Top all-time · #18346
tali
Personal blog · math.tali.linkmathprogramming
tali is a personal blog at math.tali.link about math and programming. Since 2023, 4 different Hacker News readers have linked it 16 times, most often “Classical Array Algebra”. The last post was in 2023, but the archive is still widely read.
Too few sampled comments (1) to say how often HN recommends it.?
Why HN links it
HN readers link this blog for posts on array-language thinking, such as APL-family design. The one comment contrasts functional programming's fine-grained types with array programming's minimal type distinctions.
Summarised by Claude from a sample of 1 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
Most-linked posts?
- Classical Array Algebra3 people · 6 mentions · first linked 2023-09-18
- Rainbow Array Algebra2 people · 2 mentions · first linked 2024-01-06
What Hacker News says?
There's a fundamental opposition between the functional programming approach to types and array programming principles, as I see it. In functional programming (particularly Haskell), types are used to make fine distinctions for safety. Even if an existing type would work for something, it's often recommended to make a new one so two different use cases don't get mixed up. But the APL family works to make as few type…
Comment linking /classical-array-algebra/
on “Thinking in an array language”Submitted Classical Array Algebra as a story · 3 points
HN discussionWhile I applaud the OP's exposition, imagine that instead of having axis names live as single-letter variables within einsum, our arrays themselves had these names attached to their axes? It's almost like when we moved from writing machine code to structured programming: instead of being content to document that certain registers corresponding to certain semantically meaningful quantities at particular times during…
Comment linking /rainbow-array-algebra/
on “Einsum for Tensor Manipulation”Submitted Classical Array Algebra as a story · 3 points
HN discussionThat is an excellent explanation full of great intuition building! If anyone is interested in a kind of tensor network-y diagrammatic notation for array programs (of which transformers and other deep neural nets are examples), I wrote a post recently that introduces a kind of "colorful" tensor network notation (where the colors correspond to axis names) and then uses it to describe self-attention and transformers. T…
Comment linking /rainbow-array-algebra
on “The Illustrated GPT-2”Submitted Rainbow Array Algebra as a story · 3 points
HN discussionWow, I love the interactive wizzing around and the animation, very neat! Way more explanations should work like this. I've recently finished an unorthodox kind of visualization / explanation of transformers. It's sadly not interactive, but it does have some maybe unique strengths. First, it gives array axis semantic names , represented in the diagrams as colors (which this post also uses). So sequence axis is red, k…
Comment linking /rainbow-array-algebra/
on “LLM Visualization”Submitted Classical Array Algebra as a story · 1 points
HN discussionGreat to see this kind of visualization gaining prominence! Thinking about matrix algebra in higher dimensions makes everything much more intuitive. I started along this road when I was creating 3D visualizations for the Deep Learning Indaba workshop [1], but I've spent some time since then trying to pin down the algebraic aspects of array manipulation in this blog post series that includes lots of visualizations [2…
Comment linking /classical-array-algebra/
on “Inside the Matrix: Visualizing Matrix Multiplication, Attention and Beyond”I have yet to find an adequate replacement for Mathematica and its graphics DSL. To create the visualizations in https://math.tali.link/classical-array-algebra/ takes a fair amount of interplay of code and data, I shudder to think how I would do this in a non-term-rewriting language.
Comment linking /classical-array-algebra/
on “Simple Drawings with Mathematica”