This went okay until they pushed on the inference behavior.
Start by defining Batch Normalization and its purpose, then explain the mechanics during training and inference, emphasizing the learnable parameters and running statistics. Use a clear structure: training behavior, inference behavior, and the role of parameters and statistics. Conclude with practical implications and trade-offs.
Pro tip: Mention that Batch Normalization reduces internal covariate shift but its primary benefit is smoothing the optimization landscape, enabling higher learning rates. Also, note that the choice of momentum for running statistics affects performance, especially with small batch sizes.
Explain that Batch Normalization normalizes the input to a layer by re-centering and re-scaling using the mean and variance computed over the current mini-batch. This stabilizes learning and accelerates training.
During training, compute the mean and variance of each feature across the mini-batch. Normalize using these statistics, then apply the learnable scale (gamma) and shift (beta) parameters to allow the network to recover representational power.
At inference, use fixed population statistics (running mean and variance) instead of batch statistics, since batches may not be available or should not affect predictions. This ensures deterministic outputs.
During training, maintain exponential moving averages of the batch means and variances. These running statistics are updated with a momentum term and used at inference time.
The learnable parameters gamma and beta allow the network to scale and shift the normalized activations, preserving the capacity to represent complex functions. Without them, normalization might restrict the model's expressiveness.
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Probably my strongest answer of the three.
Start by grouping the optimizers into families: basic SGD, SGD with momentum, adaptive methods (RMSProp, Adam), and Adam with decoupled weight decay (AdamW). Then compare them along key dimensions: convergence speed, generalization, memory overhead, hyperparameter sensitivity, and suitability for different architectures (e.g., CNNs vs. Transformers). Finally, discuss practical trade-offs and when to choose each, referencing real-world examples like Snapchat's use of AdamW for training large-scale recommendation models.
Pro tip: Mention that AdamW often outperforms Adam with L2 regularization because decoupled weight decay prevents overfitting more effectively, especially in transformers. Also, note that SGD with momentum can generalize better than adaptive methods in some vision tasks, but requires careful learning rate tuning and longer training.
Group them into non-adaptive (SGD, SGD with momentum) and adaptive (RMSProp, Adam, AdamW) methods, highlighting the core idea behind each.
For each optimizer, describe how it updates weights: SGD uses raw gradients; momentum adds velocity; RMSProp scales by recent gradient magnitude; Adam combines momentum and RMSProp with bias correction; AdamW decouples weight decay from gradient updates.
Discuss convergence speed, generalization, memory usage, hyperparameter tuning, and robustness to learning rate choices. For example, Adam converges fast but may generalize worse; SGD with momentum generalizes well but is slow and sensitive to LR.
Recommend optimizers for specific scenarios: Adam/AdamW for transformers and sparse gradients; SGD with momentum for CNNs and when generalization is critical; RMSProp for RNNs or non-stationary problems.
Summarize that AdamW is often the default for modern deep learning, but SGD with momentum remains strong for vision tasks; emphasize that the choice depends on model, data, and compute budget.
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Blanked for a second on the geometry part.
Start by defining L1 and L2 regularization mathematically, then explain their geometric interpretations (diamond vs. circle constraints) and how these lead to sparsity differences. Finally, discuss gradient behavior and practical implications, using examples to illustrate.
Pro tip: Mention that L1 regularization can be solved efficiently using proximal gradient methods, and that in practice, L2 is often preferred for deep learning due to smoother optimization, while L1 is used for feature selection.
Define L1 (Lasso) as adding the sum of absolute weights to the loss, and L2 (Ridge) as adding the sum of squared weights. Mention the regularization parameter lambda.
Explain that L1 constraint region is a diamond (or polytope) with corners on axes, while L2 is a circle (or hypersphere). The loss contours touch the constraint region at corners for L1, leading to zero weights, and at tangent points for L2, leading to small but non-zero weights.
Discuss that L1 promotes sparsity because the optimal solution often lies at a corner where some weights are exactly zero, effectively performing feature selection. L2 shrinks weights uniformly but rarely sets them exactly to zero.
Explain that L1 gradient is constant (sign of weight) leading to constant force towards zero, while L2 gradient is proportional to weight, leading to gradual shrinkage. This affects optimization dynamics and convergence.
Summarize when to use each: L1 for feature selection and interpretability, L2 for preventing overfitting and handling correlated features. Mention Elastic Net as a combination.
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