feedforward-dynamics-stimulus-encoding

# Feedforward Dynamics Stimulus Encoding ## Description Research demonstrating that the feedforward pass in neural networks is not a simple static transformation but involves complex dynamical processes. Challenges the common assumption of feedforward computation as simple matrix multiplication. ## Key Concepts ### Dynamical Feedforward Computation - Feedforward computation involves iterative convergence dynamics - Neurons approach fixed points through temporal evolution - Static view misses temporal computation aspects ### Stimulus Encoding Dynamics - Neural representations evolve over time during feedforward pass - Encoding quality improves through dynamical settling - Time-dependent information transformation ### Illusory Simplicity - Apparent simplicity of feedforward masks underlying complexity - Each layer performs iterative refinement, not just transformation - Dynamics enable richer computation than static models suggest ## Activation Keywords - feedforward dynamics - stimulus encoding - temporal computation - dynamical neural networks - illusory simplicity - iterative convergence - neural dynamics ## Workflow ### Step 1: Analyze Feedforward Dynamics ```python import numpy as np def feedforward_with_dynamics(x, weights, n_steps=10): """Feedforward computation with explicit dynamics.""" h = x.copy() trajectory = [h] for W in weights: # Instead of instant update, model convergence target = W @ h h_current = h.copy() for _ in range(n_steps): h_current = 0.9 * h_current + 0.1 * target # Convergence dynamics trajectory.append(h_current.copy()) h = h_current return h, trajectory ``` ### Step 2: Measure Information Evolution ```python def track_information(trajectory, targets): """Track how information evolves through dynamics.""" information = [] for h in trajectory: # Measure alignment with target representation info = np.dot(h.flatten(), targets.flatten()) information.append(info) return information ``` ### Step 3: Compare Static vs Dynamic Models ```python def compare_models(x, weights, targets): """Compare static and dynamical feedforward computation.""" # Static computation h_static = x.copy() for W in weights: h_static = W @ h_static # Dynamic computation h_dynamic, trajectory = feedforward_with_dynamics(x, weights) # Compare accuracy static_error = np.linalg.norm(h_static - targets) dynamic_error = np.linalg.norm(h_dynamic - targets) return { 'static_error': static_error, 'dynamic_error': dynamic_error, 'improvement': (static_error - dynamic_error) / static_error } ``` ## Applications 1. **Neural network interpretability** — understanding feedforward computation 2. **Computational neuroscience** — modeling temporal processing 3. **Network architecture design** — incorporating dynamical elements 4. **Theoretical analysis** — understanding neural computation ## References - arXiv:2604.12825 — The illusory simplicity of the feedforward pass: evidence for the dynamical nature of stimulus encoding