Immortal MachineA technical publicationShivam Pandey

Immortal Machine / Writing

From formulation
to evidence.

Mathematical references, derivations, implementations, and experiments. Explore the Mathematical Foundations references and the KERNELIZED archive.

  1. 01

    Mathematical Foundations · Mathematics · Calculus · Autodiff

    Calculus: Integrals, Derivatives and Tensor Operators

    A detailed reference to integration, differentiation, Einstein notation, automatic differentiation, and integral operators, with assumptions and worked derivations.
  2. 06

    KERNELIZED · FlashAttention · Transformers · Attention

    FlashAttention Kernel: Backward Pass (Parallelism)

    Mapping the backward pass into dependency graphs, loop-carried constraints, and parallel execution.
  3. 05

    KERNELIZED · FlashAttention · Transformers · Attention

    FlashAttention Kernel: Forward Pass (Parallelism)

    A dependency-led path from the forward-pass equations toward the CUDA programming model.
  4. 04

    KERNELIZED · FlashAttention · Transformers · Attention

    FlashAttention Kernel: Backward Pass (MATH)

    Deriving attention gradients from tensor differentiation to a computable backward pass.
  5. 03

    KERNELIZED · FlashAttention · Transformers · Attention

    FlashAttention Kernel: Forward Pass (MATH)

    A first-principles derivation of the online, numerically stable FlashAttention forward pass.
  6. 02

    KERNELIZED · AI · Compute · Autograd

    SoftMax Kernel: Forward and Backward Pass (MATH)

    A compact derivation of softmax forward and backward operations for later kernel work.
  7. 01

    KERNELIZED · AI · Compute · Autograd

    Max Kernel: Forward and Backward Pass (MATH)

    The forward and backward mathematics of a max-reduction kernel using indexed tensor notation.