---
language:
- en
tags:
- ColBERT
- PyLate
- sentence-transformers
- sentence-similarity
- feature-extraction
- late-interaction
- reasoning-retrieval
- edge
- loss:CachedContrastive
base_model: mixedbread-ai/mxbai-edge-colbert-v0-32m
datasets:
- reasonir/reasonir-data
- hanhainebula/bge-reasoner-data
pipeline_tag: sentence-similarity
library_name: PyLate
license: cc-by-nc-4.0
---

# SmallReason-ColBERT (32M)

An ultra-small late-interaction retriever for **reasoning-intensive** retrieval.
32M parameters, plus a **129-parameter query-side importance head**.

**21.41 mean nDCG@10 on BRIGHT** — above every ≤33M ColBERT we evaluated, and within
1.21 of the 4.7× larger 150M Reason-ModernColBERT.

---

## ⚠ Read this before loading

This model is a ColBERT base **plus a small importance head** stored in
`importance_head/`. The head is *not* part of `modules.json`, so a standard PyLate /
sentence-transformers load **silently ignores it** and gives you the un-headed base:

| How you load it | What you get | BRIGHT mean |
|---|---|---:|
| `pylate.models.ColBERT(...)` — plain load | base only, head ignored, **no error** | 19.61 |
| `WeightedColBERT.from_base(...)` — see below | full model | **21.41** |

There is no warning when the head is skipped, so if you are reproducing the paper
number, use the second path. `WeightedColBERT.from_base` resolves the head from this
repo automatically and **raises** if it cannot find one, so that path cannot fail
silently. Pass `require_head=False` if you deliberately want the base.

---

## Usage

The loader is a single file, [`weighted_colbert.py`](https://github.com/DataScience-UIBK/SmallReason-ColBERT/blob/main/src/weighted_colbert.py),
from the companion repository.

```python
from weighted_colbert import WeightedColBERT

model = WeightedColBERT.from_base(
    "DataScience-UIBK/SmallReason-ColBERT-32M",   # auto-detects importance_head/
    query_length=256,
    document_length=2048,
    device="cuda:0",
)

queries = ["What factors affect the number of Hadley cells a planet has, and how?"]
docs = [
    "Hadley cells are driven by differential solar heating; their number scales with "
    "planetary rotation rate and atmospheric depth.",
    "The best pasta recipe uses semolina flour and plenty of salted boiling water.",
]

q_embs, q_weights = model.encode(queries, is_query=True, return_weights=True)
d_embs = model.encode(docs, is_query=False)

for i, d in enumerate(d_embs):
    score = WeightedColBERT.weighted_maxsim(q_embs[0], q_weights[0], d)
    print(i, float(score))
```

`weighted_maxsim` implements the evaluation-time score

$$s(q,d) = \frac{\sum_t w_t \cdot \max_j \mathbf{Q}_t \cdot \mathbf{D}_j}{\sum_t w_t}$$

where $w_t = \sigma(\mathbf{W}\mathbf{Q}_t + b)$ is the learned per-query-token gate.
The `1/\sum_t w_t` factor is constant across documents for a fixed query, so it does not
change ranking — it only keeps scores comparable across queries of different length.

### Base only (no head)

If you want the reasoning-tuned base without the gate (19.61 on BRIGHT), load it as an
ordinary PyLate ColBERT — the head files are simply unused:

```python
from pylate import models
base = models.ColBERT("DataScience-UIBK/SmallReason-ColBERT-32M",
                      query_length=256, document_length=2048)
```

---

## Results

### BRIGHT (nDCG@10 ×100)

Evaluated with brute-force MaxSim, `query_length=256` (Pony: 32), `document_length=2048`.

| Split | upstream 32M | base (no head) | **SmallReason-ColBERT** |
|---|---:|---:|---:|
| biology | 28.70 | 33.16 | **34.17** |
| earth_science | 42.29 | 44.28 | **45.03** |
| economics | 17.65 | **20.25** | 19.99 |
| psychology | 21.93 | 24.91 | **24.94** |
| robotics | 18.09 | **18.65** | 18.14 |
| stackoverflow | 16.49 | 16.66 | **17.21** |
| sustainable_living | 18.64 | 20.11 | **21.07** |
| pony | 12.90 | **22.77** | 19.33 |
| leetcode | 16.15 | 17.40 | **29.98** |
| aops | 9.80 | 4.89 | **10.29** |
| theoremqa_questions | 12.51 | 9.04 | **13.00** |
| theoremqa_theorems | 2.76 | 3.19 | **3.74** |
| **Mean** | 18.16 | 19.61 | **21.41** |

The head is worth **+1.80** mean nDCG@10 over the same base, concentrated in the long,
symbol-dense splits: LeetCode +12.58, AoPS +5.40, TheoremQA-questions +3.96.

### Reference points

| Model | Params | BRIGHT mean |
|---|---:|---:|
| **SmallReason-ColBERT** | **32M** | **21.41** |
| answerai-colbert-small-v1 | 33M | 18.49 |
| mxbai-edge-colbert-v0-17m | 17M | 18.60 |
| GTE-ModernColBERT-v1 | 150M | 21.72 |
| Reason-ModernColBERT | 150M | 21.97 (our protocol) / 22.62 (published) |

### NanoBEIR sanity (classical IR)

The gate is trained on long reasoning queries, so it is expected to give a little back
on short keyword queries. It does, but not much:

| Model | All 13 | Excl. Touche-2020 |
|---|---:|---:|
| upstream 32M | 60.47 | 65.51 |
| base (no head) | 60.93 | 65.35 |
| **SmallReason-ColBERT** | 60.00 | 65.00 |

---

## How it works

Three stages, on top of `mixedbread-ai/mxbai-edge-colbert-v0-32m`:

1. **Widen the projection** 64 → 128 dims. The first 64 rows are inherited; the new 64
   are initialised from `N(0, σ²)` with `σ` at 10% of the original weight-matrix std —
   small enough to leave MaxSim ≈ unchanged at step 0, non-zero so the new channels
   actually receive gradient.
2. **Two-stage base training** — a varied-length warmup on ReasonIR-VL, then a
   hard-negative polish on merged ReasonIR-HQ + BGE-Reasoner. Both stages use PyLate's
   `CachedContrastive` loss over in-batch negatives.
3. **Importance head** — freeze the base, train a single `Linear(128, 1)` + sigmoid
   (129 parameters) to weight each query token.

### The one non-obvious trick

The head is **trained against the un-normalised** weighted score
`Σ w_t · max_j(Q_t · D_j)` but **evaluated against the length-normalised** one.

This asymmetry is the single most consequential choice in the recipe. Train against the
normalised score instead and the per-pair score difference is bounded by one token's
cosine range, the cross-entropy gradient collapses, the loss stalls near `ln 2`, the
gates never leave their initialisation — and BRIGHT drops by **3.59** nDCG@10.

The head is initialised `W = 0`, `b = 5`, so every gate starts at `σ(5) ≈ 0.993` and the
head is a no-op against the frozen base at step zero.

### What the head actually learns

Not soft-IDF. Across ~199K BRIGHT query tokens the gate–IDF Spearman correlation is
**ρ = −0.02** — statistically detectable, practically zero. Per-split mean gate sits in
0.43–0.47 with std ≈ 0.10: the head is a soft re-weighting, not a selector. A fixed IDF
gate on the same base reaches only 20.06, against 21.41 for the learned head.

---

## Training

| | Warmup | Polish | Head |
|---|---|---|---|
| Data | ReasonIR-VL (~245K) | merged ReasonIR-HQ + BGE-Reasoner (~2.7M) | same merged set |
| Loss | CachedContrastive | CachedContrastive | CE over `[s_pos, s_neg]` |
| LR | 1e-5 | 5e-6 | 5e-4 (AdamW, wd=0) |
| Batch | 32/GPU × accum 4 × 8 GPU | 32/GPU × accum 2 × 8 GPU | 16 triples/step, 1 GPU |
| Steps | 1 epoch (~8 h) | 1 epoch (~16 h) | 3,000 steps (~12 min) |
| Lengths | q 256 / doc 2048 | q 256 / doc 2048 | q 256 / doc 2048 |
| Precision | bf16 + FA2 | bf16 + FA2 | fp32 head, frozen bf16 base |

Base training: 8× H100 across two nodes, ~24 h total. Head training: one H100, ~12 min.

---

## Limitations

- **Scale.** The recipe was developed and validated at 32M. It does not transfer for
  free — the same head at 17M gives **no** gain.
- **Frozen base.** The head is trained on a frozen base; joint fine-tuning is unexplored.
- **Late-interaction cost.** The head is nearly free, but the model still carries
  multi-vector storage and scoring costs. The efficiency claim is about parameter count,
  not about matching single-vector retrieval.
- **Short queries.** Pony (32-token queries) regresses relative to the un-headed base —
  a per-token gate needs tokens to discriminate between.
- **Oblique queries.** On OBLIQ-Bench (stance / intent / tip-of-the-tongue) the model is
  near zero (mean 3.66) and is beaten by every baseline there. Reported as a deliberate
  negative result; embedding similarity is the wrong tool for that class of query.
- **Synthetic teacher data.** Training data is synthetic with cross-encoder-mined hard
  negatives; biases in that mining can propagate.

## License

**CC-BY-NC-4.0**, inherited from the ReasonIR and BGE-Reasoner training data.
The upstream base model (`mixedbread-ai/mxbai-edge-colbert-v0-32m`) is Apache-2.0, and
the companion training/inference **code** is released under Apache-2.0 — but these
**weights** are non-commercial.

## Citation

```bibtex
@inproceedings{smallreason-colbert,
  title     = {SmallReason-ColBERT: An Ultra-Small Late-Interaction Retriever
               for Reasoning Intensive Retrieval},
  author    = {Abdallah, Abdelrahman and Ali, Mohammed and Jatowt, Adam},
  booktitle = {Proceedings of the 2026 Conference on Empirical Methods in
               Natural Language Processing (EMNLP)},
  year      = {2026}
}
```

## Acknowledgements

Thanks to Antoine Chaffin (LightOn, Reason-ModernColBERT) for flagging the upstream
`2_Dense/use_residual` config bug in `mxbai-edge-colbert-v0-32m` — the base weights were
trained with a residual on that layer while the shipped config said otherwise. This
model uses the patched config (`use_residual: true`).