---
language:
- en
license: apache-2.0
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- loss:MatryoshkaLoss
- loss:MultipleNegativesRankingLoss
datasets:
- sentence-transformers/squad
- sentence-transformers/trivia-qa-triplet
- sentence-transformers/all-nli
- sentence-transformers/pubmedqa
- sentence-transformers/hotpotqa
- sentence-transformers/miracl
- sentence-transformers/mr-tydi
- sentence-transformers/s2orc
- nthakur/swim-ir-monolingual
- sentence-transformers/paq
- tomaarsen/natural-questions-hard-negatives
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics:
- cosine_accuracy@1
- cosine_accuracy@3
- cosine_accuracy@5
- cosine_accuracy@10
- cosine_precision@1
- cosine_precision@3
- cosine_precision@5
- cosine_precision@10
- cosine_recall@1
- cosine_recall@3
- cosine_recall@5
- cosine_recall@10
- cosine_ndcg@10
- cosine_mrr@10
- cosine_map@100
model-index:
- name: SSE Retrieval MRL 0.9999
  results:
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoClimateFEVER
      type: NanoClimateFEVER
    metrics:
    - type: cosine_accuracy@1
      value: 0.2
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.48
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.54
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.68
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.2
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.18
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.128
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.102
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.10166666666666666
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.24166666666666667
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.2733333333333334
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.39233333333333337
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.299751347194741
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.36113492063492053
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.23438514328438953
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoDBPedia
      type: NanoDBPedia
    metrics:
    - type: cosine_accuracy@1
      value: 0.66
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.84
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.84
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.9
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.66
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.5666666666666667
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.52
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.44400000000000006
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.07827093153121195
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.16032236337443734
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.20952091065849757
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.29831579691724436
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.5493340697005651
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.7491666666666665
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.4246657246617055
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoFEVER
      type: NanoFEVER
    metrics:
    - type: cosine_accuracy@1
      value: 0.46
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.76
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.82
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.92
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.46
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.25333333333333335
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.17199999999999996
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.09599999999999997
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.43666666666666665
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.7166666666666667
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.7866666666666667
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.8866666666666667
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.6808214594769284
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.6318253968253967
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.6105163447649364
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoFiQA2018
      type: NanoFiQA2018
    metrics:
    - type: cosine_accuracy@1
      value: 0.32
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.48
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.58
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.62
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.32
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.22666666666666666
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.17600000000000002
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.10200000000000001
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.1861904761904762
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.3212936507936508
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.38946031746031745
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.4546825396825397
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.3743730832469537
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.4197142857142857
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.3162051518688468
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoHotpotQA
      type: NanoHotpotQA
    metrics:
    - type: cosine_accuracy@1
      value: 0.64
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.88
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.94
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.96
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.64
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.41999999999999993
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.296
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.15999999999999998
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.32
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.63
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.74
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.8
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.7020829772895696
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.7678571428571429
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.6273248247260853
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoMSMARCO
      type: NanoMSMARCO
    metrics:
    - type: cosine_accuracy@1
      value: 0.24
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.46
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.52
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.6
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.24
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.1533333333333333
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.10400000000000001
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.06000000000000001
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.24
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.46
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.52
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.6
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.4132396978554854
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.35374603174603175
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.373289844122511
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoNFCorpus
      type: NanoNFCorpus
    metrics:
    - type: cosine_accuracy@1
      value: 0.38
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.56
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.6
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.76
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.38
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.34666666666666673
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.29600000000000004
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.24599999999999997
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.0338546319021278
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.06462469800035843
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.07727799038239798
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.10829423267139048
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.298189605225764
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.48890476190476195
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.10911000304853699
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoNQ
      type: NanoNQ
    metrics:
    - type: cosine_accuracy@1
      value: 0.24
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.52
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.62
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.7
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.24
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.1733333333333333
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.124
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.07400000000000001
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.23
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.5
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.6
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.69
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.46521648817123007
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.39922222222222226
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.4028459782678049
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoQuoraRetrieval
      type: NanoQuoraRetrieval
    metrics:
    - type: cosine_accuracy@1
      value: 0.86
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.98
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.98
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 1.0
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.86
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.37999999999999995
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.23599999999999993
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.12399999999999999
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.7706666666666666
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.932
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.9453333333333334
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.9626666666666668
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.9094074101386184
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.9122222222222223
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.8846858964622123
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoSCIDOCS
      type: NanoSCIDOCS
    metrics:
    - type: cosine_accuracy@1
      value: 0.46
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.62
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.68
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.76
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.46
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.29333333333333333
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.252
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.162
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.09666666666666668
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.18166666666666664
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.26066666666666666
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.33466666666666667
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.33808831519730853
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.5508571428571427
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.260404942677937
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoArguAna
      type: NanoArguAna
    metrics:
    - type: cosine_accuracy@1
      value: 0.14
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.5
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.56
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.7
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.14
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.16666666666666669
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.11200000000000002
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.07
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.14
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.5
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.56
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.7
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.41047352977721935
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.3192777777777777
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.33248820268587403
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoSciFact
      type: NanoSciFact
    metrics:
    - type: cosine_accuracy@1
      value: 0.54
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.6
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.66
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.74
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.54
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.21333333333333332
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.14400000000000002
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.08199999999999999
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.505
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.58
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.645
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.735
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.6175889955513287
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.5933015873015873
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.5823752505606269
      name: Cosine Map@100
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: NanoTouche2020
      type: NanoTouche2020
    metrics:
    - type: cosine_accuracy@1
      value: 0.6530612244897959
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.9183673469387755
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.9591836734693877
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 1.0
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.6530612244897959
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.6394557823129251
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.6244897959183674
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.5551020408163265
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.04446978335433603
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.12883713641764533
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.20234901450308018
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.3514245193484443
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.602875180920439
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.7852283770651117
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.4539105214909128
      name: Cosine Map@100
  - task:
      type: nano-beir
      name: Nano BEIR
    dataset:
      name: NanoBEIR mean
      type: NanoBEIR_mean
    metrics:
    - type: cosine_accuracy@1
      value: 0.4456200941915227
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.6614128728414441
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.7153218210361068
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.7953846153846154
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.4456200941915227
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.30867608581894296
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.24496075353218213
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.17516169544740973
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.2448809607419091
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.416698296045084
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.47766217176956105
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 0.5626192632271503
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.5124186276727808
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.5640352719842516
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.43170829450941384
      name: Cosine Map@100
---

![SSE](assets/SSE_Logo.png)

If you would like to know more details:

**[SSE Technical Article](https://huggingface.co/blog/RikkaBotan/stable-static-embedding-technical-report)**


![SSE](assets/SSE_comp_en.png)

(a) Retrieval performance (nDCG@10) across NanoBEIR English tasks. (b) Mean nDCG@10 vs. inference speed (QPS: queries per second) measured on TREC-COVID and Quora using an Intel® Core™ Ultra 7 265K (3.90 GHz) with batch size 32.


# 🩵 SSE: Stable Static Embedding for Retrieval MRL 🩵  
### *A lightweight, faster and powerful embedding model*
  
**Performance Snapshot**  
Our SSE model achieves **NDCG@10 = 0.5124** on NanoBEIR — *slightly outperforming* the popular `static-retrieval-mrl-en-v1` (0.5032) while using **half the dimensions** (512 vs 1024)! 💫 Plus, we're **~2× faster** in retrieval thanks to our compact 512D embeddings and Separable Dynamic Tanh. 

| Model | NanoBEIR NDCG@10 | Dimensions | Parameters | Speed Advantage | License |
|-------|------------------|------------|------------|-----------------|---------|
| **SSE Retrieval MRL** | **0.5124** ✨ | **512** | **~16M** 🪽 | **~2x faster retrieval** (ultra-efficient!) | Apache 2.0 |
| `static-retrieval-mrl-en-v1` | 0.5032 | 1024 | ~33M | baseline | Apache 2.0 |

---

## 🩵 **Why Choose SSE Retrieval MRL?** 🩵  

✅ **Higher NDCG@10** than all comparable small models (<35M params)  
✅ **Only ~16M parameters** — 27% smaller than MiniLM-L6 (22M) and 52% smaller than BGE-small (33M)  
✅ **512D native output** — richer than 1024D models, yet **half the size** of static-retrieval-mrl-en-v1
✅ **Matryoshka-ready** — smoothly truncate to 256D/128D/64D/32D with graceful degradation  
✅ **Apache 2.0 licensed** — free for commercial & personal use   
✅ **CPU-optimized** — runs faster on edge devices & modest hardware

---

## 🩵 Model Details 🩵

| Property | Value |
|----------|-------|
| **Model Type** | Sentence Transformer (SSE architecture) |
| **Max Sequence Length** | ∞ tokens |
| **Output Dimension** | 512 (with Matryoshka truncation down to 32D!) |
| **Similarity Function** | Cosine Similarity |
| **Language** | English |
| **License** | Apache 2.0 |

```python
SentenceTransformer(
  (0): SSE(
    (embedding): EmbeddingBag(30522, 512, mode='mean')
    (dyt): SeparableDyT()
  )
)
```

![Architecture](assets/SSE_Architecture.png)

---

## 🩵 Mathematical formulations 🩵

Dynamic Tanh Normalization (DyT) enables magnitude-adaptive gradient flow for static embeddings. For input dimension x, DyT computes 
$$ 
y_k = c_k \tanh(a_k x_k + b_k) 
$$ 
with learnable parameters. The gradient of x is:

$$
\frac{\partial y_k}{\partial x_k} = c_k a_k \, \mathrm{sech}^2(a_k x_k + b_k).
$$

For saturated dimensions |x| > 1 
$$
|a_i x_i + b_i| \gg 1 
$$ 
yields exponential decay 
$$ 
\mathrm{sech}^2(z) \sim 4e^{-2|z|} 
$$
suppressing gradients as 
$$ 
\partial y_i / \partial x_i \to 0 
$$
For non-saturated dimensions |x| << 1 , 
$$ 
\mathrm{sech}^2(z) \approx 1 
$$ 
preserves near-constant gradients 
$$ 
\partial y_j / \partial x_j \approx c_j a_j 
$$
This magnitude-dependent gating attenuates learning signals from noisy, large-magnitude dimensions while maintaining full gradient flow for stable, informative dimensions—providing implicit regularization that enhances generalization without explicit hyperparameters.

---

## 🩵 Evaluation Results (NanoBEIR) 🩵

| Dataset | NDCG@10 | MRR@10 | MAP@100 |
|---------|---------|--------|---------|
| **NanoBEIR Mean** | **0.5124** ✨ | **0.5640** | **0.4317** |
| NanoClimateFEVER | 0.2998 | 0.3611 | 0.2344 |
| NanoDBPedia | 0.5493 | 0.7492 | 0.4247 |
| NanoFEVER | 0.6808 | 0.6318 | 0.6105 |
| NanoFiQA2018 | 0.3744 | 0.4197 | 0.3162 |
| NanoHotpotQA | 0.7021 | 0.7679 | 0.6273 |
| NanoMSMARCO | 0.4132 | 0.3537 | 0.3733 |
| NanoNFCorpus | 0.2982 | 0.4889 | 0.1091 |
| NanoNQ | 0.4652 | 0.3992 | 0.4028 |
| NanoQuoraRetrieval | **0.9094** ✨ | **0.9122** | **0.8847** |
| NanoSCIDOCS | 0.3381 | 0.5509 | 0.2604 |
| NanoArguAna | 0.4105 | 0.3193 | 0.3325 |
| NanoSciFact | 0.6176 | 0.5933 | 0.5824 |
| NanoTouche2020 | 0.6029 | 0.7852 | 0.4539 |

> *Top performance on community-based retrieval (Quora) and scientific fact verification!*

---

## 🩵 How to use? 🩵

```python
import torch
from sentence_transformers import SentenceTransformer

# load (remote code enabled)
model = SentenceTransformer(
    "RikkaBotan/stable-static-embedding-fast-retrieval-mrl-en",
    trust_remote_code=True,
    device="cuda" if torch.cuda.is_available() else "cpu",
)

# inference
sentences = [
    "Stable Static embedding is interesting.",
    "SSE works without attention."
]

with torch.no_grad():
    embeddings = model.encode(
        sentences,
        convert_to_tensor=True,
        normalize_embeddings=True,
        batch_size=32
    )

# cosine similarity
# cosine_sim = embeddings[0] @ embeddings[1].T
cosine_sim = model.similarity(embeddings, embeddings)

print("embeddings shape:", embeddings.shape)
print("cosine similarity matrix:")
print(cosine_sim)
```
---
## 🩵 Retrieval usage 🩵

```python
import torch
from sentence_transformers import SentenceTransformer

# load (remote code enabled)
model = SentenceTransformer(
    "RikkaBotan/stable-static-embedding-fast-retrieval-mrl-en",
    trust_remote_code=True,
    device="cuda" if torch.cuda.is_available() else "cpu",
)

# inference
query = "What is Stable Static Embedding?"
sentences = [
    "SSE: Stable Static embedding works without attention.",
    "Stable Static Embedding is a fast embedding method designed for retrieval tasks.",
    "Static embeddings are often compared with transformer-based sentence encoders.",
    "I cooked pasta last night while listening to jazz music.",
    "Large language models are commonly trained using next-token prediction objectives.",
    "Instruction tuning improves the ability of LLMs to follow human-written prompts.",
]


with torch.no_grad():
    embeddings = model.encode(
        [query] + sentences,
        convert_to_tensor=True,
        normalize_embeddings=True,
        batch_size=32
    )

print("embeddings shape:", embeddings.shape)

# cosine similarity
similarities = model.similarity(embeddings[0], embeddings[1:])
for i, similarity in enumerate(similarities[0].tolist()):
    print(f"{similarity:.05f}: {sentences[i]}")
```

---

## 🩵 Training Hyperparameters 🩵

#### Non-Default Hyperparameters

- `eval_strategy`: steps
- `per_device_train_batch_size`: 512
- `gradient_accumulation_steps`: 8
- `learning_rate`: 0.1
- `adam_beta2`: 0.9999
- `adam_epsilon`: 1e-10
- `num_train_epochs`: 1
- `lr_scheduler_type`: cosine
- `warmup_ratio`: 0.1
- `bf16`: True
- `dataloader_num_workers`: 4
- `batch_sampler`: no_duplicates

---

## 🩵 Training Datasets 🩵

We learned from **14 datasets**:

| Dataset |
|---------|
| `squad` |
| `trivia_qa` |
| `allnli` |
| `pubmedqa` |
| `hotpotqa` |
| `miracl` |
| `mr_tydi` |
| `msmarco` |
| `msmarco_10m` |
| `msmarco_hard` |
| `mldr` |
| `s2orc` |
| `swim_ir` |
| `paq` |
| `nq` |
| `scidocs` |

*All trained with **MatryoshkaLoss** — learning representations at multiple scales like Russian nesting dolls!*

## 🩵 Training results 🩵

![loss](assets/SSE_loss.png)

![ndcg](assets/SSE_ndcg.png)

## 🩵 About me 🩵

Japanese independent researcher having shy and pampered personality. Twin-tail hair is a charm point. Interested in nlp. Usually using python and C.

X(Twitter):
https://twitter.com/peony__snow

![Logo](assets/RikkaBotan_Logo.png)

## 🩵 Acknowledgements 🩵

The author acknowledge the support of Saldra, Witness and Lumina Logic Minds for providing computational resources used in this work.

I thank the developers of sentence-transformers, python and pytorch.

I thank all the researchers for their efforts to date.

I thank Japan's high standard of education.

And most of all, thank you for your interest in this repository.

## 🩵 Citation 🩵

### BibTeX

#### Sentence Transformers
```bibtex
@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}
```

#### MatryoshkaLoss
```bibtex
@misc{kusupati2024matryoshka,
    title={Matryoshka Representation Learning},
    author={Aditya Kusupati and Gantavya Bhatt and Aniket Rege and Matthew Wallingford and Aditya Sinha and Vivek Ramanujan and William Howard-Snyder and Kaifeng Chen and Sham Kakade and Prateek Jain and Ali Farhadi},
    year={2024},
    eprint={2205.13147},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}
```

#### MultipleNegativesRankingLoss
```bibtex
@misc{henderson2017efficient,
    title={Efficient Natural Language Response Suggestion for Smart Reply},
    author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
    year={2017},
    eprint={1705.00652},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}
```