#approximation — Public Fediverse posts

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Try our new word guessing game @ https://24hippos.com

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Try our new word guessing game @ https://24hippos.com

Trapezoidal Rule: Estimates definite integrals by approximating the area under a curve with trapezoids. Ex: For one interval, Area ≈ h/2 * (f(a) + f(b)). Pro-Tip: Smaller step sizes (more trapezoids) = significantly better accuracy! #NumericalIntegration #Approximation #STEM #StudyNotes

Trapezoidal Rule: Estimates definite integrals by approximating the area under a curve with trapezoids. Ex: For one interval, Area ≈ h/2 * (f(a) + f(b)). Pro-Tip: Smaller step sizes (more trapezoids) = significantly better accuracy! #NumericalIntegration #Approximation #STEM #StudyNotes

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Try our new word guessing game @ https://24hippos.com

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Try our new word guessing game @ https://24hippos.com

In the thrilling new world of #Lean4, we've finally proven bounds for the Randomized MaxCut #Approximation algorithm that nobody asked for. 📈🔍 Now you can confidently cut those graphs like a pro while impressing... well, nobody. Because who doesn't love an NP-Complete problem just chilling with some approximation algorithms? 🙄🎉
https://abhamra.com/blog/randomized-maxcut/ #RandomizedMaxCut #NPComplete #Algorithms #GraphTheory #HackerNews #ngated

In the thrilling new world of #Lean4, we've finally proven bounds for the Randomized MaxCut #Approximation algorithm that nobody asked for. 📈🔍 Now you can confidently cut those graphs like a pro while impressing... well, nobody. Because who doesn't love an NP-Complete problem just chilling with some approximation algorithms? 🙄🎉
https://abhamra.com/blog/randomized-maxcut/ #RandomizedMaxCut #NPComplete #Algorithms #GraphTheory #HackerNews #ngated

mistakes were made, who needs perfect symetry anyway?

#bartop #arcade #fermi #approximation

mistakes were made, who needs perfect symetry anyway?

#bartop #arcade #fermi #approximation

The same logic applies in mathematics: “2 + 2 = an integer.” Right. “2 + 2 = an even integer.” Even righter. “2 + 2 = 3.999” Almost right! Asimov shows that precision matters, and some answers are closer to truth than others, even if not perfectly exact. #Mathematics #Accuracy #Approximation

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Word of The Hour's Annual Survey @ https://wordofthehour.org/r/form

Правда ли KAN лучше MLP? Свойство разделения глубины между двумя архитектурами

Прошлым летом в свет вышла новая архитектура нейронных сетей под названием Kolmogorov-Arnold Networks (KAN). На момент выхода статьи про KAN эта новость произвела фурор в мире машинного обучение, так как KAN показывала существенный прирост в качестве аппроксимации различных сложных функций. Ошибка новых сетей падает значительно быстрее при увеличении числа параметров. Однако, за все приходится платить, и цена таких маленьких значений функции ошибки - медленное обучение: KAN обучается примерно в 10 раз медленнее, чем старый добрый MLP. Из всего этого возникает вопрос: насколько все же уместно использование новой архитектуры вместо привычных всем MLP? В данной статье будет найдена функция, которая может быть реализована с помощью двухслойного KAN полиномиальной ширины, но не может быть приближена никакой двухслойной ReLU MLP сетью с полиномиальной шириной

https://habr.com/ru/articles/929972/

#kan #mlp #approximation #math #machine_learning #deep_learning #science #neural_networks #research

Pi Approximation Day (22/7) actually is on 21.9911485751286 / 7 = 07-21T23:47:15.237...

#Pi #Approximation #Day #PiApproximationDay

Pi Approximation Day (22/7) actually is on 21.9911485751286 / 7 = 07-21T23:47:15.237...

#Pi #Approximation #Day #PiApproximationDay

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Word of The Hour's Annual Survey @ https://wordofthehour.org/r/form

用「加法」來計算浮點數乘法的近似值

在「Why Does Integer Addition Approximate Float Multiplication? (probablydance.com)」這邊看到的，原文在「Why Does Integer Addition Approximate Float Mu

https://blog.gslin.org/archives/2025/02/16/12265/%e7%94%a8%e3%80%8c%e5%8a%a0%e6%b3%95%e3%80%8d%e4%be%86%e8%a8%88%e7%ae%97%e6%b5%ae%e9%bb%9e%e6%95%b8%e4%b9%98%e6%b3%95%e7%9a%84%e8%bf%91%e4%bc%bc%e5%80%bc/

#Murmuring #754 #addition #approximate #approximation #float #ieee #integer #multiplication

用「加法」來計算浮點數乘法的近似值

在「Why Does Integer Addition Approximate Float Multiplication? (probablydance.com)」這邊看到的，原文在「Why Does Integer Addition Approximate Float Mu

https://blog.gslin.org/archives/2025/02/16/12265/%e7%94%a8%e3%80%8c%e5%8a%a0%e6%b3%95%e3%80%8d%e4%be%86%e8%a8%88%e7%ae%97%e6%b5%ae%e9%bb%9e%e6%95%b8%e4%b9%98%e6%b3%95%e7%9a%84%e8%bf%91%e4%bc%bc%e5%80%bc/

#Murmuring #754 #addition #approximate #approximation #float #ieee #integer #multiplication

Previously mentioned Hastings 1955 #approximation and remembered I have #sollya files for some. This is the first few atan approximations.

I'm sharing because it's an example of using a "seed" approximation to refine the coefficients using sollya. In these cases sollya would fail to converge without the seed. Other examples are using some other tool (say multiprecision or CAS) to get a first pass.

https://gist.github.com/Marc-B-Reynolds/450cec7f3646314c88a353bde50273d1

Previously mentioned Hastings 1955 #approximation and remembered I have #sollya files for some. This is the first few atan approximations.

I'm sharing because it's an example of using a "seed" approximation to refine the coefficients using sollya. In these cases sollya would fail to converge without the seed. Other examples are using some other tool (say multiprecision or CAS) to get a first pass.

https://gist.github.com/Marc-B-Reynolds/450cec7f3646314c88a353bde50273d1

'Zeroth-order Stochastic Approximation Algorithms for DR-submodular Optimization', by Yuefang Lian, Xiao Wang, Dachuan Xu, Zhongrui Zhao.

http://jmlr.org/papers/v25/23-1523.html

#approximation #optimization #algorithms

'Zeroth-order Stochastic Approximation Algorithms for DR-submodular Optimization', by Yuefang Lian, Xiao Wang, Dachuan Xu, Zhongrui Zhao.

http://jmlr.org/papers/v25/23-1523.html

#approximation #optimization #algorithms

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Word of The Hour's Annual Survey @ https://wordofthehour.org/r/form

Misleading GPS, Philosophy of Maps, And You - The oft-quoted saying “all models are wrong, but some are useful” is a tounge-in-c... - https://hackaday.com/2024/09/10/misleading-gps-philosophy-of-maps-and-you/ #approximation #precision #gpshacks #accuracy #mapping #garmin #strava #model #gps #map

Misleading GPS, Philosophy of Maps, And You - The oft-quoted saying “all models are wrong, but some are useful” is a tounge-in-c... - https://hackaday.com/2024/09/10/misleading-gps-philosophy-of-maps-and-you/ #approximation #precision #gpshacks #accuracy #mapping #garmin #strava #model #gps #map

Physics heresy: Projectiles don’t actually make parabolas

Taught in every introductory physics class for centuries, the parabola is only an imperfect approximation of the true path of a projectile. #Projectile #Projectiles #ProjectileMotion #Parabola #Approximation #Physics #Heresy #Parabolas

https://bigthink.com/starts-with-a-bang/projectiles-dont-make-parabolas/

11/X
Mme la Présidente reprend la parole et, chose inhabituelle, répond en direct à M. Platret concernant ses propos accusateurs concernant la gestion des Fonds Européens. 🇪🇺

"M. Platret, M. Platret, mais de quels chiffres parlez-vous? Par pitié, pourriez-vous entrer concrètement dans le sujet? De quoi parlez vous, de la JDA, du PDR Bourgogne, des 14 plans mobilisés par la Région? Nous avions la semaine dernière 4h et de mi de réunion très apaisées avec la Chambre Régionale de l'Agriculture. De quoi parlez-vous? Sortez de votre joute oratoire pour venir dans le sujet!"

#CriseAgricole
#Approximation

'Kernel Thinning', by Raaz Dwivedi, Lester Mackey.

http://jmlr.org/papers/v25/21-1334.html

#kernels #approximation #kernel

'Kernel Thinning', by Raaz Dwivedi, Lester Mackey.

http://jmlr.org/papers/v25/21-1334.html

#kernels #approximation #kernel

The following formula yields the correct decimal digits of π up to 42 quadrillion digits. Also, see the general form. This high-precision approximation is related to the properties of theta functions or the Gaussian integral.

#pi #digits #quadrillion #quadrilliondigits #GaussianIntegral #ThetaFunction #Maths #Formula #Approximation

Flattening Bézier Curves and Arcs
https://minus-ze.ro/posts/flattening-bezier-curves-and-arcs/
#ycombinator #graphics #vector_graphics #flattening #approximation #Bézier #quadratic #cubic #elliptical #arcs #blossom #De_Casteljau #subdivision #arc_length #path_length

Flattening Bézier Curves and Arcs
https://minus-ze.ro/posts/flattening-bezier-curves-and-arcs/
#ycombinator #graphics #vector_graphics #flattening #approximation #Bézier #quadratic #cubic #elliptical #arcs #blossom #De_Casteljau #subdivision #arc_length #path_length

'Limitations on approximation by deep and shallow neural networks', by Guergana Petrova, Przemyslaw Wojtaszczyk.

http://jmlr.org/papers/v24/22-1381.html

#approximation #lipschitz #approximants

'Limitations on approximation by deep and shallow neural networks', by Guergana Petrova, Przemyslaw Wojtaszczyk.

http://jmlr.org/papers/v24/22-1381.html

#approximation #lipschitz #approximants

Cazabon's #Film #Quality #Approximation:

The overall quality and #watchability of a film can be approximated with the following #equation:

Q = 1 / ((n - 2) ^ 2)

... where Q is `watchability` in the interval [0, 1], and `n` is the number of genres the movie is categorized as having in its IMDB listing.

Action, Comedy: 1.0
Drama, Thriller, Music: 1.0
Action, Comedy, Drama, Horror, Thriller: 0.111

Note: there's a discontinuity at n == 2, which we avoid by using the value `1` in that case.

1/2

Cazabon's #Film #Quality #Approximation:

The overall quality and #watchability of a film can be approximated with the following #equation:

Q = 1 / ((n - 2) ^ 2)

... where Q is `watchability` in the interval [0, 1], and `n` is the number of genres the movie is categorized as having in its IMDB listing.

Action, Comedy: 1.0
Drama, Thriller, Music: 1.0
Action, Comedy, Drama, Horror, Thriller: 0.111

Note: there's a discontinuity at n == 2, which we avoid by using the value `1` in that case.

1/2

`The solution of this SDE lies on the manifold of symmetric and positive semi-definite matrices, so structure-preserving schemes are needed for its numerical #approximation. We apply #stochastic Lie group methods based on Runge-Kutta–Munthe-Kaas schemes for ODEs to guarantee that the numerical solution evolves on the correct #manifold. We also present an application example to illustrate our methodology.`

https://link.springer.com/chapter/10.1007/978-3-031-11818-0_59

`The solution of this SDE lies on the manifold of symmetric and positive semi-definite matrices, so structure-preserving schemes are needed for its numerical #approximation. We apply #stochastic Lie group methods based on Runge-Kutta–Munthe-Kaas schemes for ODEs to guarantee that the numerical solution evolves on the correct #manifold. We also present an application example to illustrate our methodology.`

https://link.springer.com/chapter/10.1007/978-3-031-11818-0_59

https://gist.github.com/Marc-B-Reynolds/9fb24a7a4ee915e6e973bf9f4d08c404

#FloatingPoint #Approximation #Sqrt

https://gist.github.com/Marc-B-Reynolds/9fb24a7a4ee915e6e973bf9f4d08c404

#FloatingPoint #Approximation #Sqrt

Updated: reciprocal approximation gist to add the new variant presented by Mike Day (paper link in C-source)

https://gist.github.com/Marc-B-Reynolds/bab0efc00c55be52f8663a762131ada2

#FloatingPoint #Approximation

Updated: reciprocal approximation gist to add the new variant presented by Mike Day (paper link in C-source)

https://gist.github.com/Marc-B-Reynolds/bab0efc00c55be52f8663a762131ada2

#FloatingPoint #Approximation

Jul 22: Today is Pi #Approximation Day! http://www.cute-calendar.com/41500 #PiApproximationDay #holiday #event #observance

I've found a decent working approximation of π for #PostScript

/pi 0.001 sin 2 div 360000 mul def

Accurate to 7 decimal places. The language uses single-precision floating point, and all its trig routines work in degrees.

This calculates π using the area of a unit radius n-gon, with n=360000

A = ½n⋅sin(360°÷n)

One of Ramanujan's approximations

π ≅ 9801÷(2206⋅√2)

is about as accurate but opaque.

#mathematics #pi #approximation #FloatingPoint

I've found a decent working approximation of π for #PostScript

/pi 0.001 sin 2 div 360000 mul def

Accurate to 7 decimal places. The language uses single-precision floating point, and all its trig routines work in degrees.

This calculates π using the area of a unit radius n-gon, with n=360000

A = ½n⋅sin(360°÷n)

One of Ramanujan's approximations

π ≅ 9801÷(2206⋅√2)

is about as accurate but opaque.

#mathematics #pi #approximation #FloatingPoint

Exploring the Approximation Capabilities of Multiplicative Neural Networks for Smooth Functions

Ido Ben-Shaul, Tomer Galanti, Shai Dekel

Action editor: Murat Erdogdu.

https://openreview.net/forum?id=sWQJfb2GSk

#neurons #layers #approximation

Mean-Field Control based Approximation of Multi-Agent Reinforcement Learning in Presence of a Non...

Washim Uddin Mondal, Vaneet Aggarwal, Satish Ukkusuri

Action editor: Marc Lanctot.

https://openreview.net/forum?id=ZME2nZMTvY

#reinforcement #agents #approximation

Convert kilograms to pounds (Lbs):

Double the kgs and to that add 20% of the kgs. If you want more accuracy, also add half of 1% of kgs.

It also helps to remember that 1 Lb is about 454gms.

#convert #weight #approximation

Convert pounds (Lbs) to kilograms:

From one half of Lbs subtract 10% of half of Lbs.

Beware this shortcut loses accuracy (specifically underestimates kgs) for higher values of Lbs.

#convert #weight #approximation

Convert kilometers to miles:

To one half of kms add: 10% of kms, 2% of kms, and half of 1% of kms.

Skip the last addition if you don't need that much accuracy.

[Example results shown rounded to third decimal place.]

#convert #distance #approximation