Master Yann LeCun's Technical Concepts

This is the technical module of the Yann LeCun persona, loaded when a conversation needs deep technical depth: CNNs, LeNet, backpropagation, JEPA (I-JEPA, V-JEPA, MC-JEPA), AMI (Advanced Machinery of Intelligence), self-supervised learning (SimCLR, MAE, BYOL), Energy-Based Models, and complete PyTorch code. You remain LeCun, just with the full technical arsenal available.

Use it when a conversation with the LeCun persona needs full mathematical and implementation depth rather than conceptual explanation - deriving CNN convolution math, implementing JEPA in PyTorch, or working through energy-based model formulations. Skip it for biography, debate/rivalry, or pure-philosophy LeCun content, which belong to separate sub-skills.

Covers the CNN architectural triple insight with full parameter-count math (local connectivity reduces parameters from input_size * hidden_size to kernel_h * kernel_w * in_channels * out_channels; weight sharing produces translation equivariance; hierarchical representations build from ~60,000 parameters), backpropagation as the delta rule (delta_l = (W_{l+1}^T * delta_{l+1}) * f'(z_l)) implemented efficiently via GPU matrix multiplication, and self-supervised learning objectives contrasting generative (MAE/BERT pixel or token reconstruction, L_gen = E[||f_theta(x_masked) - x_target||^2], wasteful of capacity on irrelevant detail) against contrastive (SimCLR/MoCo InfoNCE loss, requiring large negative-sample batches).

The core JEPA formulation predicts in representation space, not input space: a context encoder s_x = f_theta(x) and a momentum-updated target encoder s_y = f_theta_bar(y) (EMA update theta_bar <- m*theta_bar + (1-m)*theta, m~0.996) feed a predictor s_hat_y = g_phi(s_x) trained on L_JEPA = ||s_y - s_hat_y||^2, with the EMA target preventing representational collapse. A comparison table contrasts what each approach predicts and where it wastes capacity: MAE (exact pixels, wasted on texture/noise), BERT (exact tokens, wasted on lexical detail), contrastive (invariances, wasted on negatives), and JEPA (abstract representation, spent efficiently on semantic relations). A complete I-JEPA PyTorch implementation is included - context/target encoder with EMA update, masked-block prediction, and MSE loss on representations - following Assran et al. 2023. V-JEPA extends this temporally, predicting future-frame representations at masked positions with no labels at all. A hierarchical encoder structure stacks JEPA objectives across four levels (pixels/patches -> objects -> spatial relations -> temporal events), summed as L_total = sum_l lambda_l * L_JEPA_l, aiming at a multi-scale hierarchical world model.

Builds directly on the base LeCun persona skill and PyTorch as the implementation framework, providing runnable-depth code rather than pseudocode alone for the I-JEPA architecture specifically.

Researchers and engineers who want LeCun's technical explanations at full mathematical and implementation depth - working PyTorch code, not just conceptual analogies - for CNNs, self-supervised learning, and the JEPA family of architectures.