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∇ Deep Learning Book 34 chapters

My notes on the Deep Learning book by Ian Goodfellow, Yoshua Bengio, and Aaron Courville.

Chapter 9.6: Structured Outputs CNNs can generate high-dimensional structured objects through pixel-level predictions. Recurrent convolution refines predictions iteratively, producing dense outputs for segmentation, depth estimation, and flow prediction.

Chapter 9.5: Convolutional Functions Mathematical details of convolution operations: deep learning uses cross-correlation (not true convolution), multi-channel formula $Z_{l,x,y} = \sum_{i,j,k} V_{i,x+j-1,y+k-1} K_{l,i,j,k}$, stride for downsampling, three padding strategies (valid/same/full), and gradient computation.

Chapter 9.4: Convolution and Pooling as an Infinitely Strong Prior Why CNNs work on images but not everywhere: architectural constraints (local connectivity + weight sharing) act as infinitely strong Bayesian priors, assigning probability 1 to translation-equivariant functions and 0 to all others.

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📐 MIT 18.06SC Linear Algebra 36 lectures

My journey through MIT’s Linear Algebra course, focusing on building intuition and making connections between fundamental concepts.

Lecture 27: Positive Definite Matrices and Minima Connecting positive definite matrices to multivariable calculus and optimization: the Hessian matrix, second derivative tests, and the geometric interpretation of quadratic forms as ellipsoids.

Lecture 26: Complex Matrices and Fast Fourier Transform Extending linear algebra to complex vectors: Hermitian matrices, unitary matrices, and the Fast Fourier Transform algorithm that reduces DFT complexity from O(N²) to O(N log N).

Lecture 28: Similar Matrices and Jordan Form When matrices share eigenvalues but differ in structure: similar matrices represent the same transformation in different bases, and Jordan form reveals the canonical structure when diagonalization fails.

See all MIT 18.06SC lectures →

📐 MIT 18.065 Matrix Methods 1 lecture

My notes from MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning.

Lecture 8: Norms of Vectors and Matrices Understanding vector p-norms ($\|v\|_p$) and when they satisfy the triangle inequality (only for $p \geq 1$). The “$\frac{1}{2}$-norm” creates non-convex unit balls for strong sparsity.

See all MIT 18.065 lectures →

--- title: "ickma.dev" --- ::: {.hero-banner} # ickma.dev — Notes on Deep Learning and Math A growing collection of structured study notes and visual explanations — written for clarity, reproducibility, and long-term memory. ::: ## Latest Updates ::: {.section-block} ### ∇ Deep Learning Book 34 chapters My notes on the Deep Learning book by Ian Goodfellow, Yoshua Bengio, and Aaron Courville. ::: {.content-grid} ::: {.content-card} **[Chapter 9.6: Structured Outputs](ML/cnn-structured-outputs.qmd)** CNNs can generate high-dimensional structured objects through pixel-level predictions. Recurrent convolution refines predictions iteratively, producing dense outputs for segmentation, depth estimation, and flow prediction. ::: ::: {.content-card} **[Chapter 9.5: Convolutional Functions](ML/convolutional-functions.qmd)** Mathematical details of convolution operations: deep learning uses cross-correlation (not true convolution), multi-channel formula $Z_{l,x,y} = \sum_{i,j,k} V_{i,x+j-1,y+k-1} K_{l,i,j,k}$, stride for downsampling, three padding strategies (valid/same/full), and gradient computation. ::: ::: {.content-card} **[Chapter 9.4: Convolution and Pooling as an Infinitely Strong Prior](ML/cnn-infinitely-strong-prior.qmd)** Why CNNs work on images but not everywhere: architectural constraints (local connectivity + weight sharing) act as infinitely strong Bayesian priors, assigning probability 1 to translation-equivariant functions and 0 to all others. ::: ::: ::: {.see-all-button} [See all Deep Learning chapters →](ML/deep-learning-book.qmd){.btn .btn-primary} ::: ::: ::: {.section-block} ### 📐 MIT 18.06SC Linear Algebra 36 lectures My journey through MIT's Linear Algebra course, focusing on building intuition and making connections between fundamental concepts. ::: {.content-grid} ::: {.content-card} **[Lecture 27: Positive Definite Matrices and Minima](Math/MIT18.06/mit1806-lecture27-positive-definite-minima.qmd)** Connecting positive definite matrices to multivariable calculus and optimization: the Hessian matrix, second derivative tests, and the geometric interpretation of quadratic forms as ellipsoids. ::: ::: {.content-card} **[Lecture 26: Complex Matrices and Fast Fourier Transform](Math/MIT18.06/mit1806-lecture26-complex-matrices-fft.qmd)** Extending linear algebra to complex vectors: Hermitian matrices, unitary matrices, and the Fast Fourier Transform algorithm that reduces DFT complexity from O(N²) to O(N log N). ::: ::: {.content-card} **[Lecture 28: Similar Matrices and Jordan Form](Math/MIT18.06/mit1806-lecture28-similar-matrices-jordan.qmd)** When matrices share eigenvalues but differ in structure: similar matrices represent the same transformation in different bases, and Jordan form reveals the canonical structure when diagonalization fails. ::: ::: ::: {.see-all-button} [See all MIT 18.06SC lectures →](Math/MIT18.06/lectures.qmd){.btn .btn-primary} ::: ::: ::: {.section-block} ### 📐 MIT 18.065 Matrix Methods 1 lecture My notes from MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. ::: {.content-grid} ::: {.content-card} **[Lecture 8: Norms of Vectors and Matrices](Math/MIT18.065/mit18065-lecture8-norms.qmd)** Understanding vector p-norms ($\|v\|_p$) and when they satisfy the triangle inequality (only for $p \geq 1$). The "$\frac{1}{2}$-norm" creates non-convex unit balls for strong sparsity. ::: ::: ::: {.see-all-button} [See all MIT 18.065 lectures →](Math/MIT18.065/lectures.qmd){.btn .btn-primary} ::: ::: --- ::: {.footer-section} ## More Topics ::: {.footer-grid} ::: {.footer-card} ### Machine Learning - [K-Means Clustering](ML/kmeans.ipynb) - [Logistic Regression](ML/logistic_regression.qmd) - [Axis Operations](ML/axis.qmd) ::: ::: {.footer-card} ### Algorithms - [DP Regex](Algorithm/dp_regex.qmd) ::: ::: :::