tranz

Point-embedding knowledge graph models: TransE, RotatE, ComplEx, and DistMult. GPU training via Burn (wgpu/Metal).

[dependencies]
tranz = "0.5"

Dual-licensed under MIT or Apache-2.0.

For context on how point embeddings relate to region-based approaches, see Why Regions, Not Points.

Models

Each model scores a triple (head, relation, tail) differently:

Model	Scoring function	Intuition	Reference
TransE	$\lVert \mathbf{h} + \mathbf{r} - \mathbf{t} \rVert$	Translation: tail = head + relation	Bordes et al., 2013
RotatE	$\lVert \mathbf{h} \circ \mathbf{r} - \mathbf{t} \rVert$	Rotation in complex plane	Sun et al., 2019
ComplEx	$\text{Re}(\langle \mathbf{h}, \mathbf{r}, \bar{\mathbf{t}} \rangle)$	Asymmetric via complex conjugate	Trouillon et al., 2016
DistMult	$\langle \mathbf{h}, \mathbf{r}, \mathbf{t} \rangle$	Element-wise product, symmetric	Yang et al., 2015

$\mathbf{h}, \mathbf{r}, \mathbf{t}$ are learned embedding vectors for head, relation, and tail. $\lVert \cdot \rVert$ is the L2 norm, $\circ$ is element-wise product, $\langle \cdot \rangle$ is the trilinear dot product, $\bar{\mathbf{t}}$ is the complex conjugate.

Quick start

Install with cargo install tranz --features burn-ndarray (CPU) or --features burn-wgpu (GPU/Metal). Training uses Burn's 1-N (1vsAll) cross-entropy with AdamW.

# Train (ComplEx is the strongest recipe with label smoothing + reciprocals)
tranz train --data data/WN18RR/ --model complex --dim 200 \
    --label-smoothing 0.1 --reciprocals \
    --epochs 100 --lr 0.001 --output embeddings/ --eval

# Train from a single triple file (auto-split 80/10/10)
tranz train --triples my_graph.tsv --model transe --dim 200 \
    --epochs 500 --output embeddings/ --eval

# Predict from saved embeddings
tranz predict --embeddings embeddings/ --model distmult \
    --head "aspirin" --relation "treats" --k 10

Benchmark: WN18RR

Trained with the Burn 1-N (1vsAll) cross-entropy trainer (AdamW), full filtered evaluation on the test split.

Model	Config	Dim	Epochs	MRR	H@1	H@10
ComplEx	1-N + label smoothing + reciprocals	100	50	0.424	0.398	0.476

Published ComplEx MRR on WN18RR is 0.475 (Lacroix et al. 2018, with Adagrad + N3 regularization, which the Burn 1-N trainer does not implement).

Reproduce (about 20 min on Metal: dim 100, 50 epochs over full WN18RR):

cargo run --release --features "burn-ndarray,burn-wgpu" --bin tranz -- \
    train --data data/WN18RR/ --model complex --dim 100 \
    --label-smoothing 0.1 --reciprocals --epochs 50 --lr 0.001 --eval

The other three models train end to end on WN18RR too; see the wn18rr_kge_burn example for a four-model relative comparison.

Library usage

use tranz::{TransE, DistMult, Scorer};
use tranz::dataset::{load_dataset, FilterIndex, InternedDatasetExt};
use tranz::eval::evaluate_link_prediction;

// Load dataset (types from lattix::kge)
let ds = load_dataset("data/WN18RR".as_ref()).unwrap();
let mut interned = ds.into_interned();
interned.add_reciprocals();

// Create model and query
let model = DistMult::new(interned.num_entities(), interned.num_relations(), 200);
let top10 = model.top_k_tails(0, 0, 10);

// Evaluate (filtered link prediction)
let filter = FilterIndex::from_dataset(&interned);
let metrics = evaluate_link_prediction(&model, &interned.test, &filter, interned.num_entities());

Generic triple loading

use tranz::dataset::{Dataset, DatasetExt};

let ds = Dataset::load_flexible("my_graph.tsv".as_ref()).unwrap();
let ds = ds.split(0.1, 0.1); // 80/10/10
let interned = ds.into_interned();

Embedding export

use tranz::io::{export_embeddings, flatten_matrix};

// Export to w2v TSV
export_embeddings("output/".as_ref(), &names, &vecs, &rel_names, &rel_vecs).unwrap();

// Flat f32 matrix for FAISS/Qdrant
let flat: Vec<f32> = flatten_matrix(&vecs);

Multi-hop query answering

Answers conjunctive, disjunctive, and negation queries by decomposing them into atomic link prediction calls composed with t-norm fuzzy logic (CQD-Beam, Arakelyan et al. 2021). No complex-query training needed.

use tranz::query::{Query, QueryConfig, answer_query_topk};
use tranz::DistMult;

let model = DistMult::new(1000, 50, 200);

// 2-hop chain: entity 0 -rel 0-> V -rel 1-> ?
let q = Query::anchor(0, 0).then(1);

// Intersection: (0 -r0-> ?) AND (1 -r1-> ?)
let q = Query::intersection(vec![Query::anchor(0, 0), Query::anchor(1, 1)]);

// Intersect-then-project (pi): (0 -r0-> V AND 1 -r1-> V) -r2-> ?
let q = Query::intersection(vec![Query::anchor(0, 0), Query::anchor(1, 1)]).then(2);

let top10 = answer_query_topk(&model, &q, &QueryConfig::default(), 10);

Ensemble scoring

Average scores from multiple models (snapshots, different seeds).

use tranz::{DistMult, EnsembledScorer, Scorer};

let models: Vec<Box<dyn Scorer>> = vec![
    Box::new(DistMult::new(100, 10, 50)),
    Box::new(DistMult::new(100, 10, 50)),
];
let ensemble = EnsembledScorer::new(models);
let top5 = ensemble.top_k_tails(0, 0, 5);

Training

Training runs on the Burn backend, selected by feature:

Feature	Backend	GPU	Best for
burn-ndarray	Burn + ndarray	--	CPU training, all 4 models
burn-wgpu	Burn + WGPU	Metal/Vulkan	macOS/GPU training, all 4 models

All four models train with 1-N (1vsAll) scoring: every entity is scored per query via matmul + softmax cross-entropy, optimized with AdamW. Label smoothing is optional.

use tranz::burn_train::{train_kge, BurnModelType, BurnTrainConfig};

type B = burn::backend::Autodiff<burn_ndarray::NdArray>;
let device = burn_ndarray::NdArrayDevice::Cpu;

let config = BurnTrainConfig {
    dim: 200,
    label_smoothing: 0.1,
    epochs: 100,
    ..BurnTrainConfig::default()
};

let result = train_kge::<B>(
    &triples,
    num_entities,
    num_relations,
    BurnModelType::DistMult,
    &config,
    &device,
);

Examples

See examples/README.md for the full gallery, where each example states the question it answers, the run command, and real sample output. Highlights:

• wn18rr_kge_burn trains all four models on real WN18RR with the Burn backend (Metal-accelerated) and reports MRR/Hits, the real-data check that the Burn trainers learn.
• wn18rr_vicinity trains point embeddings and serves nearest-neighbour queries through a vicinity HNSW index.
• score is the smallest way to use a trained model; bench_wgpu times Metal vs CPU; bench_scoring and bench_f32_vs_f64 measure the scoring hot path.

Companion to subsume

subsume embeds entities as geometric regions (boxes, cones) where containment encodes subsumption. tranz embeds entities as points where distance/similarity encodes relational facts.

• subsume: ontology completion, taxonomy expansion, logical query answering
• tranz: link prediction, relation extraction, knowledge base completion