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Biotech and life sciences
protein-structure
protein structure prediction
AlphaFold
System
Techniques · 6
Primitives · 36
protein-structure
Se3 equivariant networks
machine-learning · medium: Networks equivariant to rotations and translations (invariant point attention, EGNN)
Multiple sequence alignment
search-sort · medium: Aligns N sequences into columns by merging them pairwise up a guide tree as profiles, optionally refined or guided by consistency; exact search is NP-hard.
›
Profile hmm search
search-sort · medium: Profile HMMs (HMMER, HHblits) for sensitive homology search
Smith-Waterman local alignment
search-sort · medium: Dynamic programming that finds the highest-scoring pair of similar substrings of two sequences under a substitution score and affine gap penalties, in O(nm) time.
›
Graph neural networks
machine-learning · medium: Message-passing neural networks over graphs (GCN, GAT, equivariant) for molecules and relations
Spherical harmonic transform
numerics · medium: Fast spherical harmonic transforms via FFT in longitude and Legendre in latitude
Attention variants
machine-learning · low: Multi-head, multi-query, grouped-query, sliding-window and latent attention; same softmax(QKᵀ/√d)V core, different trade-offs between quality and KV-cache size.
›
Kabsch rmsd alignment
geometry · low: Optimal rigid superposition of point sets by SVD; RMSD computation
Loss functions
machine-learning · low: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.
›
Diffusion models
ml-training · low: Train a network to undo Gaussian noise at every noise level, then generate by integrating from pure noise to data; the standard for images, video and audio.
›
FlashAttention
ml-training · low: Exact attention computed tile by tile in on-chip SRAM with online softmax, so the N×N score matrix never touches HBM; 2-4x faster, O(N) memory.
›
Gradient checkpointing
ml-training · low: Save only some activations in the forward pass and recompute the rest during backward, trading about 33% extra compute for O(√n) activation memory.
›
Mixed-precision training
ml-training · low: Run matmuls in bf16/fp16/fp8 on tensor cores while keeping master weights, optimizer state and reductions in fp32; about 2x speed, half the activation memory.
›
Transformer block
ml-training · low: The decoder-only pre-norm block (attention plus MLP on a residual stream) behind every modern LLM, with exact shapes, parameter, FLOP and KV-cache counts.
›
ZeRO and FSDP sharding
ml-training · low: Data parallelism that shards optimizer state, gradients and weights across ranks and gathers weights just in time; per-GPU model memory drops from 16Ψ to 16Ψ/N.
›
L-BFGS
numerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.
›
Force field terms
physics · low: Bonded and nonbonded MD potentials: bonds, angles, torsions, Lennard-Jones, Coulomb with cutoffs
Rigid-body transforms (SE(3) poses)
robotics · low: Represent, compose, invert, integrate and interpolate 3D poses as unit quaternion plus translation, with exp/log maps for small motions and uncertainty.
›
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
SIMD programming
hardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
Convolutional codes and the Viterbi…
signal-processing · low: Streaming error-correcting code: each output bit is a parity of the last K input bits; the Viterbi decoder finds the most likely path through a 2^(K-1)-state trellis.
›
+ 20 more primitives
System
Techniques · 6
Primitives · 36
protein-structure
Se3 equivariant networks
machine-learning · medium: Networks equivariant to rotations and translations (invariant point attention, EGNN)
Multiple sequence alignment
search-sort · medium: Aligns N sequences into columns by merging them pairwise up a guide tree as profiles, optionally refined or guided by consistency; exact search is NP-hard.
›
Profile hmm search
search-sort · medium: Profile HMMs (HMMER, HHblits) for sensitive homology search
Smith-Waterman local alignment
search-sort · medium: Dynamic programming that finds the highest-scoring pair of similar substrings of two sequences under a substitution score and affine gap penalties, in O(nm) time.
›
Graph neural networks
machine-learning · medium: Message-passing neural networks over graphs (GCN, GAT, equivariant) for molecules and relations
Spherical harmonic transform
numerics · medium: Fast spherical harmonic transforms via FFT in longitude and Legendre in latitude
Attention variants
machine-learning · low: Multi-head, multi-query, grouped-query, sliding-window and latent attention; same softmax(QKᵀ/√d)V core, different trade-offs between quality and KV-cache size.
›
Kabsch rmsd alignment
geometry · low: Optimal rigid superposition of point sets by SVD; RMSD computation
Loss functions
machine-learning · low: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.
›
Diffusion models
ml-training · low: Train a network to undo Gaussian noise at every noise level, then generate by integrating from pure noise to data; the standard for images, video and audio.
›
FlashAttention
ml-training · low: Exact attention computed tile by tile in on-chip SRAM with online softmax, so the N×N score matrix never touches HBM; 2-4x faster, O(N) memory.
›
Gradient checkpointing
ml-training · low: Save only some activations in the forward pass and recompute the rest during backward, trading about 33% extra compute for O(√n) activation memory.
›
Mixed-precision training
ml-training · low: Run matmuls in bf16/fp16/fp8 on tensor cores while keeping master weights, optimizer state and reductions in fp32; about 2x speed, half the activation memory.
›
Transformer block
ml-training · low: The decoder-only pre-norm block (attention plus MLP on a residual stream) behind every modern LLM, with exact shapes, parameter, FLOP and KV-cache counts.
›
ZeRO and FSDP sharding
ml-training · low: Data parallelism that shards optimizer state, gradients and weights across ranks and gathers weights just in time; per-GPU model memory drops from 16Ψ to 16Ψ/N.
›
L-BFGS
numerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.
›
Force field terms
physics · low: Bonded and nonbonded MD potentials: bonds, angles, torsions, Lennard-Jones, Coulomb with cutoffs
Rigid-body transforms (SE(3) poses)
robotics · low: Represent, compose, invert, integrate and interpolate 3D poses as unit quaternion plus translation, with exp/log maps for small motions and uncertainty.
›
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
SIMD programming
hardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
Convolutional codes and the Viterbi…
signal-processing · low: Streaming error-correcting code: each output bit is a parity of the last K input bits; the Viterbi decoder finds the most likely path through a 2^(K-1)-state trellis.
›
Edit distance
search-sort · low: Levenshtein/Damerau distance by DP, bit-parallel Myers variant
Embeddings
machine-learning · low: A learned table mapping discrete ids to dense vectors: gather forward, sparse scatter-add backward, row-wise optimizers to keep huge tables cheap.
›
Normalization layers
machine-learning · low: Standardize activations per batch, token or group with a learned scale so deep nets train fast and stably; RMSNorm in LLMs, BatchNorm in convnets.
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Fast Fourier transform
numerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.
›
Gaussian quadrature
numerics · low: Approximate an integral by a weighted sum of n function values at roots of orthogonal polynomials; exact for polynomials up to degree 2n-1.
›
Spherical grids
numerics · low: Lat-lon, cubed-sphere and icosahedral grids for global models; pole and area issues
Homogeneous transforms
geometry · low: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matrices
Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
›
Gpu memory coalescing banking
hardware-os · low: Coalesced global loads, shared memory bank conflicts, L2 and HBM bandwidth on GPUs
CUDA and GPU languages
languages · low: Programming GPUs: thousands of lockstep threads, bound by memory bandwidth; libraries first, Triton for fused kernels, CUDA C++ for peak speed.
›
AdamW
ml-training · low: Adam's per-parameter adaptive steps with weight decay applied directly to the weights; the default optimizer for transformers and LLM pretraining.
›
Collective communication
ml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.
›
Convolutional networks
ml-training · low: Layers that slide a small shared kernel over a grid, giving translation equivariance and few parameters; still the most compute-efficient choice for many vision tasks.
›
Cuda graphs
ml-training · low: Capturing a sequence of GPU kernel launches once and replaying it to remove CPU launch overhead
Kernel fusion
ml-training · low: Merge chains of memory-bound GPU ops into one kernel, so intermediates stay in registers instead of round-tripping through HBM.
›
Reverse-mode automatic differentiat…
ml-training · low: Record the forward computation on a tape, then sweep it backwards once to get the gradient of a scalar loss for all inputs.
›
Ring all-reduce
ml-training · low: Sum a buffer across N workers via reduce-scatter then all-gather around a ring; each link carries 2(N−1)/N of the buffer, which is bandwidth-optimal.
›
Tiled matrix multiplication
ml-training · low: Block GEMM into tiles held in shared memory and registers, so each byte loaded from DRAM feeds many FMAs; the core of fast GEMM.
›
Low precision number formats
numerics · low: Bf16, fp16, fp8 (E4M3, E5M2), MX block formats and int4: ranges, rounding, scaling
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