TRIADS (Tiny Recursive Information-Attention with Deep Supervision) is a parameter-efficient recursive architecture for materials property prediction, purpose-built for the small-data regime (312–5,680 samples).

GitHub

Live Demo

Try the interactive demo with all 6 benchmarks → Launch App

Results Summary

Task	N	TRIADS	Params	Rank
`matbench_steels` (yield strength)	312	91.20 MPa	225K	#3
`matbench_expt_gap` (band gap)	4,604	0.3068 eV	100K	#2 composition-only
`matbench_expt_ismetal` (metal?)	4,921	0.9655 ROC-AUC	100K	#1 composition-only
`matbench_glass` (glass forming)	5,680	0.9285 ROC-AUC	44K	#2
`matbench_jdft2d` (exfol. energy)	636	35.89 meV/atom	75K	#1 no-pretraining
`matbench_phonons` (phonon freq.)	1,265	41.91 cm⁻¹	247K	#1 no-pretraining

Two Model Variants

HybridTRIADS (composition tasks: steels, gap, ismetal, glass, jdft2d)

Input: Chemical formula → Magpie + Mat2Vec (composition tokens)
Core: 2-layer self-attention cell, iterated T=16-20 times with shared weights
Training: Per-cycle deep supervision (w_t ∝ t)

GraphTRIADS (structural task: phonons)

Input: CIF/structure → 3-order hierarchical crystal graph (atoms, bonds, triplet angles, dihedral angles)
Core: Hierarchical GNN message-passing stack inside the shared recursive cell
Halting: Gate-based adaptive halting (4–16 cycles per sample)

Pretrained Checkpoints

Weights are organized by benchmark. Download via huggingface_hub:

python

from huggingface_hub import hf_hub_download
import torch

# Download one benchmark's weights (contains all folds compiled)
ckpt = torch.load(
    hf_hub_download("Rtx09/TRIADS", "steels/weights.pt"),
    map_location="cpu"
)
# ckpt['folds']   -> list of fold dicts, each with 'model_state' and 'test_mae'
# ckpt['n_extra'] -> int  (needed for model init)
# ckpt['config']  -> dict (d_attn, d_hidden, ff_dim, dropout, max_steps)

Checkpoint Index

Benchmark	File	Folds	Notes
matbench_steels	`steels/weights.pt`	5	HybridTRIADS V13A · 225K · 5-seed ensemble compiled
matbench_expt_gap	`expt_gap/weights.pt`	5	HybridTRIADS V3 · 100K
matbench_expt_ismetal	`is_metal/weights.pt`	5	HybridTRIADS · 100K
matbench_glass	`glass/weights.pt`	5	HybridTRIADS · 44K
matbench_jdft2d	`jdft2d/weights.pt`	5	HybridTRIADS V4 · 75K · 5-seed ensemble compiled
matbench_phonons	`phonons/weights.pt`	5	GraphTRIADS V6 · 247K · also needs `phonons/dataset.pt`

Citation

bibtex

@article{tiwari2026triads,
  author  = {Rudra Tiwari},
  title   = {TRIADS: Tiny Recursive Information-Attention with Deep Supervision},
  year    = {2026},
  doi     = {10.5281/zenodo.19200579},
  url     = {https://doi.org/10.5281/zenodo.19200579},
  note    = {Code: https://github.com/Rtx09x/TRIADS; Models: https://huggingface.co/Rtx09/TRIADS}
}

License

MIT License — see GitHub repository.