RNA/ATAC integration tutorial

This tutorial demonstrates how to use Champollion on a PBMC dataset with RNA and ATAC modalities. The dataset used here is already preprocessed. For guidance on preparing a new dataset, see the Data Inputs section of the documentation.

This tutorial aims at illustrating on a concrete example the different steps of the workflow, focusing specifically on the integration of unpaired cells. For more details on interpretability of the learnt parameters, see the interpretability tutorial. Here, Champollion learns the cross-modality cost on the bridge, then uses it to integrate the unpaired cells, transfer annotations, and build joint visualizations.

import warnings
warnings.filterwarnings("ignore")

import os
from pathlib import Path

import anndata as ad
import matplotlib.pyplot as plt
import muon as mu
import numpy as np
import pandas as pd
import scanpy as sc
import seaborn as sns
from sklearn.metrics import accuracy_score, confusion_matrix

from champollion import Champollion
from champollion.plot import plot_ordered_transport_plan

[KeOps] Warning : CUDA libraries not found or could not be loaded; Switching to CPU only.

Configuration

DATA_PATH = Path("../semi-paired/data/pbmc_all/incomplete.h5mu")

RNA_MOD = "rna"
ATAC_MOD = "atac"
CELLTYPE_KEY = "celltype"

Load the data

mdata = mu.read_h5mu(DATA_PATH)
print(mdata)
print("modalities:", list(mdata.mod.keys()))

MuData object with n_obs × n_vars = 5637 × 145834
  obs:  'celltype', 'paired_mask'
  var:  'gene_ids', 'interval', 'n_cells', 'highly_variable', 'means', 'dispersions', 'dispersions_norm', 'variability_score', 'mean', 'std'
  uns:  'dataset_name'
  2 modalities
    atac:       5637 × 130417
      obs:      'celltype', 'batch', 'n_genes'
      var:      'gene_ids', 'interval', 'n_cells', 'highly_variable', 'means', 'dispersions', 'dispersions_norm', 'variability_score', 'mean', 'std'
      uns:      'gene_activities_var_names', 'hvg', 'log1p'
      obsm:     'X_pca', 'gene_activities', 'prior_data'
      layers:   'counts', 'scaled'
    rna:        5637 × 15417
      obs:      'celltype', 'batch', 'n_genes'
      var:      'gene_ids', 'interval', 'strand', 'n_cells', 'highly_variable', 'means', 'dispersions', 'dispersions_norm', 'variability_score', 'mean', 'std'
      uns:      'hvg', 'log1p'
      obsm:     'X_pca', 'prior_data'
      layers:   'counts', 'scaled'
modalities: ['atac', 'rna']

Prepare the tutorial inputs

For simplicity, we used a paired available Multiome dataset. Because this dataset is fully paired, every cell has both modalities. To mimic the setting Champollion is designed for, we use part of the cells as the paired bridge and treat the remaining cells as pseudo-unpaired RNA and ATAC profiles.

In a typical application, the bridge would come from a paired assay such as multiome, while the unpaired cells could come from separate scRNA-seq and scATAC-seq experiments.

The paired_mask column is used here only to construct a tutorial split: cells marked as paired form the bridge, and the remaining cells are copied into two modality-specific AnnData objects that we deliberately treat as unpaired. After this preparation step (whose details will not interest most users), we will have three objects: one bridge MuData object used for fitting, plus one pseudo-unpaired RNA object and one pseudo-unpaired ADT object used for transport and interpretation.

# Debug mode keeps the notebook executable on a cpu. Set DEBUG = False on the cluster.
DEBUG = False
DEBUG_TRAIN_CELLS = 120
DEBUG_TEST_CELLS = 180

PAIRED_MASK_KEY = "paired_mask"
paired_mask = np.asarray(mdata.obs[PAIRED_MASK_KEY].to_numpy(), dtype=bool)
celltypes = mdata.obs[CELLTYPE_KEY].astype(str).to_numpy()

def stratified_indices(mask, labels, n=None, random_state=0):
    """Return indices within mask, optionally stratified down to n cells."""
    idx = np.flatnonzero(mask)
    if n is None or n >= len(idx):
        return idx
    rng = np.random.default_rng(random_state)
    selected = []
    present_labels = [
        label for label in pd.unique(labels[idx]) if np.any(labels[idx] == label)
    ]
    per_group = max(1, int(np.ceil(n / len(present_labels))))
    for label in present_labels:
        label_idx = idx[labels[idx] == label]
        take = min(per_group, len(label_idx))
        selected.extend(rng.choice(label_idx, size=take, replace=False))
    selected = np.asarray(selected, dtype=int)
    if len(selected) > n:
        selected = rng.choice(selected, size=n, replace=False)
    return np.sort(selected)


train_idx = stratified_indices(
    paired_mask,
    labels=celltypes,
    n=DEBUG_TRAIN_CELLS if DEBUG else None,
    random_state=0,
)
test_idx = stratified_indices(
    ~paired_mask,
    labels=celltypes,
    n=DEBUG_TEST_CELLS if DEBUG else None,
    random_state=1,
)

bridge_mdata = mu.MuData(
    {
        RNA_MOD: mdata.mod[RNA_MOD][train_idx].copy(),
        ATAC_MOD: mdata.mod[ATAC_MOD][train_idx].copy(),
    }
)

adata_rna = mdata.mod[RNA_MOD][test_idx].copy()
adata_atac = mdata.mod[ATAC_MOD][test_idx].copy()

pd.crosstab(mdata.obs[CELLTYPE_KEY], mdata.obs[PAIRED_MASK_KEY], colnames=["paired"])

paired	False	True
celltype
CD56 (bright) NK cells	400	0
CD56 (dim) NK cells	452	0
classical monocytes	911	912
memory CD4 T cells	766	766
naive CD8 T cells	715	715

print(bridge_mdata)
print("pseudo-unpaired RNA:", adata_rna.shape)
print("pseudo-unpaired ATAC:", adata_atac.shape)

MuData object with n_obs × n_vars = 2393 × 145834
  var:  'gene_ids', 'interval', 'n_cells', 'highly_variable', 'means', 'dispersions', 'dispersions_norm', 'variability_score', 'mean', 'std'
  2 modalities
    rna:        2393 × 15417
      obs:      'celltype', 'batch', 'n_genes'
      var:      'gene_ids', 'interval', 'strand', 'n_cells', 'highly_variable', 'means', 'dispersions', 'dispersions_norm', 'variability_score', 'mean', 'std'
      uns:      'hvg', 'log1p'
      obsm:     'X_pca', 'prior_data'
      layers:   'counts', 'scaled'
    atac:       2393 × 130417
      obs:      'celltype', 'batch', 'n_genes'
      var:      'gene_ids', 'interval', 'n_cells', 'highly_variable', 'means', 'dispersions', 'dispersions_norm', 'variability_score', 'mean', 'std'
      uns:      'gene_activities_var_names', 'hvg', 'log1p'
      obsm:     'X_pca', 'gene_activities', 'prior_data'
      layers:   'counts', 'scaled'
pseudo-unpaired RNA: (3244, 15417)
pseudo-unpaired ATAC: (3244, 130417)

Fit Champollion on the paired bridge

The representations used here are low-dimensional RNA/ATAC embeddings stored in .obsm; the prior representation provides a common space used to compute a prior cost, it was obtained by computing gene activities for ATAC profiles with Signac.

Champollion learns the sparse cross-modality matrix A from the bridge cells. The bridge contains matched RNA and ATAC profiles for the same cells, so it provides the supervision needed to learn how the two representation spaces should be compared.

The verbose optimization log from the server run is shortened in this rendered notebook to keep the tutorial readable.

model = Champollion(
    epsilon=1.0,
    gamma=0.01,
    lambda_prior=20.0,
    use_keops=False,
    device="auto",
    random_state=0,
    max_iter=3 if DEBUG else 300_000,
    learning_rate=1e-3,
    sinkhorn_tol=1e-3,
    log_every=1 if DEBUG else 40,
    verbose=True
)
model.fit(
    bridge_mdata,
    modality_1=RNA_MOD,
    modality_2=ATAC_MOD,
    x_1_rep="obsm/X_pca",
    x_2_rep="obsm/X_pca",
    y_prior_1_rep="obsm/prior_data",
    y_prior_2_rep="obsm/prior_data",
)

print("A shape:", tuple(model.A_.shape))
print("A device:", model.A_.device)
pd.DataFrame(
    {key: pd.Series(value) for key, value in model.training_history_.items()}
).tail()

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train_total_loss: 23.648801803588867
train_obj_loss: 23.396228790283203
train_reg_loss: 0.2525726854801178
train_trace_term: -7.785801887512207
train_err_1: 1.797552227973938
train_plan_mass: 1.0000007152557373
train_total_loss: -9.479005813598633
train_obj_loss: -9.688580513000488
train_reg_loss: 0.20957428216934204
train_trace_term: -20.96923065185547
train_err_1: 1.535330057144165
train_plan_mass: 1.0000001192092896

  0%|          | 152/300000 [00:00<16:32, 302.05it/s]

train_total_loss: -16.77338218688965
train_obj_loss: -16.960758209228516
train_reg_loss: 0.18737666308879852
train_trace_term: -21.96637725830078
train_err_1: 1.1960947513580322
train_plan_mass: 1.0000001192092896
train_total_loss: -19.098215103149414
train_obj_loss: -19.268360137939453
train_reg_loss: 0.17014560103416443
train_trace_term: -19.65060806274414
train_err_1: 0.9687426090240479
train_plan_mass: 1.0

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train_total_loss: -20.113895416259766
train_obj_loss: -20.268245697021484
train_reg_loss: 0.15435002744197845
train_trace_term: -17.178295135498047
train_err_1: 0.8365817666053772
train_plan_mass: 1.0
train_total_loss: -20.66097068786621
train_obj_loss: -20.80193328857422
train_reg_loss: 0.14096195995807648
train_trace_term: -14.985442161560059
train_err_1: 0.739343523979187
train_plan_mass: 1.0

  0%|          | 301/300000 [00:01<14:06, 354.01it/s]

train_total_loss: -20.9902400970459
train_obj_loss: -21.12067222595215
train_reg_loss: 0.13043266534805298
train_trace_term: -13.415166854858398
train_err_1: 0.6697760820388794
train_plan_mass: 1.0
train_total_loss: -21.201112747192383
train_obj_loss: -21.323062896728516
train_reg_loss: 0.12194988131523132
train_trace_term: -12.392513275146484
train_err_1: 0.6202847957611084
train_plan_mass: 1.0

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train_total_loss: -21.34274673461914
train_obj_loss: -21.45783233642578
train_reg_loss: 0.11508643627166748
train_trace_term: -11.720455169677734
train_err_1: 0.5844957828521729
train_plan_mass: 1.0
train_total_loss: -21.441850662231445
train_obj_loss: -21.551212310791016
train_reg_loss: 0.10936126112937927
train_trace_term: -11.278448104858398
train_err_1: 0.5577296018600464
train_plan_mass: 1.0

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train_total_loss: -21.51506996154785
train_obj_loss: -21.619674682617188
train_reg_loss: 0.10460472106933594
train_trace_term: -10.983266830444336
train_err_1: 0.5357381105422974
train_plan_mass: 0.9999999403953552
train_total_loss: -21.572368621826172
train_obj_loss: -21.67304229736328
train_reg_loss: 0.1006736159324646
train_trace_term: -10.795778274536133
train_err_1: 0.517228901386261
train_plan_mass: 1.0

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train_total_loss: -21.618986129760742
train_obj_loss: -21.716381072998047
train_reg_loss: 0.09739574044942856
train_trace_term: -10.688013076782227
train_err_1: 0.5013983249664307
train_plan_mass: 1.0
train_total_loss: -21.65798568725586
train_obj_loss: -21.752574920654297
train_reg_loss: 0.09458954632282257
train_trace_term: -10.63742446899414
train_err_1: 0.48766660690307617
train_plan_mass: 1.0

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train_total_loss: -21.691633224487305
train_obj_loss: -21.78377914428711
train_reg_loss: 0.09214557707309723
train_trace_term: -10.628158569335938
train_err_1: 0.4751521348953247
train_plan_mass: 0.9999999403953552
train_total_loss: -21.721410751342773
train_obj_loss: -21.811424255371094
train_reg_loss: 0.0900135189294815
train_trace_term: -10.649930000305176
train_err_1: 0.4637792110443115
train_plan_mass: 1.0

  0%|          | 679/300000 [00:02<13:23, 372.61it/s]

train_total_loss: -21.748111724853516
train_obj_loss: -21.836261749267578
train_reg_loss: 0.08814920485019684
train_trace_term: -10.69873046875
train_err_1: 0.45325756072998047
train_plan_mass: 1.0
train_total_loss: -21.772388458251953
train_obj_loss: -21.85890007019043
train_reg_loss: 0.08651196956634521
train_trace_term: -10.770689010620117
train_err_1: 0.4434119164943695
train_plan_mass: 1.0

  0%|          | 793/300000 [00:02<13:23, 372.58it/s]

train_total_loss: -21.79474449157715
train_obj_loss: -21.879802703857422
train_reg_loss: 0.08505821228027344
train_trace_term: -10.857400894165039
train_err_1: 0.43415313959121704
train_plan_mass: 0.9999999403953552
train_total_loss: -21.81538963317871
train_obj_loss: -21.89913558959961
train_reg_loss: 0.08374650776386261
train_trace_term: -10.953367233276367
train_err_1: 0.42526012659072876
train_plan_mass: 1.0

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train_total_loss: -21.83462142944336
train_obj_loss: -21.917179107666016
train_reg_loss: 0.0825580358505249
train_trace_term: -11.053585052490234
train_err_1: 0.416704386472702
train_plan_mass: 1.0
train_total_loss: -21.85276985168457
train_obj_loss: -21.93425750732422
train_reg_loss: 0.08148731291294098
train_trace_term: -11.154322624206543
train_err_1: 0.40846821665763855
train_plan_mass: 1.0

  0%|          | 944/300000 [00:02<13:27, 370.55it/s]

train_total_loss: -21.869956970214844
train_obj_loss: -21.950485229492188
train_reg_loss: 0.08052785694599152
train_trace_term: -11.251028060913086
train_err_1: 0.4003918766975403
train_plan_mass: 0.9999999403953552
train_total_loss: -21.886167526245117
train_obj_loss: -21.96581268310547
train_reg_loss: 0.0796460509300232
train_trace_term: -11.345672607421875
train_err_1: 0.3922446668148041
train_plan_mass: 1.0

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train_total_loss: -21.901578903198242
train_obj_loss: -21.980411529541016
train_reg_loss: 0.07883284240961075
train_trace_term: -11.443656921386719
train_err_1: 0.38424453139305115
train_plan_mass: 1.0
train_total_loss: -21.91631317138672
train_obj_loss: -21.994403839111328
train_reg_loss: 0.07809115201234818
train_trace_term: -11.544727325439453
train_err_1: 0.37642911076545715
train_plan_mass: 1.0

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train_total_loss: -21.930452346801758
train_obj_loss: -22.007869720458984
train_reg_loss: 0.07741706818342209
train_trace_term: -11.648677825927734
train_err_1: 0.3688519597053528
train_plan_mass: 1.0
train_total_loss: -21.944042205810547
train_obj_loss: -22.020845413208008
train_reg_loss: 0.07680284976959229
train_trace_term: -11.756366729736328
train_err_1: 0.361512690782547
train_plan_mass: 1.0

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train_total_loss: -21.957120895385742
train_obj_loss: -22.033363342285156
train_reg_loss: 0.07624220103025436
train_trace_term: -11.867315292358398
train_err_1: 0.35442131757736206
train_plan_mass: 1.0
train_total_loss: -21.9697208404541
train_obj_loss: -22.045455932617188
train_reg_loss: 0.07573415338993073
train_trace_term: -11.980310440063477
train_err_1: 0.3476138114929199
train_plan_mass: 1.0

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train_total_loss: -21.981861114501953
train_obj_loss: -22.05713653564453
train_reg_loss: 0.0752745121717453
train_trace_term: -12.094630241394043
train_err_1: 0.34109342098236084
train_plan_mass: 0.9999999403953552
train_total_loss: -21.99355125427246
train_obj_loss: -22.06840705871582
train_reg_loss: 0.07485640048980713
train_trace_term: -12.209512710571289
train_err_1: 0.33485865592956543
train_plan_mass: 1.0

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train_total_loss: -22.004812240600586
train_obj_loss: -22.07928466796875
train_reg_loss: 0.07447304576635361
train_trace_term: -12.324151039123535
train_err_1: 0.32885515689849854
train_plan_mass: 1.0
train_total_loss: -22.015670776367188
train_obj_loss: -22.08979034423828
train_reg_loss: 0.07411942631006241
train_trace_term: -12.437982559204102
train_err_1: 0.323002427816391
train_plan_mass: 1.0

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train_total_loss: -22.026168823242188
train_obj_loss: -22.09996223449707
train_reg_loss: 0.07379252463579178
train_trace_term: -12.550725936889648
train_err_1: 0.3173070549964905
train_plan_mass: 0.9999999403953552
train_total_loss: -22.03633689880371
train_obj_loss: -22.109827041625977
train_reg_loss: 0.07349036633968353
train_trace_term: -12.662286758422852
train_err_1: 0.31177693605422974
train_plan_mass: 1.0

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train_total_loss: -22.04620361328125
train_obj_loss: -22.119415283203125
train_reg_loss: 0.07321120798587799
train_trace_term: -12.772721290588379
train_err_1: 0.30638837814331055
train_plan_mass: 0.9999999403953552
train_total_loss: -22.05579376220703
train_obj_loss: -22.128747940063477
train_reg_loss: 0.0729532241821289
train_trace_term: -12.88215160369873
train_err_1: 0.3011646270751953
train_plan_mass: 1.0

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train_total_loss: -22.065126419067383
train_obj_loss: -22.137840270996094
train_reg_loss: 0.07271452993154526
train_trace_term: -12.990642547607422
train_err_1: 0.2961099445819855
train_plan_mass: 0.9999999403953552
train_total_loss: -22.074207305908203
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train_reg_loss: 0.07249334454536438
train_trace_term: -13.098224639892578
train_err_1: 0.29119741916656494
train_plan_mass: 0.9999999403953552

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train_total_loss: -22.08306312561035
train_obj_loss: -22.155351638793945
train_reg_loss: 0.07228837162256241
train_trace_term: -13.20500373840332
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train_plan_mass: 1.0
train_total_loss: -22.091703414916992
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train_reg_loss: 0.07209879904985428
train_trace_term: -13.311088562011719
train_err_1: 0.28172656893730164
train_plan_mass: 1.0

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train_total_loss: -22.10013771057129
train_obj_loss: -22.172061920166016
train_reg_loss: 0.07192397117614746
train_trace_term: -13.416547775268555
train_err_1: 0.2771507501602173
train_plan_mass: 1.0
train_total_loss: -22.108379364013672
train_obj_loss: -22.180143356323242
train_reg_loss: 0.07176323980093002
train_trace_term: -13.521430969238281
train_err_1: 0.2726709246635437
train_plan_mass: 1.0

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train_total_loss: -22.11644172668457
train_obj_loss: -22.18805694580078
train_reg_loss: 0.07161600142717361
train_trace_term: -13.62582015991211
train_err_1: 0.26827794313430786
train_plan_mass: 0.9999999403953552
train_total_loss: -22.124326705932617
train_obj_loss: -22.19580841064453
train_reg_loss: 0.07148166745901108
train_trace_term: -13.72980785369873
train_err_1: 0.2639927268028259
train_plan_mass: 1.0

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train_total_loss: -22.132051467895508
train_obj_loss: -22.203411102294922
train_reg_loss: 0.07135986536741257
train_trace_term: -13.833505630493164
train_err_1: 0.2598132789134979
train_plan_mass: 1.0
train_total_loss: -22.139619827270508
train_obj_loss: -22.21087074279785
train_reg_loss: 0.07125025242567062
train_trace_term: -13.937017440795898
train_err_1: 0.2557391822338104
train_plan_mass: 1.0

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train_total_loss: -22.147045135498047
train_obj_loss: -22.218196868896484
train_reg_loss: 0.07115244120359421
train_trace_term: -14.040420532226562
train_err_1: 0.25176388025283813
train_plan_mass: 1.0
train_total_loss: -22.154329299926758
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  1%|          | 2041/300000 [00:05<13:18, 372.98it/s]

train_total_loss: -22.16147804260254
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  1%|          | 2155/300000 [00:06<13:21, 371.75it/s]

train_total_loss: -22.175392150878906
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  1%|          | 2193/300000 [00:06<13:22, 370.91it/s]

train_total_loss: -22.188817977905273
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  1%|          | 2305/300000 [00:06<13:51, 357.88it/s]

train_total_loss: -22.201791763305664
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  1%|          | 2381/300000 [00:06<13:34, 365.38it/s]

train_total_loss: -22.214344024658203
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  1%|          | 2456/300000 [00:06<13:26, 368.88it/s]

train_total_loss: -22.226520538330078
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  1%|          | 2532/300000 [00:07<13:21, 371.16it/s]

train_total_loss: -22.238374710083008
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  1%|          | 2608/300000 [00:07<13:20, 371.66it/s]

train_total_loss: -22.24994468688965
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  1%|          | 2684/300000 [00:07<13:17, 372.82it/s]

train_total_loss: -22.261205673217773
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  1%|          | 2760/300000 [00:07<13:16, 373.14it/s]

train_total_loss: -22.272130966186523
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  1%|          | 2874/300000 [00:08<13:17, 372.62it/s]

train_total_loss: -22.282737731933594
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  1%|          | 2950/300000 [00:08<13:17, 372.33it/s]

train_total_loss: -22.293045043945312
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  1%|          | 3026/300000 [00:08<13:17, 372.43it/s]

train_total_loss: -22.30307388305664
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  1%|          | 3102/300000 [00:08<13:15, 373.04it/s]

train_total_loss: -22.31283950805664
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  1%|          | 3178/300000 [00:08<13:16, 372.43it/s]

train_total_loss: -22.32235336303711
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  1%|          | 3254/300000 [00:09<13:16, 372.78it/s]

train_total_loss: -22.331621170043945
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  1%|          | 3330/300000 [00:09<13:15, 372.78it/s]

train_total_loss: -22.34065818786621
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  1%|          | 3406/300000 [00:09<13:17, 372.00it/s]

train_total_loss: -22.34947395324707
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  1%|          | 3482/300000 [00:09<13:16, 372.27it/s]

train_total_loss: -22.358076095581055
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  1%|          | 3596/300000 [00:09<13:13, 373.44it/s]

train_total_loss: -22.366474151611328
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  1%|          | 3672/300000 [00:10<13:14, 373.14it/s]

train_total_loss: -22.374675750732422
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  1%|          | 3748/300000 [00:10<13:13, 373.58it/s]

train_total_loss: -22.382688522338867
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  1%|▏         | 3824/300000 [00:10<13:13, 373.09it/s]

train_total_loss: -22.390522003173828
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  1%|▏         | 3900/300000 [00:10<13:12, 373.46it/s]

train_total_loss: -22.398178100585938
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  1%|▏         | 3976/300000 [00:10<13:14, 372.56it/s]

train_total_loss: -22.405664443969727
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  1%|▏         | 4052/300000 [00:11<13:12, 373.26it/s]

train_total_loss: -22.412986755371094
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  1%|▏         | 4128/300000 [00:11<13:15, 371.73it/s]

train_total_loss: -22.420146942138672
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  1%|▏         | 4204/300000 [00:11<13:14, 372.34it/s]

train_total_loss: -22.427154541015625
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  1%|▏         | 4280/300000 [00:11<13:11, 373.67it/s]

train_total_loss: -22.43400764465332
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  1%|▏         | 4394/300000 [00:12<13:10, 373.91it/s]

train_total_loss: -22.44072151184082
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  1%|▏         | 4470/300000 [00:12<13:13, 372.38it/s]

train_total_loss: -22.44729232788086
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  2%|▏         | 4546/300000 [00:12<13:17, 370.62it/s]

train_total_loss: -22.45372200012207
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  2%|▏         | 4622/300000 [00:12<13:14, 371.61it/s]

train_total_loss: -22.46001625061035
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  2%|▏         | 4698/300000 [00:12<13:13, 371.96it/s]

train_total_loss: -22.46617889404297
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  2%|▏         | 4774/300000 [00:13<13:14, 371.56it/s]

train_total_loss: -22.472213745117188
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  2%|▏         | 4850/300000 [00:13<13:13, 371.75it/s]

train_total_loss: -22.478126525878906
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  2%|▏         | 4926/300000 [00:13<13:13, 372.07it/s]

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  2%|▏         | 5002/300000 [00:13<13:12, 372.24it/s]

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  2%|▏         | 5116/300000 [00:14<13:10, 373.05it/s]

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  2%|▏         | 5192/300000 [00:14<13:11, 372.43it/s]

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  2%|▏         | 5268/300000 [00:14<13:12, 372.06it/s]

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  2%|▏         | 5344/300000 [00:14<13:12, 371.91it/s]

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  2%|▏         | 5419/300000 [00:14<13:59, 350.93it/s]

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  2%|▏         | 5494/300000 [00:15<13:37, 360.14it/s]

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  2%|▏         | 5569/300000 [00:15<13:24, 366.20it/s]

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  2%|▏         | 5645/300000 [00:15<13:16, 369.61it/s]

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  2%|▏         | 5721/300000 [00:15<13:10, 372.06it/s]

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  2%|▏         | 5835/300000 [00:15<13:07, 373.38it/s]

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  2%|▏         | 5911/300000 [00:16<13:09, 372.71it/s]

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  2%|▏         | 5987/300000 [00:16<13:41, 357.73it/s]

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  2%|▏         | 6063/300000 [00:16<13:24, 365.24it/s]

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  2%|▏         | 6139/300000 [00:16<13:17, 368.65it/s]

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  2%|▏         | 6215/300000 [00:17<13:12, 370.68it/s]

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  2%|▏         | 6291/300000 [00:17<13:09, 372.04it/s]

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  2%|▏         | 6367/300000 [00:17<13:08, 372.55it/s]

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  2%|▏         | 6443/300000 [00:17<13:07, 372.83it/s]

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  2%|▏         | 6519/300000 [00:17<13:06, 373.37it/s]

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  2%|▏         | 6633/300000 [00:18<13:06, 373.07it/s]

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  2%|▏         | 6709/300000 [00:18<13:06, 372.86it/s]

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  2%|▏         | 6785/300000 [00:18<13:05, 373.44it/s]

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  2%|▏         | 6861/300000 [00:18<13:06, 372.73it/s]

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  2%|▏         | 6937/300000 [00:18<13:06, 372.53it/s]

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  2%|▏         | 7013/300000 [00:19<13:06, 372.60it/s]

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  2%|▏         | 7089/300000 [00:19<13:06, 372.40it/s]

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  2%|▏         | 7165/300000 [00:19<13:08, 371.15it/s]

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  2%|▏         | 7241/300000 [00:19<13:06, 372.07it/s]

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  2%|▏         | 7355/300000 [00:20<13:03, 373.38it/s]

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  2%|▏         | 7431/300000 [00:20<13:05, 372.64it/s]

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  3%|▎         | 7507/300000 [00:20<13:04, 372.68it/s]

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  3%|▎         | 7583/300000 [00:20<13:04, 372.66it/s]

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  3%|▎         | 7659/300000 [00:20<13:04, 372.44it/s]

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  3%|▎         | 7735/300000 [00:21<13:04, 372.32it/s]

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  3%|▎         | 7811/300000 [00:21<13:04, 372.46it/s]

train_total_loss: -22.631332397460938
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  3%|▎         | 7887/300000 [00:21<13:05, 371.95it/s]

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  3%|▎         | 7963/300000 [00:21<13:03, 372.77it/s]

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  3%|▎         | 8039/300000 [00:21<13:01, 373.56it/s]

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  3%|▎         | 8153/300000 [00:22<13:03, 372.28it/s]

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  3%|▎         | 8229/300000 [00:22<13:05, 371.64it/s]

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  3%|▎         | 8305/300000 [00:22<13:06, 370.95it/s]

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  3%|▎         | 8381/300000 [00:22<13:03, 372.26it/s]

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  3%|▎         | 8457/300000 [00:23<13:02, 372.70it/s]

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  3%|▎         | 8533/300000 [00:23<13:01, 372.80it/s]

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  3%|▎         | 8609/300000 [00:23<13:00, 373.35it/s]

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  3%|▎         | 8685/300000 [00:23<13:05, 370.88it/s]

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  3%|▎         | 8761/300000 [00:23<13:01, 372.45it/s]

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  3%|▎         | 8875/300000 [00:24<12:58, 373.93it/s]

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  3%|▎         | 8951/300000 [00:24<12:59, 373.18it/s]

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  3%|▎         | 9027/300000 [00:24<12:58, 373.57it/s]

train_total_loss: -22.667680740356445
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  3%|▎         | 9103/300000 [00:24<12:59, 373.03it/s]

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  3%|▎         | 9179/300000 [00:24<13:02, 371.64it/s]

train_total_loss: -22.671743392944336
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  3%|▎         | 9255/300000 [00:25<12:59, 372.90it/s]

train_total_loss: -22.6737117767334
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  3%|▎         | 9331/300000 [00:25<12:58, 373.56it/s]

train_total_loss: -22.675626754760742
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  3%|▎         | 9407/300000 [00:25<12:58, 373.43it/s]

train_total_loss: -22.67751121520996
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  3%|▎         | 9483/300000 [00:25<12:57, 373.76it/s]

train_total_loss: -22.679367065429688
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  3%|▎         | 9559/300000 [00:26<12:56, 374.06it/s]

train_total_loss: -22.681182861328125
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  3%|▎         | 9673/300000 [00:26<13:01, 371.54it/s]

train_total_loss: -22.67974090576172
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  3%|▎         | 9748/300000 [00:26<13:34, 356.28it/s]

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  3%|▎         | 9822/300000 [00:26<13:27, 359.44it/s]

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  3%|▎         | 9896/300000 [00:26<13:19, 362.82it/s]

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  3%|▎         | 9971/300000 [00:27<13:12, 366.05it/s]

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  3%|▎         | 10046/300000 [00:27<13:05, 369.04it/s]

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  3%|▎         | 10122/300000 [00:27<13:00, 371.22it/s]

train_total_loss: -22.69284439086914
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  3%|▎         | 10198/300000 [00:27<12:58, 372.46it/s]

train_total_loss: -22.694374084472656
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  3%|▎         | 10312/300000 [00:28<12:56, 372.95it/s]

train_total_loss: -22.695878982543945
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  3%|▎         | 10388/300000 [00:28<12:56, 373.08it/s]

train_total_loss: -22.697219848632812
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  3%|▎         | 10464/300000 [00:28<12:56, 372.75it/s]

train_total_loss: -22.698793411254883
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  4%|▎         | 10540/300000 [00:28<12:55, 373.35it/s]

train_total_loss: -22.70020866394043
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  4%|▎         | 10616/300000 [00:28<12:55, 373.10it/s]

train_total_loss: -22.70159339904785
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  4%|▎         | 10692/300000 [00:29<12:53, 373.79it/s]

train_total_loss: -22.702953338623047
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  4%|▎         | 10768/300000 [00:29<12:54, 373.24it/s]

train_total_loss: -22.704116821289062
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  4%|▎         | 10844/300000 [00:29<12:54, 373.39it/s]

train_total_loss: -22.70557975769043
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  4%|▎         | 10920/300000 [00:29<12:53, 373.65it/s]

train_total_loss: -22.70354461669922
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  4%|▎         | 11034/300000 [00:30<12:53, 373.64it/s]

train_total_loss: -22.707090377807617
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  4%|▎         | 11110/300000 [00:30<12:52, 373.77it/s]

train_total_loss: -22.70887565612793
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  4%|▎         | 11186/300000 [00:30<12:54, 372.99it/s]

train_total_loss: -22.70937728881836
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  4%|▍         | 11262/300000 [00:30<12:52, 373.63it/s]

train_total_loss: -22.71138572692871
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  4%|▍         | 11338/300000 [00:30<12:55, 372.36it/s]

train_total_loss: -22.712844848632812
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  4%|▍         | 11414/300000 [00:31<12:54, 372.48it/s]

train_total_loss: -22.713973999023438
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  4%|▍         | 11490/300000 [00:31<12:54, 372.44it/s]

train_total_loss: -22.715051651000977
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  4%|▍         | 11566/300000 [00:31<12:57, 371.10it/s]

train_total_loss: -22.716163635253906
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  4%|▍         | 11642/300000 [00:31<12:54, 372.10it/s]

train_total_loss: -22.717187881469727
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  4%|▍         | 11756/300000 [00:31<12:52, 372.99it/s]

train_total_loss: -22.718259811401367
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  4%|▍         | 11832/300000 [00:32<12:53, 372.32it/s]

train_total_loss: -22.719280242919922
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  4%|▍         | 11908/300000 [00:32<12:54, 371.78it/s]

train_total_loss: -22.720130920410156
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  4%|▍         | 11984/300000 [00:32<12:54, 372.03it/s]

train_total_loss: -22.721256256103516
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  4%|▍         | 12060/300000 [00:32<12:58, 369.90it/s]

train_total_loss: -22.722209930419922
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  4%|▍         | 12136/300000 [00:32<12:54, 371.80it/s]

train_total_loss: -22.723146438598633
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  4%|▍         | 12212/300000 [00:33<12:52, 372.61it/s]

train_total_loss: -22.72404670715332
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  4%|▍         | 12288/300000 [00:33<12:51, 372.81it/s]

train_total_loss: -22.72496795654297
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  4%|▍         | 12364/300000 [00:33<12:50, 373.18it/s]

train_total_loss: -22.725841522216797
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  4%|▍         | 12440/300000 [00:33<12:49, 373.74it/s]

train_total_loss: -22.723163604736328
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  4%|▍         | 12554/300000 [00:34<12:49, 373.65it/s]

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  4%|▍         | 12630/300000 [00:34<12:49, 373.62it/s]

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  4%|▍         | 12706/300000 [00:34<12:49, 373.54it/s]

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  4%|▍         | 12782/300000 [00:34<12:49, 373.19it/s]

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  4%|▍         | 12858/300000 [00:34<12:49, 373.28it/s]

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  4%|▍         | 12934/300000 [00:35<12:47, 373.97it/s]

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  4%|▍         | 13010/300000 [00:35<12:48, 373.24it/s]

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  4%|▍         | 13086/300000 [00:35<12:49, 373.01it/s]

train_total_loss: -22.732948303222656
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  4%|▍         | 13162/300000 [00:35<12:49, 372.89it/s]

train_total_loss: -22.73366355895996
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  4%|▍         | 13276/300000 [00:36<12:48, 372.91it/s]

train_total_loss: -22.734363555908203
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  4%|▍         | 13352/300000 [00:36<12:47, 373.37it/s]

train_total_loss: -22.735048294067383
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  4%|▍         | 13428/300000 [00:36<12:48, 372.93it/s]

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  5%|▍         | 13504/300000 [00:36<12:48, 372.84it/s]

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  5%|▍         | 13580/300000 [00:36<13:36, 350.96it/s]

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  5%|▍         | 13655/300000 [00:37<13:13, 360.99it/s]

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  5%|▍         | 13731/300000 [00:37<13:00, 367.00it/s]

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  5%|▍         | 13807/300000 [00:37<12:51, 371.04it/s]

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  5%|▍         | 13883/300000 [00:37<12:48, 372.28it/s]

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  5%|▍         | 13959/300000 [00:37<12:46, 373.18it/s]

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  5%|▍         | 14073/300000 [00:38<12:44, 373.80it/s]

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  5%|▍         | 14149/300000 [00:38<12:46, 372.92it/s]

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  5%|▍         | 14225/300000 [00:38<12:45, 373.35it/s]

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  5%|▍         | 14301/300000 [00:38<12:46, 372.78it/s]

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  5%|▍         | 14377/300000 [00:38<12:45, 373.16it/s]

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  5%|▍         | 14452/300000 [00:39<13:32, 351.29it/s]

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  5%|▍         | 14527/300000 [00:39<13:11, 360.74it/s]

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  5%|▍         | 14602/300000 [00:39<12:59, 366.14it/s]

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  5%|▍         | 14716/300000 [00:39<12:50, 370.47it/s]

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  5%|▍         | 14792/300000 [00:40<12:47, 371.65it/s]

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  5%|▍         | 14868/300000 [00:40<12:46, 372.05it/s]

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  5%|▍         | 14944/300000 [00:40<12:45, 372.54it/s]

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  5%|▌         | 15020/300000 [00:40<12:46, 372.02it/s]

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  5%|▌         | 15096/300000 [00:40<13:29, 351.89it/s]

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  5%|▌         | 15171/300000 [00:41<13:07, 361.73it/s]

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  5%|▌         | 15245/300000 [00:41<12:58, 365.55it/s]

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  5%|▌         | 15320/300000 [00:41<12:49, 369.84it/s]

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  5%|▌         | 15434/300000 [00:41<12:46, 371.20it/s]

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  5%|▌         | 15510/300000 [00:42<12:45, 371.72it/s]

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  5%|▌         | 15586/300000 [00:42<12:44, 371.83it/s]

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  5%|▌         | 15660/300000 [00:42<13:28, 351.68it/s]

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  5%|▌         | 15735/300000 [00:42<13:06, 361.58it/s]

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  5%|▌         | 15810/300000 [00:42<12:54, 366.89it/s]

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  5%|▌         | 15885/300000 [00:43<12:48, 369.90it/s]

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  5%|▌         | 15961/300000 [00:43<12:44, 371.57it/s]

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  5%|▌         | 16075/300000 [00:43<12:41, 373.07it/s]

train_total_loss: -22.751514434814453
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  5%|▌         | 16113/300000 [00:43<13:27, 351.55it/s]

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  5%|▌         | 16226/300000 [00:44<12:56, 365.43it/s]

train_total_loss: -22.752168655395508
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  5%|▌         | 16302/300000 [00:44<12:47, 369.44it/s]

train_total_loss: -22.752485275268555
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  5%|▌         | 16378/300000 [00:44<12:46, 370.25it/s]

train_total_loss: -22.75275993347168
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  5%|▌         | 16453/300000 [00:44<13:31, 349.52it/s]

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  6%|▌         | 16529/300000 [00:44<13:04, 361.22it/s]

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  6%|▌         | 16605/300000 [00:45<12:51, 367.34it/s]

train_total_loss: -22.753692626953125
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  6%|▌         | 16681/300000 [00:45<12:44, 370.44it/s]

train_total_loss: -22.753986358642578
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  6%|▌         | 16795/300000 [00:45<12:39, 372.86it/s]

train_total_loss: -22.75423812866211
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  6%|▌         | 16871/300000 [00:45<12:40, 372.46it/s]

train_total_loss: -22.754520416259766
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  6%|▌         | 16947/300000 [00:46<12:38, 373.10it/s]

train_total_loss: -22.75480842590332
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  6%|▌         | 17023/300000 [00:46<12:38, 373.27it/s]

train_total_loss: -22.754989624023438
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  6%|▌         | 17099/300000 [00:46<12:39, 372.67it/s]

train_total_loss: -22.750411987304688
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  6%|▌         | 17175/300000 [00:46<12:39, 372.59it/s]

train_total_loss: -22.755552291870117
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  6%|▌         | 17251/300000 [00:46<12:39, 372.37it/s]

train_total_loss: -22.755813598632812
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  6%|▌         | 17327/300000 [00:47<12:36, 373.67it/s]

train_total_loss: -22.755985260009766
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  6%|▌         | 17403/300000 [00:47<12:35, 373.86it/s]

train_total_loss: -22.75627326965332
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  6%|▌         | 17479/300000 [00:47<12:36, 373.57it/s]

train_total_loss: -22.75649642944336
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  6%|▌         | 17593/300000 [00:47<12:36, 373.11it/s]

train_total_loss: -22.75670051574707
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  6%|▌         | 17669/300000 [00:47<12:37, 372.47it/s]

train_total_loss: -22.756925582885742
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  6%|▌         | 17745/300000 [00:48<12:37, 372.54it/s]

train_total_loss: -22.75714111328125
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  6%|▌         | 17821/300000 [00:48<12:37, 372.73it/s]

train_total_loss: -22.757347106933594
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  6%|▌         | 17897/300000 [00:48<12:35, 373.39it/s]

train_total_loss: -22.757556915283203
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  6%|▌         | 17935/300000 [00:48<13:25, 349.97it/s]

train_total_loss: -22.75774574279785
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  6%|▌         | 18029/300000 [00:49<20:43, 226.81it/s]

train_total_loss: -22.757949829101562
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  6%|▌         | 18078/300000 [00:49<21:19, 220.34it/s]

train_total_loss: -22.757946014404297
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  6%|▌         | 18123/300000 [00:49<23:32, 199.63it/s]

train_total_loss: -22.758214950561523
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  6%|▌         | 18179/300000 [00:50<30:45, 152.69it/s]

train_total_loss: -22.75832748413086
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  6%|▌         | 18227/300000 [00:50<31:38, 148.42it/s]

train_total_loss: -22.75841522216797
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  6%|▌         | 18259/300000 [00:50<31:33, 148.78it/s]

train_total_loss: -22.758522033691406
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  6%|▌         | 18307/300000 [00:51<32:14, 145.64it/s]

train_total_loss: -22.758573532104492
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  6%|▌         | 18340/300000 [00:51<30:29, 153.97it/s]

train_total_loss: -22.758691787719727
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  6%|▌         | 18388/300000 [00:51<30:35, 153.42it/s]

train_total_loss: -22.75874137878418
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  6%|▌         | 18420/300000 [00:51<30:33, 153.57it/s]

train_total_loss: -22.75883674621582
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  6%|▌         | 18468/300000 [00:52<30:29, 153.87it/s]

train_total_loss: -22.758878707885742
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  6%|▌         | 18500/300000 [00:52<30:39, 153.02it/s]

train_total_loss: -22.758678436279297
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  6%|▌         | 18550/300000 [00:52<30:48, 152.27it/s]

train_total_loss: -22.751611709594727
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  6%|▌         | 18584/300000 [00:52<29:48, 157.34it/s]

train_total_loss: -22.758193969726562
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  6%|▌         | 18632/300000 [00:53<29:33, 158.66it/s]

train_total_loss: -22.75799560546875
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  6%|▌         | 18665/300000 [00:53<29:11, 160.59it/s]

train_total_loss: -22.759309768676758
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  6%|▌         | 18710/300000 [00:53<24:27, 191.69it/s]

train_total_loss: -22.759441375732422
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  6%|▋         | 18800/300000 [00:53<21:52, 214.27it/s]

train_total_loss: -22.759597778320312
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  6%|▋         | 18867/300000 [00:54<21:32, 217.57it/s]

train_total_loss: -22.75973892211914
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  6%|▋         | 18959/300000 [00:54<21:13, 220.76it/s]

train_total_loss: -22.759885787963867
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  6%|▋         | 19028/300000 [00:54<21:16, 220.14it/s]

train_total_loss: -22.760028839111328
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  6%|▋         | 19120/300000 [00:55<21:03, 222.37it/s]

train_total_loss: -22.76016616821289
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  6%|▋         | 19189/300000 [00:55<21:04, 222.11it/s]

train_total_loss: -22.760305404663086
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  6%|▋         | 19281/300000 [00:56<21:08, 221.35it/s]

train_total_loss: -22.760419845581055
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  6%|▋         | 19350/300000 [00:56<21:02, 222.37it/s]

train_total_loss: -22.760358810424805
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  6%|▋         | 19429/300000 [00:56<20:28, 228.34it/s]

train_total_loss: -22.760700225830078
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  7%|▋         | 19521/300000 [00:57<21:07, 221.28it/s]

train_total_loss: -22.76082992553711
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  7%|▋         | 19589/300000 [00:57<21:40, 215.65it/s]

train_total_loss: -22.760953903198242
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  7%|▋         | 19680/300000 [00:57<21:41, 215.37it/s]

train_total_loss: -22.76107406616211
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  7%|▋         | 19750/300000 [00:58<21:26, 217.88it/s]

train_total_loss: -22.761165618896484
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  7%|▋         | 19838/300000 [00:58<21:41, 215.34it/s]

train_total_loss: -22.76129913330078
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  7%|▋         | 19911/300000 [00:58<20:01, 233.15it/s]

train_total_loss: -22.758434295654297
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  7%|▋         | 20005/300000 [00:59<16:21, 285.37it/s]

train_total_loss: -22.761438369750977
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  7%|▋         | 20081/300000 [00:59<14:09, 329.65it/s]

train_total_loss: -22.761621475219727
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  7%|▋         | 20195/300000 [00:59<13:00, 358.66it/s]

train_total_loss: -22.761674880981445
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  7%|▋         | 20270/300000 [00:59<12:44, 365.82it/s]

train_total_loss: -22.761831283569336
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  7%|▋         | 20345/300000 [01:00<12:37, 368.96it/s]

train_total_loss: -22.761926651000977
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  7%|▋         | 20420/300000 [01:00<12:33, 370.84it/s]

train_total_loss: -22.762025833129883
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  7%|▋         | 20496/300000 [01:00<12:32, 371.55it/s]

train_total_loss: -22.762115478515625
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  7%|▋         | 20572/300000 [01:00<12:33, 370.90it/s]

train_total_loss: -22.762184143066406
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  7%|▋         | 20648/300000 [01:00<12:33, 370.63it/s]

train_total_loss: -22.762277603149414
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  7%|▋         | 20724/300000 [01:01<12:32, 371.24it/s]

train_total_loss: -22.762371063232422
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  7%|▋         | 20800/300000 [01:01<12:31, 371.46it/s]

train_total_loss: -22.76246452331543
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  7%|▋         | 20914/300000 [01:01<12:27, 373.41it/s]

train_total_loss: -22.76255989074707
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  7%|▋         | 20952/300000 [01:01<12:36, 369.06it/s]

train_total_loss: -22.762577056884766
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  7%|▋         | 21022/300000 [01:02<16:43, 278.10it/s]

train_total_loss: -22.762680053710938
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  7%|▋         | 21128/300000 [01:02<14:23, 322.86it/s]

train_total_loss: -22.76273536682129
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  7%|▋         | 21203/300000 [01:02<13:23, 346.88it/s]

train_total_loss: -22.757692337036133
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  7%|▋         | 21279/300000 [01:02<12:56, 359.17it/s]

train_total_loss: -22.762853622436523
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  7%|▋         | 21354/300000 [01:03<13:07, 354.05it/s]

train_total_loss: -22.763010025024414
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  7%|▋         | 21422/300000 [01:03<17:40, 262.58it/s]

train_total_loss: -22.763076782226562
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  7%|▋         | 21501/300000 [01:03<20:07, 230.72it/s]

train_total_loss: -22.76314353942871
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  7%|▋         | 21593/300000 [01:04<21:34, 215.05it/s]

train_total_loss: -22.76283073425293
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  7%|▋         | 21684/300000 [01:04<16:39, 278.38it/s]

train_total_loss: -22.763273239135742
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  7%|▋         | 21759/300000 [01:04<14:14, 325.79it/s]

train_total_loss: -22.76333236694336
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  7%|▋         | 21872/300000 [01:04<13:02, 355.55it/s]

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  7%|▋         | 21948/300000 [01:05<12:42, 364.65it/s]

train_total_loss: -22.763456344604492
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  7%|▋         | 22023/300000 [01:05<12:34, 368.54it/s]

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  7%|▋         | 22099/300000 [01:05<12:30, 370.47it/s]

train_total_loss: -22.763551712036133
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  7%|▋         | 22175/300000 [01:05<13:54, 332.79it/s]

train_total_loss: -22.76362419128418
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  7%|▋         | 22248/300000 [01:06<14:17, 323.84it/s]

train_total_loss: -22.76367950439453
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  7%|▋         | 22323/300000 [01:06<13:20, 346.71it/s]

train_total_loss: -22.76372528076172
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  7%|▋         | 22399/300000 [01:06<12:54, 358.59it/s]

train_total_loss: -22.763774871826172
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  8%|▊         | 22512/300000 [01:06<12:36, 366.71it/s]

train_total_loss: -22.75878143310547
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  8%|▊         | 22587/300000 [01:06<12:31, 369.00it/s]

train_total_loss: -22.763639450073242
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  8%|▊         | 22663/300000 [01:07<12:26, 371.55it/s]

train_total_loss: -22.76393699645996
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  8%|▊         | 22739/300000 [01:07<12:33, 367.83it/s]

train_total_loss: -22.763946533203125
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  8%|▊         | 22815/300000 [01:07<12:28, 370.42it/s]

train_total_loss: -22.76402473449707
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  8%|▊         | 22891/300000 [01:07<12:25, 371.79it/s]

train_total_loss: -22.76407241821289
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  8%|▊         | 22967/300000 [01:08<12:24, 372.22it/s]

train_total_loss: -22.76411247253418
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  8%|▊         | 23043/300000 [01:08<12:21, 373.54it/s]

train_total_loss: -22.76416015625
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  8%|▊         | 23119/300000 [01:08<12:20, 373.99it/s]

train_total_loss: -22.76405143737793
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  8%|▊         | 23233/300000 [01:08<12:19, 374.45it/s]

train_total_loss: -22.764236450195312
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  8%|▊         | 23309/300000 [01:08<12:23, 372.36it/s]

train_total_loss: -22.7642765045166
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  8%|▊         | 23385/300000 [01:09<13:05, 352.01it/s]

train_total_loss: -22.76432228088379
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  8%|▊         | 23460/300000 [01:09<12:43, 362.28it/s]

train_total_loss: -22.76434898376465
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  8%|▊         | 23535/300000 [01:09<12:31, 367.67it/s]

train_total_loss: -22.764394760131836
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  8%|▊         | 23610/300000 [01:09<12:35, 365.90it/s]

train_total_loss: -22.76443099975586
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  8%|▊         | 23685/300000 [01:09<12:57, 355.57it/s]

train_total_loss: -22.76447868347168
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  8%|▊         | 23761/300000 [01:10<12:36, 365.21it/s]

train_total_loss: -22.764423370361328
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  8%|▊         | 23875/300000 [01:10<12:24, 371.00it/s]

train_total_loss: -22.7645320892334
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  8%|▊         | 23951/300000 [01:10<12:21, 372.31it/s]

train_total_loss: -22.763010025024414
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  8%|▊         | 24027/300000 [01:10<12:20, 372.74it/s]

train_total_loss: -22.762210845947266
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  8%|▊         | 24103/300000 [01:11<12:18, 373.40it/s]

train_total_loss: -22.764646530151367
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  8%|▊         | 24179/300000 [01:11<12:17, 373.97it/s]

train_total_loss: -22.76468276977539
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  8%|▊         | 24255/300000 [01:11<12:19, 372.69it/s]

train_total_loss: -22.764680862426758
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  8%|▊         | 24331/300000 [01:11<12:17, 373.70it/s]

train_total_loss: -22.764741897583008
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  8%|▊         | 24407/300000 [01:11<12:18, 373.22it/s]

train_total_loss: -22.764774322509766
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train_total_loss: -22.7647762298584
train_obj_loss: -22.86414337158203
train_reg_loss: 0.09936796128749847
train_trace_term: -47.30144500732422
train_err_1: 0.0030975029803812504
train_plan_mass: 1.0000004768371582

  8%|▊         | 24483/300000 [01:12<12:16, 373.96it/s]

train_total_loss: -22.764789581298828
train_obj_loss: -22.86416244506836
train_reg_loss: 0.09937360882759094
train_trace_term: -47.30636978149414
train_err_1: 0.0035237916745245457
train_plan_mass: 1.000000238418579
train_total_loss: -22.764816284179688
train_obj_loss: -22.864194869995117
train_reg_loss: 0.09937930852174759
train_trace_term: -47.31604766845703
train_err_1: 0.0011834728065878153
train_plan_mass: 1.0000003576278687

  8%|▊         | 24559/300000 [01:12<12:17, 373.29it/s]

train_total_loss: -22.764833450317383
train_obj_loss: -22.864219665527344
train_reg_loss: 0.09938550740480423
train_trace_term: -47.32213592529297
train_err_1: 0.0011416298802942038
train_plan_mass: 1.0000003576278687
train_total_loss: -22.76484489440918
train_obj_loss: -22.86423683166504
train_reg_loss: 0.09939151257276535
train_trace_term: -47.32801818847656
train_err_1: 0.0011345307575538754
train_plan_mass: 1.0000003576278687

  8%|▊         | 24673/300000 [01:12<12:16, 374.00it/s]

train_total_loss: -22.764713287353516
train_obj_loss: -22.864112854003906
train_reg_loss: 0.09940028935670853
train_trace_term: -47.31980895996094
train_err_1: 0.010367462411522865
train_plan_mass: 1.0000004768371582
train_total_loss: -22.764867782592773
train_obj_loss: -22.864269256591797
train_reg_loss: 0.09940079599618912
train_trace_term: -47.34062576293945
train_err_1: 0.003010024316608906
train_plan_mass: 1.0000003576278687

  8%|▊         | 24749/300000 [01:12<12:16, 373.69it/s]

train_total_loss: -22.764888763427734
train_obj_loss: -22.864295959472656
train_reg_loss: 0.09940668195486069
train_trace_term: -47.344573974609375
train_err_1: 0.0012221019715070724
train_plan_mass: 1.0000003576278687
train_total_loss: -22.764902114868164
train_obj_loss: -22.864315032958984
train_reg_loss: 0.0994124561548233
train_trace_term: -47.34960174560547
train_err_1: 0.00110993895214051
train_plan_mass: 1.0000003576278687

  8%|▊         | 24825/300000 [01:13<12:15, 374.31it/s]

train_total_loss: -22.764923095703125
train_obj_loss: -22.864341735839844
train_reg_loss: 0.09941943734884262
train_trace_term: -47.354896545410156
train_err_1: 0.0012022975133731961
train_plan_mass: 1.0000003576278687
train_total_loss: -22.76492691040039
train_obj_loss: -22.864349365234375
train_reg_loss: 0.09942308068275452
train_trace_term: -47.362125396728516
train_err_1: 0.002823765855282545
train_plan_mass: 1.0000004768371582

  8%|▊         | 24901/300000 [01:13<12:14, 374.36it/s]

train_total_loss: -22.76494789123535
train_obj_loss: -22.864376068115234
train_reg_loss: 0.099428690969944
train_trace_term: -47.36452102661133
train_err_1: 0.0012652699369937181
train_plan_mass: 1.0000004768371582
train_total_loss: -22.764930725097656
train_obj_loss: -22.86436653137207
train_reg_loss: 0.0994361862540245
train_trace_term: -47.36460494995117
train_err_1: 0.005332715809345245
train_plan_mass: 1.0000003576278687

  8%|▊         | 24977/300000 [01:13<12:14, 374.60it/s]

train_total_loss: -22.764965057373047
train_obj_loss: -22.864402770996094
train_reg_loss: 0.09943708032369614
train_trace_term: -47.37793731689453
train_err_1: 0.002885080175474286
train_plan_mass: 1.000000238418579
train_total_loss: -22.76498794555664
train_obj_loss: -22.864431381225586
train_reg_loss: 0.09944303333759308
train_trace_term: -47.379608154296875
train_err_1: 0.0012228023260831833
train_plan_mass: 1.0000003576278687

  8%|▊         | 25053/300000 [01:13<12:15, 373.90it/s]

train_total_loss: -22.765005111694336
train_obj_loss: -22.864452362060547
train_reg_loss: 0.0994475707411766
train_trace_term: -47.385276794433594
train_err_1: 0.0016777795972302556
train_plan_mass: 1.0000003576278687
train_total_loss: -22.7650089263916
train_obj_loss: -22.864459991455078
train_reg_loss: 0.09945039451122284
train_trace_term: -47.39162826538086
train_err_1: 0.003166094422340393
train_plan_mass: 1.0000003576278687

  8%|▊         | 25129/300000 [01:13<12:13, 374.53it/s]

train_total_loss: -22.765031814575195
train_obj_loss: -22.86448860168457
train_reg_loss: 0.09945686161518097
train_trace_term: -47.39250564575195
train_err_1: 0.0011985664023086429
train_plan_mass: 1.0000004768371582
train_total_loss: -22.765029907226562
train_obj_loss: -22.864490509033203
train_reg_loss: 0.09946039319038391
train_trace_term: -47.40273666381836
train_err_1: 0.0035768512170761824
train_plan_mass: 1.0000003576278687

  8%|▊         | 25205/300000 [01:14<12:14, 374.11it/s]

train_total_loss: -22.765050888061523
train_obj_loss: -22.86451530456543
train_reg_loss: 0.09946534782648087
train_trace_term: -47.397727966308594
train_err_1: 0.0026654298417270184
train_plan_mass: 1.0000004768371582
train_total_loss: -22.765066146850586
train_obj_loss: -22.864534378051758
train_reg_loss: 0.09946893155574799
train_trace_term: -47.40449523925781
train_err_1: 0.0024959836155176163
train_plan_mass: 1.0000004768371582

  8%|▊         | 25281/300000 [01:14<15:17, 299.55it/s]

train_total_loss: -22.765045166015625
train_obj_loss: -22.864517211914062
train_reg_loss: 0.0994715467095375
train_trace_term: -47.41459655761719
train_err_1: 0.00487096980214119
train_plan_mass: 1.000000238418579
train_total_loss: -22.76509666442871
train_obj_loss: -22.864574432373047
train_reg_loss: 0.09947725385427475
train_trace_term: -47.414268493652344
train_err_1: 0.00183482829015702
train_plan_mass: 1.0000003576278687

  8%|▊         | 25343/300000 [01:14<18:17, 250.19it/s]

train_total_loss: -22.76504898071289
train_obj_loss: -22.864532470703125
train_reg_loss: 0.09948268532752991
train_trace_term: -47.40671920776367
train_err_1: 0.00668372493237257
train_plan_mass: 1.0000003576278687
train_total_loss: -22.765117645263672
train_obj_loss: -22.86460304260254
train_reg_loss: 0.0994856208562851
train_trace_term: -47.42011260986328
train_err_1: 0.00214449898339808
train_plan_mass: 1.0000004768371582

  8%|▊         | 25443/300000 [01:15<20:23, 224.36it/s]

train_total_loss: -22.765104293823242
train_obj_loss: -22.864591598510742
train_reg_loss: 0.09948734939098358
train_trace_term: -47.42652893066406
train_err_1: 0.0041792127303779125
train_plan_mass: 1.0000004768371582
train_total_loss: -22.765132904052734
train_obj_loss: -22.8646240234375
train_reg_loss: 0.09949077665805817
train_trace_term: -47.43416213989258
train_err_1: 0.0032768133096396923
train_plan_mass: 1.0000004768371582

  9%|▊         | 25527/300000 [01:15<17:39, 258.94it/s]

train_total_loss: -22.763296127319336
train_obj_loss: -22.862743377685547
train_reg_loss: 0.0994463711977005
train_trace_term: -47.43132781982422
train_err_1: 0.012963908724486828
train_plan_mass: 1.0000003576278687
train_total_loss: -22.756450653076172
train_obj_loss: -22.855369567871094
train_reg_loss: 0.09891930967569351
train_trace_term: -47.58799743652344
train_err_1: 0.035422999411821365
train_plan_mass: 1.000000238418579

  9%|▊         | 25602/300000 [01:15<14:33, 314.08it/s]

train_total_loss: -22.761919021606445
train_obj_loss: -22.860797882080078
train_reg_loss: 0.09887843579053879
train_trace_term: -47.56159973144531
train_err_1: 0.01935384050011635
train_plan_mass: 1.0000003576278687
train_total_loss: -22.764158248901367
train_obj_loss: -22.86339569091797
train_reg_loss: 0.09923727065324783
train_trace_term: -47.513336181640625
train_err_1: 0.009653383865952492
train_plan_mass: 1.0000003576278687

  9%|▊         | 25716/300000 [01:15<12:57, 352.85it/s]

train_total_loss: -22.76490020751953
train_obj_loss: -22.864221572875977
train_reg_loss: 0.09932103008031845
train_trace_term: -47.50249481201172
train_err_1: 0.005859344266355038
train_plan_mass: 1.0000003576278687
train_total_loss: -22.76514434814453
train_obj_loss: -22.864578247070312
train_reg_loss: 0.09943322092294693
train_trace_term: -47.503509521484375
train_err_1: 0.0034643467515707016
train_plan_mass: 1.0000003576278687

  9%|▊         | 25792/300000 [01:16<12:35, 363.18it/s]

train_total_loss: -22.765235900878906
train_obj_loss: -22.864723205566406
train_reg_loss: 0.09948763996362686
train_trace_term: -47.49488067626953
train_err_1: 0.0012764855055138469
train_plan_mass: 1.0000003576278687
train_total_loss: -22.76525115966797
train_obj_loss: -22.86475372314453
train_reg_loss: 0.09950309246778488
train_trace_term: -47.49058532714844
train_err_1: 0.001034261891618371
train_plan_mass: 1.0000003576278687

  9%|▊         | 25868/300000 [01:16<12:24, 368.13it/s]

train_total_loss: -22.764774322509766
train_obj_loss: -22.864282608032227
train_reg_loss: 0.0995083600282669
train_trace_term: -47.513328552246094
train_err_1: 0.015511035919189453
train_plan_mass: 1.0000004768371582
train_total_loss: -22.76526641845703
train_obj_loss: -22.864784240722656
train_reg_loss: 0.09951744973659515
train_trace_term: -47.49102783203125
train_err_1: 0.0020169296767562628
train_plan_mass: 1.000000238418579

  9%|▊         | 25920/300000 [01:16<13:28, 338.88it/s]

train_total_loss: -22.765281677246094
train_obj_loss: -22.864805221557617
train_reg_loss: 0.09952424466609955
train_trace_term: -47.48903274536133
train_err_1: 0.001074271509423852
train_plan_mass: 1.0000003576278687
train_total_loss: -22.765295028686523
train_obj_loss: -22.864826202392578
train_reg_loss: 0.09953080862760544
train_trace_term: -47.48905944824219
train_err_1: 0.0009939862648025155
train_plan_mass: 1.0000003576278687
Converged after 25921 iterations
train_n_iterations: 25921
train_err_1: 0.0009890461806207895
train_plan_mass: 1.0000003576278687
train_A_final_norm: 9.95309829711914
train_plan_entropy_ratio: tensor([0.7478], device='cuda:0', grad_fn=<DivBackward0>)
A shape: (50, 50)
A device: cuda:0

	train_total_loss	train_obj_loss	train_reg_loss	train_trace_term	train_err_1	train_plan_mass
645	-22.764774	-22.864283	0.099508	-47.513329	0.015511	1.0
646	-22.765266	-22.864784	0.099517	-47.491028	0.002017	1.0
647	-22.765282	-22.864805	0.099524	-47.489033	0.001074	1.0
648	-22.765295	-22.864826	0.099531	-47.489059	0.000994	1.0
649	NaN	NaN	NaN	NaN	0.000989	1.0

Integrate pseudo-unpaired cells

We now apply the learned cost to the RNA and ATAC cells held out from the bridge in order to infer a transport plan matching those unpaired profiles.

transport = model.transport(
    {RNA_MOD: adata_rna, ATAC_MOD: adata_atac},
    x_reps={RNA_MOD: "obsm/X_pca", ATAC_MOD: "obsm/X_pca"},
    y_prior_reps={RNA_MOD: "obsm/prior_data", ATAC_MOD: "obsm/prior_data"},
    store_cost=True,
    store_plan=True,
    max_iter_sink=30 if DEBUG else 1000,
)

plan = (
    transport.materialize_plan()
    .detach()
    .cpu()
    .numpy()
)
print("plan shape:", plan.shape)
print("plan mass:", plan.sum())
transport.plan_diagnostics

Transport sinkhorn loop reached max_iter_sink
plan shape: (3244, 3244)
plan mass: 1.0000007

{'mass': 1.0000007152557373,
 'mass_abs_error': 7.152557373046875e-07,
 'x_1_marginal_l1_error': 0.006189633160829544,
 'x_2_marginal_l1_error': 1.7432321328669786e-06,
 'finite': True,
 'passed': False,
 'tol': 0.001}

Inspect the transport plan

The transport plan summarizes how mass is assigned between RNA and ATAC cells. Reordering cells by known labels is a useful diagnostic: a good integration should concentrate mass between biologically matching populations.

rna_labels = adata_rna.obs[CELLTYPE_KEY].astype(str).to_numpy()
atac_labels = adata_atac.obs[CELLTYPE_KEY].astype(str).to_numpy()
celltype_order = sorted(pd.unique(np.concatenate([rna_labels, atac_labels])))

_, _, _, fig, ax = plot_ordered_transport_plan(
    heat_mtx=plan,
    annotations=rna_labels,
    annotations_ordered=celltype_order,
    annotations_2=atac_labels,
    annotations_ordered_2=celltype_order,
    cmap="magma",
    figsize=(7, 7),
    vmin=1e-16,
    xlabel="ATAC cells",
    ylabel="RNA cells",
)
plt.show()

Transfer cell type annotations from RNA to ATAC

A common use case is to transfer annotations from a well-annotated modality to another modality. Here we transfer RNA cell type labels to ATAC cells through the transport plan and compare the predictions with the known labels of ATAC cells.

transfer = transport.transfer_obs(
    CELLTYPE_KEY,
    source=RNA_MOD,
    kind="categorical",
    inplace=True,
    target_key="celltype_champollion",
    return_probabilities=True,
)

predicted = transfer["prediction"].astype(str)
true = adata_atac.obs[CELLTYPE_KEY].astype(str)
print("cell type transfer accuracy:", accuracy_score(true, predicted))
transfer["probabilities"].head()

cell type transfer accuracy: 0.9778051787916153

	CD56 (bright) NK cells	CD56 (dim) NK cells	classical monocytes	memory CD4 T cells	naive CD8 T cells
AAACAGCCAATCCCTT-1	5.878114e-25	2.227206e-18	9.914182e-07	9.995016e-01	4.973546e-04
AAACATGCAAGGTCCT-1	4.730245e-34	6.667834e-30	5.848635e-08	4.016490e-05	9.999597e-01
AAACATGCACCGGCTA-1	1.000000e+00	7.871149e-09	0.000000e+00	0.000000e+00	0.000000e+00
AAACATGCAGGGAGCT-1	9.305187e-01	6.948131e-02	0.000000e+00	3.143325e-34	9.091624e-42
AAACCAACATTGTGCA-1	0.000000e+00	0.000000e+00	9.999999e-01	3.689943e-23	3.264675e-28

labels = [
    label
    for label in celltype_order
    if (true.eq(label).any() or predicted.eq(label).any())
]
cm = confusion_matrix(true, predicted, labels=labels)

fig, ax = plt.subplots(figsize=(9, 7))
sns.heatmap(
    cm,
    annot=True,
    fmt="d",
    cmap="Blues",
    xticklabels=labels,
    yticklabels=labels,
    cbar=False,
    ax=ax,
)
ax.set_xlabel("Predicted ATAC label")
ax.set_ylabel("True ATAC label")
ax.set_title("RNA-to-ATAC cell type transfer")
ax.set_xticklabels(ax.get_xticklabels(), rotation=45, ha="right")
ax.set_yticklabels(ax.get_yticklabels(), rotation=0)
plt.tight_layout()
plt.show()

Barycentric projection into RNA PCA space

The same transport plan can also project continuous representations across modalities. Here each ATAC cell is represented as a barycenter of RNA cells in RNA PCA space, which enables a joint visualization of original RNA cells and projected ATAC cells.

projected_atac_in_rna_pca = transport.project(rep="obsm/X_pca", source=RNA_MOD)

joint = ad.AnnData(X=np.vstack([adata_rna.obsm["X_pca"], projected_atac_in_rna_pca]))
joint.obs["modality"] = pd.Categorical(
    ["RNA"] * adata_rna.n_obs + ["ATAC projected"] * adata_atac.n_obs
)
joint.obs[CELLTYPE_KEY] = pd.Categorical(np.concatenate([rna_labels, atac_labels]))

sc.pp.neighbors(joint, n_neighbors=15, use_rep="X")
sc.tl.umap(joint, min_dist=0.2, random_state=0)

sc.pl.umap(joint, color=["modality", CELLTYPE_KEY], alpha=0.65, wspace=0.35)