[Verse 1]
Gaussian sources whisper secrets through the noise
Target distributions dancing with mathematical poise
Information bottleneck squeezes data through a gate
Mutual information balanced with compression rate
Beta parameter controls the trade-off that we make
Lagrangian optimization for relevance sake
[Chorus]
Sparse codes orthogonal, dimensions climbing high
Bottleneck solutions where the patterns never lie
Autoencoder learning, weights become so thin
Cortical columns computing, let the math begin
Storage scales exponential when the sparsity's right
Neural architectures gleaming in algorithmic light
[Verse 2]
Derivation starts with variational bound so tight
Conditional distributions parameterized just right
Gaussian assumption simplifies the complex scene
Covariance matrices paint the statistical machine
Eigenvalue decomposition reveals the hidden truth
Information geometry guides us to the proof
[Chorus]
Sparse codes orthogonal, dimensions climbing high
Bottleneck solutions where the patterns never lie
Autoencoder learning, weights become so thin
Cortical columns computing, let the math begin
Storage scales exponential when the sparsity's right
Neural architectures gleaming in algorithmic light
[Verse 3]
Implementation time, sparse autoencoder built
Rectified linear units prevent the gradient tilt
L1 regularization makes the activations rare
Weight matrices converge to vectors in the air
Orthogonality emerges from the learning game
High dimensional spaces never look the same
[Verse 4]
Biological inspiration drives the model's core
Cortical microcircuits processing more and more
Pyramidal neurons firing in selective arrays
Sparse representation guides the neural pathways
Feature detectors tuned to minimal response
Efficiency encoded in each synaptic correspondence
[Bridge]
Co-storable patterns multiply with every added node
Sparsity percentage determines the memory load
Empirical investigation reveals the scaling law
Dimensionality increases storage without a flaw
Hopfield networks dreaming in distributed arrays
Cortical computation through these neural maze
[Chorus]
Sparse codes orthogonal, dimensions climbing high
Bottleneck solutions where the patterns never lie
Autoencoder learning, weights become so thin
Cortical columns computing, let the math begin
Storage scales exponential when the sparsity's right
Neural architectures gleaming in algorithmic light
[Outro]
Mathematics dancing through biological design
Computational units working in perfect line
Information theory meets the neural plasticity
Distributed processing shows us what the brain can be