Published on: 2025-04-23 20:30:47
Differentiable Programming from Scratch Differentiable programming has become a hot research topic, and not only due to the popularity of machine learning frameworks like TensorFlow, PyTorch, and JAX. Many fields apart from machine learning are finding differentiable programming to be a useful tool for solving optimization problems. In computer graphics, differentiable rendering, differentiable physics, and neural representations are all gaining popularity. This article received an honorable m
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Find related items on AmazonPublished on: 2025-04-26 10:01:41
Let's remove Quaternions from every 3D Engine (An Interactive Introduction to Rotors from Geometric Algebra) The clearest explanation of 3D geometric algebra within 15 minutes that I've seen so far —BrokenSymmetry I am sold. While I can understand quaternions to an extent, this way of thinking is a much more intuitive and elegant approach. —Jack Rasksilver This sets a high standard for educational material, and is a shining example of how we can improve education with today's technologies. —Se
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Find related items on AmazonPublished on: 2025-04-29 14:54:51
Monte Carlo Crash Course Sampling In the previous chapter, we assumed that we can uniformly randomly sample our domain. However, it’s not obvious how to actually do so—in fact, how can a deterministic computer even generate random numbers? Pseudo-Random Numbers Fortunately, Monte Carlo methods don’t need truly random numbers. Instead, we can use a pseudo-random number generator (PRNG). A PRNG produces a deterministic stream of numbers that look uniformly random: By “look uniformly random,”
Keywords: f_ frac mathbf mathcal omega
Find related items on AmazonPublished on: 2025-06-01 08:26:05
authored by Premmi and Beguène Previous Topic: An Axiomatic Study of Numbers Introduction Thinking of numbers intuitively brings to mind the simplest and most fundamental set of numbers, namely the set of natural numbers. These numbers are used to count objects like cars, books, pens, etc. If we associate natural numbers such as 1, 2, 3, etc. with counting, then with what corresponding concepts do we relate numbers like -4, \sqrt{3} \text{ and } \frac{22}{7}? To reason about all kinds of num
Keywords: axioms mathbb natural numbers set
Find related items on AmazonPublished on: 2025-06-02 09:26:05
authored by Premmi and Beguène Previous Topic: An Axiomatic Study of Numbers Introduction Thinking of numbers intuitively brings to mind the simplest and most fundamental set of numbers, namely the set of natural numbers. These numbers are used to count objects like cars, books, pens, etc. If we associate natural numbers such as 1, 2, 3, etc. with counting, then with what corresponding concepts do we relate numbers like -4, \sqrt{3} \text{ and } \frac{22}{7}? To reason about all kinds of num
Keywords: axioms mathbb natural numbers set
Find related items on AmazonPublished on: 2025-06-14 16:39:31
A hypernetwork estimates parameters $\{\mathbf{b}_1, \mathbf{W}_2\}^{(i,j)}$ of pixel-wise, local neural heat fields. The phase shifts $\mathbf{b}_1$ operate on globally learned components, before thermal activations scale each component depending on their frequency and the desired scaling factor. The components are then linearly combined using coefficients $\mathbf{W}_2$, resulting in an appropriately-blurred, continuous local neural field. This field is then rasterized at the appropriate sampl
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Find related items on AmazonPublished on: 2025-07-09 15:20:40
MathB.in Is Shutting Down By Susam Pal on 23 Feb 2025 Thirteen years ago, on a quiet Saturday night, I sat down and began developing MathB.in. After coding all through the night, as the sun rose on Sunday, 25 March 2012, the website was ready. I registered a new domain name and shared it with a few friends who loved mathematics. Back then, we spent hours discussing fascinating mathematics problems, and this website became a simple way for us to share snippets with each other. Word spread quick
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