrent Neural Networks for Long Sequences
    • CKConv: Continuous Kernel Convolution For Sequential Data
    • FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes
    • Towards a General Purpose CNN for Long Range Dependencies in ND
  • Rnn
    • When Attention Meets Fast Recurrence: Training Language Models with Reduced Compute
    • Linear Transformers Are Secretly Fast Weight Programmers
    • Going Beyond Linear Transformers with Recurrent Fast Weight Programmers
    • Parallelizing Linear Recurrent Neural Nets Over Sequence Length
    • Quasi-recurrent neural networks
  • CrossAttention
    • Neural Machine Translation in Linear Time
  • Inference
    • Extrapolation
      • Parallel Context Windows for Large Language Models
      • Structured Prompting: Scaling In-Context Learning to 1,000 Examples
      • Naive Bayes-based Context Extension
  • Peft
    • Parameter-Efficient Fine-Tuning without Introducing New Latency
    • Make Your Pre-trained Model Reversible: From Parameter to Memory Efficient Fine-Tuning
  • LLM
    • LLM Details Summary
    • What Language Model to Train if You Have One Million GPU Hours?
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数学符号

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Last updated 2 years ago

这里统一规定笔记中的数学记号。

基本符号

  1. 向量用小写mathbf字体表示：x∈Rd\mathbf x \in \mathbb R^dx∈Rd(所有向量均为列向量，即x∈Rd×1\mathbf x \in \mathbb R^{d\times 1}x∈Rd×1)；

  2. 矩阵用大写mathbf字体表示，X∈Rn×d\mathbf X\in \mathbb R^{n\times d}X∈Rn×d：

    X=[x1⊤⋮xn⊤]∈Rn×d;\begin{aligned} \mathbf X&= \left[ \begin{matrix} \mathbf x_1^{\top} \\ \vdots \\ \mathbf x_n^{\top} \end{matrix} \right]\in \mathbb R^{n\times d}; \end{aligned}X​=​x1⊤​⋮xn⊤​​​∈Rn×d;​

  3. xi\mathbf x_ixi​表示矩阵X\mathbf XX的第iii行的转置；

  4. 标量用常规字体表示α,β\alpha, \betaα,β；

  5. 默认用nnn表示序列长度，ddd表示嵌入维度，bbb表示batch size；

  6. Score Matrix：S=QK⊤\mathbf S=\mathbf Q \mathbf K^{\top}S=QK⊤；

  7. Attention Matrix：A=f(S)\mathbf A = f(\mathbf S)A=f(S)；

    • 一般场景下f=Softmaxf=\mathrm{Softmax}f=Softmax，但是也可以有别的选择；

  8. 一些常用算子符号：

    • Softmax(X,d=−1):Rn×d→Rn×d\mathrm{Softmax}(\mathbf X,d=-1): \mathbb R^{n\times d}\to \mathbb R^{n\times d}Softmax(X,d=−1):Rn×d→Rn×d：

      • ddd为归一化维度，不指定时为最后一维，这里表示映射时没有考虑ddd，做个不严格的简化定义；

    • Norm(X,d=−1):Rn×d→Rn×d\mathrm{Norm}(\mathbf X,d=-1): \mathbb R^{n\times d}\to \mathbb R^{n\times d}Norm(X,d=−1):Rn×d→Rn×d：

      • 各种归一化方式，具体类型使用文字说明，符号中不体现，ddd为归一化维度，不指定时为最后一维;

    • MHA(X,Y):Rn×d×Rm×d→Rn×d\mathrm{MHA}(\mathbf X, \mathbf Y):\mathbb R^{n\times d}\times \mathbb R^{m\times d}\to \mathbb R^{n\times d}MHA(X,Y):Rn×d×Rm×d→Rn×d：

      • 一种MHA\mathrm {MHA}MHA的接口，最具体来说X\mathbf XX对应query，Y\mathbf YY对应key, value；

    • MHA(Q,K,V):Rn×d×Rm×d×Rm×d→Rn×d\mathrm{MHA}(\mathbf Q, \mathbf K,\mathbf V):\mathbb R^{n\times d}\times \mathbb R^{m\times d}\times \mathbb R^{m\times d}\to \mathbb R^{n\times d}MHA(Q,K,V):Rn×d×Rm×d×Rm×d→Rn×d：

      • 另一种MHA\mathrm{MHA}MHA的接口，不常使用；

    • Tran(X,Y):Rn×d×Rm×d→Rn×d\mathrm{Tran}(\mathbf X, \mathbf Y):\mathbb R^{n\times d}\times \mathbb R^{m\times d}\to \mathbb R^{n\times d}Tran(X,Y):Rn×d×Rm×d→Rn×d

      • Transformer的接口；

    • FFN(X):Rn×d→Rn×d\mathrm {FFN}(\mathbf{X}): \mathbb R^{n\times d} \to \mathbb R^{n\times d}FFN(X):Rn×d→Rn×d：

      • Transformer中FFN层；

  9. Sum(X,d=0):Rn×d→Rd\mathrm{Sum}(\mathbf X,d=0): \mathbb R^{n\times d} \to \mathbb R^{d}Sum(X,d=0):Rn×d→Rd

目前先定义这些，后续再进行补充。