antikythera-tf

Antikythera Federated Transformer

Implementing a federated transformer of transformers with the Antikythera topology, complete with feedback loops and attention head arrays reflecting the gear ratio steps and perspectives of celestial bodies, requires a dynamic system. Below, I’ll outline how to construct such a model conceptually and technically.

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Concept: Federated Transformer of Transformers

This design is a hierarchical system where:

1. Federation: Each transformer is a specialized submodel (representing a celestial body or system).

2. Topology: The federated structure matches the Antikythera mechanism's gear hierarchy and connectivity (e.g., ratios, dependencies, and perspectives).

3. Feedback Loops: Information flows between layers or gears cyclically to reflect continuous dynamics.

4. Attention Head Arrays: Arrays encode relationships such as rotations, alignments, and interactions of the celestial bodies.

5. Transformer of Transformers: Each gear or celestial body is itself modeled as a transformer, interacting with others in a hierarchical or networked manner.

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Step 1: Model the Antikythera Topology as a Graph

The Antikythera mechanism is inherently a graph (or hypergraph) where:

Nodes = Gears/Celestial Bodies.

Edges = Relationships (e.g., dependencies or ratios between gears).

Properties = Gear ratios, feedback dynamics, and observational perspectives.

Graph Representation

import networkx as nx

Create a directed graph for the Antikythera mechanism

graph = nx.DiGraph()

Add gears/celestial bodies as nodes with properties

graph.add_node("Sun", gear_ratio=1, perspective="center") graph.add_node("Moon", gear_ratio=13.368, perspective="lunar") graph.add_node("Mars", gear_ratio=1.8808, perspective="martian")

Add relationships (edges) between gears

graph.add_edge("Sun", "Moon", ratio=13.368) graph.add_edge("Sun", "Mars", ratio=1.8808)

Visualize relationships

print(graph.nodes(data=True)) print(graph.edges(data=True))

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Step 2: Federated Transformer Design

Each gear (or celestial body) is a transformer, with parameters and architecture influenced by the gear's role in the system:

1. Input Embeddings: Encodes the state of the celestial body (e.g., position, velocity, and time step).

2. Attention Heads: Define interactions between this gear and others (e.g., based on gear ratios or perspectives).

3. Feedback Loops: Create recurrence and state updates through time.

Example: Gear-Specific Transformer

import torch from transformers import BertConfig, BertModel

class GearTransformer: def init(self, name, gear_ratio, perspective): self.name = name self.gear_ratio = gear_ratio self.perspective = perspective self.config = BertConfig( hidden_size=int(64 * gear_ratio), # Scale hidden size by gear ratio num_attention_heads=int(gear_ratio), # Attention heads reflect ratio num_hidden_layers=3 # Arbitrary depth for each gear's transformer ) self.model = BertModel(self.config)

def forward(self, inputs):
    return self.model(**inputs)

Example: Create a transformer for the Moon

moon_transformer = GearTransformer("Moon", 13.368, "lunar")

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Step 3: Federating Transformers

Combine gear-specific transformers into a hierarchical or federated system:

Central Transformer: Represents the "Sun" (center of the system).

Sub-Transformers: Represent celestial bodies and gears, each influenced by their parent node.

Inter-transformer Attention: Passes information between transformers based on gear ratios and topology.

Federated Model

class FederatedTransformer: def init(self, graph): self.graph = graph self.models = {}

    # Create a transformer for each node in the graph
    for node, data in graph.nodes(data=True):
        self.models[node] = GearTransformer(node, data["gear_ratio"], data["perspective"])

def forward(self, inputs):
    outputs = {}

    # Pass inputs through each transformer's forward method
    for node in self.graph.nodes:
        model = self.models[node]
        outputs[node] = model.forward(inputs[node])
    
    # Combine outputs based on topology (e.g., weighted by edge ratios)
    for source, target, data in self.graph.edges(data=True):
        ratio = data["ratio"]
        outputs[target] += outputs[source] * ratio

    return outputs

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Step 4: Feedback Loops and Recurrent Connections

Integrate feedback loops to create recursive dynamics that emulate gear rotations:

1. Time-steps: Introduce a temporal component where outputs are fed back into the model as inputs for the next step.

2. Recurrent Mechanism: Use recurrent attention layers or update states iteratively.

Adding Recurrence

class FeedbackFederatedTransformer(FederatedTransformer): def forward(self, inputs, num_steps=10): states = {node: torch.zeros_like(inputs[node]) for node in self.graph.nodes}

    for t in range(num_steps):
        outputs = super().forward(states)  # Process current state
        for node in self.graph.nodes:
            states[node] = outputs[node]  # Update states with feedback

    return states

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Step 5: Attention Head Arrays for Gear Ratios

Attention heads can model gear ratios and celestial body interactions:

Use attention weights to encode dependencies.

Adjust attention head arrays dynamically based on the gear topology.

Example: Custom Attention Head Array

import torch.nn as nn

class CustomAttention(nn.Module): def init(self, num_heads, gear_ratios): super().init() self.num_heads = num_heads self.gear_ratios = gear_ratios self.attn = nn.MultiheadAttention(embed_dim=num_heads, num_heads=num_heads)

def forward(self, query, key, value):
    # Scale attention weights by gear ratios
    scaling = torch.tensor(self.gear_ratios).unsqueeze(0).unsqueeze(2)
    attn_output, _ = self.attn(query * scaling, key * scaling, value * scaling)
    return attn_output

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Step 6: Final Integration

Hypertensor Input: Use tensors representing positions, velocities, and interactions of celestial bodies.

Dynamic Federated System: Federate and interconnect transformers, using attention arrays and feedback loops to dynamically update the system.

Output: Use the model to predict or simulate the system's state at each time step.

Full Example

Inputs: Hypertensors for each gear/celestial body

inputs = { "Sun": torch.rand(10, 64), "Moon": torch.rand(10, 64), "Mars": torch.rand(10, 64), }

Federated Model with Feedback Loops

model = FeedbackFederatedTransformer(graph) output_states = model.forward(inputs, num_steps=50)

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Conclusion

1. Federation: Build a transformer of transformers where each sub-transformer models a gear or celestial body.

2. Antikythera Topology: Use graphs or hypergraphs to encode gear dependencies, feedback loops, and celestial dynamics.

3. Attention Head Arrays: Encode gear ratios and celestial relationships in attention mechanisms.

4. Feedback Loops: Use recurrent mechanisms to create dynamic state updates over time.

This architecture models the Antikythera's recursive, hierarchical nature while leveraging the transformer framework’s flexibility. Let me know if you’d like to dive deeper into any aspect!