rienet 1.0.9

A Compact Recurrent-Invariant Eigenvalue Network for Portfolio Optimization

RIEnet: A Rotational Invariant Estimator Network for GMV Optimization

This library implements the neural estimators introduced in:

• Bongiorno, C., Manolakis, E., & Mantegna, R. N. (2025). End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning (arXiv:2507.01918). https://arxiv.org/abs/2507.01918
• Bongiorno, C., Manolakis, E., & Mantegna, R. N. (2025). Neural Network-Driven Volatility Drag Mitigation under Aggressive Leverage. In Proceedings of the 6th ACM International Conference on AI in Finance (ICAIF ’25). https://doi.org/10.1145/3768292.3770370

RIEnet is a end-to-end neural estimator for Global Minimum-Variance (GMV) portfolios. The architecture couples a lag-kernel with a bidirectional RNN spectral denoiser and a marginal-volatility head to produce cleaned inverse covariances and analytic GMV weights. By design, the number of learnable parameters can be independent of the look-back window length and the asset-universe size, enabling immediate transfer across universes and sampling frequencies without retraining. The model can be trained directly on a realized-variance objective and can export its cleaned covariance for constrained optimizations.

Key Features

• End-to-End Variance Objective – Trains on the realized out-of-sample variance, yielding GMV weights analytically from the learned inverse covariance.
• Parameter Efficiency – Fixed-size modules (5-parameter lag kernel; BiGRU eigencleaning; lightweight volatility head) keep the model at ≈2k parameters.
• Size-Invariant Design – Complexity does not scale with look-back length or cross-sectional dimension; deploy on new universes without architecture changes.
• RIE-Style Covariance Cleaning – Rotation-invariant mapping of the correlation spectrum with a BiGRU (16 units per direction by default).
• Practical Outputs – Retrieve GMV weights and the cleaned precision/covariance; the latter can be plugged into long-only QP solvers when needed.
• Reproducible Defaults – TensorFlow/Keras reference implementation with paper-consistent hyperparameters and tests.

Module Organization

• rienet.trainable_layers: layers with trainable parameters (RIEnetLayer, LagTransformLayer, DeepLayer, DeepRecurrentLayer, CorrelationEigenTransformLayer).
• rienet.ops_layers: deterministic operation layers (statistics, normalization, eigensystem algebra, weight post-processing).

Installation

Install from PyPI:

pip install rienet

Or install from source:

git clone https://github.com/bongiornoc/RIEnet.git
cd RIEnet
pip install -e .

Quick Start

Basic Usage

import tensorflow as tf
from rienet import RIEnetLayer, variance_loss_function

# Defaults reproduce the compact GMV architecture (bidirectional GRU with 16 units)
rienet_layer = RIEnetLayer(output_type=['weights', 'precision'])

# Sample data: (batch_size, n_stocks, n_days)
returns = tf.random.normal((32, 10, 60), stddev=0.02)

# Retrieve GMV weights and cleaned precision in one pass
outputs = rienet_layer(returns)
weights = outputs['weights']          # (32, 10, 1)
precision = outputs['precision']      # (32, 10, 10)

# GMV training objective
covariance = tf.random.normal((32, 10, 10))
covariance = tf.matmul(covariance, covariance, transpose_b=True)
loss = variance_loss_function(covariance, weights)
print(loss.shape)  # (32, 1, 1)

Training with the GMV Variance Loss

import tensorflow as tf
from rienet import RIEnetLayer, variance_loss_function

def create_portfolio_model():
    inputs = tf.keras.Input(shape=(None, None))
    weights = RIEnetLayer(output_type='weights')(inputs)
    return tf.keras.Model(inputs=inputs, outputs=weights)

model = create_portfolio_model()

# Synthetic training data
X_train = tf.random.normal((1000, 10, 60), stddev=0.02)
Sigma_train = tf.random.normal((1000, 10, 10))
Sigma_train = tf.matmul(Sigma_train, Sigma_train, transpose_b=True)

optimizer = tf.keras.optimizers.Adam(learning_rate=1e-4, clipnorm=1.0)
model.compile(optimizer=optimizer, loss=variance_loss_function)

model.fit(X_train, Sigma_train, epochs=10, batch_size=32, verbose=True)

Tip: When you intend to deploy RIEnet on portfolios of varying size, train on batches that span different asset universes. The RIE-based architecture is dimension agnostic and benefits from heterogeneous training shapes.

Using Different Output Types

# GMV weights only
weights = RIEnetLayer(output_type='weights')(returns)

# Precision matrix only
precision_matrix = RIEnetLayer(output_type='precision')(returns)

# Precision, covariance, and the lag-transformed inputs in one pass
outputs = RIEnetLayer(
    output_type=['precision', 'covariance', 'input_transformed']
)(returns)
precision_matrix = outputs['precision']
covariance_matrix = outputs['covariance']
lagged_inputs = outputs['input_transformed']

# Spectral components (non-inverse)
spectral = RIEnetLayer(
    output_type=['eigenvalues', 'eigenvectors', 'transformed_std']
)(returns)
cleaned_eigenvalues = spectral['eigenvalues']   # (batch, n_stocks, 1)
eigenvectors = spectral['eigenvectors']         # (batch, n_stocks, n_stocks)
transformed_std = spectral['transformed_std']   # (batch, n_stocks, 1)

# Optional: disable variance normalisation (do not use it with end-to-end GMV training)
raw_covariance = RIEnetLayer(
    output_type='covariance',
    normalize_transformed_variance=False
)(returns)

⚠️ When RIEnet is trained end-to-end on the GMV variance loss, leave normalize_transformed_variance=True (the default). The loss is invariant to global covariance rescalings and the layer keeps the implied variance scale centred around one. Disable the normalisation only when using alternative objectives where the absolute volatility scale must be preserved.

Using LagTransformLayer Directly

LagTransformLayer is exposed both at package root and in the dedicated module:

import tensorflow as tf
from rienet import LagTransformLayer
# or: from rienet.lag_transform import LagTransformLayer

# Dynamic lookback (T can change call-by-call)
compact = LagTransformLayer(variant="compact")
y1 = compact(tf.random.normal((4, 12, 20)))
y2 = compact(tf.random.normal((4, 12, 40)))

# Fixed lookback inferred at first build/call (requires static T)
per_lag = LagTransformLayer(variant="per_lag")
z1 = per_lag(tf.random.normal((4, 12, 20)))
z2 = per_lag(tf.random.normal((4, 8, 20)))   # n_assets can change

Using EigenWeightsLayer Directly

EigenWeightsLayer is part of the public API and can be imported directly:

import tensorflow as tf
from rienet import EigenWeightsLayer

layer = EigenWeightsLayer(name="gmv_weights")

# Inputs
eigenvectors = tf.random.normal((8, 20, 20))         # (..., n_assets, n_assets)
inverse_eigenvalues = tf.random.uniform((8, 20, 1))  # (..., n_assets) or (..., n_assets, 1)
inverse_std = tf.random.uniform((8, 20, 1))          # optional

# Full GMV-like branch (includes inverse_std scaling)
weights = layer(eigenvectors, inverse_eigenvalues, inverse_std)

# Covariance-eigensystem branch (inverse_std omitted)
weights_cov = layer(eigenvectors, inverse_eigenvalues)

Notes:

• inverse_std is optional by design.
• If inverse_std is omitted, the layer uses a dedicated branch with fewer operations (it does not materialize a vector of ones).
• Output shape is always (..., n_assets, 1), normalized to sum to one along assets.

Using CorrelationEigenTransformLayer Directly

import tensorflow as tf
from rienet import CorrelationEigenTransformLayer

layer = CorrelationEigenTransformLayer(name="corr_cleaner")

# Correlation matrix: (batch, n_assets, n_assets)
corr = tf.eye(6, batch_shape=[4])

# Optional attributes: (batch, k) e.g. q, lookback, regime flags, etc.
attrs = tf.constant([
    [0.5, 60.0],
    [0.7, 60.0],
    [1.2, 30.0],
    [0.9, 90.0],
], dtype=tf.float32)

# With attributes (default output_type='correlation')
cleaned_corr = layer(corr, attributes=attrs)

# Request multiple outputs
details = layer(
    corr,
    attributes=attrs,
    output_type=[
        'correlation',
        'inverse_correlation',
        'eigenvalues',
        'eigenvectors',
        'inverse_eigenvalues',
    ],
)
cleaned_eigvals = details['eigenvalues']              # (batch, n_assets, 1)
cleaned_inv_eigvals = details['inverse_eigenvalues']  # (batch, n_assets, 1)
inv_corr = details['inverse_correlation']             # (batch, n_assets, n_assets)

# Without attributes
cleaned_corr_no_attr = CorrelationEigenTransformLayer(name="corr_cleaner_no_attr")(corr)

Notes:

• attributes is optional and can have shape (batch, k) or (batch, n_assets, k).
• The output is a cleaned correlation matrix (batch, n_assets, n_assets).
• If you change attribute width k, use a new layer instance.

Loss Function

Variance Loss Function

from rienet import variance_loss_function

loss = variance_loss_function(
    covariance_true=true_covariance,    # (batch_size, n_assets, n_assets)
    weights_predicted=predicted_weights # (batch_size, n_assets, 1)
)

Mathematical Formula:

Loss = n_assets × wᵀ Σ w

Where w are the portfolio weights and Σ is the realised covariance matrix.

Architecture Details

The RIEnet pipeline consists of:

1. Input Scaling – Annualise returns by 252
2. Lag Transformation – Five-parameter memory kernel for temporal weighting
3. Covariance Estimation – Sample covariance across assets
4. Eigenvalue Decomposition – Spectral analysis of the covariance matrix
5. Recurrent Cleaning – Bidirectional GRU/LSTM processing of eigen spectra
6. Marginal Volatility Head – Dense network forecasting inverse standard deviations
7. Matrix Reconstruction – RIE-based synthesis of Σ⁻¹ and GMV weight normalisation

Paper defaults use a single bidirectional GRU layer with 16 units per direction and a marginal-volatility head with 8 hidden units, matching the compact network described in Bongiorno et al. (2025).

Requirements

• Python ≥ 3.8
• TensorFlow ≥ 2.10.0
• Keras ≥ 2.10.0
• NumPy ≥ 1.21.0

Development

git clone https://github.com/bongiornoc/RIEnet.git
cd RIEnet
pip install -e ".[dev]"
pytest tests/

Citation

Please cite the following references when using RIEnet:

@article{bongiorno2025covariance,
  title={End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning},
  author={Bongiorno, Christian and Manolakis, Efstratios and Mantegna, Rosario N.},
  journal={arXiv preprint arXiv:2507.01918},
  year={2025}
}

@inproceedings{bongiorno2025compact,
  author = {Bongiorno, Christian and Manolakis, Efstratios and Mantegna, Rosario Nunzio},
  title = {Neural Network-Driven Volatility Drag Mitigation under Aggressive Leverage},
  year = {2025},
  isbn = {9798400722202},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  url = {https://doi.org/10.1145/3768292.3770370},
  doi = {10.1145/3768292.3770370},
  booktitle = {Proceedings of the 6th ACM International Conference on AI in Finance},
  pages = {449–455},
  numpages = {7},
  location = {},
  series = {ICAIF '25}
  }

For software citation:

@software{rienet2025,
  title={RIEnet: A Rotational Invariant Estimator Network for Global Minimum-Variance Optimisation},
  author={Bongiorno, Christian},
  year={2026},
  version={1.0.0},
  url={https://github.com/bongiornoc/RIEnet}
}

You can print citation information programmatically:

import rienet
rienet.print_citation()

Support

For questions, issues, or contributions, please:

• Open an issue on GitHub
• Check the documentation
• Contact Prof. Christian Bongiorno ([e-mail]) for calibrated model weights or collaboration requests