Holographic theory and AI technology

What is holographic theory?

Holographic theory (holographic principle) is a theory of physics that is particularly relevant to the conservation of information in the universe. It is concerned with fundamental ideas about the conservation of information in physics, and is closely related in particular to the theory of quantum gravity, black hole thermodynamics and the theory of higher dimensional space.

The central idea of the theory is the notion that ‘higher dimensional information can be perfectly recorded on lower dimensional surfaces’, which suggests that physical phenomena in three or more dimensions of space may be described in lower dimensional space (e.g. two-dimensional surfaces).

Holographic theory suggests how the conservation of physical laws and information can be established by ‘projecting’ physical space and events onto lower dimensional boundaries. In this way, for example, all information in the three-dimensional space we inhabit is supposed to be recorded like a ‘hologram’ on a two-dimensional surface (e.g. the boundary of a black hole).

This idea has its origins primarily in research on the thermodynamics of black holes and was popularised through Hawking radiation research in the 1970s. Holographic theory played an important role in what was later called string theory, and is regarded as one of the key theories to solving many unsolved problems in physics.

The holographic principle is based on the following concepts

• The principle of information conservation: the idea is that information in physical space (e.g. the position, kinetic state and energy of matter) is actually recorded on the boundary surfaces of that space (e.g. the event horizon of a black hole), so that all information in a three-dimensional physical space is compressed onto a two-dimensional surface.
• Black holes and the storage of information: conventionally, it was thought that when an object is sucked into a black hole, the object’s information is recorded on the event horizon (boundary plane) of the black hole, trapping it within the black hole. However, holographic theory suggests that instead of information being lost inside the black hole, that information is recorded on the event horizon and may be retrieved by an external observer.
• String theory and the holographic principle: The holographic principle is also related to string theory. One interpretation of string theory, the AdS/CFT correspondence (Anti-de Sitter space/Conformal Field Theory correspondence), shows that physical phenomena in some higher dimensional space (AdS space) can be described by a lower dimensional boundary surface, which This is supposed to make it possible to understand higher-dimensional theories, such as string theory, in terms of lower-dimensional theories.

The holographic principle has had a major impact on the study of quantum gravity and black holes in particular, and the theory has attracted attention as a means of resolving the black hole information paradox concerning the problem of the non-lost storage of information. Showing that information can be recorded without loss is one of the key challenges in modern physics.

Mathematically, holographic theory is generally described using quantum field theory and string theory. In particular, the AdS/CFT correspondence is based on the correspondence that exists between quantum field theory (CFT) and gravitational theory (AdS space), which is a powerful tool for integrating and interpreting different fields of physics.

Possible applications of holographic theory include

• Information science: holographic representations of information can be useful in relation to compression and efficient storage methods for high-dimensional data.
• Artificial intelligence (AI): applicable to methods for mapping data in high-dimensional space to low-dimensional space and extracting important features and patterns. For example, algorithms inspired by holographic theory could be used for data compression, feature extraction and generative modelling.
• Quantum computers: holographic theory is also related to the issue of quantum gravity and is important to link with quantum computer theory to understand how information is handled.

Holographic theory offers a revolutionary perspective on the storage of information and the understanding of higher dimensional spaces, with potential applications not only in physics and mathematics, but also in information science and AI. In particular, the theory is expected to bring new ideas related to data compression, knowledge representation and efficiency of distributed systems.

Applying hologram theory to AI technology

Let us examine some specific applications of this approach to applying hologram theory to AI technology.

First, information compression and efficient data representation

• Hologram theory and data compression: borrowing from the holographic principle, the notion that information in a three-dimensional space is reduced to a two-dimensional boundary, we can consider data compression and dimensionality reduction in AI, for example, to optimise the information in a huge data set (images, audio, text, etc.), low dimensional features It is possible to ‘encode’ data into a space and retain high dimensional information, while reducing computation and storage.
• Application example: using dimensionality reduction techniques such as Principal Component Analysis (PCA)* and t-SNE, important features of high-dimensional data can be mapped into low-dimensional spaces to save computational resources while retaining important information. Techniques have also been developed for image and audio data compression, which in principle take a holographic approach to compressing information efficiently.

Secondly, in terms of distributed learning and knowledge ‘encoding’, the following can be considered

• Knowledge integration in distributed AI systems: by applying the principles of hologram theory to distributed AI systems, methods can be developed to share and integrate knowledge and information between different agents. In terms of hologram theory, the approach could be to efficiently ‘encode’ and transfer important information between different distributed systems (AI agents) and optimise it through interactions in the overall system.
• APPLICATION: The idea of holographic knowledge integration can be used in processes such as Distributed Reinforcement Learning or Federated Learning, where models learned locally by multiple agents (devices) are aggregated and optimised on a central server. Here, the ‘low-dimensional’ information (parameters and model weights) that each agent has locally is used as a basis for aggregating ‘high-dimensional’ information to make the overall learning more efficient.

This can also be applied to natural language processing.

• Hologram theory and semantic compression: in language models, approaches can efficiently compress information and map high-dimensional semantic information onto low-dimensional space in order to understand the meaning of sentences and words. In a manner similar to hologram theory, semantically important information can be retained in low-dimensional vector spaces to reconstruct meaning.
• Application example: embedding techniques such as Word2Vec and BERT compress high-dimensional word spaces into low-dimensional vectors to efficiently represent word meaning and context information. Borrowing from the perspective of hologram theory, there is the potential for advances in technologies that reconstruct whole sentences or conversational contexts with a minimum of features.

AI-based reconstruction of high-dimensional space

• Technology to represent and reconstruct spatial information in low-dimensional space: an approach where AI has spatial and temporal information in high-dimensional space and reconstructs its essential information in low-dimensional space as required, applying hologram theory to encode the complex dynamics of the environment (e.g. environmental awareness in automated vehicles) as low-dimensional data, which can be used to control the vehicle.
• Application: in methods such as Self-supervised learning and Variational Autoencoders (VAE), where high-dimensional data in the input space (e.g. visual or sensor data) is compressed, mapped and reconstructed in low-dimensional latent space, hologram theory Ideas can be used. This allows the model to use computational resources efficiently while maintaining the necessary information.

Virtual space and holographic representation of knowledge

• Knowledge representation in virtual environments: the hologram theory approach can be applied to AI to compress and encode knowledge in virtual space, enabling AI agents to understand physical laws and human intentions in virtual environments. In particular, it can utilise virtual reality (VR) and augmented reality (AR) technologies to visually represent complex information in a holographic manner.
• Application examples: in VR and AR systems, data based on user behaviour and interaction with the environment can be reproduced in a holographic manner, compressing and displaying the knowledge required for the user to efficiently manipulate the virtual space; AI agents can learn user behaviour and provide low-dimensional feedback can be given.

The application of holographic theory to AI enables new approaches in areas such as information compression, data integration, knowledge representation and distributed systems. A holographic perspective can be a powerful framework, especially for dealing with huge amounts of data and efficient information abstraction; understanding models based on holographic theory will play an important role in helping AI to learn and optimise more efficiently.

implementation example

Specific details and implementation overviews of distributed learning and knowledge ‘encoding’ implementation examples are given below.

1. overview of distributed learning: distributed learning is a way of performing machine learning in an environment where data and computational resources are distributed, and this approach is particularly useful when dealing with large data sets and resource-intensive models. Common distributed learning methods include

• Data parallel distributed learning: splitting the data into multiple nodes, training the model on each node and then aggregating its weights. Examples: Horovod and TensorFlow MirroredStrategy.
• Model parallel distributed learning: the model itself is split into multiple nodes and trained. Effective for large models, but requires complex coordination.
  Federated Learning: data is held locally and a central server updates the model by aggregating updates from each client.

2. knowledge ‘encoding’.

Encoding’ refers to the process of converting knowledge into a specific format. In machine learning and deep learning, knowledge is encoded through the parameters of the model (weights and biases), whereas encoding in distributed learning is specifically concerned with how data is processed and models are shared.

• Knowledge compression: methods that reduce the size of models and improve communication and storage efficiency. Examples: model pruning and quantisation.
  Knowledge transfer: the process of transferring learned knowledge between different models. Examples: knowledge distillation.
• Knowledge sharing coding: methods for efficiently sharing knowledge between different nodes in a distributed environment.

3. Example implementation: the following is an example implementation of distributed learning and knowledge encoding using TensorFlow and Keras. The example shows how distributed learning can be used to aggregate the weights of the models computed at each node and how knowledge distillation can be used to transfer the learned knowledge.

a. Implementing distributed learning: in TensorFlow 2.x, distributed learning can be easily performed using tf.distribute.Strategy. Here, data parallel learning is implemented using the MirroredStrategy.

import tensorflow as tf
from tensorflow.keras import layers, models

# Initialisation of the diversification strategy
strategy = tf.distribute.MirroredStrategy()

# Train models in a distributed environment.
with strategy.scope():
    # Model definition.
    model = models.Sequential([
        layers.InputLayer(input_shape=(784,)),
        layers.Dense(128, activation='relu'),
        layers.Dropout(0.2),
        layers.Dense(10, activation='softmax')
    ])

    # Compiling the model
    model.compile(optimizer='adam',
                  loss='sparse_categorical_crossentropy',
                  metrics=['accuracy'])

# Prepare dataset 
# Use MNIST data as an example here
(train_images, train_labels), (test_images, test_labels) = tf.keras.datasets.mnist.load_data()
train_images = train_images / 255.0
test_images = test_images / 255.0

# Perform distributed learning
model.fit(train_images, train_labels, epochs=5, batch_size=64)

The code uses MirroredStrategy to run training across multiple GPUs in parallel. Data is distributed across multiple nodes and the weights trained on each node are automatically synchronised.

b. Knowledge transfer through knowledge distillation

Knowledge distillation becomes a technique for transferring knowledge from a large Teacher Model (Teacher Model) to a smaller Student Model (Student Model). This is a way of using the output of the Teacher Model to train the Student Model.

import tensorflow as tf
from tensorflow.keras import layers, models

# Definition of teacher models (larger models)
teacher_model = models.Sequential([
    layers.InputLayer(input_shape=(784,)),
    layers.Dense(256, activation='relu'),
    layers.Dense(10, activation='softmax')
])

# Definition of the pupil model (small model)
student_model = models.Sequential([
    layers.InputLayer(input_shape=(784,)),
    layers.Dense(128, activation='relu'),
    layers.Dense(10, activation='softmax')
])

# Training of teacher models.
teacher_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy'])
# Train a teacher model using MNIST data (e.g.)
teacher_model.fit(train_images, train_labels, epochs=5)

# Loss functions for knowledge distillation.
def distillation_loss(y_true, y_pred, teacher_predictions, temperature=3):
    # Use predictions from supervised models
    teacher_predictions = tf.nn.softmax(teacher_predictions / temperature)
    y_pred = tf.nn.softmax(y_pred / temperature)
    
    # Calculating cross-entropy
    distillation_loss = tf.reduce_mean(tf.keras.losses.categorical_crossentropy(teacher_predictions, y_pred))
    return distillation_loss

# Train student models.
student_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy'])

# Get predictions from teacher models and train student models
teacher_predictions = teacher_model.predict(train_images)
student_model.fit(train_images, train_labels, epochs=5, batch_size=64, 
                  loss=distillation_loss(teacher_predictions=teacher_predictions))

The code trains the teacher model (large network) and then trains the student model (small network) with the predictions of the teacher model. This allows the student models to take over the knowledge of the teacher models and learn more efficiently.

4. practical applications

• Distributed learning:
  • Large-scale natural language processing (NLP) models: using distributed learning to train models such as GPT and BERT on large amounts of textual data.
  • Image classification: large image datasets can be trained efficiently by distributed learning, significantly reducing training time.
• Knowledge encoding:
  • Model compression and transfer learning: using knowledge distillation to transfer knowledge from large teacher models to lightweight student models for highly accurate prediction in resource-limited environments.
  • Model transfer: using knowledge distillation to transfer knowledge from teacher models appropriately for different tasks, building task-specific models.

5. conclusions.

Distributed learning and knowledge coding (in particular knowledge distillation) are very powerful techniques for efficiently utilising data and computational resources and improving model performance, distributed learning allows large data sets to be processed in parallel, and through knowledge distillation, highly accurate models can be used even in resource-constrained environments This makes it possible to use models with high accuracy even in resource-constrained environments.

Application examples

The convergence of holographic theory and AI techniques offers interesting applications, particularly in the areas of physics, information theory and data analysis. Some specific applications are discussed below.

1. analysis of the black hole information paradox

• Abstract: AI techniques are helping to improve the efficiency of simulations when solving black hole information paradoxes using holographic principles (especially AdS/CFT support) AI is used to speed up the huge amount of calculations related to black hole entropy and information conservation and to It is used to make predictions.
• Role of AI:
  Use of deep learning models in modelling quantum fields.
  Reducing computational costs and improving the accuracy of results.
• Related research:
  ‘Holography as deep learning’ (arXiv paper).

2. numerical simulation of AdS/CFT support

• Abstract: The AdS/CFT correspondence in holographic theory is an important way to link field theory and gravity theory, and AI assists in the analysis of complex CFT (conformal field theory) and numerically challenging calculations in AdS space.
• Role of AI:
  Visualising the geometric structure of the AdS space using deep generative models (e.g. GANs).
  Parameter optimisation when solving holographic reconstruction problems.
• Concrete examples:
  Simulations using AI to analyse gravity wave data to confirm the theory of AdS/CFT correspondence.

3. holographic image reconstruction

• Abstract: Holographic theory is increasingly being used in combination with AI for medical image processing and 3D hologram generation, enabling accurate reconstruction of complex 3D structures.
• Role of AI:
  Analyses holographic image data with neural networks and reconstructs highly accurate 3D images.
  Reduction of data noise and improvement of reconstruction accuracy.
• Applications:
  Medical holographic image analysis.
  Next-generation display technology.

4. data analysis in cosmology

• Abstract: Research is underway to analyse cosmological data (e.g. cosmic microwave background radiation and galaxy distributions) using holographic principles, and AI can help to estimate physical parameters from vast amounts of data.
• Role of AI:
  Extracting features of observed data using anomaly detection algorithms.
  Compares theoretical predictions with observed data in a generative model.
• Specific examples:
  AI analysis based on cosmic expansion models.
  Validation of holographic correspondence theories based on observational data.

5. quantum computing and the holographic principle

• Abstract: In quantum computing, some research has applied holographic theory to improve the efficiency of information processing and error correction.
• Role of AI:
  Deep learning is used to generate quantum error-correcting codes.
  Holographic modelling of quantum states.
• Related projects:
  Quantum simulation research by Google and IBM.

6. application to Physics Informed Neural Networks (PINN)

• Abstract: PINN is a technique for incorporating physical laws into neural networks, which has also been applied to numerical analysis of holographic theory.
• Role of AI:
  Fast solution of physical systems based on partial differential equations.
  Optimisation of boundary conditions for holographic simulations.
• Specific examples:
  Numerical simulation of gravitational wave analysis and black hole thermodynamics.

reference book

This section describes reference books related to holographic theory and its application to AI technology.

Books related to holographic theory.
1. Leonard Susskind, ‘The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics’.
– Learn about the background of holographic principles and their relation to the black hole information paradox.

2. “The Holographic Principle”

3. Juan Maldacena, ‘The Large N Limit of Superconformal Field Theories and Supergravity’.
– The first paper to present the AdS/CFT correspondence (the basis of holographic theory). Technical, but essential for understanding the theory.

4.Brian Greene, ‘The Elegant Universe ’
– An introductory book that provides background on superstring theory and holographic principles for the general reader.

Books related to AI technology.
1. Ian Goodfellow, Yoshua Bengio, Aaron Courville, ‘Deep Learning’.
– A comprehensive overview of deep learning technology, from the basics to applications. Also useful when considering numerical simulation applications with holographic theory.

2. marcus du Sautoy, ‘The Creativity Code: art and Innovation in the Age of AI’.
– A book for the general public on how AI can help create new ideas and theories.

3. ‘Neural Networks and Deep Learning’
– Helps to better understand mathematical models and to design AI algorithms.

Books with articles and chapters related to the integration of holographic theory and AI.
1. Simone Severini, Giuseppe Di Bari, ‘Quantum Machine Learning: An Applied Approach’.
– Describes the fusion of quantum mechanical approaches and AI. Useful for mathematical modelling of holographic theory.

2. Seth Lloyd, ‘Programming the Universe’.
– Explains the idea of the universe as a quantum computer. Useful for exploring the links between holographic theory and information processing.

3. Vlatko Vedral, ‘Decoding Reality: the Universe as Quantum Information’.
– Suitable for considering the interface between AI and holographic principles from the perspective of interpreting the universe in terms of information theory.

Papers (good ones to look for online)
– ‘Holography and Deep Learning’.
– Look for recent research papers focusing on the combination of holographic principles and numerical simulation of AI (arXiv is recommended).