Quantum-Inspired Attention Mechanism

This project proposes a novel synthesis between two fundamental theories of consciousness: Attention Schema Theory (AST) and Orchestrated Objective Reduction (OrchOR). While AST suggests consciousness emerges from the brain's model of attention itself, OrchOR provides a quantum mechanical basis for consciousness through orchestrated collapse of quantum states in neural microtubules. We propose these theories are describing the same phenomenon from different perspectives - AST describing the functional mechanism of consciousness, and OrchOR describing its physical implementation.

We implement this theoretical synthesis in a transformer architecture by modifying the attention mechanism to incorporate quantum collapse operations in Hilbert space. This quantum attention mechanism models consciousness as the orchestrated reduction of superposed attention states, providing a computational framework that bridges quantum consciousness theories with modern machine learning architectures. Our implementation suggests that the quantum computations described by OrchOR may be the physical basis for the attention schema described by AST, offering a unified model of consciousness that is both theoretically grounded and computationally implementable.

This work explores the possibility that consciousness and attention are fundamentally the same process, with quantum mechanics providing the physical mechanism for both. By implementing these principles in an artificial neural network, we aim to better understand consciousness while potentially advancing towards more conscious-like artificial intelligence systems.

Theoretical Foundation

Mathematical Framework

Standard Attention

The traditional transformer attention mechanism is defined as:

$$ \text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V $$

where Q, K, and V are query, key and value matrices, and $$d_k$$ is the dimension of the key vectors.

Hilbert Space Inner Product

In Hilbert space, the inner product between two vectors x and y is defined as:

$$ \langle x,y \rangle = \sum_{i=1}^n x_i\overline{y_i} $$

For complex-valued vectors, where $$\overline{y_i}$$ represents the complex conjugate.

Quantum Attention

Our implementation approximates quantum mechanical processes using computationally efficient classical operations:

$$ \text{QuantumAttention}(Q,K,V) = \text{CollapseFn}\left(\frac{QK^T}{\sqrt{d_k}}\right)V $$

Where CollapseFn implements a threshold-based collapse operation that mirrors orchestrated reduction:

$$ \text{CollapseFn}(x) = \text{normalize}(\text{threshold}(\text{softmax}(x))) $$

Unifying OrchOR and AST Through Mathematical Structure

The striking similarity between attention mechanisms and Hilbert space operations suggests a deeper connection between OrchOR and AST. The attention mechanism's mathematical structure mirrors quantum mechanical processes in several key ways:

Structural Parallels

• The attention mechanism's dot product operation provides a computationally efficient approximation of Hilbert space inner products
• Softmax followed by threshold-based collapse approximates quantum probability amplitude reduction
• The threshold in our collapse function mirrors the critical threshold for orchestrated reduction in biological systems

Biological Implementation

In biological systems, this mathematical parallel manifests through:

• Microtubules maintaining quantum superpositions of attention states
• Orchestrated collapse events corresponding to discrete moments of conscious attention
• The attention schema being physically implemented through quantum computations

Theoretical Synthesis

This mathematical and structural similarity suggests that OrchOR may describe the physical mechanism by which the brain implements its attention schema:

• Quantum superpositions in microtubules represent potential attention states
• Orchestrated reduction selects specific attention states, corresponding to conscious awareness
• The collapse process implements the attention control mechanisms described by AST

This unified view suggests that consciousness arises from quantum mechanical attention processes, with OrchOR providing the physical mechanism for the computational process described by AST. The mathematical similarity between attention mechanisms and quantum mechanics isn't merely coincidental - it reflects the fundamental nature of consciousness as a quantum attention process.

Consciousness Through Attention

Attention Schema Theory

This implementation bridges two theories of consciousness:

• Attention Schema Theory (AST), which proposes that consciousness is fundamentally an attention mechanism
• OrchOR, which provides a quantum mechanical basis for consciousness

By implementing OrchOR-style quantum collapse in an attention mechanism, we aim to demonstrate that these theories may be describing the same phenomenon from different perspectives.

Implementation

Quantum Attention Mechanism

The core implementation provides a drop-in replacement for standard transformer attention.

Key Features

• Quantum collapse simulation through orchestrated reduction
• Hilbert space representation of attention states
• Threshold-based collapse mechanism
• Multi-head attention structure

Implementation Benefits

• Maintains the essential properties of quantum collapse (discreteness, probability-based selection)
• Achieves computational efficiency while preserving theoretical parallels
• Provides a practical framework for testing consciousness-related hypotheses

Usage in Transformers

To use this attention mechanism in a transformer:

import torch
import torch.nn as nn
from quantumattention import QuantumAttention

class QuantumTransformer(nn.Module):
    def __init__(self, d_model=512, nhead=8, num_layers=6):
        super().__init__()
        self.d_model = d_model
        
        # Replace standard attention with quantum attention
        encoder_layer = nn.TransformerEncoderLayer(
            d_model=d_model,
            nhead=nhead,
            dim_feedforward=4*d_model,
            dropout=0.1,
            batch_first=True
        )
        
        # Replace the self-attention in encoder layer
        encoder_layer.self_attn = QuantumAttention(
            embed_dim=d_model,
            num_heads=nhead
        )
        
        self.transformer = nn.TransformerEncoder(
            encoder_layer,
            num_layers=num_layers
        )
        
    def forward(self, x, mask=None):
        return self.transformer(x, mask)

# Example usage
model = QuantumTransformer()
x = torch.randn(32, 100, 512)  # batch_size=32, seq_len=100, d_model=512
output = model(x)

Research Implications

This implementation suggests several testable hypotheses:

• Quantum collapse-based attention might show different patterns of information processing
• The discrete nature of quantum collapse could provide natural chunking of information
• The relationship between attention and consciousness might be experimentally observable

Future Directions

• Optimization of the collapse function for better computational efficiency
• Investigation of different collapse thresholds and their effects
• Integration with other quantum-inspired neural network components
• Empirical testing of consciousness-like behaviors in networks using this mechanism

Installation and Usage

[Installation instructions to be added]

References

1. Webb, T. W., & Graziano, M. S. A. (2015). The attention schema theory: A mechanistic account of subjective awareness. Frontiers in Psychology, 6, 500.

2. Hameroff, S., & Penrose, R. (2014). Consciousness in the universe: A review of the 'Orch OR' theory. Physics of Life Reviews, 11(1), 39-78.

3. Hameroff, S. (2007). Orchestrated reduction of quantum coherence in brain microtubules: A model for consciousness. NeuroQuantology, 5(1), 1-8.

4. Tomic, M. (2020). Quantum Computational Psychoanalysis -- Quantum logic approach to Bi-logic. arXiv:2010.04550.

5. Gao, S. (2022). Orch OR and the Quantum Biology of Consciousness. In Consciousness and Quantum Mechanics. Oxford University Press.

6. Chen, Z., Xue, Y., Duan, R., & Chen, J. (2024). Quantum linear algebra is all you need for Transformer architectures. arXiv:2402.16714.

The first three papers provide the foundational theories of consciousness (AST and Orch OR). Paper 4 demonstrates how quantum logic and Hilbert spaces can represent mental processes. Paper 5 explores the quantum biological basis of consciousness. Paper 6 provides the quantum computing framework we build upon for implementing consciousness-aware transformers.