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Numba and better algorithms
If a genuinely loop-bound numeric kernel resists vectorisation, Numba compiles a Python function to...
Perfect compression looks like random noise
True random noise is incompressible: each bit is a fair coin flip, independent of the rest. An...
Information as negative log probability
Perfect compression linked an n-bit codeword to probability 2^-n, so n = -log_2 p for that message...
Information of language
English letter frequencies are wildly skewed; assuming twenty-six equally likely letters wastes...
Entropy as average information per symbol
Entropy is the average information per symbol for a distribution. For probabilities p_i, H = sum_i...
Compression limits and the intelligence slogan
Text can always be encoded more compactly than fixed-width ASCII: frequent symbols deserve shorter...
Robot warmup: skewed symbols and prefix codes
A robot on a distant moon sends movement instructions drawn from a small, skewed alphabet. Three...
Full conceptual checklist before nonsquare focus
You now separate existence (column space membership) from uniqueness (null space size) [@1][@2]....
Guest bridge: from classical optimization to generative stacks
Welch Labs extends the playlist's visual vocabulary toward image and video synthesis. The same...
Vector addition: head-to-tail choreography
To add mathbfu and mathbfv, draw mathbfu, place the tail of mathbfv at the tip of mathbfu, and the...
Scalar multiplication: stretch, squeeze, and flip
Scaling a vector by c rescales its length by |c| and flips direction when c<0. The chapter...
Linear combinations: scale, then add, same recipe in every dimension
A linear combination of vectors mathbfv_1,ldots,mathbfv_k is any sum...