---
base_model: answerdotai/ModernBERT-base
datasets:
- lightonai/ms-marco-en-bge
language:
- en
library_name: PyLate
pipeline_tag: sentence-similarity
model-index:
- name: ColBERT based on answerdotai/ModernBERT-base
results:
- dataset:
name: FiQA
split: test
type: beir/fiqa
metrics:
- type: ndcg_at_10
value: 39.86
task:
type: Retrieval
- dataset:
name: SciFact
split: test
type: beir/scifact
metrics:
- type: ndcg_at_10
value: 73.67
task:
type: Retrieval
- dataset:
name: nfcorpus
split: test
type: beir/nfcorpus
metrics:
- type: ndcg_at_10
value: 33.98
task:
type: Retrieval
- dataset:
name: arguana
split: test
type: beir/arguana
metrics:
- type: ndcg_at_10
value: 30.98
task:
type: Retrieval
tags:
- ColBERT
- PyLate
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:808728
- loss:Distillation
---
# PyLate model based on answerdotai/ModernBERT-base
This is a [PyLate](https://github.com/lightonai/pylate) model finetuned from [answerdotai/ModernBERT-base](https://huggingface.co/answerdotai/ModernBERT-base) on the [train](https://huggingface.co/datasets/lightonai/ms-marco-en-bge) dataset. It maps sentences & paragraphs to sequences of 128-dimensional dense vectors and can be used for semantic textual similarity using the MaxSim operator.
I finetuned the model with official script [examples/train_pylate.py](https://github.com/AnswerDotAI/ModernBERT/blob/main/examples/train_pylate.py) on a RTX 4090 GPU in 12 hours. See more details in [trianing logs](https://wandb.ai/joe32140/col-modernbert-msmarco/workspace?nw=nwuserjoe32140).
The finetuned model performance is on par with numbers reported in the paper.
## Model Details
### Model Description
- **Model Type:** PyLate model
- **Base model:** [answerdotai/ModernBERT-base](https://huggingface.co/answerdotai/ModernBERT-base)
- **Document Length:** 180 tokens
- **Query Length:** 32 tokens
- **Output Dimensionality:** 128 tokens
- **Similarity Function:** MaxSim
- **Training Dataset:**
- [train](https://huggingface.co/datasets/lightonai/ms-marco-en-bge)
- **Language:** en
### Model Sources
- **Documentation:** [PyLate Documentation](https://lightonai.github.io/pylate/)
- **Repository:** [PyLate on GitHub](https://github.com/lightonai/pylate)
- **Hugging Face:** [PyLate models on Hugging Face](https://huggingface.co/models?library=PyLate)
### Full Model Architecture
```
ColBERT(
(0): Transformer({'max_seq_length': 179, 'do_lower_case': False}) with Transformer model: ModernBertModel
(1): Dense({'in_features': 768, 'out_features': 128, 'bias': False, 'activation_function': 'torch.nn.modules.linear.Identity'})
)
```
## Usage
First install the PyLate library:
```bash
pip install -U pylate
```
### Retrieval
PyLate provides a streamlined interface to index and retrieve documents using ColBERT models. The index leverages the Voyager HNSW index to efficiently handle document embeddings and enable fast retrieval.
#### Indexing documents
First, load the ColBERT model and initialize the Voyager index, then encode and index your documents:
```python
from pylate import indexes, models, retrieve
# Step 1: Load the ColBERT model
model = models.ColBERT(
model_name_or_path=pylate_model_id,
)
# Step 2: Initialize the Voyager index
index = indexes.Voyager(
index_folder="pylate-index",
index_name="index",
override=True, # This overwrites the existing index if any
)
# Step 3: Encode the documents
documents_ids = ["1", "2", "3"]
documents = ["document 1 text", "document 2 text", "document 3 text"]
documents_embeddings = model.encode(
documents,
batch_size=32,
is_query=False, # Ensure that it is set to False to indicate that these are documents, not queries
show_progress_bar=True,
)
# Step 4: Add document embeddings to the index by providing embeddings and corresponding ids
index.add_documents(
documents_ids=documents_ids,
documents_embeddings=documents_embeddings,
)
```
Note that you do not have to recreate the index and encode the documents every time. Once you have created an index and added the documents, you can re-use the index later by loading it:
```python
# To load an index, simply instantiate it with the correct folder/name and without overriding it
index = indexes.Voyager(
index_folder="pylate-index",
index_name="index",
)
```
#### Retrieving top-k documents for queries
Once the documents are indexed, you can retrieve the top-k most relevant documents for a given set of queries.
To do so, initialize the ColBERT retriever with the index you want to search in, encode the queries and then retrieve the top-k documents to get the top matches ids and relevance scores:
```python
# Step 1: Initialize the ColBERT retriever
retriever = retrieve.ColBERT(index=index)
# Step 2: Encode the queries
queries_embeddings = model.encode(
["query for document 3", "query for document 1"],
batch_size=32,
is_query=True, # # Ensure that it is set to False to indicate that these are queries
show_progress_bar=True,
)
# Step 3: Retrieve top-k documents
scores = retriever.retrieve(
queries_embeddings=queries_embeddings,
k=10, # Retrieve the top 10 matches for each query
)
```
### Reranking
If you only want to use the ColBERT model to perform reranking on top of your first-stage retrieval pipeline without building an index, you can simply use rank function and pass the queries and documents to rerank:
```python
from pylate import rank, models
queries = [
"query A",
"query B",
]
documents = [
["document A", "document B"],
["document 1", "document C", "document B"],
]
documents_ids = [
[1, 2],
[1, 3, 2],
]
model = models.ColBERT(
model_name_or_path=pylate_model_id,
)
queries_embeddings = model.encode(
queries,
is_query=True,
)
documents_embeddings = model.encode(
documents,
is_query=False,
)
reranked_documents = rank.rerank(
documents_ids=documents_ids,
queries_embeddings=queries_embeddings,
documents_embeddings=documents_embeddings,
)
```
## Evaluation
NDCG@10
|Dataset | Score|
|:-------|------|
|FiQA | 0.3986|
|SciFact | 0.7367|
|nfcorpus | 0.3398 |
|arguana|0.3098|
## Training Details
### Training Dataset
#### train
* Dataset: [train](https://huggingface.co/datasets/lightonai/ms-marco-en-bge) at [11e6ffa](https://huggingface.co/datasets/lightonai/ms-marco-en-bge/tree/11e6ffa1d22f461579f451eb31bdc964244cb61f)
* Size: 808,728 training samples
* Columns: query_id, document_ids, and scores
* Approximate statistics based on the first 1000 samples:
| | query_id | document_ids | scores |
|:--------|:--------------------------------------------------------------------------------|:------------------------------------|:------------------------------------|
| type | string | list | list |
| details | - min: 5 tokens
- mean: 5.59 tokens
- max: 6 tokens
| | |
* Samples:
| query_id | document_ids | scores |
|:--------------------|:--------------------------------------------------------------------------|:-----------------------------------------------------------------------------------------------------------------------|
| 121352 | ['2259784', '4923159', '40211', '1545154', '8527175', ...] | [0.2343463897705078, 0.639204204082489, 0.3806908428668976, 0.5623092651367188, 0.8051995635032654, ...] |
| 634306 | ['7723525', '1874779', '379307', '2738583', '7599583', ...] | [0.7124203443527222, 0.7379189729690552, 0.5786551237106323, 0.6142299175262451, 0.6755089163780212, ...] |
| 920825 | ['5976297', '2866112', '3560294', '3285659', '4706740', ...] | [0.6462352871894836, 0.7880821228027344, 0.791019856929779, 0.7709633111953735, 0.8284491300582886, ...] |
* Loss: pylate.losses.distillation.Distillation
### Training Hyperparameters
#### Non-Default Hyperparameters
- `per_device_train_batch_size`: 4
- `gradient_accumulation_steps`: 4
- `learning_rate`: 8e-05
- `num_train_epochs`: 1
- `warmup_ratio`: 0.05
- `bf16`: True
- `tf32`: True
#### All Hyperparameters
Click to expand
- `overwrite_output_dir`: False
- `do_predict`: False
- `eval_strategy`: no
- `prediction_loss_only`: True
- `per_device_train_batch_size`: 4
- `per_device_eval_batch_size`: 8
- `per_gpu_train_batch_size`: None
- `per_gpu_eval_batch_size`: None
- `gradient_accumulation_steps`: 4
- `eval_accumulation_steps`: None
- `torch_empty_cache_steps`: None
- `learning_rate`: 8e-05
- `weight_decay`: 0.0
- `adam_beta1`: 0.9
- `adam_beta2`: 0.999
- `adam_epsilon`: 1e-08
- `max_grad_norm`: 1.0
- `num_train_epochs`: 1
- `max_steps`: -1
- `lr_scheduler_type`: linear
- `lr_scheduler_kwargs`: {}
- `warmup_ratio`: 0.05
- `warmup_steps`: 0
- `log_level`: passive
- `log_level_replica`: warning
- `log_on_each_node`: True
- `logging_nan_inf_filter`: True
- `save_safetensors`: True
- `save_on_each_node`: False
- `save_only_model`: False
- `restore_callback_states_from_checkpoint`: False
- `no_cuda`: False
- `use_cpu`: False
- `use_mps_device`: False
- `seed`: 42
- `data_seed`: None
- `jit_mode_eval`: False
- `use_ipex`: False
- `bf16`: True
- `fp16`: False
- `fp16_opt_level`: O1
- `half_precision_backend`: auto
- `bf16_full_eval`: False
- `fp16_full_eval`: False
- `tf32`: True
- `local_rank`: 0
- `ddp_backend`: None
- `tpu_num_cores`: None
- `tpu_metrics_debug`: False
- `debug`: []
- `dataloader_drop_last`: False
- `dataloader_num_workers`: 0
- `dataloader_prefetch_factor`: None
- `past_index`: -1
- `disable_tqdm`: False
- `remove_unused_columns`: True
- `label_names`: None
- `load_best_model_at_end`: False
- `ignore_data_skip`: False
- `fsdp`: []
- `fsdp_min_num_params`: 0
- `fsdp_config`: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
- `fsdp_transformer_layer_cls_to_wrap`: None
- `accelerator_config`: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
- `deepspeed`: None
- `label_smoothing_factor`: 0.0
- `optim`: adamw_torch
- `optim_args`: None
- `adafactor`: False
- `group_by_length`: False
- `length_column_name`: length
- `ddp_find_unused_parameters`: None
- `ddp_bucket_cap_mb`: None
- `ddp_broadcast_buffers`: False
- `dataloader_pin_memory`: True
- `dataloader_persistent_workers`: False
- `skip_memory_metrics`: True
- `use_legacy_prediction_loop`: False
- `push_to_hub`: False
- `resume_from_checkpoint`: None
- `hub_model_id`: None
- `hub_strategy`: every_save
- `hub_private_repo`: None
- `hub_always_push`: False
- `gradient_checkpointing`: False
- `gradient_checkpointing_kwargs`: None
- `include_inputs_for_metrics`: False
- `include_for_metrics`: []
- `eval_do_concat_batches`: True
- `fp16_backend`: auto
- `push_to_hub_model_id`: None
- `push_to_hub_organization`: None
- `mp_parameters`:
- `auto_find_batch_size`: False
- `full_determinism`: False
- `torchdynamo`: None
- `ray_scope`: last
- `ddp_timeout`: 1800
- `torch_compile`: False
- `torch_compile_backend`: None
- `torch_compile_mode`: None
- `dispatch_batches`: None
- `split_batches`: None
- `include_tokens_per_second`: False
- `include_num_input_tokens_seen`: False
- `neftune_noise_alpha`: None
- `optim_target_modules`: None
- `batch_eval_metrics`: False
- `eval_on_start`: False
- `use_liger_kernel`: False
- `eval_use_gather_object`: False
- `average_tokens_across_devices`: False
- `prompts`: None
- `batch_sampler`: batch_sampler
- `multi_dataset_batch_sampler`: proportional
Click to expand
| Epoch | Step | Training Loss |
|:------:|:-----:|:-------------:|
| 0.0020 | 100 | 0.0524 |
| 0.0040 | 200 | 0.0482 |
| 0.0059 | 300 | 0.0464 |
| 0.0079 | 400 | 0.043 |
| 0.0099 | 500 | 0.0387 |
| 0.0119 | 600 | 0.0383 |
| 0.0138 | 700 | 0.0345 |
| 0.0158 | 800 | 0.0307 |
| 0.0178 | 900 | 0.0294 |
| 0.0198 | 1000 | 0.0275 |
| 0.0218 | 1100 | 0.0271 |
| 0.0237 | 1200 | 0.0264 |
| 0.0257 | 1300 | 0.0258 |
| 0.0277 | 1400 | 0.0246 |
| 0.0297 | 1500 | 0.0239 |
| 0.0317 | 1600 | 0.023 |
| 0.0336 | 1700 | 0.0216 |
| 0.0356 | 1800 | 0.0282 |
| 0.0376 | 1900 | 0.0211 |
| 0.0396 | 2000 | 0.0205 |
| 0.0415 | 2100 | 0.0197 |
| 0.0435 | 2200 | 0.0187 |
| 0.0455 | 2300 | 0.0184 |
| 0.0475 | 2400 | 0.0177 |
| 0.0495 | 2500 | 0.0179 |
| 0.0514 | 2600 | 0.0173 |
| 0.0534 | 2700 | 0.0169 |
| 0.0554 | 2800 | 0.0163 |
| 0.0574 | 2900 | 0.016 |
| 0.0594 | 3000 | 0.016 |
| 0.0613 | 3100 | 0.0147 |
| 0.0633 | 3200 | 0.0148 |
| 0.0653 | 3300 | 0.0155 |
| 0.0673 | 3400 | 0.0149 |
| 0.0692 | 3500 | 0.0149 |
| 0.0712 | 3600 | 0.0141 |
| 0.0732 | 3700 | 0.0145 |
| 0.0752 | 3800 | 0.0142 |
| 0.0772 | 3900 | 0.0143 |
| 0.0791 | 4000 | 0.0137 |
| 0.0811 | 4100 | 0.0134 |
| 0.0831 | 4200 | 0.0129 |
| 0.0851 | 4300 | 0.0133 |
| 0.0871 | 4400 | 0.0135 |
| 0.0890 | 4500 | 0.0128 |
| 0.0910 | 4600 | 0.0126 |
| 0.0930 | 4700 | 0.0126 |
| 0.0950 | 4800 | 0.0129 |
| 0.0969 | 4900 | 0.0127 |
| 0.0989 | 5000 | 0.0127 |
| 0.1009 | 5100 | 0.0125 |
| 0.1029 | 5200 | 0.0119 |
| 0.1049 | 5300 | 0.0124 |
| 0.1068 | 5400 | 0.012 |
| 0.1088 | 5500 | 0.013 |
| 0.1108 | 5600 | 0.0119 |
| 0.1128 | 5700 | 0.0118 |
| 0.1147 | 5800 | 0.0121 |
| 0.1167 | 5900 | 0.0119 |
| 0.1187 | 6000 | 0.0116 |
| 0.1207 | 6100 | 0.0112 |
| 0.1227 | 6200 | 0.0116 |
| 0.1246 | 6300 | 0.0115 |
| 0.1266 | 6400 | 0.0119 |
| 0.1286 | 6500 | 0.0115 |
| 0.1306 | 6600 | 0.0109 |
| 0.1326 | 6700 | 0.0114 |
| 0.1345 | 6800 | 0.0114 |
| 0.1365 | 6900 | 0.0109 |
| 0.1385 | 7000 | 0.011 |
| 0.1405 | 7100 | 0.0111 |
| 0.1424 | 7200 | 0.0109 |
| 0.1444 | 7300 | 0.0108 |
| 0.1464 | 7400 | 0.0112 |
| 0.1484 | 7500 | 0.0106 |
| 0.1504 | 7600 | 0.011 |
| 0.1523 | 7700 | 0.0106 |
| 0.1543 | 7800 | 0.0107 |
| 0.1563 | 7900 | 0.0108 |
| 0.1583 | 8000 | 0.0106 |
| 0.1603 | 8100 | 0.0107 |
| 0.1622 | 8200 | 0.0108 |
| 0.1642 | 8300 | 0.0103 |
| 0.1662 | 8400 | 0.0107 |
| 0.1682 | 8500 | 0.0104 |
| 0.1701 | 8600 | 0.011 |
| 0.1721 | 8700 | 0.0105 |
| 0.1741 | 8800 | 0.0105 |
| 0.1761 | 8900 | 0.01 |
| 0.1781 | 9000 | 0.0106 |
| 0.1800 | 9100 | 0.0105 |
| 0.1820 | 9200 | 0.0104 |
| 0.1840 | 9300 | 0.0104 |
| 0.1860 | 9400 | 0.0107 |
| 0.1879 | 9500 | 0.0102 |
| 0.1899 | 9600 | 0.0103 |
| 0.1919 | 9700 | 0.0105 |
| 0.1939 | 9800 | 0.01 |
| 0.1959 | 9900 | 0.0098 |
| 0.1978 | 10000 | 0.0099 |
| 0.1998 | 10100 | 0.0099 |
| 0.2018 | 10200 | 0.0099 |
| 0.2038 | 10300 | 0.0098 |
| 0.2058 | 10400 | 0.01 |
| 0.2077 | 10500 | 0.0101 |
| 0.2097 | 10600 | 0.0098 |
| 0.2117 | 10700 | 0.0101 |
| 0.2137 | 10800 | 0.0098 |
| 0.2156 | 10900 | 0.0101 |
| 0.2176 | 11000 | 0.01 |
| 0.2196 | 11100 | 0.01 |
| 0.2216 | 11200 | 0.0096 |
| 0.2236 | 11300 | 0.0096 |
| 0.2255 | 11400 | 0.0096 |
| 0.2275 | 11500 | 0.0098 |
| 0.2295 | 11600 | 0.0099 |
| 0.2315 | 11700 | 0.0094 |
| 0.2335 | 11800 | 0.0096 |
| 0.2354 | 11900 | 0.0094 |
| 0.2374 | 12000 | 0.0098 |
| 0.2394 | 12100 | 0.0095 |
| 0.2414 | 12200 | 0.0095 |
| 0.2433 | 12300 | 0.0098 |
| 0.2453 | 12400 | 0.0097 |
| 0.2473 | 12500 | 0.0094 |
| 0.2493 | 12600 | 0.0093 |
| 0.2513 | 12700 | 0.0093 |
| 0.2532 | 12800 | 0.0092 |
| 0.2552 | 12900 | 0.0094 |
| 0.2572 | 13000 | 0.0095 |
| 0.2592 | 13100 | 0.0093 |
| 0.2612 | 13200 | 0.009 |
| 0.2631 | 13300 | 0.0087 |
| 0.2651 | 13400 | 0.0089 |
| 0.2671 | 13500 | 0.009 |
| 0.2691 | 13600 | 0.0091 |
| 0.2710 | 13700 | 0.0092 |
| 0.2730 | 13800 | 0.0089 |
| 0.2750 | 13900 | 0.0091 |
| 0.2770 | 14000 | 0.0092 |
| 0.2790 | 14100 | 0.0088 |
| 0.2809 | 14200 | 0.009 |
| 0.2829 | 14300 | 0.0091 |
| 0.2849 | 14400 | 0.0086 |
| 0.2869 | 14500 | 0.009 |
| 0.2888 | 14600 | 0.0088 |
| 0.2908 | 14700 | 0.0092 |
| 0.2928 | 14800 | 0.009 |
| 0.2948 | 14900 | 0.0088 |
| 0.2968 | 15000 | 0.0087 |
| 0.2987 | 15100 | 0.0085 |
| 0.3007 | 15200 | 0.009 |
| 0.3027 | 15300 | 0.0088 |
| 0.3047 | 15400 | 0.0086 |
| 0.3067 | 15500 | 0.0087 |
| 0.3086 | 15600 | 0.0088 |
| 0.3106 | 15700 | 0.0085 |
| 0.3126 | 15800 | 0.0088 |
| 0.3146 | 15900 | 0.0085 |
| 0.3165 | 16000 | 0.0086 |
| 0.3185 | 16100 | 0.0086 |
| 0.3205 | 16200 | 0.0087 |
| 0.3225 | 16300 | 0.0088 |
| 0.3245 | 16400 | 0.0087 |
| 0.3264 | 16500 | 0.0087 |
| 0.3284 | 16600 | 0.0086 |
| 0.3304 | 16700 | 0.0087 |
| 0.3324 | 16800 | 0.0092 |
| 0.3344 | 16900 | 0.0085 |
| 0.3363 | 17000 | 0.0088 |
| 0.3383 | 17100 | 0.0084 |
| 0.3403 | 17200 | 0.0088 |
| 0.3423 | 17300 | 0.0083 |
| 0.3442 | 17400 | 0.0085 |
| 0.3462 | 17500 | 0.0083 |
| 0.3482 | 17600 | 0.0084 |
| 0.3502 | 17700 | 0.0084 |
| 0.3522 | 17800 | 0.0083 |
| 0.3541 | 17900 | 0.0087 |
| 0.3561 | 18000 | 0.0083 |
| 0.3581 | 18100 | 0.0085 |
| 0.3601 | 18200 | 0.0082 |
| 0.3621 | 18300 | 0.0079 |
| 0.3640 | 18400 | 0.0085 |
| 0.3660 | 18500 | 0.0084 |
| 0.3680 | 18600 | 0.0082 |
| 0.3700 | 18700 | 0.0083 |
| 0.3719 | 18800 | 0.0082 |
| 0.3739 | 18900 | 0.0082 |
| 0.3759 | 19000 | 0.0083 |
| 0.3779 | 19100 | 0.0081 |
| 0.3799 | 19200 | 0.0083 |
| 0.3818 | 19300 | 0.0079 |
| 0.3838 | 19400 | 0.0083 |
| 0.3858 | 19500 | 0.0082 |
| 0.3878 | 19600 | 0.0084 |
| 0.3897 | 19700 | 0.0084 |
| 0.3917 | 19800 | 0.008 |
| 0.3937 | 19900 | 0.0081 |
| 0.3957 | 20000 | 0.0083 |
| 0.3977 | 20100 | 0.0082 |
| 0.3996 | 20200 | 0.0078 |
| 0.4016 | 20300 | 0.0079 |
| 0.4036 | 20400 | 0.0081 |
| 0.4056 | 20500 | 0.0085 |
| 0.4076 | 20600 | 0.0082 |
| 0.4095 | 20700 | 0.008 |
| 0.4115 | 20800 | 0.0079 |
| 0.4135 | 20900 | 0.0081 |
| 0.4155 | 21000 | 0.008 |
| 0.4174 | 21100 | 0.0079 |
| 0.4194 | 21200 | 0.0077 |
| 0.4214 | 21300 | 0.0078 |
| 0.4234 | 21400 | 0.0082 |
| 0.4254 | 21500 | 0.008 |
| 0.4273 | 21600 | 0.0076 |
| 0.4293 | 21700 | 0.0075 |
| 0.4313 | 21800 | 0.0078 |
| 0.4333 | 21900 | 0.0081 |
| 0.4353 | 22000 | 0.0077 |
| 0.4372 | 22100 | 0.0079 |
| 0.4392 | 22200 | 0.0078 |
| 0.4412 | 22300 | 0.0078 |
| 0.4432 | 22400 | 0.0077 |
| 0.4451 | 22500 | 0.0078 |
| 0.4471 | 22600 | 0.0079 |
| 0.4491 | 22700 | 0.0078 |
| 0.4511 | 22800 | 0.0079 |
| 0.4531 | 22900 | 0.0075 |
| 0.4550 | 23000 | 0.0077 |
| 0.4570 | 23100 | 0.0076 |
| 0.4590 | 23200 | 0.0078 |
| 0.4610 | 23300 | 0.0075 |
| 0.4629 | 23400 | 0.0075 |
| 0.4649 | 23500 | 0.0078 |
| 0.4669 | 23600 | 0.0075 |
| 0.4689 | 23700 | 0.0076 |
| 0.4709 | 23800 | 0.0075 |
| 0.4728 | 23900 | 0.0075 |
| 0.4748 | 24000 | 0.0075 |
| 0.4768 | 24100 | 0.0076 |
| 0.4788 | 24200 | 0.0079 |
| 0.4808 | 24300 | 0.0076 |
| 0.4827 | 24400 | 0.0077 |
| 0.4847 | 24500 | 0.0077 |
| 0.4867 | 24600 | 0.0073 |
| 0.4887 | 24700 | 0.0077 |
| 0.4906 | 24800 | 0.0076 |
| 0.4926 | 24900 | 0.0075 |
| 0.4946 | 25000 | 0.0076 |
| 0.4966 | 25100 | 0.0078 |
| 0.4986 | 25200 | 0.0077 |
| 0.5005 | 25300 | 0.0076 |
| 0.5025 | 25400 | 0.0076 |
| 0.5045 | 25500 | 0.0076 |
| 0.5065 | 25600 | 0.0073 |
| 0.5085 | 25700 | 0.0075 |
| 0.5104 | 25800 | 0.0072 |
| 0.5124 | 25900 | 0.0074 |
| 0.5144 | 26000 | 0.0075 |
| 0.5164 | 26100 | 0.0075 |
| 0.5183 | 26200 | 0.0072 |
| 0.5203 | 26300 | 0.0073 |
| 0.5223 | 26400 | 0.0073 |
| 0.5243 | 26500 | 0.0073 |
| 0.5263 | 26600 | 0.0076 |
| 0.5282 | 26700 | 0.0075 |
| 0.5302 | 26800 | 0.0075 |
| 0.5322 | 26900 | 0.0071 |
| 0.5342 | 27000 | 0.0074 |
| 0.5362 | 27100 | 0.0073 |
| 0.5381 | 27200 | 0.0072 |
| 0.5401 | 27300 | 0.0071 |
| 0.5421 | 27400 | 0.0073 |
| 0.5441 | 27500 | 0.0072 |
| 0.5460 | 27600 | 0.0076 |
| 0.5480 | 27700 | 0.0072 |
| 0.5500 | 27800 | 0.0074 |
| 0.5520 | 27900 | 0.0072 |
| 0.5540 | 28000 | 0.0072 |
| 0.5559 | 28100 | 0.0071 |
| 0.5579 | 28200 | 0.0069 |
| 0.5599 | 28300 | 0.0071 |
| 0.5619 | 28400 | 0.0075 |
| 0.5638 | 28500 | 0.0074 |
| 0.5658 | 28600 | 0.0072 |
| 0.5678 | 28700 | 0.0074 |
| 0.5698 | 28800 | 0.0072 |
| 0.5718 | 28900 | 0.0072 |
| 0.5737 | 29000 | 0.0073 |
| 0.5757 | 29100 | 0.0072 |
| 0.5777 | 29200 | 0.0069 |
| 0.5797 | 29300 | 0.0069 |
| 0.5817 | 29400 | 0.007 |
| 0.5836 | 29500 | 0.0071 |
| 0.5856 | 29600 | 0.007 |
| 0.5876 | 29700 | 0.0069 |
| 0.5896 | 29800 | 0.0072 |
| 0.5915 | 29900 | 0.007 |
| 0.5935 | 30000 | 0.007 |
| 0.5955 | 30100 | 0.007 |
| 0.5975 | 30200 | 0.0069 |
| 0.5995 | 30300 | 0.0068 |
| 0.6014 | 30400 | 0.0071 |
| 0.6034 | 30500 | 0.007 |
| 0.6054 | 30600 | 0.0071 |
| 0.6074 | 30700 | 0.007 |
| 0.6094 | 30800 | 0.0069 |
| 0.6113 | 30900 | 0.007 |
| 0.6133 | 31000 | 0.0071 |
| 0.6153 | 31100 | 0.0069 |
| 0.6173 | 31200 | 0.007 |
| 0.6192 | 31300 | 0.0068 |
| 0.6212 | 31400 | 0.0069 |
| 0.6232 | 31500 | 0.0068 |
| 0.6252 | 31600 | 0.0068 |
| 0.6272 | 31700 | 0.007 |
| 0.6291 | 31800 | 0.0068 |
| 0.6311 | 31900 | 0.0069 |
| 0.6331 | 32000 | 0.0068 |
| 0.6351 | 32100 | 0.0069 |
| 0.6370 | 32200 | 0.0066 |
| 0.6390 | 32300 | 0.0068 |
| 0.6410 | 32400 | 0.0067 |
| 0.6430 | 32500 | 0.0068 |
| 0.6450 | 32600 | 0.0069 |
| 0.6469 | 32700 | 0.0068 |
| 0.6489 | 32800 | 0.0065 |
| 0.6509 | 32900 | 0.0068 |
| 0.6529 | 33000 | 0.0067 |
| 0.6549 | 33100 | 0.0066 |
| 0.6568 | 33200 | 0.0069 |
| 0.6588 | 33300 | 0.0067 |
| 0.6608 | 33400 | 0.0067 |
| 0.6628 | 33500 | 0.0068 |
| 0.6647 | 33600 | 0.0066 |
| 0.6667 | 33700 | 0.0069 |
| 0.6687 | 33800 | 0.0069 |
| 0.6707 | 33900 | 0.0064 |
| 0.6727 | 34000 | 0.0065 |
| 0.6746 | 34100 | 0.0067 |
| 0.6766 | 34200 | 0.0063 |
| 0.6786 | 34300 | 0.0067 |
| 0.6806 | 34400 | 0.0066 |
| 0.6826 | 34500 | 0.0065 |
| 0.6845 | 34600 | 0.0064 |
| 0.6865 | 34700 | 0.0066 |
| 0.6885 | 34800 | 0.0065 |
| 0.6905 | 34900 | 0.0064 |
| 0.6924 | 35000 | 0.0066 |
| 0.6944 | 35100 | 0.0064 |
| 0.6964 | 35200 | 0.0064 |
| 0.6984 | 35300 | 0.0066 |
| 0.7004 | 35400 | 0.0065 |
| 0.7023 | 35500 | 0.0067 |
| 0.7043 | 35600 | 0.0065 |
| 0.7063 | 35700 | 0.0064 |
| 0.7083 | 35800 | 0.0066 |
| 0.7103 | 35900 | 0.0065 |
| 0.7122 | 36000 | 0.0067 |
| 0.7142 | 36100 | 0.0069 |
| 0.7162 | 36200 | 0.0065 |
| 0.7182 | 36300 | 0.0064 |
| 0.7201 | 36400 | 0.0064 |
| 0.7221 | 36500 | 0.0066 |
| 0.7241 | 36600 | 0.0065 |
| 0.7261 | 36700 | 0.0062 |
| 0.7281 | 36800 | 0.0068 |
| 0.7300 | 36900 | 0.0064 |
| 0.7320 | 37000 | 0.0067 |
| 0.7340 | 37100 | 0.0063 |
| 0.7360 | 37200 | 0.0063 |
| 0.7379 | 37300 | 0.0064 |
| 0.7399 | 37400 | 0.0066 |
| 0.7419 | 37500 | 0.0065 |
| 0.7439 | 37600 | 0.0064 |
| 0.7459 | 37700 | 0.0065 |
| 0.7478 | 37800 | 0.0064 |
| 0.7498 | 37900 | 0.0063 |
| 0.7518 | 38000 | 0.0062 |
| 0.7538 | 38100 | 0.0064 |
| 0.7558 | 38200 | 0.0062 |
| 0.7577 | 38300 | 0.0064 |
| 0.7597 | 38400 | 0.0063 |
| 0.7617 | 38500 | 0.0063 |
| 0.7637 | 38600 | 0.0065 |
| 0.7656 | 38700 | 0.0063 |
| 0.7676 | 38800 | 0.0064 |
| 0.7696 | 38900 | 0.0062 |
| 0.7716 | 39000 | 0.0062 |
| 0.7736 | 39100 | 0.0062 |
| 0.7755 | 39200 | 0.0063 |
| 0.7775 | 39300 | 0.0065 |
| 0.7795 | 39400 | 0.0061 |
| 0.7815 | 39500 | 0.0062 |
| 0.7835 | 39600 | 0.0063 |
| 0.7854 | 39700 | 0.0062 |
| 0.7874 | 39800 | 0.0062 |
| 0.7894 | 39900 | 0.0063 |
| 0.7914 | 40000 | 0.0059 |
| 0.7933 | 40100 | 0.0063 |
| 0.7953 | 40200 | 0.0064 |
| 0.7973 | 40300 | 0.006 |
| 0.7993 | 40400 | 0.0063 |
| 0.8013 | 40500 | 0.0061 |
| 0.8032 | 40600 | 0.0061 |
| 0.8052 | 40700 | 0.0062 |
| 0.8072 | 40800 | 0.0062 |
| 0.8092 | 40900 | 0.006 |
| 0.8112 | 41000 | 0.0061 |
| 0.8131 | 41100 | 0.0063 |
| 0.8151 | 41200 | 0.0059 |
| 0.8171 | 41300 | 0.0062 |
| 0.8191 | 41400 | 0.0062 |
| 0.8210 | 41500 | 0.0062 |
| 0.8230 | 41600 | 0.0062 |
| 0.8250 | 41700 | 0.0061 |
| 0.8270 | 41800 | 0.0061 |
| 0.8290 | 41900 | 0.0061 |
| 0.8309 | 42000 | 0.0063 |
| 0.8329 | 42100 | 0.0064 |
| 0.8349 | 42200 | 0.0063 |
| 0.8369 | 42300 | 0.0063 |
| 0.8388 | 42400 | 0.0061 |
| 0.8408 | 42500 | 0.0062 |
| 0.8428 | 42600 | 0.0062 |
| 0.8448 | 42700 | 0.0061 |
| 0.8468 | 42800 | 0.0059 |
| 0.8487 | 42900 | 0.006 |
| 0.8507 | 43000 | 0.0061 |
| 0.8527 | 43100 | 0.0062 |
| 0.8547 | 43200 | 0.0058 |
| 0.8567 | 43300 | 0.0065 |
| 0.8586 | 43400 | 0.0064 |
| 0.8606 | 43500 | 0.006 |
| 0.8626 | 43600 | 0.0061 |
| 0.8646 | 43700 | 0.0059 |
| 0.8665 | 43800 | 0.0063 |
| 0.8685 | 43900 | 0.0061 |
| 0.8705 | 44000 | 0.006 |
| 0.8725 | 44100 | 0.0061 |
| 0.8745 | 44200 | 0.0061 |
| 0.8764 | 44300 | 0.0059 |
| 0.8784 | 44400 | 0.006 |
| 0.8804 | 44500 | 0.006 |
| 0.8824 | 44600 | 0.0059 |
| 0.8844 | 44700 | 0.0062 |
| 0.8863 | 44800 | 0.006 |
| 0.8883 | 44900 | 0.006 |
| 0.8903 | 45000 | 0.0058 |
| 0.8923 | 45100 | 0.006 |
| 0.8942 | 45200 | 0.0061 |
| 0.8962 | 45300 | 0.006 |
| 0.8982 | 45400 | 0.0059 |
| 0.9002 | 45500 | 0.0059 |
| 0.9022 | 45600 | 0.006 |
| 0.9041 | 45700 | 0.0062 |
| 0.9061 | 45800 | 0.0056 |
| 0.9081 | 45900 | 0.0057 |
| 0.9101 | 46000 | 0.006 |
| 0.9120 | 46100 | 0.0059 |
| 0.9140 | 46200 | 0.006 |
| 0.9160 | 46300 | 0.0059 |
| 0.9180 | 46400 | 0.0062 |
| 0.9200 | 46500 | 0.0059 |
| 0.9219 | 46600 | 0.0059 |
| 0.9239 | 46700 | 0.006 |
| 0.9259 | 46800 | 0.0059 |
| 0.9279 | 46900 | 0.0058 |
| 0.9299 | 47000 | 0.0057 |
| 0.9318 | 47100 | 0.0058 |
| 0.9338 | 47200 | 0.0058 |
| 0.9358 | 47300 | 0.0059 |
| 0.9378 | 47400 | 0.0059 |
| 0.9397 | 47500 | 0.0058 |
| 0.9417 | 47600 | 0.006 |
| 0.9437 | 47700 | 0.0058 |
| 0.9457 | 47800 | 0.006 |
| 0.9477 | 47900 | 0.0059 |
| 0.9496 | 48000 | 0.0058 |
| 0.9516 | 48100 | 0.0057 |
| 0.9536 | 48200 | 0.006 |
| 0.9556 | 48300 | 0.0057 |
| 0.9576 | 48400 | 0.006 |
| 0.9595 | 48500 | 0.0058 |
| 0.9615 | 48600 | 0.0058 |
| 0.9635 | 48700 | 0.0058 |
| 0.9655 | 48800 | 0.0057 |
| 0.9674 | 48900 | 0.0058 |
| 0.9694 | 49000 | 0.006 |
| 0.9714 | 49100 | 0.0055 |
| 0.9734 | 49200 | 0.0058 |
| 0.9754 | 49300 | 0.0059 |
| 0.9773 | 49400 | 0.0057 |
| 0.9793 | 49500 | 0.0055 |
| 0.9813 | 49600 | 0.0059 |
| 0.9833 | 49700 | 0.0058 |
| 0.9853 | 49800 | 0.0059 |
| 0.9872 | 49900 | 0.0058 |
| 0.9892 | 50000 | 0.0056 |
| 0.9912 | 50100 | 0.0058 |
| 0.9932 | 50200 | 0.0058 |
| 0.9951 | 50300 | 0.0059 |
| 0.9971 | 50400 | 0.0059 |
| 0.9991 | 50500 | 0.006 |