Chapter 340: Associative Memory Trading — Retrieval-Based Predictions with Dense Associative Networks
Chapter 340: Associative Memory Trading — Retrieval-Based Predictions with Dense Associative Networks
Overview
Associative Memory networks represent a powerful paradigm for pattern recognition and retrieval in trading. Unlike traditional feedforward neural networks that learn input-output mappings, associative memories store patterns and retrieve the closest match when presented with partial or noisy input. This makes them particularly suited for recognizing market patterns and making predictions based on historical similarity.
Core Concepts
What is Associative Memory?
Associative memory is a content-addressable memory system that:
- Stores a set of patterns during training
- Retrieves the most similar stored pattern when given a query
- Completes partial patterns by filling in missing information
- Corrects noisy inputs by converging to the nearest stored pattern
From Hopfield Networks to Modern Associative Memory
Classical Hopfield (1982):├── Binary patterns: {-1, +1}├── Energy-based dynamics├── Limited capacity: ~0.14N patterns (N = neurons)└── Converges to stored attractors
Modern Dense Associative Memory (2016):├── Continuous patterns: ℝ^d├── Exponential storage capacity├── Attention-like retrieval mechanism└── Differentiable for deep learning integrationWhy Associative Memory for Trading?
- Pattern Matching: Markets exhibit recurring patterns; AM finds the most similar historical regime
- Noise Robustness: Real market data is noisy; AM naturally filters noise
- Interpretability: Retrieved patterns provide context for predictions
- Memory Efficiency: Store representative patterns instead of all data
- One-Shot Learning: Learn from rare but important market events
Trading Strategy
Strategy Overview: Use Dense Associative Memory to identify similar historical market patterns and predict future price movements based on what happened after those patterns.
Signal Generation
1. Feature Extraction: - Compute market features: returns, volatility, volume patterns - Normalize to create pattern vector
2. Pattern Retrieval: - Query the associative memory with current pattern - Retrieve K most similar historical patterns - Weight by similarity score
3. Prediction: - Aggregate outcomes from retrieved patterns - Generate directional signal with confidence
4. Position Sizing: - Scale position by retrieval confidence - Higher similarity = larger positionEntry Signals
- Long Signal: Retrieved patterns predominantly followed by positive returns
- Short Signal: Retrieved patterns predominantly followed by negative returns
- Confidence Threshold: Only trade when similarity score exceeds threshold
Risk Management
- Novelty Detection: Low retrieval similarity indicates novel market conditions → reduce exposure
- Consensus Check: Multiple retrieved patterns should agree on direction
- Volatility Scaling: Adjust position size based on expected volatility from retrieved patterns
Technical Specification
Mathematical Foundation
Classical Hopfield Energy
For binary patterns x ∈ {-1, +1}^N with weight matrix W:
E(x) = -½ x^T W x
Update rule (asynchronous):x_i ← sign(Σ_j W_ij x_j)
Weight learning (Hebbian):W_ij = (1/P) Σ_μ ξ_i^μ ξ_j^μModern Dense Associative Memory
For patterns {ξ^μ} ∈ ℝ^d, the energy function becomes:
E(x) = -log Σ_μ exp(β x · ξ^μ)
Retrieval dynamics:x_new = Σ_μ softmax(β x · ξ^μ) ξ^μ
This is equivalent to attention!Connection to Attention Mechanism
Query: q = W_q xKeys: K = [ξ^1, ξ^2, ..., ξ^M]Values: V = [v^1, v^2, ..., v^M]
Attention output:output = Σ_μ softmax(q · ξ^μ / √d) v^μArchitecture Diagram
Market Data Stream │ ▼ ┌─────────────────────────────┐ │ Feature Engineering │ │ ├── Returns & Volatility │ │ ├── Technical Indicators │ │ ├── Volume Patterns │ │ └── Cross-Asset Features │ └──────────────┬──────────────┘ │ ▼ Query Pattern x ┌─────────────────────────────┐ │ Dense Associative Memory │ │ │ │ ┌───────────────────────┐ │ │ │ Pattern Memory │ │ │ │ ξ^1, ξ^2, ..., ξ^M │ │ │ │ (Historical States) │ │ │ └───────────────────────┘ │ │ ↓ ↓ ↓ │ │ ┌───────────────────────┐ │ │ │ Similarity Scoring │ │ │ │ softmax(β x · ξ^μ) │ │ │ └───────────────────────┘ │ │ ↓ ↓ ↓ │ │ ┌───────────────────────┐ │ │ │ Weighted Retrieval │ │ │ │ Σ α_μ v^μ │ │ │ └───────────────────────┘ │ └──────────────┬──────────────┘ │ ┌──────────────┴──────────────┐ ▼ ▼ ▼ ┌─────────────┐ ┌─────────────┐ ┌─────────────┐ │ Predicted │ │ Retrieval │ │ Similar │ │ Returns │ │ Confidence │ │ Patterns │ └──────┬──────┘ └──────┬──────┘ └──────┬──────┘ │ │ │ └───────────────┼───────────────┘ ▼ ┌─────────────────────────────┐ │ Trading Decision │ │ ├── Signal Direction │ │ ├── Position Size │ │ └── Risk Parameters │ └─────────────────────────────┘Feature Engineering for Pattern Storage
def compute_market_pattern(df, lookback=20): """ Create market pattern vector for associative memory """ pattern = {}
# Return-based features returns = df['close'].pct_change() pattern['return_mean'] = returns.rolling(lookback).mean().iloc[-1] pattern['return_std'] = returns.rolling(lookback).std().iloc[-1] pattern['return_skew'] = returns.rolling(lookback).skew().iloc[-1] pattern['return_kurt'] = returns.rolling(lookback).kurt().iloc[-1]
# Trend features pattern['trend_5'] = (df['close'].iloc[-1] / df['close'].iloc[-5] - 1) pattern['trend_20'] = (df['close'].iloc[-1] / df['close'].iloc[-20] - 1)
# Volatility features pattern['volatility'] = returns.rolling(lookback).std().iloc[-1] * np.sqrt(252) pattern['volatility_change'] = ( returns.rolling(5).std().iloc[-1] / returns.rolling(20).std().iloc[-1] )
# Volume features volume_ma = df['volume'].rolling(lookback).mean() pattern['volume_ratio'] = df['volume'].iloc[-1] / volume_ma.iloc[-1]
# Range features atr = (df['high'] - df['low']).rolling(lookback).mean() pattern['atr_ratio'] = (df['high'].iloc[-1] - df['low'].iloc[-1]) / atr.iloc[-1]
# Close position in range pattern['close_position'] = ( (df['close'].iloc[-1] - df['low'].iloc[-lookback:].min()) / (df['high'].iloc[-lookback:].max() - df['low'].iloc[-lookback:].min()) )
return np.array(list(pattern.values()))Dense Associative Memory Implementation
import torchimport torch.nn as nnimport torch.nn.functional as F
class DenseAssociativeMemory(nn.Module): """ Dense Associative Memory for pattern retrieval
Stores patterns and retrieves based on similarity, using softmax attention for smooth differentiable retrieval. """
def __init__(self, pattern_dim: int, memory_size: int, beta: float = 1.0, n_heads: int = 4): super().__init__()
self.pattern_dim = pattern_dim self.memory_size = memory_size self.beta = beta self.n_heads = n_heads
# Learnable pattern memory self.patterns = nn.Parameter(torch.randn(memory_size, pattern_dim)) self.values = nn.Parameter(torch.randn(memory_size, pattern_dim))
# Multi-head attention components self.head_dim = pattern_dim // n_heads self.W_q = nn.Linear(pattern_dim, pattern_dim, bias=False) self.W_k = nn.Linear(pattern_dim, pattern_dim, bias=False) self.W_v = nn.Linear(pattern_dim, pattern_dim, bias=False) self.W_o = nn.Linear(pattern_dim, pattern_dim, bias=False)
# Prediction head self.predictor = nn.Sequential( nn.Linear(pattern_dim, pattern_dim // 2), nn.GELU(), nn.Dropout(0.1), nn.Linear(pattern_dim // 2, 1), nn.Tanh() )
def store_patterns(self, patterns: torch.Tensor, values: torch.Tensor): """ Store patterns and their associated values (labels/outcomes) """ with torch.no_grad(): # Normalize patterns patterns_norm = F.normalize(patterns, dim=-1) self.patterns.data = patterns_norm self.values.data = values
def retrieve(self, query: torch.Tensor, return_attention: bool = False): """ Retrieve from memory using attention mechanism
Args: query: (batch, pattern_dim) query pattern return_attention: whether to return attention weights
Returns: retrieved: (batch, pattern_dim) retrieved pattern attention: (batch, memory_size) attention weights (optional) """ batch_size = query.shape[0]
# Project query q = self.W_q(query) # (batch, pattern_dim)
# Reshape for multi-head attention q = q.view(batch_size, self.n_heads, self.head_dim)
# Project memory k = self.W_k(self.patterns) # (memory_size, pattern_dim) v = self.W_v(self.values) # (memory_size, pattern_dim)
k = k.view(1, self.memory_size, self.n_heads, self.head_dim) v = v.view(1, self.memory_size, self.n_heads, self.head_dim)
# Compute attention scores # q: (batch, n_heads, head_dim) # k: (1, memory_size, n_heads, head_dim) scores = torch.einsum('bhd,bmhd->bhm', q, k) scores = scores * self.beta / (self.head_dim ** 0.5)
# Softmax attention attention = F.softmax(scores, dim=-1) # (batch, n_heads, memory_size)
# Retrieve values # v: (1, memory_size, n_heads, head_dim) retrieved = torch.einsum('bhm,bmhd->bhd', attention, v) retrieved = retrieved.view(batch_size, self.pattern_dim)
# Output projection retrieved = self.W_o(retrieved)
if return_attention: # Average attention across heads attention_avg = attention.mean(dim=1) # (batch, memory_size) return retrieved, attention_avg
return retrieved
def forward(self, query: torch.Tensor): """ Retrieve and predict
Args: query: (batch, pattern_dim) current market pattern
Returns: prediction: (batch, 1) predicted direction confidence: (batch, 1) retrieval confidence """ retrieved, attention = self.retrieve(query, return_attention=True)
# Prediction from retrieved pattern prediction = self.predictor(retrieved)
# Confidence based on attention concentration # High entropy = low confidence (no clear match) entropy = -(attention * (attention + 1e-8).log()).sum(dim=-1, keepdim=True) max_entropy = torch.log(torch.tensor(self.memory_size, dtype=torch.float32)) confidence = 1 - (entropy / max_entropy)
return prediction, confidence
def get_similar_patterns(self, query: torch.Tensor, k: int = 5): """ Get k most similar stored patterns
Args: query: (pattern_dim,) query pattern k: number of patterns to retrieve
Returns: indices: (k,) indices of similar patterns similarities: (k,) similarity scores """ query = F.normalize(query.unsqueeze(0), dim=-1) patterns = F.normalize(self.patterns, dim=-1)
similarities = (query @ patterns.T).squeeze(0) topk = torch.topk(similarities, k=min(k, self.memory_size))
return topk.indices, topk.values
class AssociativeMemoryTrader: """ Trading system based on Dense Associative Memory """
def __init__(self, memory: DenseAssociativeMemory, confidence_threshold: float = 0.3, position_scale: float = 1.0): self.memory = memory self.confidence_threshold = confidence_threshold self.position_scale = position_scale
def generate_signal(self, current_pattern: torch.Tensor): """ Generate trading signal from current market pattern
Returns: signal: float in [-1, 1], direction and strength confidence: float in [0, 1], retrieval confidence similar_patterns: list of (index, similarity) tuples """ self.memory.eval()
with torch.no_grad(): prediction, confidence = self.memory(current_pattern.unsqueeze(0)) indices, similarities = self.memory.get_similar_patterns( current_pattern, k=5 )
prediction = prediction.item() confidence = confidence.item()
# Only trade if confidence exceeds threshold if confidence < self.confidence_threshold: return 0.0, confidence, list(zip(indices.tolist(), similarities.tolist()))
# Scale signal by confidence signal = prediction * confidence * self.position_scale
return signal, confidence, list(zip(indices.tolist(), similarities.tolist()))Continuous Hopfield Network (Modern Version)
class ContinuousHopfieldNetwork(nn.Module): """ Continuous Hopfield Network with exponential storage capacity
Based on "Hopfield Networks is All You Need" (Ramsauer et al., 2020) """
def __init__(self, input_dim: int, hidden_dim: int = 64, beta: float = None): super().__init__()
self.input_dim = input_dim self.hidden_dim = hidden_dim self.beta = beta if beta else (1.0 / (hidden_dim ** 0.5))
# Pattern projection self.W_pattern = nn.Linear(input_dim, hidden_dim) self.W_query = nn.Linear(input_dim, hidden_dim)
# Output projection self.W_out = nn.Linear(hidden_dim, input_dim)
# Pattern memory (set during training) self.register_buffer('stored_patterns', None)
def store(self, patterns: torch.Tensor): """ Store patterns in memory
Args: patterns: (N, input_dim) patterns to store """ with torch.no_grad(): projected = self.W_pattern(patterns) # (N, hidden_dim) self.stored_patterns = F.normalize(projected, dim=-1)
def energy(self, state: torch.Tensor) -> torch.Tensor: """ Compute energy of current state
E(x) = -log Σ exp(β ξ^T x)
Lower energy = closer to stored patterns """ if self.stored_patterns is None: raise ValueError("No patterns stored")
state_proj = self.W_query(state) # (batch, hidden_dim) state_proj = F.normalize(state_proj, dim=-1)
# Compute similarities similarities = state_proj @ self.stored_patterns.T # (batch, N)
# Log-sum-exp for energy energy = -torch.logsumexp(self.beta * similarities, dim=-1)
return energy
def update(self, state: torch.Tensor, n_steps: int = 1) -> torch.Tensor: """ Update state towards stored patterns
Uses softmax-weighted combination of patterns """ if self.stored_patterns is None: raise ValueError("No patterns stored")
for _ in range(n_steps): state_proj = self.W_query(state) state_proj = F.normalize(state_proj, dim=-1)
# Attention over stored patterns similarities = state_proj @ self.stored_patterns.T attention = F.softmax(self.beta * similarities, dim=-1)
# Weighted combination new_state_proj = attention @ self.stored_patterns
# Project back state = self.W_out(new_state_proj)
return state
def retrieve(self, query: torch.Tensor) -> torch.Tensor: """ Retrieve closest pattern to query """ return self.update(query, n_steps=3)
class HopfieldPooling(nn.Module): """ Hopfield-based pooling for sequence encoding
Useful for encoding price sequences into fixed-size patterns """
def __init__(self, input_dim: int, n_patterns: int, beta: float = None): super().__init__()
self.input_dim = input_dim self.n_patterns = n_patterns self.beta = beta if beta else (1.0 / (input_dim ** 0.5))
# Learnable prototype patterns (queries) self.prototypes = nn.Parameter(torch.randn(n_patterns, input_dim))
def forward(self, sequence: torch.Tensor) -> torch.Tensor: """ Pool sequence into fixed-size representation
Args: sequence: (batch, seq_len, input_dim)
Returns: pooled: (batch, n_patterns * input_dim) """ batch_size, seq_len, _ = sequence.shape
# Normalize seq_norm = F.normalize(sequence, dim=-1) proto_norm = F.normalize(self.prototypes, dim=-1)
# Compute attention: each prototype attends to sequence # proto_norm: (n_patterns, input_dim) # seq_norm: (batch, seq_len, input_dim) attention = torch.einsum('pd,bsd->bps', proto_norm, seq_norm) attention = F.softmax(self.beta * attention, dim=-1) # (batch, n_patterns, seq_len)
# Weighted sum of sequence pooled = torch.einsum('bps,bsd->bpd', attention, sequence) # (batch, n_patterns, input_dim)
return pooled.view(batch_size, -1)Pattern Memory Management
class PatternMemoryManager: """ Manages pattern storage with capacity limits and relevance scoring """
def __init__(self, max_patterns: int, pattern_dim: int, similarity_threshold: float = 0.95): self.max_patterns = max_patterns self.pattern_dim = pattern_dim self.similarity_threshold = similarity_threshold
self.patterns = [] self.outcomes = [] self.timestamps = [] self.retrieval_counts = []
def add_pattern(self, pattern: np.ndarray, outcome: float, timestamp): """ Add pattern to memory, potentially replacing old/similar ones """ pattern = pattern / (np.linalg.norm(pattern) + 1e-8)
# Check for similar existing patterns if len(self.patterns) > 0: patterns_arr = np.array(self.patterns) similarities = patterns_arr @ pattern
# If very similar pattern exists, update it instead if np.max(similarities) > self.similarity_threshold: idx = np.argmax(similarities) # Exponential moving average update alpha = 0.3 self.patterns[idx] = alpha * pattern + (1 - alpha) * self.patterns[idx] self.patterns[idx] /= np.linalg.norm(self.patterns[idx]) self.outcomes[idx] = alpha * outcome + (1 - alpha) * self.outcomes[idx] return
# Add new pattern if len(self.patterns) >= self.max_patterns: self._evict_pattern()
self.patterns.append(pattern) self.outcomes.append(outcome) self.timestamps.append(timestamp) self.retrieval_counts.append(0)
def _evict_pattern(self): """ Remove least useful pattern based on recency and usage """ if len(self.patterns) == 0: return
# Score based on recency and usage n = len(self.patterns) recency_scores = np.arange(n) / n # Older = lower score usage_scores = np.array(self.retrieval_counts) usage_scores = usage_scores / (usage_scores.max() + 1)
scores = 0.5 * recency_scores + 0.5 * usage_scores
# Remove pattern with lowest score remove_idx = np.argmin(scores) self.patterns.pop(remove_idx) self.outcomes.pop(remove_idx) self.timestamps.pop(remove_idx) self.retrieval_counts.pop(remove_idx)
def query(self, query: np.ndarray, k: int = 5): """ Query memory for similar patterns """ if len(self.patterns) == 0: return [], [], []
query = query / (np.linalg.norm(query) + 1e-8) patterns_arr = np.array(self.patterns)
similarities = patterns_arr @ query
k = min(k, len(self.patterns)) top_k_idx = np.argsort(similarities)[-k:][::-1]
# Update retrieval counts for idx in top_k_idx: self.retrieval_counts[idx] += 1
return ( [self.patterns[i] for i in top_k_idx], [self.outcomes[i] for i in top_k_idx], [similarities[i] for i in top_k_idx] )
def predict(self, query: np.ndarray, k: int = 5) -> tuple: """ Predict outcome based on similar patterns """ patterns, outcomes, similarities = self.query(query, k)
if len(patterns) == 0: return 0.0, 0.0
# Weighted average of outcomes similarities = np.array(similarities) weights = similarities / (similarities.sum() + 1e-8) prediction = np.sum(weights * np.array(outcomes))
# Confidence based on average similarity confidence = np.mean(similarities)
return prediction, confidence
def to_tensors(self): """ Convert to PyTorch tensors for neural network """ if len(self.patterns) == 0: return None, None
patterns = torch.tensor(np.array(self.patterns), dtype=torch.float32) outcomes = torch.tensor(np.array(self.outcomes), dtype=torch.float32)
return patterns, outcomesTraining Loop
def train_associative_memory( model: DenseAssociativeMemory, train_patterns: torch.Tensor, train_labels: torch.Tensor, val_patterns: torch.Tensor, val_labels: torch.Tensor, epochs: int = 100, lr: float = 0.001, batch_size: int = 64): """ Train the associative memory model """ optimizer = torch.optim.AdamW(model.parameters(), lr=lr, weight_decay=0.01) scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, epochs) criterion = nn.MSELoss()
# Store patterns in memory model.store_patterns(train_patterns, train_patterns)
best_val_loss = float('inf')
for epoch in range(epochs): model.train() total_loss = 0 n_batches = 0
# Shuffle training data perm = torch.randperm(len(train_patterns))
for i in range(0, len(train_patterns), batch_size): batch_idx = perm[i:i+batch_size] patterns = train_patterns[batch_idx] labels = train_labels[batch_idx].unsqueeze(-1)
optimizer.zero_grad()
predictions, confidence = model(patterns)
# Loss: weighted MSE by confidence loss = (confidence * (predictions - labels).pow(2)).mean()
# Add regularization for memory diversity patterns_norm = F.normalize(model.patterns, dim=-1) similarity_matrix = patterns_norm @ patterns_norm.T diversity_loss = (similarity_matrix - torch.eye(model.memory_size)).pow(2).mean()
total_loss = loss + 0.1 * diversity_loss total_loss.backward()
torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0) optimizer.step()
total_loss += loss.item() n_batches += 1
scheduler.step()
# Validation model.eval() with torch.no_grad(): val_pred, val_conf = model(val_patterns) val_loss = criterion(val_pred.squeeze(), val_labels)
# Direction accuracy direction_acc = ((val_pred.squeeze() > 0) == (val_labels > 0)).float().mean()
if val_loss < best_val_loss: best_val_loss = val_loss best_state = model.state_dict().copy()
if (epoch + 1) % 10 == 0: print(f"Epoch {epoch+1}/{epochs}: " f"Loss={total_loss/n_batches:.4f}, " f"Val Loss={val_loss:.4f}, " f"Direction Acc={direction_acc:.2%}")
model.load_state_dict(best_state) return modelBacktesting Framework
class AssociativeMemoryBacktest: """ Backtest trading strategy based on associative memory """
def __init__(self, model: DenseAssociativeMemory, pattern_lookback: int = 20, min_confidence: float = 0.3, position_size: float = 0.1): self.model = model self.pattern_lookback = pattern_lookback self.min_confidence = min_confidence self.position_size = position_size
def run(self, prices: pd.DataFrame, warmup: int = 100): """ Run backtest on price data
Args: prices: DataFrame with OHLCV columns warmup: Number of periods for warmup """ results = { 'timestamp': [], 'price': [], 'signal': [], 'confidence': [], 'position': [], 'pnl': [], 'cumulative_pnl': [] }
position = 0.0 cumulative_pnl = 0.0
self.model.eval()
for i in range(warmup, len(prices)): # Compute current pattern window = prices.iloc[i-self.pattern_lookback:i] pattern = compute_market_pattern(window) pattern_tensor = torch.tensor(pattern, dtype=torch.float32)
# Get prediction with torch.no_grad(): pred, conf = self.model(pattern_tensor.unsqueeze(0))
pred = pred.item() conf = conf.item()
# Determine position if conf >= self.min_confidence: target_position = np.sign(pred) * self.position_size * conf else: target_position = 0.0
# Calculate PnL (assumes daily returns) if i > warmup: daily_return = (prices['close'].iloc[i] / prices['close'].iloc[i-1]) - 1 pnl = position * daily_return cumulative_pnl += pnl else: pnl = 0.0
# Update position position = target_position
# Store results results['timestamp'].append(prices.index[i]) results['price'].append(prices['close'].iloc[i]) results['signal'].append(pred) results['confidence'].append(conf) results['position'].append(position) results['pnl'].append(pnl) results['cumulative_pnl'].append(cumulative_pnl)
return pd.DataFrame(results)
def calculate_metrics(self, results: pd.DataFrame) -> dict: """ Calculate performance metrics """ returns = results['pnl']
# Basic metrics total_return = results['cumulative_pnl'].iloc[-1] n_days = len(results)
# Sharpe Ratio (annualized) if returns.std() > 0: sharpe = returns.mean() / returns.std() * np.sqrt(252) else: sharpe = 0.0
# Sortino Ratio downside = returns[returns < 0] if len(downside) > 0 and downside.std() > 0: sortino = returns.mean() / downside.std() * np.sqrt(252) else: sortino = 0.0
# Maximum Drawdown cumulative = results['cumulative_pnl'] rolling_max = cumulative.expanding().max() drawdown = cumulative - rolling_max max_drawdown = drawdown.min()
# Win Rate winning = returns[returns > 0] win_rate = len(winning) / len(returns[returns != 0]) if len(returns[returns != 0]) > 0 else 0
# Average confidence when trading trading_conf = results[results['position'] != 0]['confidence'] avg_confidence = trading_conf.mean() if len(trading_conf) > 0 else 0
return { 'total_return': total_return, 'sharpe_ratio': sharpe, 'sortino_ratio': sortino, 'max_drawdown': max_drawdown, 'win_rate': win_rate, 'n_trades': (results['position'].diff() != 0).sum(), 'avg_confidence': avg_confidence }Data Requirements
Historical OHLCV Data:├── Minimum: 1 year of hourly data├── Recommended: 3+ years for diverse patterns├── Frequency: 1-hour to daily recommended└── Source: Bybit, Binance, or other exchanges
Required Fields:├── timestamp├── open, high, low, close├── volume└── Optional: turnover, trades count
Pattern Construction:├── Lookback: 20-60 periods for pattern├── Features: 10-50 dimensions├── Normalization: Z-score or min-max└── Update: Rolling windowKey Metrics
- Retrieval Accuracy: Percentage of times correct pattern is in top-K
- Pattern Coverage: Percentage of market conditions covered by stored patterns
- Confidence Calibration: Correlation between confidence and accuracy
- Sharpe Ratio: Risk-adjusted returns
- Maximum Drawdown: Largest peak-to-trough decline
- Win Rate: Percentage of profitable trades
Dependencies
# Corenumpy>=1.23.0pandas>=1.5.0scipy>=1.10.0
# Deep Learningtorch>=2.0.0pytorch-lightning>=2.0.0
# Visualizationmatplotlib>=3.6.0seaborn>=0.12.0plotly>=5.10.0
# Market Dataccxt>=4.0.0websocket-client>=1.4.0
# Utilitiesscikit-learn>=1.2.0tqdm>=4.65.0Expected Outcomes
- Pattern Recognition System with exponential storage capacity
- Retrieval-Based Predictions using attention mechanisms
- Confidence-Calibrated Trading with novelty detection
- Interpretable Decisions through similar pattern analysis
- Backtest Results: Expected Sharpe Ratio 1.0-2.0 with proper tuning
References
-
Dense Associative Memory for Pattern Recognition (Krotov & Hopfield, 2016)
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Hopfield Networks is All You Need (Ramsauer et al., 2020)
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Modern Hopfield Networks and Attention for Immune Repertoire Classification (Widrich et al., 2020)
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Associative Memory in Machine Learning - Survey and Applications
-
Neural Networks and Deep Learning (Michael Nielsen) - Chapter on Hopfield Networks
Rust Implementation
This chapter includes a complete Rust implementation for high-performance associative memory trading on cryptocurrency data from Bybit. See rust/ directory.
Features:
- Real-time data fetching from Bybit
- Dense Associative Memory implementation
- Pattern storage and retrieval
- Confidence-based trading signals
- Backtesting framework
- Modular and extensible design
Difficulty Level
⭐⭐⭐⭐⭐ (Expert)
Requires understanding of: Neural Networks, Attention Mechanisms, Energy-Based Models, Pattern Recognition, Trading Systems