Reason-ModernColBERT

Reason-ModernColBERT is a late interaction model trained on the reasonir-hq dataset. It achieves extremely competitive performance on the BRIGHT benchmark aimed at evaluating reasoning-intensive retrieval performance, outperforming all existing models up to 7B (more than 45 times its size) and even surprisingly improving performance of ReasonIR-8B (a 8B model trained on the same data) by more than 2.5 NDCG@10 on average on Stack Exchange splits. We attribute such strong results to late-interaction, see evaluation section.

License

Unfortunately, since the ReasonIR data has been released under a cc-by-nc-4.0 license, we cannot release this model under an Apache 2.0 license. However, the authors of ReasonIR released code to generate the data. Anyone willing to reproduce the data could then easily reproduce this model under an Apache 2.0 license by running a fine-tuning lasting lower than 2 hours using this boilerplate.

PyLate model based on lightonai/GTE-ModernColBERT-v1

This is a PyLate model finetuned from lightonai/GTE-ModernColBERT-v1 on the reasonir-hq dataset. It maps sentences & paragraphs to sequences of 128-dimensional dense vectors and can be used for semantic textual similarity using the MaxSim operator.

Model Details

Model Description

  • Model Type: PyLate model
  • Base model: lightonai/GTE-ModernColBERT-v1
  • Document Length: 8192 tokens
  • Query Length: 128 tokens
  • Output Dimensionality: 128 tokens
  • Similarity Function: MaxSim
  • Training Dataset:
  • Language: en

Model Sources

Full Model Architecture

ColBERT(
  (0): Transformer({'max_seq_length': 127, '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:

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:

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:

# 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:

# 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:

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

BRIGHT Benchmark

The BRIGHT benchmark is aimed at evaluating reasoning-intensive retrieval performance. Reason-ModernColBERT outperforms all existing models up to 7B (more than 45 times its size) and even surprisingly improving performance of ReasonIR-8B (a 8B model trained on the same data) by more than 2.5 NDCG@10 on average on Stack Exchange splits. We attribute such strong results to late-interaction compared to usual dense (single vector) retrieval performed by other models as highlighted in the next section.

Model / Metric Biology Earth Economics Psychology Robotics Stackoverflow Sustainable Leetcode Pony AoPS Theorem - Q Theorem - T Mean StackExchange Mean coding Mean theorem Full mean
BM25 18.9 27.2 14.9 12.5 13.6 18.4 15 24.4 7.9 6.2 10.4 4.9 17.21 16.15 7.17 14.53
< 1B OS
BGE 11.7 24.6 16.6 17.5 11.7 10.8 13.3 26.7 5.7 6 13 6.9 15.17 16.2 8.63 13.71
Inst-L 15.2 21.2 14.7 22.3 11.4 13.3 13.5 19.5 1.3 8.1 20.9 9.1 15.94 10.4 12.7 14.21
SBERT 15.1 20.4 16.6 22.7 8.2 11 15.3 26.4 7 5.3 20 10.8 15.61 16.7 12.03 14.9
> 1B OS
E5 18.6 26 15.5 15.8 16.3 11.2 18.1 28.7 4.9 7.1 26.1 26.8 17.36 16.8 20 17.93
SFR 19.1 26.7 17.8 19 16.3 14.4 19.2 27.4 2 7.4 24.3 26 18.93 14.7 19.23 18.3
Inst-XL 21.6 34.3 22.4 27.4 18.2 21.2 19.1 27.5 5 8.5 15.6 5.9 23.46 16.25 10 18.89
GritLM 24.8 32.3 18.9 19.8 17.1 13.6 17.8 29.9 22 8.8 25.2 21.2 20.61 25.95 18.4 20.95
Qwen 30.6 36.4 17.8 24.6 13.2 22.2 14.8 25.5 9.9 14.4 27.8 32.9 22.8 17.7 25.03 22.51
Proprietary
Cohere 18.7 28.4 20.4 21.6 16.3 18.3 17.6 26.8 1.9 6.3 15.7 7.2 20.19 14.35 9.73 16.6
OpenAI 23.3 26.7 19.5 27.6 12.8 14.3 20.5 23.6 2.4 8.5 23.5 11.7 20.67 13 14.57 17.87
Voyage 23.1 25.4 19.9 24.9 10.8 16.8 15.4 30.6 1.5 7.5 27.4 11.6 19.47 16.05 15.5 17.91
Google 22.7 34.8 19.6 27.8 15.7 20.1 17.1 29.6 3.6 9.3 23.8 15.9 22.54 16.6 16.33 20
ReasonIR data
ReasonIR-8B 26.2 31.4 23.3 30 18 23.9 20.5 35 10.5 14.7 31.9 27.2 24.76 22.75 24.6 24.38
Reason-ModernColBERT (150M) 33.25 41.02 24.93 30.73 21.12 20.62 20.31 31.07 8.51 9.17 19.51 11.24 27.43 19.79 15.38 22.62

Comparison with a dense model

A fair claim would be that the performance of Reason-ModernColBERT are mostly due to the ReasonIR data. Although the differences between ReasonIR-8B and Reason-ModernColBERT already hint that it is most likely more than just that, we conducted a small experiment by training a dense (single vector) model in the same setup using Sentence Transformers as a multi-vector one trained using PyLate. This experiment highlights a very large gap in performance. Obviously, more rigourous experiments are required to draw conclusion (e.g, both models could have been further tuned and the training could have been enhanced (e.g, we did not gather negatives from other GPUs in these experiments because ST do not supports it for now)) but the gap seems really big and it does correlate pretty well with Reason-ModernColBERT being competitive with ReasonIR-8B while being more than 50 times smaller.

Model/Split Biology Earth Economics Psychology Robotics Stackoverflow Sustainable Leetcode Pony AoPS Theorem Q Theorem T Mean StackExchange Mean coding Mean theorem Full mean
Dense (single vector) model 7.51 16.92 13.43 17.18 10.23 8.93 8.85 24.88 1.43 9.81 18.83 9.71 11.86 13.16 12.78 12.31
Late-interaction (multi vector model) 28.02 39.25 21.51 27.05 19.86 17.23 21.1 27.37 3.76 6.87 16.06 7.21 24.86 15.57 10.05 19.61

Training Details

Training Dataset

reasonir-hq

  • Dataset: train at 0275f82
  • Size: 100,521 training samples
  • Columns: query, pos, and neg
  • Approximate statistics based on the first 1000 samples:
    query pos neg
    type string string string
    details
    • min: 38 tokens
    • mean: 97.84 tokens
    • max: 128 tokens
    • min: 85 tokens
    • mean: 127.63 tokens
    • max: 128 tokens
    • min: 81 tokens
    • mean: 127.77 tokens
    • max: 128 tokens
  • Samples:
    query pos neg
    Given this reasoning-intensive query, find relevant documents that could help answer the question. A researcher is analyzing a sound signal represented by the equation f(t) = 2sin(3πt) + sin(5πt) + 0.5sin(7πt). Using the Fourier transform, what are the frequencies, amplitudes, and phases of the individual sinusoidal components in the signal? A sound signal is given by the equation f(t) = sin(2πt) + sin(4πt) + sin(6πt) where t is time in seconds. Use Fourier transform to find the frequencies, amplitudes, and phases of the individual sinusoidal components in the signal.
    To find the frequencies, amplitudes, and phases of the individual sinusoidal components in the signal f(t) = sin(2πt) + sin(4πt) + sin(6πt), we can use the Fourier transform. The Fourier transform of a continuous function f(t) is given by:

    F(ω) = ∫[f(t) * e^(-jωt)] dt

    where F(ω) is the Fourier transform of f(t), ω is the angular frequency, and j is the imaginary unit (j^2 = -1). In this case, f(t) is already given as a sum of sinusoidal functions, so we can directly identify the frequencies, amplitudes, and phases of the individual components.

    1. First component: sin(2πt)
    - Frequency: The angular frequency is 2π, so the frequency is ω/(2π) = 1 Hz.
    - Amplitude: The coefficient of the sine function is 1, so the amplitude is 1.
    - Phase: There is no phase shi...
    The Fourier transform is widely used in various fields, including engineering, physics, and data analysis. It is a powerful tool for decomposing a signal into its constituent frequencies. In music, for example, the Fourier transform can be used to analyze the frequency components of a sound wave. By applying the Fourier transform to a sound signal, one can identify the different frequencies present in the signal, as well as their relative amplitudes. This information can be useful in a variety of applications, such as sound filtering and audio processing. The Fourier transform can also be used to analyze images and other types of data. In image processing, the Fourier transform can be used to filter out noise and other unwanted features from an image. It can also be used to compress images by representing them in the frequency domain. In addition to its many practical applications, the Fourier transform also has a number of interesting theoretical properties. For example, it has been ...
    Given this reasoning-intensive query, find relevant documents that could help answer the question. A manufacturer is designing a cone-shaped container with a fixed volume of 200π cubic centimeters. The container's height is 12 centimeters, and the radius of the base is unknown. If the manufacturer wants to minimize the surface area of the container while maintaining its volume, what should be the radius of the base? A right circular cone has a radius of 6cm and a slant height of 10cm. Determine the surface area of the cone.
    To find the surface area of a right circular cone, we need to calculate the area of the base and the lateral surface area, and then add them together.

    The base of the cone is a circle with radius r = 6 cm. The area of the base (A_base) can be found using the formula for the area of a circle:

    A_base = πr^2
    A_base = π(6 cm)^2
    A_base = 36π cm^2

    The lateral surface area (A_lateral) can be found using the formula for the lateral surface area of a cone:

    A_lateral = πrs, where r is the radius and s is the slant height.

    Given that the slant height s = 10 cm, we can calculate the lateral surface area:

    A_lateral = π(6 cm)(10 cm)
    A_lateral = 60π cm^2

    Now, we can find the total surface area (A_total) by adding the base area and the lateral surface area:

    A_total = A_base + A_lateral
    A_total = 36π cm^2 + 60π cm^2
    A_total = 96π cm^2

    The surface area of the cone is 96π cm^2.
    Torus-Shaped Containers in Chemical Engineering - New Designs and ApplicationsTorus-shaped containers are commonly used in chemical engineering for storing and transporting fluids. These containers have a distinctive doughnut shape, with a central hole and a circular cross-section. In this article, we will explore the design and applications of torus-shaped containers in chemical engineering.One of the main advantages of torus-shaped containers is their high volume-to-surface-area ratio. This makes them ideal for storing large quantities of fluids while minimizing the amount of material needed for construction. Additionally, the curved shape of the container provides added strength and stability, making it less prone to rupture or leakage.The design of torus-shaped containers typically involves the use of computer-aided design (CAD) software to create detailed models of the container's geometry. Engineers can then use these models to simulate various scenarios, such as fluid flow and ...
    Given this reasoning-intensive query, find relevant documents that could help answer the question. On the xy-coordinate plane, points A and B are given as A(2, 4) and B(8, -3). Determine the coordinates of the point on line segment AB that is three times as far from A as it is from B. On the xy co-ordinate plane, point C is (5,-2) and point D is (-1,1.5). The point on line segment CD that is twice as far from C as from D is:
    Answer Choices: (A) (1,-1) (B) (1,1) (C) (2,0.25) (D) (3,0.5) (E) (3,1)
    Let's think about the multi-choice question step by step.
    We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
    *It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
    Taking the x-coordinate first, the distance between C and D is
    (x-coordinate ofC - (x-coordinate ofD
  • Loss: pylate.losses.cached_contrastive.CachedContrastive

Training Hyperparameters

Non-Default Hyperparameters

  • per_device_train_batch_size: 256
  • per_device_eval_batch_size: 256
  • learning_rate: 1e-05
  • bf16: True
  • dataloader_num_workers: 8

All Hyperparameters

Click to expand
  • overwrite_output_dir: False
  • do_predict: False
  • eval_strategy: no
  • prediction_loss_only: True
  • per_device_train_batch_size: 256
  • per_device_eval_batch_size: 256
  • per_gpu_train_batch_size: None
  • per_gpu_eval_batch_size: None
  • gradient_accumulation_steps: 1
  • eval_accumulation_steps: None
  • torch_empty_cache_steps: None
  • learning_rate: 1e-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: 3
  • max_steps: -1
  • lr_scheduler_type: linear
  • lr_scheduler_kwargs: {}
  • warmup_ratio: 0.0
  • 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: None
  • local_rank: 0
  • ddp_backend: None
  • tpu_num_cores: None
  • tpu_metrics_debug: False
  • debug: []
  • dataloader_drop_last: False
  • dataloader_num_workers: 8
  • 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

Training Logs

Click to expand
Epoch Step Training Loss
0.0025 1 4.9684
0.0051 2 4.6956
0.0076 3 4.5076
0.0102 4 4.3723
0.0127 5 4.3305
0.0153 6 4.0355
0.0178 7 3.7886
0.0204 8 3.6133
0.0229 9 3.2395
0.0254 10 3.1481
0.0280 11 2.7444
0.0305 12 2.4946
0.0331 13 2.333
0.0356 14 2.2471
0.0382 15 1.9117
0.0407 16 1.6753
0.0433 17 1.2413
0.0458 18 1.1201
0.0483 19 1.0335
0.0509 20 1.0583
0.0534 21 1.067
0.0560 22 0.7056
0.0585 23 0.761
0.0611 24 0.5501
0.0636 25 0.6486
0.0662 26 0.4639
0.0687 27 0.3885
0.0712 28 0.4982
0.0738 29 0.4784
0.0763 30 0.5189
0.0789 31 0.4824
0.0814 32 0.4183
0.0840 33 0.4945
0.0865 34 0.2579
0.0891 35 0.3312
0.0916 36 0.4035
0.0941 37 0.305
0.0967 38 0.2898
0.0992 39 0.2899
0.1018 40 0.2713
0.1043 41 0.3017
0.1069 42 0.2395
0.1094 43 0.1548
0.1120 44 0.2468
0.1145 45 0.1876
0.1170 46 0.2322
0.1196 47 0.2823
0.1221 48 0.2158
0.1247 49 0.2679
0.1272 50 0.273
0.1298 51 0.2876
0.1323 52 0.197
0.1349 53 0.1282
0.1374 54 0.3355
0.1399 55 0.1941
0.1425 56 0.1873
0.1450 57 0.2288
0.1476 58 0.2802
0.1501 59 0.2087
0.1527 60 0.2239
0.1552 61 0.225
0.1578 62 0.1582
0.1603 63 0.1972
0.1628 64 0.1632
0.1654 65 0.2101
0.1679 66 0.2084
0.1705 67 0.1499
0.1730 68 0.1467
0.1756 69 0.1428
0.1781 70 0.2298
0.1807 71 0.1883
0.1832 72 0.22
0.1858 73 0.1988
0.1883 74 0.2091
0.1908 75 0.1948
0.1934 76 0.1348
0.1959 77 0.112
0.1985 78 0.1474
0.2010 79 0.1949
0.2036 80 0.1664
0.2061 81 0.1807
0.2087 82 0.1403
0.2112 83 0.1225
0.2137 84 0.1919
0.2163 85 0.1403
0.2188 86 0.1402
0.2214 87 0.0981
0.2239 88 0.1214
0.2265 89 0.1755
0.2290 90 0.1509
0.2316 91 0.1551
0.2341 92 0.176
0.2366 93 0.1648
0.2392 94 0.1622
0.2417 95 0.1372
0.2443 96 0.1016
0.2468 97 0.1134
0.2494 98 0.1436
0.2519 99 0.1478
0.2545 100 0.2065
0.2570 101 0.1901
0.2595 102 0.1859
0.2621 103 0.212
0.2646 104 0.2179
0.2672 105 0.2471
0.2697 106 0.1769
0.2723 107 0.1593
0.2748 108 0.204
0.2774 109 0.1496
0.2799 110 0.1212
0.2824 111 0.1282
0.2850 112 0.1126
0.2875 113 0.1254
0.2901 114 0.1422
0.2926 115 0.1266
0.2952 116 0.1305
0.2977 117 0.1283
0.3003 118 0.0737
0.3028 119 0.1237
0.3053 120 0.1185
0.3079 121 0.0891
0.3104 122 0.2312
0.3130 123 0.2384
0.3155 124 0.155
0.3181 125 0.1118
0.3206 126 0.1575
0.3232 127 0.2115
0.3257 128 0.098
0.3282 129 0.1811
0.3308 130 0.1704
0.3333 131 0.1494
0.3359 132 0.1531
0.3384 133 0.1032
0.3410 134 0.1137
0.3435 135 0.1271
0.3461 136 0.1591
0.3486 137 0.1586
0.3511 138 0.1292
0.3537 139 0.1115
0.3562 140 0.1337
0.3588 141 0.1298
0.3613 142 0.1649
0.3639 143 0.0855
0.3664 144 0.1124
0.3690 145 0.0764
0.3715 146 0.1402
0.3740 147 0.137
0.3766 148 0.0736
0.3791 149 0.0772
0.3817 150 0.1689
0.3842 151 0.1371
0.3868 152 0.1195
0.3893 153 0.1536
0.3919 154 0.1421
0.3944 155 0.1222
0.3969 156 0.1121
0.3995 157 0.0892
0.4020 158 0.1516
0.4046 159 0.1071
0.4071 160 0.1593
0.4097 161 0.1078
0.4122 162 0.1112
0.4148 163 0.2101
0.4173 164 0.2096
0.4198 165 0.1337
0.4224 166 0.1501
0.4249 167 0.0989
0.4275 168 0.0992
0.4300 169 0.0926
0.4326 170 0.0692
0.4351 171 0.1235
0.4377 172 0.1029
0.4402 173 0.1351
0.4427 174 0.0899
0.4453 175 0.0844
0.4478 176 0.1167
0.4504 177 0.1355
0.4529 178 0.092
0.4555 179 0.1005
0.4580 180 0.0891
0.4606 181 0.1396
0.4631 182 0.1024
0.4656 183 0.1325
0.4682 184 0.1061
0.4707 185 0.1657
0.4733 186 0.1141
0.4758 187 0.149
0.4784 188 0.1125
0.4809 189 0.1524
0.4835 190 0.1129
0.4860 191 0.1089
0.4885 192 0.1333
0.4911 193 0.1377
0.4936 194 0.0547
0.4962 195 0.1057
0.4987 196 0.1321
0.5013 197 0.0979
0.5038 198 0.1706
0.5064 199 0.1559
0.5089 200 0.1111
0.5115 201 0.1258
0.5140 202 0.0816
0.5165 203 0.1362
0.5191 204 0.1604
0.5216 205 0.1104
0.5242 206 0.1494
0.5267 207 0.1402
0.5293 208 0.1282
0.5318 209 0.1543
0.5344 210 0.1576
0.5369 211 0.2071
0.5394 212 0.1248
0.5420 213 0.1237
0.5445 214 0.0592
0.5471 215 0.1769
0.5496 216 0.1118
0.5522 217 0.1608
0.5547 218 0.1192
0.5573 219 0.0551
0.5598 220 0.1401
0.5623 221 0.2046
0.5649 222 0.1273
0.5674 223 0.1319
0.5700 224 0.1518
0.5725 225 0.0929
0.5751 226 0.1262
0.5776 227 0.1566
0.5802 228 0.1128
0.5827 229 0.1467
0.5852 230 0.1513
0.5878 231 0.1989
0.5903 232 0.0594
0.5929 233 0.0838
0.5954 234 0.0711
0.5980 235 0.0854
0.6005 236 0.1775
0.6031 237 0.118
0.6056 238 0.1297
0.6081 239 0.1092
0.6107 240 0.1469
0.6132 241 0.1203
0.6158 242 0.0901
0.6183 243 0.1179
0.6209 244 0.0864
0.6234 245 0.1277
0.6260 246 0.1313
0.6285 247 0.089
0.6310 248 0.0727
0.6336 249 0.0556
0.6361 250 0.0782
0.6387 251 0.0869
0.6412 252 0.0988
0.6438 253 0.0818
0.6463 254 0.1013
0.6489 255 0.096
0.6514 256 0.0622
0.6539 257 0.1561
0.6565 258 0.1282
0.6590 259 0.1087
0.6616 260 0.1312
0.6641 261 0.1343
0.6667 262 0.0955
0.6692 263 0.0844
0.6718 264 0.1209
0.6743 265 0.0858
0.6768 266 0.0714
0.6794 267 0.1431
0.6819 268 0.0632
0.6845 269 0.115
0.6870 270 0.1115
0.6896 271 0.1239
0.6921 272 0.1206
0.6947 273 0.1894
0.6972 274 0.0755
0.6997 275 0.0709
0.7023 276 0.1304
0.7048 277 0.1476
0.7074 278 0.1497
0.7099 279 0.113
0.7125 280 0.1676
0.7150 281 0.0999
0.7176 282 0.2044
0.7201 283 0.1125
0.7226 284 0.0956
0.7252 285 0.0956
0.7277 286 0.0771
0.7303 287 0.0712
0.7328 288 0.0525
0.7354 289 0.0689
0.7379 290 0.0964
0.7405 291 0.1068
0.7430 292 0.0536
0.7455 293 0.0861
0.7481 294 0.0813
0.7506 295 0.0885
0.7532 296 0.1083
0.7557 297 0.1124
0.7583 298 0.1095
0.7608 299 0.08
0.7634 300 0.1081
0.7659 301 0.0719
0.7684 302 0.0933
0.7710 303 0.1143
0.7735 304 0.065
0.7761 305 0.1276
0.7786 306 0.102
0.7812 307 0.186
0.7837 308 0.0778
0.7863 309 0.1419
0.7888 310 0.0895
0.7913 311 0.1154
0.7939 312 0.1037
0.7964 313 0.0711
0.7990 314 0.1559
0.8015 315 0.0755
0.8041 316 0.0799
0.8066 317 0.1137
0.8092 318 0.0837
0.8117 319 0.1052
0.8142 320 0.0846
0.8168 321 0.0715
0.8193 322 0.0923
0.8219 323 0.1397
0.8244 324 0.0899
0.8270 325 0.1414
0.8295 326 0.0422
0.8321 327 0.0748
0.8346 328 0.0739
0.8372 329 0.0855
0.8397 330 0.071
0.8422 331 0.0557
0.8448 332 0.1055
0.8473 333 0.096
0.8499 334 0.1083
0.8524 335 0.133
0.8550 336 0.1308
0.8575 337 0.0661
0.8601 338 0.0974
0.8626 339 0.1027
0.8651 340 0.1068
0.8677 341 0.1653
0.8702 342 0.097
0.8728 343 0.0845
0.8753 344 0.0546
0.8779 345 0.1273
0.8804 346 0.0982
0.8830 347 0.0893
0.8855 348 0.1222
0.8880 349 0.1072
0.8906 350 0.1254
0.8931 351 0.0679
0.8957 352 0.0995
0.8982 353 0.0878
0.9008 354 0.0564
0.9033 355 0.113
0.9059 356 0.0567
0.9084 357 0.0968
0.9109 358 0.1023
0.9135 359 0.1106
0.9160 360 0.091
0.9186 361 0.0988
0.9211 362 0.1374
0.9237 363 0.0855
0.9262 364 0.0824
0.9288 365 0.058
0.9313 366 0.0776
0.9338 367 0.1195
0.9364 368 0.0506
0.9389 369 0.0893
0.9415 370 0.1145
0.9440 371 0.0695
0.9466 372 0.0805
0.9491 373 0.0824
0.9517 374 0.0841
0.9542 375 0.0919
0.9567 376 0.064
0.9593 377 0.2194
0.9618 378 0.1165
0.9644 379 0.0888
0.9669 380 0.0826
0.9695 381 0.0687
0.9720 382 0.0933
0.9746 383 0.1337
0.9771 384 0.0738
0.9796 385 0.0749
0.9822 386 0.0742
0.9847 387 0.1111
0.9873 388 0.093
0.9898 389 0.0877
0.9924 390 0.0637
0.9949 391 0.0897
0.9975 392 0.0818
1.0 393 0.0362
1.0025 394 0.0561
1.0051 395 0.0847
1.0076 396 0.0752
1.0102 397 0.0951
1.0127 398 0.1069
1.0153 399 0.0553
1.0178 400 0.0929
1.0204 401 0.0876
1.0229 402 0.0381
1.0254 403 0.1074
1.0280 404 0.0763
1.0305 405 0.0881
1.0331 406 0.0481
1.0356 407 0.1398
1.0382 408 0.09
1.0407 409 0.1045
1.0433 410 0.088
1.0458 411 0.0751
1.0483 412 0.0781
1.0509 413 0.0844
1.0534 414 0.0949
1.0560 415 0.0467
1.0585 416 0.1159
1.0611 417 0.0511
1.0636 418 0.0659
1.0662 419 0.043
1.0687 420 0.0468
1.0712 421 0.068
1.0738 422 0.1022
1.0763 423 0.1096
1.0789 424 0.1113
1.0814 425 0.1219
1.0840 426 0.0852
1.0865 427 0.0413
1.0891 428 0.0797
1.0916 429 0.1048
1.0941 430 0.0494
1.0967 431 0.079
1.0992 432 0.0698
1.1018 433 0.0908
1.1043 434 0.0993
1.1069 435 0.0397
1.1094 436 0.0312
1.1120 437 0.089
1.1145 438 0.0318
1.1170 439 0.0356
1.1196 440 0.0588
1.1221 441 0.0311
1.1247 442 0.0578
1.1272 443 0.1313
1.1298 444 0.0897
1.1323 445 0.0798
1.1349 446 0.0326
1.1374 447 0.143
1.1399 448 0.0661
1.1425 449 0.0433
1.1450 450 0.0782
1.1476 451 0.08
1.1501 452 0.0505
1.1527 453 0.0542
1.1552 454 0.0755
1.1578 455 0.0315
1.1603 456 0.0667
1.1628 457 0.0329
1.1654 458 0.0791
1.1679 459 0.0698
1.1705 460 0.0194
1.1730 461 0.0501
1.1756 462 0.0449
1.1781 463 0.0903
1.1807 464 0.0503
1.1832 465 0.0664
1.1858 466 0.0457
1.1883 467 0.0568
1.1908 468 0.064
1.1934 469 0.0253
1.1959 470 0.046
1.1985 471 0.0279
1.2010 472 0.0733
1.2036 473 0.0463
1.2061 474 0.07
1.2087 475 0.0281
1.2112 476 0.0373
1.2137 477 0.0738
1.2163 478 0.0412
1.2188 479 0.0545
1.2214 480 0.0247
1.2239 481 0.0293
1.2265 482 0.0845
1.2290 483 0.055
1.2316 484 0.072
1.2341 485 0.0481
1.2366 486 0.0443
1.2392 487 0.0807
1.2417 488 0.0421
1.2443 489 0.0237
1.2468 490 0.0189
1.2494 491 0.0604
1.2519 492 0.0428
1.2545 493 0.061
1.2570 494 0.0723
1.2595 495 0.0539
1.2621 496 0.0747
1.2646 497 0.0917
1.2672 498 0.1161
1.2697 499 0.087
1.2723 500 0.0616
1.2748 501 0.0756
1.2774 502 0.0674
1.2799 503 0.04
1.2824 504 0.0354
1.2850 505 0.0403
1.2875 506 0.0596
1.2901 507 0.0359
1.2926 508 0.0648
1.2952 509 0.0424
1.2977 510 0.0605
1.3003 511 0.0136
1.3028 512 0.0547
1.3053 513 0.0385
1.3079 514 0.0191
1.3104 515 0.1222
1.3130 516 0.0906
1.3155 517 0.0603
1.3181 518 0.0366
1.3206 519 0.0416
1.3232 520 0.0832
1.3257 521 0.0355
1.3282 522 0.0614
1.3308 523 0.0539
1.3333 524 0.0566
1.3359 525 0.0727
1.3384 526 0.0311
1.3410 527 0.0254
1.3435 528 0.0376
1.3461 529 0.0652
1.3486 530 0.0717
1.3511 531 0.0521
1.3537 532 0.0404
1.3562 533 0.041
1.3588 534 0.0435
1.3613 535 0.0842
1.3639 536 0.0203
1.3664 537 0.072
1.3690 538 0.0277
1.3715 539 0.0575
1.3740 540 0.0665
1.3766 541 0.024
1.3791 542 0.0202
1.3817 543 0.052
1.3842 544 0.0532
1.3868 545 0.0623
1.3893 546 0.0643
1.3919 547 0.0694
1.3944 548 0.0582
1.3969 549 0.0411
1.3995 550 0.0245
1.4020 551 0.0714
1.4046 552 0.0489
1.4071 553 0.0696
1.4097 554 0.0316
1.4122 555 0.0554
1.4148 556 0.097
1.4173 557 0.0665
1.4198 558 0.0578
1.4224 559 0.0746
1.4249 560 0.0347
1.4275 561 0.0471
1.4300 562 0.0237
1.4326 563 0.0269
1.4351 564 0.068
1.4377 565 0.0362
1.4402 566 0.059
1.4427 567 0.0321
1.4453 568 0.0469
1.4478 569 0.0445
1.4504 570 0.0804
1.4529 571 0.0387
1.4555 572 0.0358
1.4580 573 0.0322
1.4606 574 0.0673
1.4631 575 0.0302
1.4656 576 0.0612
1.4682 577 0.0553
1.4707 578 0.0998
1.4733 579 0.0396
1.4758 580 0.0764
1.4784 581 0.0427
1.4809 582 0.0785
1.4835 583 0.0419
1.4860 584 0.0584
1.4885 585 0.0437
1.4911 586 0.0561
1.4936 587 0.0131
1.4962 588 0.0472
1.4987 589 0.0479
1.5013 590 0.0477
1.5038 591 0.0745
1.5064 592 0.0918
1.5089 593 0.041
1.5115 594 0.0463
1.5140 595 0.0227
1.5165 596 0.0427
1.5191 597 0.0754
1.5216 598 0.0489
1.5242 599 0.0765
1.5267 600 0.0651
1.5293 601 0.0544
1.5318 602 0.0777
1.5344 603 0.0638
1.5369 604 0.1198
1.5394 605 0.0882
1.5420 606 0.0236
1.5445 607 0.0202
1.5471 608 0.0955
1.5496 609 0.0366
1.5522 610 0.1021
1.5547 611 0.0669
1.5573 612 0.0185
1.5598 613 0.0575
1.5623 614 0.1001
1.5649 615 0.0664
1.5674 616 0.0617
1.5700 617 0.0661
1.5725 618 0.0425
1.5751 619 0.0445
1.5776 620 0.0773
1.5802 621 0.0504
1.5827 622 0.0785
1.5852 623 0.0802
1.5878 624 0.0882
1.5903 625 0.0125
1.5929 626 0.0305
1.5954 627 0.0275
1.5980 628 0.0245
1.6005 629 0.0897
1.6031 630 0.0444
1.6056 631 0.0589
1.6081 632 0.0337
1.6107 633 0.0889
1.6132 634 0.0556
1.6158 635 0.0426
1.6183 636 0.046
1.6209 637 0.0342
1.6234 638 0.0573
1.6260 639 0.0569
1.6285 640 0.0248
1.6310 641 0.0214
1.6336 642 0.0147
1.6361 643 0.0203
1.6387 644 0.0366
1.6412 645 0.0484
1.6438 646 0.0301
1.6463 647 0.0314
1.6489 648 0.0369
1.6514 649 0.0168
1.6539 650 0.0645
1.6565 651 0.0755
1.6590 652 0.0448
1.6616 653 0.0795
1.6641 654 0.0673
1.6667 655 0.0431
1.6692 656 0.0265
1.6718 657 0.0567
1.6743 658 0.0235
1.6768 659 0.034
1.6794 660 0.0812
1.6819 661 0.0157
1.6845 662 0.0448
1.6870 663 0.0488
1.6896 664 0.0515
1.6921 665 0.0531
1.6947 666 0.1166
1.6972 667 0.0264
1.6997 668 0.0325
1.7023 669 0.0784
1.7048 670 0.0859
1.7074 671 0.0981
1.7099 672 0.0411
1.7125 673 0.0915
1.7150 674 0.0396
1.7176 675 0.1381
1.7201 676 0.0547
1.7226 677 0.0436
1.7252 678 0.0519
1.7277 679 0.0305
1.7303 680 0.0356
1.7328 681 0.0173
1.7354 682 0.0299
1.7379 683 0.0424
1.7405 684 0.038
1.7430 685 0.0159
1.7455 686 0.0273
1.7481 687 0.0301
1.7506 688 0.0315
1.7532 689 0.0566
1.7557 690 0.0478
1.7583 691 0.0533
1.7608 692 0.0248
1.7634 693 0.0454
1.7659 694 0.0252
1.7684 695 0.0326
1.7710 696 0.0501
1.7735 697 0.0196
1.7761 698 0.0487
1.7786 699 0.0445
1.7812 700 0.1264
1.7837 701 0.0312
1.7863 702 0.1022
1.7888 703 0.0293
1.7913 704 0.0671
1.7939 705 0.051
1.7964 706 0.0246
1.7990 707 0.1115
1.8015 708 0.0203
1.8041 709 0.0359
1.8066 710 0.0699
1.8092 711 0.0435
1.8117 712 0.0689
1.8142 713 0.0359
1.8168 714 0.0321
1.8193 715 0.0439
1.8219 716 0.0652
1.8244 717 0.0494
1.8270 718 0.0864
1.8295 719 0.0119
1.8321 720 0.0284
1.8346 721 0.0344
1.8372 722 0.0454
1.8397 723 0.0267
1.8422 724 0.0152
1.8448 725 0.0512
1.8473 726 0.0537
1.8499 727 0.0873
1.8524 728 0.0934
1.8550 729 0.0583
1.8575 730 0.0206
1.8601 731 0.0308
1.8626 732 0.0443
1.8651 733 0.0435
1.8677 734 0.1254
1.8702 735 0.0525
1.8728 736 0.039
1.8753 737 0.0157
1.8779 738 0.0621
1.8804 739 0.0405
1.8830 740 0.0369
1.8855 741 0.0568
1.8880 742 0.0451
1.8906 743 0.0657
1.8931 744 0.0304
1.8957 745 0.047
1.8982 746 0.0457
1.9008 747 0.0239
1.9033 748 0.0669
1.9059 749 0.0252
1.9084 750 0.061
1.9109 751 0.0429
1.9135 752 0.0611
1.9160 753 0.0482
1.9186 754 0.0381
1.9211 755 0.0749
1.9237 756 0.0481
1.9262 757 0.0405
1.9288 758 0.0248
1.9313 759 0.0377
1.9338 760 0.061
1.9364 761 0.0203
1.9389 762 0.0315
1.9415 763 0.0534
1.9440 764 0.0383
1.9466 765 0.0431
1.9491 766 0.0509
1.9517 767 0.0361
1.9542 768 0.054
1.9567 769 0.0248
1.9593 770 0.1599
1.9618 771 0.0657
1.9644 772 0.0373
1.9669 773 0.0632
1.9695 774 0.0385
1.9720 775 0.0456
1.9746 776 0.0857
1.9771 777 0.0253
1.9796 778 0.0378
1.9822 779 0.0366
1.9847 780 0.0646
1.9873 781 0.062
1.9898 782 0.0513
1.9924 783 0.0291
1.9949 784 0.0466
1.9975 785 0.0345
2.0 786 0.0108
2.0025 787 0.0196
2.0051 788 0.0402
2.0076 789 0.034
2.0102 790 0.0606
2.0127 791 0.0677
2.0153 792 0.0174
2.0178 793 0.0548
2.0204 794 0.0385
2.0229 795 0.0146
2.0254 796 0.0716
2.0280 797 0.0304
2.0305 798 0.0512
2.0331 799 0.0158
2.0356 800 0.0973
2.0382 801 0.0394
2.0407 802 0.0724
2.0433 803 0.0518
2.0458 804 0.0385
2.0483 805 0.0464
2.0509 806 0.0501
2.0534 807 0.051
2.0560 808 0.0232
2.0585 809 0.0631
2.0611 810 0.0192
2.0636 811 0.0301
2.0662 812 0.0177
2.0687 813 0.0172
2.0712 814 0.0313
2.0738 815 0.0653
2.0763 816 0.0715
2.0789 817 0.0548
2.0814 818 0.0729
2.0840 819 0.0399
2.0865 820 0.0208
2.0891 821 0.0476
2.0916 822 0.054
2.0941 823 0.0174
2.0967 824 0.0431
2.0992 825 0.0361
2.1018 826 0.0514
2.1043 827 0.0513
2.1069 828 0.0099
2.1094 829 0.0137
2.1120 830 0.0493
2.1145 831 0.0133
2.1170 832 0.0087
2.1196 833 0.0306
2.1221 834 0.0092
2.1247 835 0.0242
2.1272 836 0.0905
2.1298 837 0.0544
2.1323 838 0.0462
2.1349 839 0.0107
2.1374 840 0.0846
2.1399 841 0.031
2.1425 842 0.027
2.1450 843 0.05
2.1476 844 0.0468
2.1501 845 0.0251
2.1527 846 0.031
2.1552 847 0.0343
2.1578 848 0.0149
2.1603 849 0.0347
2.1628 850 0.014
2.1654 851 0.0471
2.1679 852 0.0413
2.1705 853 0.0047
2.1730 854 0.0232
2.1756 855 0.025
2.1781 856 0.0621
2.1807 857 0.0198
2.1832 858 0.0346
2.1858 859 0.0177
2.1883 860 0.0298
2.1908 861 0.0325
2.1934 862 0.0075
2.1959 863 0.0224
2.1985 864 0.0085
2.2010 865 0.0498
2.2036 866 0.0222
2.2061 867 0.0309
2.2087 868 0.0074
2.2112 869 0.0126
2.2137 870 0.0372
2.2163 871 0.0232
2.2188 872 0.033
2.2214 873 0.0111
2.2239 874 0.0121
2.2265 875 0.0552
2.2290 876 0.0305
2.2316 877 0.042
2.2341 878 0.0147
2.2366 879 0.0222
2.2392 880 0.0341
2.2417 881 0.0163
2.2443 882 0.0084
2.2468 883 0.0081
2.2494 884 0.0312
2.2519 885 0.0153
2.2545 886 0.0262
2.2570 887 0.0404
2.2595 888 0.0198
2.2621 889 0.0304
2.2646 890 0.0544
2.2672 891 0.065
2.2697 892 0.0473
2.2723 893 0.0291
2.2748 894 0.0415
2.2774 895 0.0398
2.2799 896 0.018
2.2824 897 0.0158
2.2850 898 0.0161
2.2875 899 0.0347
2.2901 900 0.0104
2.2926 901 0.044
2.2952 902 0.019
2.2977 903 0.0416
2.3003 904 0.0039
2.3028 905 0.0246
2.3053 906 0.0133
2.3079 907 0.0053
2.3104 908 0.0992
2.3130 909 0.0569
2.3155 910 0.0326
2.3181 911 0.0189
2.3206 912 0.0115
2.3232 913 0.0417
2.3257 914 0.0161
2.3282 915 0.0308
2.3308 916 0.0234
2.3333 917 0.027
2.3359 918 0.0391
2.3384 919 0.0107
2.3410 920 0.0092
2.3435 921 0.016
2.3461 922 0.0299
2.3486 923 0.0493
2.3511 924 0.025
2.3537 925 0.0127
2.3562 926 0.0131
2.3588 927 0.0214
2.3613 928 0.0538
2.3639 929 0.0082
2.3664 930 0.043
2.3690 931 0.0074
2.3715 932 0.042
2.3740 933 0.044
2.3766 934 0.01
2.3791 935 0.0055
2.3817 936 0.0215
2.3842 937 0.0258
2.3868 938 0.0302
2.3893 939 0.0326
2.3919 940 0.0348
2.3944 941 0.0444
2.3969 942 0.019
2.3995 943 0.0098
2.4020 944 0.0283
2.4046 945 0.0306
2.4071 946 0.0316
2.4097 947 0.01
2.4122 948 0.0253
2.4148 949 0.0664
2.4173 950 0.0366
2.4198 951 0.0307
2.4224 952 0.0422
2.4249 953 0.0133
2.4275 954 0.0209
2.4300 955 0.0065
2.4326 956 0.0107
2.4351 957 0.0396
2.4377 958 0.0137
2.4402 959 0.0258
2.4427 960 0.0138
2.4453 961 0.0275
2.4478 962 0.0208
2.4504 963 0.0302
2.4529 964 0.0292
2.4555 965 0.018
2.4580 966 0.0168
2.4606 967 0.0365
2.4631 968 0.0141
2.4656 969 0.0348
2.4682 970 0.022
2.4707 971 0.0677
2.4733 972 0.0156
2.4758 973 0.0424
2.4784 974 0.0188
2.4809 975 0.0494
2.4835 976 0.0192
2.4860 977 0.0346
2.4885 978 0.0167
2.4911 979 0.0274
2.4936 980 0.0046
2.4962 981 0.0301
2.4987 982 0.0246
2.5013 983 0.0222
2.5038 984 0.0346
2.5064 985 0.0595
2.5089 986 0.0221
2.5115 987 0.0211
2.5140 988 0.0092
2.5165 989 0.0225
2.5191 990 0.0452
2.5216 991 0.0288
2.5242 992 0.044
2.5267 993 0.0308
2.5293 994 0.0309
2.5318 995 0.0495
2.5344 996 0.0384
2.5369 997 0.0834
2.5394 998 0.0866
2.5420 999 0.0076
2.5445 1000 0.0071
2.5471 1001 0.0634
2.5496 1002 0.0144
2.5522 1003 0.077
2.5547 1004 0.0347
2.5573 1005 0.0081
2.5598 1006 0.0216
2.5623 1007 0.0437
2.5649 1008 0.0367
2.5674 1009 0.0281
2.5700 1010 0.0312
2.5725 1011 0.0181
2.5751 1012 0.0226
2.5776 1013 0.0558
2.5802 1014 0.0267
2.5827 1015 0.0596
2.5852 1016 0.046
2.5878 1017 0.0465
2.5903 1018 0.0035
2.5929 1019 0.019
2.5954 1020 0.0118
2.5980 1021 0.0128
2.6005 1022 0.0458
2.6031 1023 0.0185
2.6056 1024 0.0309
2.6081 1025 0.0142
2.6107 1026 0.0732
2.6132 1027 0.0327
2.6158 1028 0.0296
2.6183 1029 0.0237
2.6209 1030 0.0169
2.6234 1031 0.0306
2.6260 1032 0.0235
2.6285 1033 0.009
2.6310 1034 0.0118
2.6336 1035 0.0067
2.6361 1036 0.008
2.6387 1037 0.0202
2.6412 1038 0.0241
2.6438 1039 0.0118
2.6463 1040 0.0161
2.6489 1041 0.0242
2.6514 1042 0.0072
2.6539 1043 0.037
2.6565 1044 0.0362
2.6590 1045 0.0213
2.6616 1046 0.0458
2.6641 1047 0.0358
2.6667 1048 0.024
2.6692 1049 0.0093
2.6718 1050 0.0306
2.6743 1051 0.0075
2.6768 1052 0.0193
2.6794 1053 0.048
2.6819 1054 0.0058
2.6845 1055 0.0233
2.6870 1056 0.0264
2.6896 1057 0.0276
2.6921 1058 0.0346
2.6947 1059 0.0854
2.6972 1060 0.0119
2.6997 1061 0.0174
2.7023 1062 0.0514
2.7048 1063 0.0628
2.7074 1064 0.0721
2.7099 1065 0.0246
2.7125 1066 0.049
2.7150 1067 0.0148
2.7176 1068 0.1024
2.7201 1069 0.0312
2.7226 1070 0.029
2.7252 1071 0.0352
2.7277 1072 0.0131
2.7303 1073 0.0195
2.7328 1074 0.0064
2.7354 1075 0.0169
2.7379 1076 0.0232
2.7405 1077 0.0216
2.7430 1078 0.0058
2.7455 1079 0.0089
2.7481 1080 0.0143
2.7506 1081 0.0168
2.7532 1082 0.0331
2.7557 1083 0.0255
2.7583 1084 0.0312
2.7608 1085 0.0125
2.7634 1086 0.0228
2.7659 1087 0.0083
2.7684 1088 0.0141
2.7710 1089 0.0189
2.7735 1090 0.0109
2.7761 1091 0.0195
2.7786 1092 0.0169
2.7812 1093 0.0937
2.7837 1094 0.019
2.7863 1095 0.0856
2.7888 1096 0.0155
2.7913 1097 0.0408
2.7939 1098 0.0279
2.7964 1099 0.008
2.7990 1100 0.086
2.8015 1101 0.0078
2.8041 1102 0.0186
2.8066 1103 0.0468
2.8092 1104 0.0255
2.8117 1105 0.0418
2.8142 1106 0.0188
2.8168 1107 0.0197
2.8193 1108 0.023
2.8219 1109 0.0421
2.8244 1110 0.0301
2.8270 1111 0.0627
2.8295 1112 0.0052
2.8321 1113 0.0163
2.8346 1114 0.0209
2.8372 1115 0.0277
2.8397 1116 0.0211
2.8422 1117 0.0066
2.8448 1118 0.0263
2.8473 1119 0.0408
2.8499 1120 0.0516
2.8524 1121 0.0748
2.8550 1122 0.0309
2.8575 1123 0.007
2.8601 1124 0.014
2.8626 1125 0.0284
2.8651 1126 0.0165
2.8677 1127 0.0975
2.8702 1128 0.0354
2.8728 1129 0.0235
2.8753 1130 0.0074
2.8779 1131 0.0386
2.8804 1132 0.0173
2.8830 1133 0.0211
2.8855 1134 0.0305
2.8880 1135 0.0219
2.8906 1136 0.0454
2.8931 1137 0.0176
2.8957 1138 0.0261
2.8982 1139 0.0274
2.9008 1140 0.0131
2.9033 1141 0.0485
2.9059 1142 0.0129
2.9084 1143 0.05
2.9109 1144 0.0306
2.9135 1145 0.0352
2.9160 1146 0.0271
2.9186 1147 0.0216
2.9211 1148 0.0567
2.9237 1149 0.0258
2.9262 1150 0.0221
2.9288 1151 0.0112
2.9313 1152 0.0199
2.9338 1153 0.0388
2.9364 1154 0.0101
2.9389 1155 0.0179
2.9415 1156 0.0358
2.9440 1157 0.0247
2.9466 1158 0.031
2.9491 1159 0.0367
2.9517 1160 0.0198
2.9542 1161 0.0346
2.9567 1162 0.011
2.9593 1163 0.139
2.9618 1164 0.0555
2.9644 1165 0.0228
2.9669 1166 0.0377
2.9695 1167 0.024
2.9720 1168 0.0331
2.9746 1169 0.0815
2.9771 1170 0.0116
2.9796 1171 0.0186
2.9822 1172 0.0153
2.9847 1173 0.0557
2.9873 1174 0.0406
2.9898 1175 0.0334
2.9924 1176 0.0265
2.9949 1177 0.0333
2.9975 1178 0.0177
3.0 1179 0.0028

Framework Versions

  • Python: 3.11.10
  • Sentence Transformers: 4.0.2
  • PyLate: 1.1.7
  • Transformers: 4.48.2
  • PyTorch: 2.5.1+cu124
  • Accelerate: 1.1.1
  • Datasets: 2.21.0
  • Tokenizers: 0.21.0

Citation

BibTeX

Reason-ModernColBERT

@misc{Reason-ModernColBERT,
title={Reason-ModernColBERT},
author={Chaffin, Antoine},
url={https://huggingface.co/lightonai/Reason-ModernColBERT},
year={2025}
}

GTE-ModernColBERT

@misc{GTE-ModernColBERT,
title={GTE-ModernColBERT},
author={Chaffin, Antoine},
url={https://huggingface.co/lightonai/GTE-ModernColBERT-v1},
year={2025}
}

Sentence Transformers

@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"
}

PyLate

@misc{PyLate,
title={PyLate: Flexible Training and Retrieval for Late Interaction Models},
author={Chaffin, Antoine and Sourty, Raphaël},
url={https://github.com/lightonai/pylate},
year={2024}
}

CachedContrastive

@misc{gao2021scaling,
    title={Scaling Deep Contrastive Learning Batch Size under Memory Limited Setup},
    author={Luyu Gao and Yunyi Zhang and Jiawei Han and Jamie Callan},
    year={2021},
    eprint={2101.06983},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}
Downloads last month
95
Safetensors
Model size
149M params
Tensor type
F32
·
Inference Providers NEW
This model isn't deployed by any Inference Provider. 🙋 Ask for provider support

Model tree for lightonai/Reason-ModernColBERT

Dataset used to train lightonai/Reason-ModernColBERT