ECG Foundation Model

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Date created: 2024/07/25

Last Modified: 2024/08/14

Description: Train, evaluate, and export an ECG foundation model

Overview

This notebook demonstrates creating a foundation model for raw ECG signals. By creating a foundation model, we can create small, down-stream classification models.

#!pip install -q --disable-pip-version-check heartkit

import os

os.environ["TF_CPP_MIN_LOG_LEVEL"] = "2"  # 3
import contextlib
from pathlib import Path
import tempfile
import keras
import heartkit as hk
import tensorflow as tf
import numpy as np
import helia_edge as helia
import matplotlib.pyplot as plt
from sklearn.manifold import TSNE

2024-08-16 18:53:16.603880: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
2024-08-16 18:53:16.611916: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
2024-08-16 18:53:16.614257: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered

Constants

Here we provide the constants that we will use throughout the guide. For better performance, adjust parameters such as BATCH_SIZE, EPOCHS, and LEARNING_RATE.

# File paths
datasets_dir = Path(os.getenv("HK_DATASET_PATH", "./datasets"))
job_dir = Path(tempfile.gettempdir()) / "hk-foundation"
model_file = job_dir / "model.keras"
val_file = job_dir / "val.pkl"

# Data settings
sampling_rate = 100  # 100 Hz
input_size = 1000  # 10 seconds
frame_size = 800  # 8 seconds

# Training settings
batch_size = 1024  # Batch size for training
buffer_size = 2000  # How many samples are shuffled each epoch
epochs = 150  # Increase this to 100+
steps_per_epoch = 25  # # Steps per epoch (must set since ds has unknown size)
samples_per_patient = 1  # Number of samples per patient
val_metric = "loss"  # Metric to monitor for early stopping
val_mode = "min"  # Mode for early stopping
val_size = 10000  # Number of samples used for validation
learning_rate = 1e-3  # Learning rate for Adam optimizer
epsilon = 0.001

# Model settings
projection_width = 128
temperature = 0.1

# Other settings
seed = 42  # Seed for reproducibility
verbose = 1  # Verbosity level
plot_theme = hk.utils.dark_theme

helia.utils.silence_tensorflow()
hk.utils.setup_plotting(plot_theme)
logger = helia.utils.setup_logger(__name__, level=verbose)

os.makedirs(job_dir, exist_ok=True)
logger.info(f"Job directory: {job_dir}")

INFO     Job directory: /tmp/hk-foundation                                                          1079341004.py:6

Configure datasets

We are going to train our model using two large datasets: the PTB-XL dataset and the large-scale arrhythmia dataset.

datasets = [
    hk.NamedParams(name="lsad", params=dict(path=datasets_dir / "lsad")),
    hk.NamedParams(name="ptbxl", params=dict(path=datasets_dir / "ptbxl")),
]

Download datasets

for dataset in datasets:
    ds = hk.DatasetFactory.get(dataset.name)(**dataset.params)
    ds.download(force=False)

Create data pipeline

Next, we will create a tf.data pipeline by performing the following steps on each dataset:

• Loading dataset class handler
• Leverage task specific data loader for given dataset
• Splittiing the dataset into training and validation sets
• Creating tf.data.Dataset objects for training and validation

After creating all the tf.data.Dataset objects, we will merge them into a single dataset for training and validation.

# Load datasets
dsets = [hk.DatasetFactory.get(ds.name)(**ds.params) for ds in datasets]

dset_weights = np.array([0.5, 0.5])

train_datasets = []
val_datasets = []
for ds in dsets:
    # Create dataloader specific to dataset
    dataloader = hk.tasks.foundation.FoundationTaskFactory.get(ds.name)(
        ds=ds,
        frame_size=frame_size,
        sampling_rate=sampling_rate,
    )

    # Split patients into train and validation sets
    train_patients, val_patients = dataloader.split_train_val_patients()

    # Create train dataset
    train_ds = dataloader.create_dataloader(
        patient_ids=train_patients, samples_per_patient=samples_per_patient, shuffle=True
    )

    # Create validation dataset
    val_ds = dataloader.create_dataloader(
        patient_ids=val_patients, samples_per_patient=samples_per_patient, shuffle=False
    )
    train_datasets.append(train_ds)
    val_datasets.append(val_ds)
# END FOR

# Combine datasets
train_ds = tf.data.Dataset.sample_from_datasets(train_datasets, weights=dset_weights)
val_ds = tf.data.Dataset.sample_from_datasets(val_datasets, weights=dset_weights)

WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1723834403.812869  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.835711  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.835842  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.837216  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.837303  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.837349  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.890424  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.890527  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723834403.890585  712291 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355

Visualize the data

Let’s visualize a sample ECG signal from the synthetic dataset. Note this contains no noise or artifacts. Augmentations will be applied later to generate noisy samples for training.

ecg1, ecg2 = next(iter(train_ds))
ecg1, ecg2 = ecg1.numpy().squeeze(), ecg2.numpy().squeeze()

ts = np.arange(0, len(ecg1)) / sampling_rate
fig, ax = plt.subplots(1, 1, figsize=(9, 4))
ax.plot(ts, ecg1, color=plot_theme.primary_color, lw=3)
ax.plot(ts, ecg2, color=plot_theme.secondary_color, lw=3)
fig.suptitle("Raw ECG Signal")
ax.set_xlabel("Time (s)")
ax.set_ylabel("Amplitude")
fig.tight_layout()
fig.show()

Create augmentation pipeline

To enable self-supervised training to learn useful features from raw ECG signals, we need to create an augmentation pipeline. Each sample will be augmented into two different ways. Using contrastive learning, the model should generate features that are similar for the same sample and different for different samples.

nstdb = hk.datasets.nstdb.NstdbNoise(target_rate=sampling_rate)
noises = np.hstack(
    (nstdb.get_noise(noise_type="bw"), nstdb.get_noise(noise_type="ma"), nstdb.get_noise(noise_type="em"))
)
noises = noises.astype(np.float32)

preprocessor = helia.layers.preprocessing.LayerNormalization1D(epsilon=epsilon, name="LayerNormalization")

augmenter = helia.layers.preprocessing.AugmentationPipeline(
    layers=[
        helia.layers.preprocessing.RandomNoiseDistortion1D(
            sample_rate=sampling_rate, amplitude=(0, 1.0), frequency=(0.5, 1.5), name="BaselineWander"
        ),
        helia.layers.preprocessing.RandomSineWave(
            sample_rate=sampling_rate, amplitude=(0, 0.05), frequency=(45, 50), name="PowerlineNoise"
        ),
        helia.layers.preprocessing.AmplitudeWarp(
            sample_rate=sampling_rate, amplitude=(0.9, 1.1), frequency=(0.5, 1.5), name="AmplitudeWarp"
        ),
        helia.layers.preprocessing.RandomGaussianNoise1D(factor=(0.05, 0.2), name="GaussianNoise"),
        helia.layers.preprocessing.RandomBackgroundNoises1D(
            noises=noises, amplitude=(0.05, 0.2), num_noises=2, name="RandomBackgroundNoises"
        ),
        helia.layers.preprocessing.RandomCutout1D(
            factor=(0.01, 0.05), cutouts=2, fill_mode="constant", fill_value=0.0, name="RandomCutout"
        ),
        helia.layers.preprocessing.RandomCrop1D(duration=frame_size, name="RandomCrop", auto_vectorize=True),
    ],
)

Visualize augmented pair

aug_ecg1 = augmenter(preprocessor(keras.ops.convert_to_tensor(np.reshape(ecg1, (1, -1, 1)))), training=True)
aug_ecg1 = aug_ecg1.numpy().squeeze()

aug_ecg2 = augmenter(preprocessor(keras.ops.convert_to_tensor(np.reshape(ecg2, (1, -1, 1)))), training=True)
aug_ecg2 = aug_ecg2.numpy().squeeze()


ts = np.arange(0, frame_size, 1) / sampling_rate

fig, ax = plt.subplots(1, 1, figsize=(9, 4))
plt.title("Augmented ECG")
plt.plot(ts, aug_ecg1, color=plot_theme.primary_color, lw=2)
plt.plot(ts, aug_ecg2, color=plot_theme.secondary_color, lw=2)
ax.set_xlabel("Time (s)")
ax.set_ylabel("Amplitude")
plt.show()

Create full data pipeline w/ augmentation

We will now create a full data pipeline by extended the original with shuffling, batching, augmentations, and prefetching.

For validation, we will cache a subset of the validation data to speed up the evaluation process.

train_ds = (
    train_ds.shuffle(
        buffer_size=buffer_size,
        reshuffle_each_iteration=True,
    )
    .batch(
        batch_size=batch_size,
        drop_remainder=True,
        num_parallel_calls=tf.data.AUTOTUNE,
    )
    .map(
        lambda x1, x2: {
            helia.trainers.SimCLRTrainer.SAMPLES: x1,
            helia.trainers.SimCLRTrainer.AUG_SAMPLES_0: augmenter(preprocessor(x1), training=True),
            helia.trainers.SimCLRTrainer.AUG_SAMPLES_1: augmenter(preprocessor(x2), training=True),
        },
        num_parallel_calls=tf.data.AUTOTUNE,
    )
    .prefetch(tf.data.AUTOTUNE)
)

val_ds = (
    val_ds.batch(
        batch_size=batch_size,
        drop_remainder=True,
        num_parallel_calls=tf.data.AUTOTUNE,
    )
    .map(
        lambda x1, x2: {
            helia.trainers.SimCLRTrainer.SAMPLES: x1,
            helia.trainers.SimCLRTrainer.AUG_SAMPLES_0: augmenter(preprocessor(x1), training=True),
            helia.trainers.SimCLRTrainer.AUG_SAMPLES_1: augmenter(preprocessor(x2), training=True),
        },
        num_parallel_calls=tf.data.AUTOTUNE,
    )
    .prefetch(tf.data.AUTOTUNE)
)

# Cache the validation dataset
val_ds = val_ds.take(val_size // batch_size).cache()

Define encoder model

For this task, we are going to leverage a customized EfficientNetV2 model architecture for the encoder that is smaller and can handle 1D signals. The model consists of 5 main MBConv blocks with a global average pooling layer and a dense layer for classification.

inputs = keras.Input(shape=(frame_size, 1), name="input")

encoder_params = dict(
    input_filters=24,
    input_kernel_size=(1, 9),
    input_strides=(1, 2),
    blocks=[
        dict(filters=32, depth=2, kernel_size=(1, 9), strides=(1, 2), ex_ratio=1, se_ratio=4, norm="layer"),
        dict(filters=48, depth=2, kernel_size=(1, 9), strides=(1, 2), ex_ratio=1, se_ratio=4, norm="layer"),
        dict(filters=64, depth=2, kernel_size=(1, 9), strides=(1, 2), ex_ratio=1, se_ratio=4, norm="layer"),
        dict(filters=80, depth=1, kernel_size=(1, 9), strides=(1, 2), ex_ratio=1, se_ratio=4, norm="layer"),
        dict(filters=96, depth=1, kernel_size=(1, 9), strides=(1, 2), ex_ratio=1, se_ratio=4, norm="layer"),
    ],
    output_filters=projection_width,
    include_top=True,
)

encoder = helia.models.efficientnet.efficientnetv2_from_object(x=inputs, params=encoder_params, num_classes=None)

Visualize the model

Let’s view the encoder to understand the architecture better.

encoder.summary(print_fn=logger.info, layer_range=("input", encoder.layers[10].name))
flops = helia.metrics.flops.get_flops(encoder, batch_size=1, fpath=os.devnull)
logger.info(f"Computation: {flops / 1e6:0.2f} MFLOPs")
encoder_output = encoder(inputs)

Saved output

INFO     Model: "EfficientNetV2"                                                               summary_utils.py:389
         ┏━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━┓
         ┃ Layer (type)        ┃ Output Shape      ┃    Param # ┃ Connected to      ┃
         ┡━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━┩
         │ input (InputLayer)  │ (None, 800, 1)    │          0 │ -                 │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ reshape (Reshape)   │ (None, 1, 800, 1) │          0 │ input[0][0]       │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stem.conv (Conv2D)  │ (None, 1, 400,    │        216 │ reshape[0][0]     │
         │                     │ 24)               │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stem.bn             │ (None, 1, 400,    │         96 │ stem.conv[0][0]   │
         │ (BatchNormalizatio… │ 24)               │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stem.act            │ (None, 1, 400,    │          0 │ stem.bn[0][0]     │
         │ (Activation)        │ 24)               │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stage1.mbconv1.dp   │ (None, 1, 400,    │        216 │ stem.act[0][0]    │
         │ (DepthwiseConv2D)   │ 24)               │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stage1.mbconv1.dp.… │ (None, 1, 400,    │         96 │ stage1.mbconv1.d… │
         │ (BatchNormalizatio… │ 24)               │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stage1.mbconv1.dp.… │ (None, 1, 400,    │          0 │ stage1.mbconv1.d… │
         │ (Activation)        │ 24)               │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ max_pooling2d       │ (None, 1, 200,    │          0 │ stage1.mbconv1.d… │
         │ (MaxPooling2D)      │ 24)               │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stage1.mbconv1.se.… │ (None, 1, 1, 24)  │          0 │ max_pooling2d[0]… │
         │ (GlobalAveragePool… │                   │            │                   │
         ├─────────────────────┼───────────────────┼────────────┼───────────────────┤
         │ stage1.mbconv1.se.… │ (None, 1, 1, 6)   │        150 │ stage1.mbconv1.s… │
         │ (Conv2D)            │                   │            │                   │
         └─────────────────────┴───────────────────┴────────────┴───────────────────┘
          Total params: 57,066 (222.91 KB)
          Trainable params: 55,050 (215.04 KB)
          Non-trainable params: 2,016 (7.88 KB)

INFO     Computation: 4.17 MFLOPs                                                                    909537700.py:3

projector_input = encoder_output
projector_output = keras.layers.Dense(projection_width, activation="relu6")(projector_input)
projector_output = keras.layers.Dense(projection_width)(projector_output)
projector = keras.Model(inputs=projector_input, outputs=projector_output, name="projector")
flops = helia.metrics.flops.get_flops(projector, batch_size=1, fpath=os.devnull)
projector.summary(print_fn=logger.info)
logger.debug(f"Projector requires {flops / 1e6:0.2f} MFLOPS")

Saved output

INFO     Model: "projector"                                                                    summary_utils.py:389
         ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
         ┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
         ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
         │ keras_tensor_109CLONE           │ (None, 128)            │             0 │
         │ (InputLayer)                    │                        │               │
         ├─────────────────────────────────┼────────────────────────┼───────────────┤
         │ dense (Dense)                   │ (None, 128)            │        16,512 │
         ├─────────────────────────────────┼────────────────────────┼───────────────┤
         │ dense_1 (Dense)                 │ (None, 128)            │        16,512 │
         └─────────────────────────────────┴────────────────────────┴───────────────┘
          Total params: 33,024 (129.00 KB)
          Trainable params: 33,024 (129.00 KB)
          Non-trainable params: 0 (0.00 B)

Create a SimCLR model to train

model = helia.trainers.SimCLRTrainer(
    encoder=encoder,
    augmenter=None,  # We augment in the data pipeline
    projector=projector,
)

Compile the model

We will compile the model using Adam optimizer with cosine learning rate scheduler and custom cosine similarity loss function. We will also attach metrics and callbacks to monitor the training process.

def get_scheduler():
    return keras.optimizers.schedules.CosineDecay(
        initial_learning_rate=learning_rate,
        decay_steps=steps_per_epoch * epochs,
    )


optimizer = keras.optimizers.Adam(get_scheduler())
loss = helia.losses.simclr.SimCLRLoss(temperature=temperature)

metrics = [
    keras.metrics.MeanSquaredError(name="mse"),
    keras.metrics.CosineSimilarity(name="cos"),
]

model_callbacks = [
    keras.callbacks.EarlyStopping(
        monitor=f"val_{val_metric}",
        patience=max(int(0.25 * epochs), 1),
        mode=val_mode,
        restore_best_weights=True,
        verbose=verbose - 1,
    ),
    keras.callbacks.ModelCheckpoint(
        filepath=str(model_file), monitor=f"val_{val_metric}", save_best_only=True, mode=val_mode, verbose=verbose - 1
    ),
    keras.callbacks.CSVLogger(job_dir / "history.csv"),
]
if helia.utils.env_flag("TENSORBOARD"):
    model_callbacks.append(
        keras.callbacks.TensorBoard(
            log_dir=job_dir,
            write_steps_per_second=True,
        )
    )

model.compile(
    encoder_optimizer=optimizer,
    encoder_loss=loss,
    encoder_metrics=metrics,
)

Train the model

history = model.fit(
    train_ds,
    steps_per_epoch=steps_per_epoch,
    verbose=verbose,
    epochs=epochs,
    validation_data=val_ds,
    callbacks=model_callbacks,
)

Epoch 1/150

2024-08-16 18:54:13.839587: E tensorflow/core/util/util.cc:131] oneDNN supports DT_INT32 only on platforms with AVX-512. Falling back to the default Eigen-based implementation if present.
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1723834463.457755  712486 service.cc:146] XLA service 0x78321c02f130 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices:
I0000 00:00:1723834463.457771  712486 service.cc:154]   StreamExecutor device (0): NVIDIA GeForce RTX 4090, Compute Capability 8.9

 1/25 ━━━━━━━━━━━━━━━━━━━━ 13:39 34s/step - cos: 0.5956 - loss: 15.6336 - mse: 0.2352

I0000 00:00:1723834487.410060  712486 device_compiler.h:188] Compiled cluster using XLA!  This line is logged at most once for the lifetime of the process.

Saved output

25/25 ━━━━━━━━━━━━━━━━━━━━ 67s 1s/step - cos: 0.6157 - loss: 14.9098 - mse: 0.2319 - val_cos: 0.6770 - val_loss: 12.6894 - val_mse: 0.2770
Epoch 2/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 6s 228ms/step - cos: 0.6928 - loss: 12.2036 - mse: 0.2814 - val_cos: 0.7274 - val_loss: 11.2915 - val_mse: 0.2797
Epoch 3/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 183ms/step - cos: 0.7322 - loss: 11.1098 - mse: 0.2783 - val_cos: 0.7428 - val_loss: 10.5851 - val_mse: 0.2743
Epoch 4/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 185ms/step - cos: 0.7449 - loss: 10.4056 - mse: 0.2715 - val_cos: 0.7517 - val_loss: 9.9517 - val_mse: 0.2724
Epoch 5/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 184ms/step - cos: 0.7523 - loss: 9.8387 - mse: 0.2707 - val_cos: 0.7568 - val_loss: 9.5624 - val_mse: 0.2703
Epoch 6/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 183ms/step - cos: 0.7548 - loss: 9.5425 - mse: 0.2690 - val_cos: 0.7591 - val_loss: 9.2802 - val_mse: 0.2633
Epoch 7/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7587 - loss: 9.2489 - mse: 0.2617 - val_cos: 0.7604 - val_loss: 9.0665 - val_mse: 0.2585
Epoch 8/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 185ms/step - cos: 0.7604 - loss: 9.0068 - mse: 0.2579 - val_cos: 0.7623 - val_loss: 8.8123 - val_mse: 0.2564
Epoch 9/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 182ms/step - cos: 0.7618 - loss: 8.7503 - mse: 0.2550 - val_cos: 0.7628 - val_loss: 8.5923 - val_mse: 0.2538
Epoch 10/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7621 - loss: 8.5523 - mse: 0.2549 - val_cos: 0.7622 - val_loss: 8.4131 - val_mse: 0.2523
Epoch 11/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 186ms/step - cos: 0.7624 - loss: 8.3957 - mse: 0.2511 - val_cos: 0.7635 - val_loss: 8.2374 - val_mse: 0.2495
Epoch 12/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7637 - loss: 8.2014 - mse: 0.2498 - val_cos: 0.7641 - val_loss: 8.0899 - val_mse: 0.2478
Epoch 13/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7639 - loss: 8.0752 - mse: 0.2456 - val_cos: 0.7645 - val_loss: 7.9631 - val_mse: 0.2451
Epoch 14/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7638 - loss: 7.9306 - mse: 0.2457 - val_cos: 0.7665 - val_loss: 7.8171 - val_mse: 0.2403
Epoch 15/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7642 - loss: 7.8377 - mse: 0.2410 - val_cos: 0.7663 - val_loss: 7.7359 - val_mse: 0.2385
Epoch 16/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 185ms/step - cos: 0.7658 - loss: 7.6886 - mse: 0.2378 - val_cos: 0.7676 - val_loss: 7.6044 - val_mse: 0.2350
Epoch 17/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 188ms/step - cos: 0.7643 - loss: 7.6359 - mse: 0.2369 - val_cos: 0.7659 - val_loss: 7.5199 - val_mse: 0.2345
Epoch 18/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 184ms/step - cos: 0.7660 - loss: 7.5126 - mse: 0.2329 - val_cos: 0.7680 - val_loss: 7.4207 - val_mse: 0.2301
Epoch 19/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7651 - loss: 7.4191 - mse: 0.2304 - val_cos: 0.7682 - val_loss: 7.3130 - val_mse: 0.2268
Epoch 20/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7651 - loss: 7.3419 - mse: 0.2291 - val_cos: 0.7664 - val_loss: 7.2225 - val_mse: 0.2272
Epoch 21/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7657 - loss: 7.2691 - mse: 0.2277 - val_cos: 0.7665 - val_loss: 7.1630 - val_mse: 0.2245
Epoch 22/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7640 - loss: 7.2177 - mse: 0.2248 - val_cos: 0.7662 - val_loss: 7.0724 - val_mse: 0.2219
Epoch 23/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7679 - loss: 7.0468 - mse: 0.2195 - val_cos: 0.7680 - val_loss: 6.9664 - val_mse: 0.2184
Epoch 24/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7667 - loss: 6.9840 - mse: 0.2171 - val_cos: 0.7669 - val_loss: 6.9237 - val_mse: 0.2178
Epoch 25/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7662 - loss: 6.9243 - mse: 0.2169 - val_cos: 0.7666 - val_loss: 6.8773 - val_mse: 0.2136
Epoch 26/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7655 - loss: 6.8518 - mse: 0.2143 - val_cos: 0.7668 - val_loss: 6.7758 - val_mse: 0.2124
Epoch 27/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7667 - loss: 6.7623 - mse: 0.2110 - val_cos: 0.7664 - val_loss: 6.7287 - val_mse: 0.2101
Epoch 28/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 184ms/step - cos: 0.7676 - loss: 6.7556 - mse: 0.2077 - val_cos: 0.7678 - val_loss: 6.6686 - val_mse: 0.2059
Epoch 29/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 191ms/step - cos: 0.7671 - loss: 6.6939 - mse: 0.2065 - val_cos: 0.7670 - val_loss: 6.6024 - val_mse: 0.2012
Epoch 30/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 186ms/step - cos: 0.7660 - loss: 6.6050 - mse: 0.2017 - val_cos: 0.7678 - val_loss: 6.5662 - val_mse: 0.1994
Epoch 31/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7667 - loss: 6.5798 - mse: 0.2007 - val_cos: 0.7677 - val_loss: 6.5317 - val_mse: 0.1979
Epoch 32/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7669 - loss: 6.5304 - mse: 0.1988 - val_cos: 0.7691 - val_loss: 6.4457 - val_mse: 0.1951
Epoch 33/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 184ms/step - cos: 0.7671 - loss: 6.4863 - mse: 0.1965 - val_cos: 0.7678 - val_loss: 6.4010 - val_mse: 0.1941
Epoch 34/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 185ms/step - cos: 0.7666 - loss: 6.4082 - mse: 0.1940 - val_cos: 0.7678 - val_loss: 6.3757 - val_mse: 0.1933
Epoch 35/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 189ms/step - cos: 0.7677 - loss: 6.3730 - mse: 0.1909 - val_cos: 0.7692 - val_loss: 6.3082 - val_mse: 0.1881
Epoch 36/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7677 - loss: 6.3429 - mse: 0.1880 - val_cos: 0.7681 - val_loss: 6.2834 - val_mse: 0.1878
Epoch 37/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7671 - loss: 6.2941 - mse: 0.1861 - val_cos: 0.7697 - val_loss: 6.2232 - val_mse: 0.1849
Epoch 38/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7670 - loss: 6.2765 - mse: 0.1862 - val_cos: 0.7684 - val_loss: 6.1971 - val_mse: 0.1828
Epoch 39/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7664 - loss: 6.2457 - mse: 0.1831 - val_cos: 0.7686 - val_loss: 6.1664 - val_mse: 0.1812
Epoch 40/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7698 - loss: 6.1896 - mse: 0.1797 - val_cos: 0.7696 - val_loss: 6.1331 - val_mse: 0.1777
Epoch 41/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7670 - loss: 6.1657 - mse: 0.1788 - val_cos: 0.7701 - val_loss: 6.1057 - val_mse: 0.1760
Epoch 42/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7690 - loss: 6.0656 - mse: 0.1760 - val_cos: 0.7693 - val_loss: 6.0554 - val_mse: 0.1738
Epoch 43/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7682 - loss: 6.0856 - mse: 0.1745 - val_cos: 0.7676 - val_loss: 6.0448 - val_mse: 0.1722
Epoch 44/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7665 - loss: 6.0528 - mse: 0.1724 - val_cos: 0.7683 - val_loss: 6.0189 - val_mse: 0.1710
Epoch 45/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 186ms/step - cos: 0.7691 - loss: 6.0253 - mse: 0.1699 - val_cos: 0.7685 - val_loss: 5.9979 - val_mse: 0.1665
Epoch 46/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7679 - loss: 5.9833 - mse: 0.1665 - val_cos: 0.7681 - val_loss: 5.9251 - val_mse: 0.1675
Epoch 47/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7680 - loss: 5.9603 - mse: 0.1664 - val_cos: 0.7698 - val_loss: 5.9433 - val_mse: 0.1651
Epoch 48/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7701 - loss: 5.9152 - mse: 0.1653 - val_cos: 0.7703 - val_loss: 5.9054 - val_mse: 0.1632
Epoch 49/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7682 - loss: 5.8829 - mse: 0.1632 - val_cos: 0.7692 - val_loss: 5.8782 - val_mse: 0.1611
Epoch 50/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7683 - loss: 5.8843 - mse: 0.1602 - val_cos: 0.7705 - val_loss: 5.8711 - val_mse: 0.1598
Epoch 51/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7687 - loss: 5.8453 - mse: 0.1596 - val_cos: 0.7680 - val_loss: 5.8498 - val_mse: 0.1603
Epoch 52/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7685 - loss: 5.8001 - mse: 0.1577 - val_cos: 0.7699 - val_loss: 5.7597 - val_mse: 0.1563
Epoch 53/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 173ms/step - cos: 0.7685 - loss: 5.7991 - mse: 0.1569 - val_cos: 0.7682 - val_loss: 5.7875 - val_mse: 0.1550
Epoch 54/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7680 - loss: 5.7853 - mse: 0.1547 - val_cos: 0.7707 - val_loss: 5.7683 - val_mse: 0.1524
Epoch 55/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7691 - loss: 5.7863 - mse: 0.1526 - val_cos: 0.7705 - val_loss: 5.7501 - val_mse: 0.1514
Epoch 56/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7692 - loss: 5.7813 - mse: 0.1511 - val_cos: 0.7694 - val_loss: 5.7335 - val_mse: 0.1502
Epoch 57/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7699 - loss: 5.7194 - mse: 0.1498 - val_cos: 0.7694 - val_loss: 5.7055 - val_mse: 0.1492
Epoch 58/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7704 - loss: 5.6757 - mse: 0.1483 - val_cos: 0.7700 - val_loss: 5.6847 - val_mse: 0.1472
Epoch 59/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7690 - loss: 5.7145 - mse: 0.1485 - val_cos: 0.7699 - val_loss: 5.6508 - val_mse: 0.1456
Epoch 60/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7673 - loss: 5.6932 - mse: 0.1473 - val_cos: 0.7707 - val_loss: 5.6501 - val_mse: 0.1436
Epoch 61/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7694 - loss: 5.6243 - mse: 0.1447 - val_cos: 0.7689 - val_loss: 5.6231 - val_mse: 0.1428
Epoch 62/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7684 - loss: 5.6316 - mse: 0.1423 - val_cos: 0.7688 - val_loss: 5.5892 - val_mse: 0.1425
Epoch 63/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7677 - loss: 5.6548 - mse: 0.1434 - val_cos: 0.7710 - val_loss: 5.5681 - val_mse: 0.1399
Epoch 64/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 174ms/step - cos: 0.7680 - loss: 5.6244 - mse: 0.1421 - val_cos: 0.7698 - val_loss: 5.5903 - val_mse: 0.1400
Epoch 65/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7681 - loss: 5.6289 - mse: 0.1406 - val_cos: 0.7687 - val_loss: 5.5534 - val_mse: 0.1409
Epoch 66/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7688 - loss: 5.5736 - mse: 0.1403 - val_cos: 0.7702 - val_loss: 5.5605 - val_mse: 0.1376
Epoch 67/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7700 - loss: 5.5189 - mse: 0.1380 - val_cos: 0.7702 - val_loss: 5.5123 - val_mse: 0.1363
Epoch 68/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7687 - loss: 5.5515 - mse: 0.1369 - val_cos: 0.7691 - val_loss: 5.5241 - val_mse: 0.1370
Epoch 69/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7702 - loss: 5.5545 - mse: 0.1357 - val_cos: 0.7699 - val_loss: 5.4955 - val_mse: 0.1362
Epoch 70/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7690 - loss: 5.4659 - mse: 0.1352 - val_cos: 0.7703 - val_loss: 5.4853 - val_mse: 0.1337
Epoch 71/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7681 - loss: 5.4991 - mse: 0.1344 - val_cos: 0.7683 - val_loss: 5.4826 - val_mse: 0.1333
Epoch 72/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7681 - loss: 5.4836 - mse: 0.1327 - val_cos: 0.7693 - val_loss: 5.4592 - val_mse: 0.1316
Epoch 73/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7702 - loss: 5.4963 - mse: 0.1315 - val_cos: 0.7706 - val_loss: 5.4468 - val_mse: 0.1308
Epoch 74/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7696 - loss: 5.3915 - mse: 0.1302 - val_cos: 0.7698 - val_loss: 5.4245 - val_mse: 0.1298
Epoch 75/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7706 - loss: 5.4288 - mse: 0.1288 - val_cos: 0.7695 - val_loss: 5.3944 - val_mse: 0.1290
Epoch 76/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7676 - loss: 5.4072 - mse: 0.1294 - val_cos: 0.7708 - val_loss: 5.3982 - val_mse: 0.1279
Epoch 77/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7688 - loss: 5.3941 - mse: 0.1292 - val_cos: 0.7698 - val_loss: 5.4304 - val_mse: 0.1282
Epoch 78/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7692 - loss: 5.4147 - mse: 0.1282 - val_cos: 0.7707 - val_loss: 5.3892 - val_mse: 0.1265
Epoch 79/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7703 - loss: 5.3819 - mse: 0.1260 - val_cos: 0.7696 - val_loss: 5.3757 - val_mse: 0.1265
Epoch 80/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7691 - loss: 5.3872 - mse: 0.1262 - val_cos: 0.7688 - val_loss: 5.3662 - val_mse: 0.1262
Epoch 81/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7701 - loss: 5.3129 - mse: 0.1245 - val_cos: 0.7701 - val_loss: 5.3568 - val_mse: 0.1245
Epoch 82/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7690 - loss: 5.3379 - mse: 0.1245 - val_cos: 0.7694 - val_loss: 5.3354 - val_mse: 0.1242
Epoch 83/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7687 - loss: 5.3438 - mse: 0.1245 - val_cos: 0.7719 - val_loss: 5.3168 - val_mse: 0.1228
Epoch 84/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7681 - loss: 5.3040 - mse: 0.1235 - val_cos: 0.7715 - val_loss: 5.3151 - val_mse: 0.1220
Epoch 85/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 183ms/step - cos: 0.7685 - loss: 5.3504 - mse: 0.1237 - val_cos: 0.7695 - val_loss: 5.3025 - val_mse: 0.1231
Epoch 86/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 174ms/step - cos: 0.7685 - loss: 5.3010 - mse: 0.1224 - val_cos: 0.7705 - val_loss: 5.3040 - val_mse: 0.1212
Epoch 87/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 183ms/step - cos: 0.7702 - loss: 5.2738 - mse: 0.1207 - val_cos: 0.7702 - val_loss: 5.2965 - val_mse: 0.1218
Epoch 88/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7689 - loss: 5.2917 - mse: 0.1206 - val_cos: 0.7699 - val_loss: 5.2888 - val_mse: 0.1208
Epoch 89/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7696 - loss: 5.3199 - mse: 0.1208 - val_cos: 0.7689 - val_loss: 5.2589 - val_mse: 0.1208
Epoch 90/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7682 - loss: 5.2979 - mse: 0.1212 - val_cos: 0.7711 - val_loss: 5.2490 - val_mse: 0.1197
Epoch 91/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 174ms/step - cos: 0.7701 - loss: 5.2316 - mse: 0.1198 - val_cos: 0.7712 - val_loss: 5.2642 - val_mse: 0.1194
Epoch 92/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7691 - loss: 5.2812 - mse: 0.1199 - val_cos: 0.7704 - val_loss: 5.2346 - val_mse: 0.1190
Epoch 93/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7688 - loss: 5.2679 - mse: 0.1191 - val_cos: 0.7693 - val_loss: 5.2493 - val_mse: 0.1184
Epoch 94/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7690 - loss: 5.2947 - mse: 0.1185 - val_cos: 0.7703 - val_loss: 5.2468 - val_mse: 0.1179
Epoch 95/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7697 - loss: 5.2224 - mse: 0.1174 - val_cos: 0.7699 - val_loss: 5.2175 - val_mse: 0.1174
Epoch 96/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7679 - loss: 5.2491 - mse: 0.1178 - val_cos: 0.7706 - val_loss: 5.2031 - val_mse: 0.1174
Epoch 97/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7704 - loss: 5.2146 - mse: 0.1168 - val_cos: 0.7690 - val_loss: 5.1959 - val_mse: 0.1174
Epoch 98/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7698 - loss: 5.1986 - mse: 0.1171 - val_cos: 0.7694 - val_loss: 5.1951 - val_mse: 0.1169
Epoch 99/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7685 - loss: 5.1510 - mse: 0.1173 - val_cos: 0.7692 - val_loss: 5.2092 - val_mse: 0.1164
Epoch 100/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 174ms/step - cos: 0.7700 - loss: 5.1515 - mse: 0.1160 - val_cos: 0.7696 - val_loss: 5.2035 - val_mse: 0.1160
Epoch 101/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7685 - loss: 5.2375 - mse: 0.1161 - val_cos: 0.7713 - val_loss: 5.1944 - val_mse: 0.1159
Epoch 102/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7689 - loss: 5.1949 - mse: 0.1157 - val_cos: 0.7705 - val_loss: 5.1947 - val_mse: 0.1150
Epoch 103/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7692 - loss: 5.1795 - mse: 0.1150 - val_cos: 0.7703 - val_loss: 5.1872 - val_mse: 0.1147
Epoch 104/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7689 - loss: 5.1701 - mse: 0.1155 - val_cos: 0.7706 - val_loss: 5.1679 - val_mse: 0.1149
Epoch 105/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 173ms/step - cos: 0.7685 - loss: 5.1989 - mse: 0.1154 - val_cos: 0.7689 - val_loss: 5.1848 - val_mse: 0.1153
Epoch 106/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7691 - loss: 5.1822 - mse: 0.1145 - val_cos: 0.7703 - val_loss: 5.1448 - val_mse: 0.1142
Epoch 107/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7695 - loss: 5.1392 - mse: 0.1146 - val_cos: 0.7708 - val_loss: 5.1465 - val_mse: 0.1139
Epoch 108/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7692 - loss: 5.2153 - mse: 0.1145 - val_cos: 0.7705 - val_loss: 5.1640 - val_mse: 0.1136
Epoch 109/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7690 - loss: 5.1583 - mse: 0.1140 - val_cos: 0.7689 - val_loss: 5.1519 - val_mse: 0.1142
Epoch 110/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7700 - loss: 5.1384 - mse: 0.1134 - val_cos: 0.7688 - val_loss: 5.1593 - val_mse: 0.1139
Epoch 111/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7695 - loss: 5.1484 - mse: 0.1134 - val_cos: 0.7709 - val_loss: 5.1299 - val_mse: 0.1132
Epoch 112/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7699 - loss: 5.1683 - mse: 0.1126 - val_cos: 0.7698 - val_loss: 5.1275 - val_mse: 0.1131
Epoch 113/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 171ms/step - cos: 0.7694 - loss: 5.1230 - mse: 0.1123 - val_cos: 0.7703 - val_loss: 5.1364 - val_mse: 0.1121
Epoch 114/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7699 - loss: 5.1434 - mse: 0.1129 - val_cos: 0.7691 - val_loss: 5.1523 - val_mse: 0.1132
Epoch 115/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7686 - loss: 5.1086 - mse: 0.1123 - val_cos: 0.7695 - val_loss: 5.1388 - val_mse: 0.1123
Epoch 116/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7700 - loss: 5.1089 - mse: 0.1121 - val_cos: 0.7698 - val_loss: 5.1056 - val_mse: 0.1125
Epoch 117/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7708 - loss: 5.0898 - mse: 0.1122 - val_cos: 0.7715 - val_loss: 5.1041 - val_mse: 0.1120
Epoch 118/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 174ms/step - cos: 0.7688 - loss: 5.1048 - mse: 0.1123 - val_cos: 0.7698 - val_loss: 5.1103 - val_mse: 0.1117
Epoch 119/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7690 - loss: 5.1339 - mse: 0.1123 - val_cos: 0.7707 - val_loss: 5.0992 - val_mse: 0.1114
Epoch 120/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 174ms/step - cos: 0.7707 - loss: 5.0996 - mse: 0.1114 - val_cos: 0.7691 - val_loss: 5.1405 - val_mse: 0.1121
Epoch 121/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7706 - loss: 5.0921 - mse: 0.1117 - val_cos: 0.7705 - val_loss: 5.1123 - val_mse: 0.1117
Epoch 122/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7694 - loss: 5.1215 - mse: 0.1118 - val_cos: 0.7730 - val_loss: 5.1020 - val_mse: 0.1101
Epoch 123/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 173ms/step - cos: 0.7694 - loss: 5.1185 - mse: 0.1113 - val_cos: 0.7713 - val_loss: 5.1067 - val_mse: 0.1113
Epoch 124/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 175ms/step - cos: 0.7676 - loss: 5.1077 - mse: 0.1121 - val_cos: 0.7699 - val_loss: 5.1011 - val_mse: 0.1119
Epoch 125/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7692 - loss: 5.1002 - mse: 0.1116 - val_cos: 0.7722 - val_loss: 5.0920 - val_mse: 0.1106
Epoch 126/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7700 - loss: 5.0861 - mse: 0.1109 - val_cos: 0.7708 - val_loss: 5.0755 - val_mse: 0.1110
Epoch 127/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7687 - loss: 5.1179 - mse: 0.1116 - val_cos: 0.7701 - val_loss: 5.0813 - val_mse: 0.1113
Epoch 128/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7691 - loss: 5.0677 - mse: 0.1114 - val_cos: 0.7712 - val_loss: 5.0920 - val_mse: 0.1111
Epoch 129/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 182ms/step - cos: 0.7693 - loss: 5.0750 - mse: 0.1109 - val_cos: 0.7697 - val_loss: 5.1003 - val_mse: 0.1117
Epoch 130/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7696 - loss: 5.1088 - mse: 0.1111 - val_cos: 0.7700 - val_loss: 5.1090 - val_mse: 0.1112
Epoch 131/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7710 - loss: 5.0843 - mse: 0.1103 - val_cos: 0.7703 - val_loss: 5.0754 - val_mse: 0.1116
Epoch 132/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7694 - loss: 5.0816 - mse: 0.1113 - val_cos: 0.7695 - val_loss: 5.0800 - val_mse: 0.1109
Epoch 133/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 183ms/step - cos: 0.7690 - loss: 5.0900 - mse: 0.1110 - val_cos: 0.7691 - val_loss: 5.1067 - val_mse: 0.1107
Epoch 134/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7687 - loss: 5.1286 - mse: 0.1116 - val_cos: 0.7706 - val_loss: 5.0937 - val_mse: 0.1104
Epoch 135/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7699 - loss: 5.0638 - mse: 0.1106 - val_cos: 0.7692 - val_loss: 5.1000 - val_mse: 0.1115
Epoch 136/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7696 - loss: 5.0928 - mse: 0.1109 - val_cos: 0.7711 - val_loss: 5.1196 - val_mse: 0.1105
Epoch 137/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7688 - loss: 5.0861 - mse: 0.1113 - val_cos: 0.7689 - val_loss: 5.0883 - val_mse: 0.1112
Epoch 138/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7705 - loss: 5.0776 - mse: 0.1104 - val_cos: 0.7706 - val_loss: 5.0706 - val_mse: 0.1108
Epoch 139/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 180ms/step - cos: 0.7708 - loss: 5.0805 - mse: 0.1106 - val_cos: 0.7694 - val_loss: 5.0848 - val_mse: 0.1114
Epoch 140/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 183ms/step - cos: 0.7709 - loss: 5.0705 - mse: 0.1100 - val_cos: 0.7696 - val_loss: 5.1025 - val_mse: 0.1108
Epoch 141/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 184ms/step - cos: 0.7689 - loss: 5.0755 - mse: 0.1111 - val_cos: 0.7695 - val_loss: 5.0697 - val_mse: 0.1109
Epoch 142/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 176ms/step - cos: 0.7693 - loss: 5.0860 - mse: 0.1110 - val_cos: 0.7698 - val_loss: 5.0901 - val_mse: 0.1108
Epoch 143/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 182ms/step - cos: 0.7703 - loss: 5.0945 - mse: 0.1105 - val_cos: 0.7703 - val_loss: 5.0849 - val_mse: 0.1110
Epoch 144/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 181ms/step - cos: 0.7682 - loss: 5.0852 - mse: 0.1109 - val_cos: 0.7705 - val_loss: 5.0823 - val_mse: 0.1107
Epoch 145/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 183ms/step - cos: 0.7700 - loss: 5.0820 - mse: 0.1099 - val_cos: 0.7691 - val_loss: 5.0824 - val_mse: 0.1114
Epoch 146/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 184ms/step - cos: 0.7698 - loss: 5.1090 - mse: 0.1105 - val_cos: 0.7697 - val_loss: 5.0849 - val_mse: 0.1113
Epoch 147/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 177ms/step - cos: 0.7699 - loss: 5.0637 - mse: 0.1106 - val_cos: 0.7702 - val_loss: 5.0996 - val_mse: 0.1107
Epoch 148/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 179ms/step - cos: 0.7708 - loss: 5.0515 - mse: 0.1101 - val_cos: 0.7695 - val_loss: 5.0811 - val_mse: 0.1111
Epoch 149/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 5s 192ms/step - cos: 0.7692 - loss: 5.0959 - mse: 0.1111 - val_cos: 0.7705 - val_loss: 5.1056 - val_mse: 0.1106
Epoch 150/150
25/25 ━━━━━━━━━━━━━━━━━━━━ 4s 178ms/step - cos: 0.7685 - loss: 5.1008 - mse: 0.1110 - val_cos: 0.7713 - val_loss: 5.0885 - val_mse: 0.1105

Visualize training history

Let’s visualize the training history to understand the model’s performance during training. This will help to ensure the model is learning and not under or overfitting.

fig, _ = helia.plotting.plot_history_metrics(
    history.history,
    metrics=["loss", "cos"],
    title="Training History",
    colors=[plot_theme.primary_color, plot_theme.secondary_color],
    stack=True,
    figsize=(9, 5),
)
fig.tight_layout()
fig.show()

Model evaluation

Now that we have trained the model, we will evaluate the model on the test dataset. The model’s built-in evaluate method will be used to calculate the loss and metrics on the dataset.

# Convert validation dataset to numpy arrays
test_x1, test_x2 = [], []
for inputs in val_ds.as_numpy_iterator():
    test_x1.append(inputs[helia.trainers.SimCLRTrainer.AUG_SAMPLES_0])
    test_x2.append(inputs[helia.trainers.SimCLRTrainer.AUG_SAMPLES_1])
test_x1 = np.concatenate(test_x1)
test_x2 = np.concatenate(test_x2)

test_y1 = encoder.predict(test_x1)
test_y2 = encoder.predict(test_x2)

288/288 ━━━━━━━━━━━━━━━━━━━━ 1s 923us/step
288/288 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step

rst = helia.metrics.compute_metrics(metrics, test_y1, test_y2)
logger.info("[VAL SET] " + ", ".join([f"{k.upper()}={v:.4f}" for k, v in rst.items()]))

INFO     [VAL SET] MSE=0.0132, COS=0.9683                                                           4122487501.py:2

Export model to TF Lite / TFLM

Once we have trained and evaluated the model, we need to export the model into a format that can be used for inference on the edge. Currently, we export the model to TensorFlow Lite flatbuffer format. This will also generate a C header file that can be used with TensorFlow Lite for Microcontrollers (TFLM).

For this model, we will export as a 32-bit floating point model.

NOTE: We utilize CONCRETE mode to lower the model to concrete functions before converting. This is because TF (MLIR) fails to properly lower the dilated convolutional layers.

converter = helia.converters.tflite.TfLiteKerasConverter(model=encoder)

# Redirect stdout and stderr to devnull since TFLite converter is very verbose
with open(os.devnull, "w") as devnull:
    with contextlib.redirect_stdout(devnull), contextlib.redirect_stderr(devnull):
        tflite_content = converter.convert(
            test_x=test_x1, quantization="FP32", io_type="float32", mode="KERAS", strict=False, verbose=verbose
        )

W0000 00:00:1723835186.987318  712291 tf_tfl_flatbuffer_helpers.cc:392] Ignored output_format.
W0000 00:00:1723835186.987329  712291 tf_tfl_flatbuffer_helpers.cc:395] Ignored drop_control_dependency.

Save TFLite model as both a file and C header

converter.export(tflite_path=job_dir / "model.tflite")

converter.export_header(
    header_path=job_dir / "model.h",
    name="model",
)

Evaluate TFLite model against TensorFlow model

We will instantiate a tflite interpreter and evaluate the model on the test dataset. This will help us ensure that the model has been exported correctly and is ready for deployment.

tflite = helia.interpreters.tflite.TfLiteKerasInterpreter(tflite_content)
tflite.compile()

INFO: Created TensorFlow Lite XNNPACK delegate for CPU.

converter = helia.converters.tflite.TfLiteKerasConverter(model=encoder)

tflite_content = converter.convert(
    test_x=test_x1, quantization="FP32", io_type="float32", mode="KERAS", strict=False, verbose=verbose
)

Saved output

Saved artifact at '/tmp/tmpserse9cu'. The following endpoints are available:

* Endpoint 'serve'
  args_0 (POSITIONAL_ONLY): TensorSpec(shape=(None, 800, 1), dtype=tf.float32, name='input')
Output Type:
  TensorSpec(shape=(None, 128), dtype=tf.float32, name=None)
Captures:
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W0000 00:00:1723835188.716817  712291 tf_tfl_flatbuffer_helpers.cc:392] Ignored output_format.
W0000 00:00:1723835188.716827  712291 tf_tfl_flatbuffer_helpers.cc:395] Ignored drop_control_dependency.

tflite = helia.interpreters.tflite.TfLiteKerasInterpreter(tflite_content)
tflite.compile()

y1_pred_tf = encoder.predict(test_x1)
y2_pred_tf = encoder.predict(test_x2)

y1_pred_tfl = tflite.predict(x=test_x1)
y2_pred_tfl = tflite.predict(x=test_x2)

  1/288 ━━━━━━━━━━━━━━━━━━━━ 2s 9ms/step

288/288 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step
288/288 ━━━━━━━━━━━━━━━━━━━━ 1s 3ms/step

tf_rst = helia.metrics.compute_metrics(metrics, y1_pred_tf, y2_pred_tf)
tfl_rst = helia.metrics.compute_metrics(metrics, y1_pred_tfl, y2_pred_tfl)
logger.info("[TF METRICS] " + " ".join([f"{k.upper()}={v:.4f}" for k, v in tf_rst.items()]))
logger.info("[TFL METRICS] " + " ".join([f"{k.upper()}={v:.4f}" for k, v in tfl_rst.items()]))

INFO     [TF METRICS] MSE=0.0132 COS=0.9683                                                         2850812944.py:3

INFO     [TFL METRICS] MSE=0.0132 COS=0.9683                                                        2850812944.py:4

ECG Foundation Demo

Finally, we will showcase the foundation model by running across lots of patients and plotting via t-SNE to view the embeddings. This will help us understand how the model is clustering the data and if it is learning useful features.

# Compute t-SNE
logger.debug("Computing t-SNE")
tsne = TSNE(n_components=2, random_state=0, n_iter=1000, perplexity=75)
x_tsne = tsne.fit_transform(test_y1)

# Plot t-SNE in matplotlib
fig, ax = plt.subplots(1, 1, figsize=(6, 6))
ax.scatter(x_tsne[:, 0], x_tsne[:, 1], c=x_tsne[:, 0] - x_tsne[:, 1], cmap="viridis")
fig.suptitle("HK Foundation: t-SNE")
ax.set_xlabel("Component 1")
ax.set_ylabel("Component 2")
fig.show()