log-depth-recurrent-modeling 0.0.4

Log Depth Recurrent Modeling (wip)

Explorations into the Log Depth Recurrent Modeling proposed by Yiqin Wang of Imperial College London

AutoregressiveGatedRecursiveCell scans a sequence in log depth by padding it to the nearest power of two and running a Blelloch scan over the resulting balanced binary tree, giving it length extrapolation for free. Setting max_seq_len (a power of two) pins the window size instead, padding and folding longer sequences into independent windows processed in parallel.

Usage

Train on the parity task at sequence length 16, then extrapolate to unseen sequence lengths

import torch
from log_depth_recurrent_modeling import ARGRC

torch.manual_seed(42)

model = ARGRC(num_tokens = 2, dim_embed = 32, dim = 32)
opt = torch.optim.AdamW(model.parameters(), lr = 3e-3)

def parity_batch(seq_len, batch_size = 64):
    bits = torch.randint(0, 2, (batch_size, seq_len))
    return bits, bits.cumsum(dim = -1) % 2

# train on sequences of length 16

for step in range(1, 201):
    bits, labels = parity_batch(16)

    loss = model(bits, labels = labels)
    loss.backward()
    opt.step()
    opt.zero_grad()

    if step % 50 == 0:
        print(f"step {step:3d} | loss: {loss.item():.4f}")

# extrapolate to unseen sequence lengths

for seq_len in (16, 64, 256, 1024):
    bits, labels = parity_batch(seq_len, 100)
    acc = (model(bits).argmax(dim = -1) == labels).float().mean().item()
    print(f"seq len {seq_len:4d} | accuracy: {acc * 100:.1f}%")

step  50 | loss: 0.6559
step 100 | loss: 0.0003
step 150 | loss: 0.0000
step 200 | loss: 0.0000
seq len   16 | accuracy: 100.0%
seq len   64 | accuracy: 100.0%
seq len  256 | accuracy: 100.0%
seq len 1024 | accuracy: 100.0%

Citations

@misc{wang2026logdepthrecurrentlanguagemodeling,
    title    = {Log-Depth Recurrent Language Modeling},
    author   = {Yiqin Wang and Nuri Cingillioglu and Charles Pert},
    year     = {2026},
    eprint   = {2609.28212},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG},
    url      = {https://arxiv.org/abs/2609.28212},
}

@misc{shen2019orderedmemory,
    title   = {Ordered Memory},
    author  = {Yikang Shen and Shawn Tan and Arian Hosseini and Zhouhan Lin and Alessandro Sordoni and Aaron Courville},
    year    = {2019},
    eprint  = {1910.13466},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG},
    url     = {https://arxiv.org/abs/1910.13466},
}

@misc{pert2026lengthgeneralizationlogdepthrecurrent,
    title     = {Length Generalization with Log-Depth Recurrent Units},
    author    = {Charles Pert and Dalal Alrajeh and Alessandra Russo},
    year      = {2026},
    eprint    = {2605.26035},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG},
    url       = {https://arxiv.org/abs/2605.26035},
}