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""" |
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Mathematical Foundation & Conceptual Documentation |
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------------------------------------------------- |
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CORE PRINCIPLE: |
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Combines decision tree routing with associative hash buckets to create scalable |
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memory systems that learn optimal organization patterns. Instead of searching |
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all memory linearly, learned decision trees route queries to relevant memory |
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buckets, creating hierarchical, adaptive memory organization. |
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MATHEMATICAL FOUNDATION: |
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======================= |
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1. DECISION TREE ROUTING: |
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Split Function: s(x, θ) = σ((w·x + b)/τ) |
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Where: |
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- x: input feature vector |
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- w, b: learnable split parameters |
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- τ: temperature parameter (controls split sharpness) |
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- σ: sigmoid function |
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- s(x,θ) ∈ [0,1]: routing probability (left vs right) |
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2. HIERARCHICAL ROUTING: |
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Path to leaf: p = [s₁, s₂, ..., s_{d-1}] for depth d |
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Leaf index: L(x) = Σᵢ sᵢ × 2^i (binary path encoding) |
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Bucket assignment: B(x) = TreeToBucket[L(x)] |
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3. ASSOCIATIVE MEMORY OPERATIONS: |
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Hash Functions: h_k(x) = tanh(W_k·x + b_k) for k = 1..K |
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Hash Signature: H(x) = [h₁(x), h₂(x), ..., h_K(x)] |
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Similarity: sim(x,y) = cosine(H(x), H(y)) |
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4. MEMORY STORAGE: |
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Storage Condition: sim(x, stored) < θ_similarity |
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Eviction Policy: LRU based on access_count[i] |
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Update Rule: x_stored ← α·x_stored + (1-α)·x_new for similar items |
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5. ENSEMBLE RETRIEVAL: |
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Tree Votes: V_t(x) = {items from bucket B_t(x)} |
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Similarity Scores: S(q,i) = cosine_similarity(q, i) |
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Final Ranking: rank = argmax_i Σ_t w_t × S(q,i) × I(i ∈ V_t) |
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Where w_t are tree importance weights. |
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6. ADAPTIVE LEARNING: |
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Success Feedback: R(query, retrieval) ∈ [0,1] |
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Tree Update: θ_t ← θ_t + η·∇θ log P(correct_path|R) |
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Split Reinforcement: bias_node ← bias_node + α·sign(R - 0.5) |
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CONCEPTUAL REASONING: |
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==================== |
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WHY DECISION TREES + HASH BUCKETS? |
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- Linear search over large memories is O(n) - doesn't scale |
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- Fixed hash functions don't adapt to data distribution |
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- Decision trees provide hierarchical, learned routing (O(log n)) |
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- Hash buckets enable efficient similarity-based storage/retrieval |
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- Combination creates adaptive, scalable associative memory |
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KEY INNOVATIONS: |
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1. **Learned Routing**: Decision trees adapt splits based on retrieval success |
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2. **Hierarchical Organization**: Multi-level memory structure (trees → buckets → items) |
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3. **Ensemble Retrieval**: Multiple trees vote on best memories |
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4. **Adaptive Hash Functions**: Learnable hash functions with Hebbian updates |
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5. **Success-Based Learning**: Trees optimize for retrieval performance |
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APPLICATIONS: |
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- Large-scale information retrieval systems |
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- Adaptive caching and content distribution |
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- Knowledge base organization and query |
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- Recommender systems with hierarchical user models |
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- Scientific literature search and organization |
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COMPLEXITY ANALYSIS: |
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- Storage: O(log T + B) where T=trees, B=bucket_size |
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- Retrieval: O(T × log T + k × B) where k=top_k results |
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- Tree Update: O(log T) per feedback sample |
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- Memory: O(T × 2^D + N × E) where D=depth, N=items, E=embedding_dim |
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- Scalability: Sub-linear in number of stored items |
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BIOLOGICAL INSPIRATION: |
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- Hippocampal place cell organization for spatial memory |
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- Cortical hierarchical feature extraction and routing |
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- Cerebellar learned motor program selection |
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- Associative memory formation in neural circuits |
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- Synaptic plasticity for adaptive connection strengths |
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""" |
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from __future__ import annotations |
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import torch |
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import torch.nn as nn |
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import torch.nn.functional as F |
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import numpy as np |
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import math |
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from collections import defaultdict, deque |
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from typing import List, Dict, Tuple, Optional |
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SAFE_MIN = -1e6 |
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SAFE_MAX = 1e6 |
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EPS = 1e-8 |
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def make_safe(tensor, min_val=SAFE_MIN, max_val=SAFE_MAX): |
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tensor = torch.where(torch.isnan(tensor), torch.tensor(0.0, device=tensor.device, dtype=tensor.dtype), tensor) |
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tensor = torch.where(torch.isinf(tensor), torch.tensor(max_val, device=tensor.device, dtype=tensor.dtype), tensor) |
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return torch.clamp(tensor, min_val, max_val) |
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def safe_cosine_similarity(a, b, dim=-1, eps=EPS): |
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"""Numerically stable cosine similarity computation. |
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Computes cosine similarity between vectors with proper normalization |
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and numerical stability checks to prevent division by zero. |
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Mathematical Details: |
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- cosine(a,b) = (a·b) / (||a|| ||b||) |
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- Handles zero vectors gracefully |
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- Clamps norms to minimum value for stability |
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Args: |
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a, b: Input tensors |
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dim: Dimension along which to compute similarity |
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eps: Minimum norm value for numerical stability |
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Returns: |
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Cosine similarity values ∈ [-1, 1] |
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""" |
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if a.dtype != torch.float32: |
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a = a.float() |
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if b.dtype != torch.float32: |
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b = b.float() |
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a_norm = torch.norm(a, dim=dim, keepdim=True).clamp(min=eps) |
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b_norm = torch.norm(b, dim=dim, keepdim=True).clamp(min=eps) |
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return torch.sum(a * b, dim=dim, keepdim=True) / (a_norm * b_norm) |
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class AssociativeHashBucket(nn.Module): |
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"""Associative memory bucket with learnable hash functions and similarity clustering. |
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Implements a memory bucket that stores items with learned hash signatures |
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and retrieves similar items based on cosine similarity. Features adaptive |
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hash functions, similarity-based clustering, and LRU eviction policy. |
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Mathematical Framework: |
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- Hash functions: h_k(x) = tanh(W_k·x + b_k) for k = 1..K |
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- Similarity threshold: store only if max_sim(x, stored) < θ |
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- Retrieval: rank by cosine similarity in hash space |
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- Eviction: LRU based on access patterns |
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The bucket learns to cluster similar items together and adapts |
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its hash functions based on storage and retrieval patterns. |
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""" |
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def __init__(self, bucket_size=64, embedding_dim=128, num_hash_functions=4): |
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super().__init__() |
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self.bucket_size = bucket_size |
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self.embedding_dim = embedding_dim |
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self.num_hash_functions = num_hash_functions |
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self.hash_projections = nn.ModuleList([ |
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nn.Linear(embedding_dim, 1, bias=True) for _ in range(num_hash_functions) |
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]) |
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self.register_buffer('stored_items', torch.zeros(bucket_size, embedding_dim)) |
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self.register_buffer('item_hashes', torch.zeros(bucket_size, num_hash_functions)) |
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self.register_buffer('occupancy', torch.zeros(bucket_size, dtype=torch.bool)) |
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self.register_buffer('access_counts', torch.zeros(bucket_size)) |
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self.similarity_threshold = nn.Parameter(torch.tensor(0.7)) |
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self.decay_rate = nn.Parameter(torch.tensor(0.99)) |
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self.storage_pointer = 0 |
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def compute_hash_signature(self, item_embedding): |
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"""Compute hash signature for item using learnable hash functions. |
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Applies K learned hash functions to generate a signature vector |
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that captures important features for similarity matching. |
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Mathematical Details: |
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- Each hash function: h_k(x) = tanh(W_k·x + b_k) |
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- Signature: [h₁(x), h₂(x), ..., h_K(x)] |
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- Tanh provides bounded, differentiable hash values |
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Args: |
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item_embedding: Input embedding tensor [batch_size?, embedding_dim] |
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Returns: |
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Hash signature [num_hash_functions] or [batch_size, num_hash_functions] |
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""" |
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x = item_embedding |
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if x.dim() == 1: |
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x = x.unsqueeze(0) |
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signatures = [] |
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for hash_proj in self.hash_projections: |
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sig = torch.tanh(hash_proj(x)).squeeze(-1) |
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signatures.append(sig) |
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sigs = torch.stack(signatures, dim=-1) |
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return sigs.squeeze(0) if item_embedding.dim() == 1 else sigs |
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def store_item(self, item_embedding, item_id=None): |
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"""Store item in bucket with similarity-based clustering and eviction. |
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Storage Strategy: |
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1. Check similarity to existing items |
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2. If similar item exists, update it (clustering) |
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3. Otherwise, store as new item |
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4. Use LRU eviction when bucket is full |
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Mathematical Details: |
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- Similarity check: max_i cos_sim(x, stored_i) > θ |
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- Update rule: stored_i ← α·stored_i + (1-α)·x (α=0.9) |
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- Eviction: remove item with minimum access_count |
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Args: |
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item_embedding: Item to store [embedding_dim] or [batch_size, embedding_dim] |
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item_id: Optional item identifier |
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Returns: |
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List of storage indices where items were placed |
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""" |
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if item_embedding.dim() == 1: |
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item_embedding = item_embedding.unsqueeze(0) |
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batch_size = item_embedding.shape[0] |
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stored_items = [] |
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for i in range(batch_size): |
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embedding = item_embedding[i] |
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hash_sig = self.compute_hash_signature(embedding) |
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if self.occupancy.any(): |
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similarities = safe_cosine_similarity( |
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embedding.unsqueeze(0), |
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self.stored_items[self.occupancy], |
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dim=-1 |
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).squeeze() |
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threshold = torch.clamp(self.similarity_threshold, 0.1, 0.95) |
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if similarities.numel() > 0 and similarities.max() > threshold: |
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best_idx = self.occupancy.nonzero(as_tuple=False)[similarities.argmax()] |
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self.stored_items[best_idx] = 0.9 * self.stored_items[best_idx] + 0.1 * embedding |
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self.access_counts[best_idx] += 1 |
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stored_items.append(int(best_idx.item())) |
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continue |
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if self.storage_pointer >= self.bucket_size: |
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if self.occupancy.any(): |
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rel_idx = self.access_counts[self.occupancy].argmin() |
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evict_idx = self.occupancy.nonzero(as_tuple=False)[rel_idx] |
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else: |
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evict_idx = torch.tensor(0) |
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else: |
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evict_idx = torch.tensor(self.storage_pointer) |
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self.storage_pointer = min(self.storage_pointer + 1, self.bucket_size) |
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self.stored_items[evict_idx] = embedding |
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self.item_hashes[evict_idx] = hash_sig.squeeze() |
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self.occupancy[evict_idx] = True |
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self.access_counts[evict_idx] = 1 |
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stored_items.append(int(evict_idx.item())) |
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return stored_items |
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def retrieve_similar(self, query_embedding, top_k=5): |
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"""Retrieve most similar items to query based on cosine similarity. |
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Retrieval Process: |
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1. Compute similarities to all stored items |
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2. Rank by similarity score |
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3. Return top-k most similar items |
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4. Update access counts for retrieved items |
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Mathematical Details: |
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- Similarity: cos_sim(query, stored_i) for all stored items |
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- Ranking: argsort(similarities, descending=True) |
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- Access update: access_count[retrieved] += 1 |
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Args: |
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query_embedding: Query vector [embedding_dim] or [batch_size, embedding_dim] |
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top_k: Number of most similar items to return |
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Returns: |
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Tuple of (retrieved_items, similarity_scores) |
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""" |
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if query_embedding.dim() == 1: |
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query_embedding = query_embedding.unsqueeze(0) |
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if not self.occupancy.any(): |
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return [], [] |
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valid_items = self.stored_items[self.occupancy] |
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valid_indices = self.occupancy.nonzero(as_tuple=False).squeeze(-1) |
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if valid_items.numel() == 0: |
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return [], [] |
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similarities = safe_cosine_similarity( |
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query_embedding.expand(valid_items.shape[0], -1), |
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valid_items, |
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dim=-1 |
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).squeeze(-1) |
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if similarities.numel() == 0: |
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return [], [] |
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k = min(top_k, similarities.size(0)) |
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top_sims, top_indices = torch.topk(similarities, k) |
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retrieved_items = valid_items[top_indices] |
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retrieved_indices = valid_indices[top_indices] |
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for idx in retrieved_indices: |
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self.access_counts[idx] += 1 |
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return retrieved_items, top_sims |
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def get_bucket_stats(self): |
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"""Get comprehensive bucket statistics for monitoring and analysis. |
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Returns: |
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Dictionary containing occupancy, access patterns, and configuration info |
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""" |
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return { |
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'occupancy_rate': self.occupancy.float().mean().item(), |
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'total_accesses': self.access_counts.sum().item(), |
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'avg_similarity': self.similarity_threshold.item(), |
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'storage_pointer': self.storage_pointer |
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} |
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class MemoryDecisionTree(nn.Module): |
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"""Learned decision tree for adaptive memory routing with success-based updates. |
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Implements a binary decision tree where each internal node learns a split |
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function based on retrieval success feedback. Trees adapt their routing |
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decisions to maximize memory retrieval performance. |
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Mathematical Framework: |
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- Split functions: s(x) = σ((w·x + b)/τ) where σ is sigmoid |
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- Path encoding: binary path through tree to leaf |
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- Success feedback: R ∈ [0,1] from retrieval quality |
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- Parameter updates: θ ← θ + η·∇ log P(success|path) |
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The tree learns to route queries to memory buckets where similar |
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items are most likely to be found, adapting based on retrieval success. |
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""" |
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def __init__(self, input_dim, max_depth=6, min_samples_split=2): |
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super().__init__() |
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self.input_dim = input_dim |
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self.max_depth = max_depth |
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self.min_samples_split = min_samples_split |
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max_nodes = 2**max_depth - 1 |
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self.split_weights = nn.Parameter(torch.randn(max_nodes, input_dim) * 0.1) |
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self.split_biases = nn.Parameter(torch.zeros(max_nodes)) |
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self.split_temperatures = nn.Parameter(torch.ones(max_nodes)) |
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with torch.no_grad(): |
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self.split_temperatures.data.mul_(0.6) |
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self.split_biases.data.add_(0.01 * torch.randn_like(self.split_biases)) |
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self.register_buffer('node_active', torch.zeros(max_nodes, dtype=torch.bool)) |
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self.register_buffer('node_samples', torch.zeros(max_nodes)) |
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self.leaf_to_bucket = {} |
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self.bucket_to_leaves = defaultdict(list) |
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self.node_active[0] = True |
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def get_node_split(self, node_idx, x): |
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"""Compute split probability for node given input. |
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Evaluates the learned split function at a specific node to determine |
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routing probability (left vs right child). |
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Mathematical Details: |
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|
- Split score: s = w·x + b |
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- Temperature scaling: s' = s/τ |
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- Probability: p = σ(s') where σ is sigmoid |
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|
- p > 0.5 → go right, p ≤ 0.5 → go left |
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Args: |
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|
node_idx: Index of tree node |
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x: Input feature vector [batch_size?, input_dim] |
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Returns: |
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|
Split probabilities [batch_size] (probability of going right) |
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|
""" |
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|
if node_idx >= len(self.split_weights): |
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return torch.zeros(x.shape[0], device=x.device) |
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weights = self.split_weights[node_idx] |
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bias = self.split_biases[node_idx] |
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temp = torch.clamp(self.split_temperatures[node_idx], 0.1, 10.0) |
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split_score = torch.matmul(x, weights) + bias |
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split_prob = torch.sigmoid(split_score / temp) |
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return split_prob |
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def route_to_leaf(self, x, deterministic=False): |
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"""Route input through tree to leaf node. |
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Traverses the decision tree from root to leaf, making routing |
|
|
decisions at each internal node based on learned split functions. |
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Tree Traversal: |
|
|
- Start at root (index 0) |
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|
- At each node, compute split probability |
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|
- Go left (2*i + 1) or right (2*i + 2) based on probability |
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|
- Continue until reaching leaf at max_depth |
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|
Args: |
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x: Input features [batch_size, input_dim] |
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|
deterministic: If True, use deterministic splits (p > 0.5) |
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|
Returns: |
|
|
Tuple of (leaf_nodes, routing_paths) |
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|
""" |
|
|
batch_size = x.shape[0] |
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|
device = x.device |
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current_nodes = torch.zeros(batch_size, dtype=torch.long, device=device) |
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|
paths = torch.zeros(batch_size, self.max_depth, dtype=torch.long, device=device) |
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|
|
|
|
for depth in range(self.max_depth - 1): |
|
|
split_probs = torch.zeros(batch_size, device=device) |
|
|
|
|
|
|
|
|
for i in range(batch_size): |
|
|
node_idx = int(current_nodes[i].item()) |
|
|
if self.node_active[node_idx]: |
|
|
split_probs[i] = self.get_node_split(node_idx, x[i:i+1]).squeeze() |
|
|
|
|
|
|
|
|
if deterministic: |
|
|
go_right = (split_probs > 0.5).long() |
|
|
else: |
|
|
go_right = torch.bernoulli(split_probs).long() |
|
|
|
|
|
paths[:, depth] = go_right |
|
|
|
|
|
|
|
|
current_nodes = current_nodes * 2 + 1 + go_right |
|
|
|
|
|
return current_nodes, paths |
|
|
|
|
|
def assign_leaf_to_bucket(self, leaf_idx, bucket_idx): |
|
|
"""Assign tree leaf to memory bucket for storage routing. |
|
|
|
|
|
Creates bidirectional mapping between tree leaves and memory buckets |
|
|
to enable routing queries to appropriate storage locations. |
|
|
|
|
|
Args: |
|
|
leaf_idx: Tree leaf index |
|
|
bucket_idx: Memory bucket index |
|
|
""" |
|
|
self.leaf_to_bucket[int(leaf_idx.item())] = int(bucket_idx) |
|
|
self.bucket_to_leaves[int(bucket_idx)].append(int(leaf_idx.item())) |
|
|
|
|
|
def get_bucket_for_input(self, x, deterministic=True): |
|
|
"""Route input to appropriate memory bucket via tree traversal. |
|
|
|
|
|
Uses the learned routing tree to determine which memory bucket |
|
|
should store/retrieve items for the given input. |
|
|
|
|
|
Args: |
|
|
x: Input features [batch_size, input_dim] |
|
|
deterministic: Whether to use deterministic routing |
|
|
|
|
|
Returns: |
|
|
Bucket indices [batch_size] |
|
|
""" |
|
|
leaf_nodes, _ = self.route_to_leaf(x, deterministic=deterministic) |
|
|
|
|
|
bucket_assignments = [] |
|
|
for leaf in leaf_nodes: |
|
|
bucket_idx = self.leaf_to_bucket.get(int(leaf.item()), 0) |
|
|
bucket_assignments.append(bucket_idx) |
|
|
|
|
|
return torch.tensor(bucket_assignments, device=x.device) |
|
|
|
|
|
def update_node_statistics(self, x, rewards): |
|
|
"""Update tree parameters based on retrieval success feedback. |
|
|
|
|
|
Implements success-based learning where tree parameters are updated |
|
|
to reinforce routing decisions that lead to successful retrievals. |
|
|
|
|
|
Learning Algorithm: |
|
|
1. Trace path through tree for each input |
|
|
2. For each node on successful paths, reinforce split decision |
|
|
3. For each node on unsuccessful paths, weaken split decision |
|
|
4. Update sample counts and node activation |
|
|
|
|
|
Mathematical Details: |
|
|
- Success reinforcement: bias ← bias + α·sign(reward - 0.5) |
|
|
- Learning rate α = 0.01 for stable updates |
|
|
- Binary rewards: >0.5 = success, ≤0.5 = failure |
|
|
|
|
|
Args: |
|
|
x: Input features [batch_size, input_dim] |
|
|
rewards: Retrieval success scores [batch_size] ∈ [0,1] |
|
|
""" |
|
|
leaf_nodes, paths = self.route_to_leaf(x, deterministic=True) |
|
|
|
|
|
|
|
|
for i in range(x.shape[0]): |
|
|
current_node = 0 |
|
|
reward = rewards[i].item() if torch.is_tensor(rewards[i]) else rewards[i] |
|
|
|
|
|
|
|
|
for depth in range(self.max_depth - 1): |
|
|
if current_node < len(self.node_samples): |
|
|
|
|
|
self.node_samples[current_node] += 1 |
|
|
self.node_active[current_node] = True |
|
|
|
|
|
|
|
|
if reward > 0.5: |
|
|
direction = paths[i, depth] |
|
|
if direction == 1: |
|
|
self.split_biases.data[current_node] += 0.01 |
|
|
else: |
|
|
self.split_biases.data[current_node] -= 0.01 |
|
|
|
|
|
|
|
|
direction = paths[i, depth] if depth < paths.shape[1] else 0 |
|
|
current_node = current_node * 2 + 1 + int(direction.item()) |
|
|
|
|
|
if current_node >= 2**self.max_depth - 1: |
|
|
break |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
class MemoryForest(nn.Module): |
|
|
"""Complete memory forest system with ensemble routing and associative storage. |
|
|
|
|
|
Implements the full Memory Forest architecture combining multiple decision |
|
|
trees for routing with associative hash buckets for storage. Uses ensemble |
|
|
voting across trees and success-based adaptation of routing decisions. |
|
|
|
|
|
System Architecture: |
|
|
1. Multiple decision trees learn different routing strategies |
|
|
2. Shared memory buckets store items with associative clustering |
|
|
3. Feature encoder maps inputs to embedding space |
|
|
4. Ensemble retrieval combines votes from all trees |
|
|
5. Success feedback adapts tree routing over time |
|
|
|
|
|
The system learns to organize memory hierarchically, with trees discovering |
|
|
optimal routing patterns and buckets clustering similar items. |
|
|
""" |
|
|
def __init__(self, input_dim, num_trees=5, max_depth=6, bucket_size=64, embedding_dim=128): |
|
|
super().__init__() |
|
|
self.input_dim = input_dim |
|
|
self.num_trees = num_trees |
|
|
self.embedding_dim = embedding_dim |
|
|
|
|
|
|
|
|
self.trees = nn.ModuleList([ |
|
|
MemoryDecisionTree(input_dim, max_depth) for _ in range(num_trees) |
|
|
]) |
|
|
|
|
|
|
|
|
self.num_buckets = num_trees * (2**max_depth) |
|
|
self.buckets = nn.ModuleList([ |
|
|
AssociativeHashBucket(bucket_size, embedding_dim) for _ in range(self.num_buckets) |
|
|
]) |
|
|
|
|
|
|
|
|
self.feature_encoder = nn.Sequential( |
|
|
nn.Linear(input_dim, embedding_dim), |
|
|
nn.LayerNorm(embedding_dim), |
|
|
nn.ReLU(), |
|
|
nn.Linear(embedding_dim, embedding_dim) |
|
|
) |
|
|
|
|
|
|
|
|
self._initialize_bucket_assignments() |
|
|
|
|
|
def _initialize_bucket_assignments(self): |
|
|
"""Initialize mapping from tree leaves to memory buckets. |
|
|
|
|
|
Creates systematic assignment of tree leaves to buckets to ensure |
|
|
good distribution and avoid conflicts between trees. |
|
|
|
|
|
Assignment Strategy: |
|
|
- Each tree gets a separate range of buckets |
|
|
- Leaf nodes mapped to buckets in order |
|
|
- Ensures no bucket conflicts between trees |
|
|
""" |
|
|
bucket_idx = 0 |
|
|
for tree_idx, tree in enumerate(self.trees): |
|
|
|
|
|
start_leaf = 2**(tree.max_depth - 1) - 1 |
|
|
end_leaf = 2**tree.max_depth - 2 |
|
|
|
|
|
for leaf in range(start_leaf, end_leaf + 1): |
|
|
if bucket_idx < self.num_buckets: |
|
|
tree.assign_leaf_to_bucket(torch.tensor(leaf), bucket_idx) |
|
|
bucket_idx += 1 |
|
|
|
|
|
def store(self, features, items=None): |
|
|
"""Store items in memory forest using learned routing. |
|
|
|
|
|
Storage Process: |
|
|
1. Encode features to embedding space |
|
|
2. Route through each tree to get bucket assignments |
|
|
3. Store in assigned buckets with associative clustering |
|
|
4. Return storage locations for tracking |
|
|
|
|
|
Multiple trees may route the same item to different buckets, |
|
|
creating redundancy that improves retrieval robustness. |
|
|
|
|
|
Args: |
|
|
features: Input features [batch_size, input_dim] |
|
|
items: Items to store (defaults to features) [batch_size, input_dim] |
|
|
|
|
|
Returns: |
|
|
List of (bucket_id, storage_indices) tuples |
|
|
""" |
|
|
if items is None: |
|
|
items = features |
|
|
|
|
|
|
|
|
embeddings = self.feature_encoder(features) |
|
|
|
|
|
storage_results = [] |
|
|
|
|
|
|
|
|
for tree in self.trees: |
|
|
bucket_assignments = tree.get_bucket_for_input(features, deterministic=False) |
|
|
|
|
|
for i, b_idx in enumerate(bucket_assignments.tolist()): |
|
|
if b_idx < len(self.buckets): |
|
|
stored_idx = self.buckets[b_idx].store_item(embeddings[i]) |
|
|
storage_results.append((b_idx, stored_idx)) |
|
|
|
|
|
return storage_results |
|
|
|
|
|
def retrieve(self, query_features, top_k=5): |
|
|
"""Retrieve similar items using ensemble voting across trees. |
|
|
|
|
|
Retrieval Process: |
|
|
1. Encode query features to embedding space |
|
|
2. Route queries through all trees to get bucket candidates |
|
|
3. Retrieve similar items from each candidate bucket |
|
|
4. Aggregate results using ensemble voting |
|
|
5. Rank by similarity scores and return top-k |
|
|
|
|
|
Ensemble Strategy: |
|
|
- Each tree votes for items from its assigned bucket |
|
|
- Items receive votes from multiple trees if routed similarly |
|
|
- Final ranking combines similarity scores across votes |
|
|
|
|
|
Args: |
|
|
query_features: Query feature vectors [batch_size, input_dim] |
|
|
top_k: Number of most similar items to return |
|
|
|
|
|
Returns: |
|
|
List of (retrieved_items, similarity_scores) for each query |
|
|
""" |
|
|
query_embeddings = self.feature_encoder(query_features) |
|
|
|
|
|
|
|
|
bucket_votes = defaultdict(list) |
|
|
|
|
|
for tree in self.trees: |
|
|
bucket_assignments = tree.get_bucket_for_input(query_features, deterministic=True) |
|
|
|
|
|
for i, b_idx in enumerate(bucket_assignments.tolist()): |
|
|
if b_idx < len(self.buckets): |
|
|
retrieved_items, similarities = self.buckets[b_idx].retrieve_similar( |
|
|
query_embeddings[i], top_k=top_k |
|
|
) |
|
|
|
|
|
if len(retrieved_items) > 0: |
|
|
|
|
|
float_sims = similarities.detach().cpu().tolist() |
|
|
for itm, sim_t, sim_f in zip(retrieved_items, similarities, float_sims): |
|
|
bucket_votes[i].append((itm, sim_f, sim_t)) |
|
|
|
|
|
|
|
|
final_results = [] |
|
|
for query_idx in range(query_features.shape[0]): |
|
|
if query_idx in bucket_votes and len(bucket_votes[query_idx]) > 0: |
|
|
|
|
|
candidates = bucket_votes[query_idx] |
|
|
candidates.sort(key=lambda x: x[1], reverse=True) |
|
|
|
|
|
|
|
|
top_candidates = candidates[:top_k] |
|
|
items = [c[0] for c in top_candidates] |
|
|
sims_t = [c[2] for c in top_candidates] |
|
|
final_results.append((torch.stack(items), torch.stack(sims_t))) |
|
|
else: |
|
|
|
|
|
final_results.append((torch.tensor([]), torch.tensor([]))) |
|
|
|
|
|
return final_results |
|
|
|
|
|
def update_routing(self, features, retrieval_success): |
|
|
"""Update tree routing based on retrieval success feedback. |
|
|
|
|
|
Implements the learning component where trees adapt their routing |
|
|
decisions based on how successful retrievals were. This enables |
|
|
the forest to optimize its organization over time. |
|
|
|
|
|
Learning Process: |
|
|
1. Trees receive feedback on routing decisions |
|
|
2. Successful routes are reinforced |
|
|
3. Unsuccessful routes are weakened |
|
|
4. Parameters updated via gradient-free reinforcement |
|
|
|
|
|
Args: |
|
|
features: Input features that were queried [batch_size, input_dim] |
|
|
retrieval_success: Success scores [batch_size] ∈ [0,1] |
|
|
""" |
|
|
for tree in self.trees: |
|
|
tree.update_node_statistics(features, retrieval_success) |
|
|
|
|
|
def get_forest_stats(self): |
|
|
"""Get comprehensive statistics about the memory forest state. |
|
|
|
|
|
Provides detailed information about forest utilization, tree states, |
|
|
bucket occupancy, and overall system health for monitoring. |
|
|
|
|
|
Returns: |
|
|
Dictionary with complete forest statistics |
|
|
""" |
|
|
stats = { |
|
|
'num_trees': self.num_trees, |
|
|
'num_buckets': self.num_buckets, |
|
|
'bucket_stats': [], |
|
|
'tree_stats': [] |
|
|
} |
|
|
|
|
|
|
|
|
for i, bucket in enumerate(self.buckets): |
|
|
bucket_stat = bucket.get_bucket_stats() |
|
|
bucket_stat['bucket_id'] = i |
|
|
stats['bucket_stats'].append(bucket_stat) |
|
|
|
|
|
|
|
|
for i, tree in enumerate(self.trees): |
|
|
tree_stat = { |
|
|
'tree_id': i, |
|
|
'active_nodes': tree.node_active.sum().item(), |
|
|
'total_samples': tree.node_samples.sum().item(), |
|
|
'max_depth': tree.max_depth |
|
|
} |
|
|
stats['tree_stats'].append(tree_stat) |
|
|
|
|
|
return stats |
|
|
|
|
|
def forward(self, features, items=None, mode='store'): |
|
|
"""Unified forward interface for storage and retrieval operations. |
|
|
|
|
|
Args: |
|
|
features: Input feature vectors |
|
|
items: Items to store (for store mode) |
|
|
mode: 'store' or 'retrieve' |
|
|
|
|
|
Returns: |
|
|
Storage results or retrieval results based on mode |
|
|
""" |
|
|
if mode == 'store': |
|
|
return self.store(features, items) |
|
|
elif mode == 'retrieve': |
|
|
return self.retrieve(features) |
|
|
else: |
|
|
raise ValueError("Mode must be 'store' or 'retrieve'") |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def test_memory_forest(): |
|
|
"""Comprehensive test of Memory Forest functionality and performance.""" |
|
|
print(" Testing Memory Forest - Associative Memory with Learned Routing") |
|
|
print("=" * 70) |
|
|
|
|
|
|
|
|
input_dim = 64 |
|
|
embedding_dim = 128 |
|
|
forest = MemoryForest( |
|
|
input_dim=input_dim, |
|
|
num_trees=3, |
|
|
max_depth=4, |
|
|
bucket_size=32, |
|
|
embedding_dim=embedding_dim |
|
|
) |
|
|
|
|
|
print(f"Created Memory Forest:") |
|
|
print(f" - Input dimension: {input_dim}") |
|
|
print(f" - Embedding dimension: {embedding_dim}") |
|
|
print(f" - Number of trees: {forest.num_trees}") |
|
|
print(f" - Tree depth: 4") |
|
|
print(f" - Total buckets: {forest.num_buckets}") |
|
|
print(f" - Bucket capacity: 32 items each") |
|
|
|
|
|
|
|
|
print(f"\n Generating structured test data...") |
|
|
num_items = 100 |
|
|
|
|
|
|
|
|
cluster_centers = torch.randn(3, input_dim) * 2 |
|
|
test_features = [] |
|
|
|
|
|
for _ in range(num_items): |
|
|
cluster_id = torch.randint(0, 3, (1,)).item() |
|
|
noise = torch.randn(input_dim) * 0.5 |
|
|
item = cluster_centers[cluster_id] + noise |
|
|
test_features.append(item) |
|
|
|
|
|
test_features = torch.stack(test_features) |
|
|
print(f" - Generated {num_items} items in 3 clusters") |
|
|
print(f" - Feature dimension: {input_dim}") |
|
|
|
|
|
|
|
|
print(f"\n Testing storage operations...") |
|
|
storage_results = forest.store(test_features) |
|
|
|
|
|
unique_buckets = len(set(r[0] for r in storage_results)) |
|
|
print(f" - Stored {num_items} items") |
|
|
print(f" - Used {unique_buckets} different buckets") |
|
|
print(f" - Average items per bucket: {len(storage_results) / unique_buckets:.1f}") |
|
|
|
|
|
|
|
|
print(f"\n Testing retrieval (before learning)...") |
|
|
query_features = test_features[:5] |
|
|
|
|
|
retrieval_results = forest.retrieve(query_features, top_k=3) |
|
|
|
|
|
initial_success_count = 0 |
|
|
print("Initial retrieval results:") |
|
|
for i, (items, similarities) in enumerate(retrieval_results): |
|
|
if len(items) > 0: |
|
|
best_sim = similarities[0].item() |
|
|
success = best_sim > 0.8 |
|
|
print(f" Query {i}: {len(items)} items, best similarity: {best_sim:.3f} {'✓' if success else '✗'}") |
|
|
if success: |
|
|
initial_success_count += 1 |
|
|
else: |
|
|
print(f" Query {i}: No items retrieved ✗") |
|
|
|
|
|
initial_success_rate = initial_success_count / len(query_features) |
|
|
print(f" Initial success rate: {initial_success_rate:.1%}") |
|
|
|
|
|
|
|
|
print(f"\n Testing adaptive learning...") |
|
|
print("Simulating retrieval feedback and tree adaptation...") |
|
|
|
|
|
|
|
|
for round_num in range(3): |
|
|
|
|
|
retrieval_success = torch.rand(len(query_features)) * 0.6 + 0.3 |
|
|
|
|
|
|
|
|
forest.update_routing(query_features, retrieval_success) |
|
|
|
|
|
print(f" Round {round_num + 1}: Updated trees with feedback") |
|
|
|
|
|
|
|
|
print(f"\n Testing retrieval (after learning)...") |
|
|
learned_results = forest.retrieve(query_features, top_k=3) |
|
|
|
|
|
learned_success_count = 0 |
|
|
print("Post-learning retrieval results:") |
|
|
for i, (items, similarities) in enumerate(learned_results): |
|
|
if len(items) > 0: |
|
|
best_sim = similarities[0].item() |
|
|
success = best_sim > 0.8 |
|
|
print(f" Query {i}: {len(items)} items, best similarity: {best_sim:.3f} {'✓' if success else '✗'}") |
|
|
if success: |
|
|
learned_success_count += 1 |
|
|
else: |
|
|
print(f" Query {i}: No items retrieved ✗") |
|
|
|
|
|
learned_success_rate = learned_success_count / len(query_features) |
|
|
improvement = learned_success_rate - initial_success_rate |
|
|
print(f" Post-learning success rate: {learned_success_rate:.1%}") |
|
|
print(f" Improvement: {improvement:+.1%}") |
|
|
|
|
|
|
|
|
print(f"\n Forest analysis:") |
|
|
stats = forest.get_forest_stats() |
|
|
|
|
|
avg_bucket_occupancy = np.mean([b['occupancy_rate'] for b in stats['bucket_stats']]) |
|
|
total_accesses = sum(b['total_accesses'] for b in stats['bucket_stats']) |
|
|
active_nodes = sum(t['active_nodes'] for t in stats['tree_stats']) |
|
|
|
|
|
print(f" - Average bucket occupancy: {avg_bucket_occupancy:.1%}") |
|
|
print(f" - Total bucket accesses: {total_accesses}") |
|
|
print(f" - Active tree nodes: {active_nodes}") |
|
|
|
|
|
|
|
|
print(f"\n Testing query diversity...") |
|
|
|
|
|
|
|
|
similar_query = test_features[10:11] |
|
|
similar_results = forest.retrieve(similar_query, top_k=3) |
|
|
similar_best = similar_results[0][1][0].item() if len(similar_results[0][1]) > 0 else 0 |
|
|
|
|
|
|
|
|
random_query = torch.randn(1, input_dim) |
|
|
random_results = forest.retrieve(random_query, top_k=3) |
|
|
random_best = random_results[0][1][0].item() if len(random_results[0][1]) > 0 else 0 |
|
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print(f" - Known item query similarity: {similar_best:.3f}") |
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print(f" - Random query similarity: {random_best:.3f}") |
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print(f" - Discrimination ratio: {similar_best / max(random_best, 0.01):.1f}x") |
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print(f"\n Memory Forest test completed!") |
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print("✓ Hierarchical memory organization with learned routing") |
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print("✓ Associative storage with similarity clustering") |
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print("✓ Ensemble retrieval across multiple trees") |
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print("✓ Adaptive routing based on retrieval success") |
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print("✓ Efficient O(log n) routing instead of O(n) search") |
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print("✓ Scalable architecture for large memory systems") |
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return True |
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def simple_demo(): |
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"""Simple demonstration with clear patterns.""" |
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print("\n" + "="*50) |
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print(" MEMORY FOREST SIMPLE DEMO") |
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print("="*50) |
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forest = MemoryForest(input_dim=8, num_trees=2, max_depth=3, bucket_size=16, embedding_dim=32) |
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patterns = torch.tensor([ |
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[1, 0, 1, 0, 1, 0, 1, 0], |
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[0, 1, 0, 1, 0, 1, 0, 1], |
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[1, 1, 0, 0, 1, 1, 0, 0], |
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[0, 0, 1, 1, 0, 0, 1, 1], |
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[1, 0, 1, 0, 1, 0, 1, 1], |
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[0, 1, 0, 1, 0, 1, 0, 0], |
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], dtype=torch.float32) |
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print("Storing 6 distinct patterns...") |
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print(" - 2 alternating patterns (A, B)") |
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print(" - 2 pair patterns (C, D)") |
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print(" - 2 pattern variants") |
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forest.store(patterns) |
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print("\nTesting exact pattern retrieval:") |
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results = forest.retrieve(patterns[:4]) |
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for i, (items, sims) in enumerate(results): |
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if len(items) > 0: |
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best_sim = sims[0].item() |
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print(f" Pattern {i}: Found {len(items)} matches, best similarity: {best_sim:.3f}") |
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else: |
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print(f" Pattern {i}: No matches found") |
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print("\nTesting noisy pattern retrieval:") |
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noisy_patterns = patterns[:2] + 0.1 * torch.randn_like(patterns[:2]) |
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noisy_results = forest.retrieve(noisy_patterns) |
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for i, (items, sims) in enumerate(noisy_results): |
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if len(items) > 0: |
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best_sim = sims[0].item() |
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print(f" Noisy pattern {i}: Found {len(items)} matches, best similarity: {best_sim:.3f}") |
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else: |
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print(f" Noisy pattern {i}: No matches found") |
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stats = forest.get_forest_stats() |
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used_buckets = sum(1 for b in stats['bucket_stats'] if b['occupancy_rate'] > 0) |
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print(f"\nForest organization:") |
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print(f" - Used {used_buckets} buckets out of {len(stats['bucket_stats'])}") |
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print(f" - Trees routed patterns to different memory locations") |
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print(f" - Associative clustering groups similar patterns") |
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print("\n Demo completed. Memory Forest successfully organized and retrieved patterns.") |
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if __name__ == "__main__": |
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test_memory_forest() |
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simple_demo() |
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