Four basis functions.

To build the MSE dataset I used four basis functions: 1, t, sin(50t), cos(50t). Why these four?

𐂅 Constant never hurts — it lets the curve shift up or down.
𐂅Linear captures any overall trend.
𐂅sin and cos with the same frequency come as a pair: by mixing their weights you set both amplitude and phase (i.e., you can place the peaks where you need them).

Why 50?
Because on 𝑡∈[0,1] the period 2π/50 roughly matches the width of the letters in the title I’m approximating, so the oscillations align with the letter shapes.

Everybody wants to be like ewe

Track on youtube

Just a small reminder:
🐑Homophones - "you" and "ewe", same pronunciation but different meanings
🐑Homographs - same spelling, different pronunciations (wind noun vs. wind verb). cat noun and cat verb...
🐑Homonyms (broad sense) umbrella term covering same-sound and/or same-spelling pairs

That's not it.

🐑Oronyms: phrases that sound alike — “ice cream” / “I scream”.
🐑Homographs: same spelling, different meanings — lead (metal) / lead (guide)
🐑Heteronyms: same spelling, different pronunciations and meanings — wind (noun) / wind (verb).
🐑Capitonyms: meaning (and sometimes pronunciation) changes with capitalization — Polish / polish, March / march.
🐑Heterographs: different spellings for words in a pair — you/ewe
🐑Polysemy: one word with related senses — head (of a person, of a department)
🐑Auto-antonyms (contronyms/Janus words): one word with opposite meanings — sanction (“approve” / “penalize”)

Mishearings

🐑Mondegreen: misheard lyric — “’Scuse me while I kiss this guy” for “kiss the sky.”
🐑Eggcorn: plausible but wrong substitution — “for all intensive purposes” for “intents and purposes.”
🐑Malapropism: wrong word, similar sound — “dance the flamingo” for flamenco.
🐑Spoonerism: swapping sounds — “You have hissed all my mystery lectures.”

The Farmer Was Replaced

In one of ML channels I'm reading, I found a reference to the game "The Farmer Was Replaced". Here you are to write programs on a language which is quite similar to Python, but is not quite Python to solve farm puzzles.

Some of them are quite essential: to chop grass and collect hay, to grow bushes and trees and collect wood. Carrot is totally normal - you just to spend some wood to seed it. Weird things starts with pumpkins: they rot with 20% probability, but when there is a patch of ready to harvest pumpkins, they merge together and when you harvest this mega-pumpkin, you have bonus harvest.

Then things go totally astray: on the picture it's a dinosaur chasing the apple. Basically you are to program automatic pilot for the famous "snake" game.

There are also cacti. You have to sort them on two-dimensional grid in order to get bonus.

I totally like it because it gives a chance to practice medium programming tasks at the Meta/Google 20-minutes level while playing the game.

It also brought back some memories I thought I'd forgotten. I will try to share them in this channel.

Memories Awakened by “The Farmer Was Replaced”

It seems like a very trivial question: “What should a drone do if it is on the lower (South) edge of the field and it has a move(South) command to perform?” But, strangely, this question leads to quite an interesting set of consequences.

In The Farmer Was Replaced the drone teleports to the other end of the field. It means that the upper edge of the field is glued to the lower edge. As I drew it, a square with upper and lower edges glued together becomes a cylinder from the topological point of view. Then the same goes for the left and right boundaries, and we have a torus.

There are other options. For instance, if the drone disappears on the lower edge and then appears on the left one (and similarly with upper and right), we have a sphere.

But that’s not all. You can play with the orientation of edges. If the drone appears at the beginning of the lower edge and then at the end of the upper edge, it means that we reversed the orientation. After we finish gluing edges, we get a Klein bottle or the projective plane. Unfortunately, you can’t embed these figures in 3D without self-intersection.

About memories. I first read about this in Anatoly Fomenko’s book. He also wrote “History: Fiction or Science?” (New Chronology) and, while he’s quite famous for that, he’s also a mathematician; his “Visual Geometry and Topology” is an interesting read. It even contains illustrations for “The Master and Margarita.” What I explained about gluing the edges of a square together is a simplified version of the introductory section of that book.

TFWR. Navigation.

In order to navigate the drone, there are get_pos_x(), get_pos_y(), and move() functions. move() takes East (x + 1), North (y + 1), West (x − 1), and South (y − 1) commands. get_world_size() is useful too. The world is square, so a single number (the side length) gives you everything you need.

nav(x, y) is a nice-to-have function. It moves the drone to position (x, y).

In the screenshot, a naive navigation function decides where to go—positive or negative direction—and moves accordingly. Why naive? Because it doesn't take into account the toroidal nature of the world (wrap-around at the boundaries).

Hello everyone!

I really appreciate that all of you have signed up for my channel. It's kinda touching, and I feel a little bit awkward just writing about GBDT and TFWR (but what else could I write about…).
So, I’d like to have a small talk with you. Let’s discuss in a comments a few things:

🤖How has the LLM revolution affected you?
🤖What do you expect in the near future?
🤖How do you see your career plans, taking into account all this hubbub?

I'll address some of these topics not to bias discussion.

Всем привет!

Я очень ценю то, что вы подписались на этот канал. Это трогательно и я чувствую себя немного неловко продолжая просто писать про градиентный бустинг и игрушку с дроном вместо фермера (правда, я не очень знаю, о чём ещё писать). Мне очень хочется со всеми поговорить. Давайте по-флудим в комментах по следующему поводу:
🤖Как тебя затронула LLM шумиха?
🤖Какие ожидания от ближайшего будущего?
🤖Влияет ли вся эта радость на карьерные планы?

Я для затравки напишу чуть-чуть чтобы ни у кого не украсть тезисы и допишу когда (если) пойдёт жара.

Eggcorn of the day

Bone apple tea → bon appétit

Some time ago my friend, who worked with native English speakers, told me that when they worked with a colleague on a piece of technical documentation, the word “she” suddenly appeared referring to the “user.” They discussed it, and it turned out the gender of this word in English is opposite to the gender of the word’s translation into Russian.

When I was on Vocabulary.com, I found the phrase above and recalled that “she-user” conversation. ChatGPT assures me that the user is gender-neutral, as is soldier in the example above.

I tried to find cases of gender reversal. In the form of “word”: (English gender) (Russian gender)

the sea: she neuter
a city: she masculine
a ship: she masculine
a car: she (“автомобиль” — муж, “машина” — жен)
a country: she
a hurricane: she

This is ChatGPT’s opinion. Do you agree? Did you have some clashes like that in your practice?

Dawn of the day

It dawned on me today that Harlequin ↔️ Harley Quinn. An example of paronomasia (a pun)—more specifically, it works like an eggcorn/mondegreen for a proper name

Torus navigation

Problem statement: issue control commands on torus map to navigate bot to a given point.

Essence
* pythonic (x2-x1) % n gives eastward toroidal distance
* easier to think in "direction first" terms
* go_bestt(East, West, (x2-x1)%n, (x1-x2)%n) is a solution


About three years ago I met this challenge on codingame platform. Now when I tried to solve it again in TFWR I totally forget the approach and here I want to make a note on what works well and what leads to a cumbersome constructions. I always try not to memorize solutions, but approaches instead. In this post I want to compare different ways of thinking about this problem and check programs we have as a result.

My first approach

def navigate(x, y):
  dx = x - get_pos_x()
  dy = y - get_pos_y()
  if dx:
    if dx > 0:
      for _ in range(dx):
        move(East)
    else:
      for _ in range(-dx):
        move(West)
  if dy:
    if dy > 0:
      for _ in range(dy):
        move(North)
    else:
      for _ in range(-dy):
        move(South)

It's a straightforward way to think about this problem: to select a direction and to walk in this direction. I think it is not bad, in general, while can be improved using functions. Then I tried to extend this approach to handle torus topology. It worked, but the result (obviously) was so cumbersome, I decided not to publish it.

Next idea was to reverse direction. Logic behind is like "we reverse our decision to go East or West if it gives not the best distance on torus". I think this trick is funny, so, let's check it closer

if (dx > 0) ^ (n - dx < dx):
  go(East, abs(dx))
else:
  go(West, abs(dx))

Here we use an interesting property of XOR gate: it gives the inversion of the first parameter, if the second is true. When I realized that ^ doesn't work in TFWR, I used == instead. (a ^ b) == (a != b).

But this way is kinda creepy and I dwelled for a while, what it the best way of thinking about this problem in a right way. The results are:
1) We are working with remainders modulo n. Indeed, possible coordinates are 0, ..., (n-1) and n is equivalent to 0
2) we can think about our positions as of positions on vertices of n-gon
3) if we have two points x1, x2 they divide the n-gon into two arcs
4) in python we can calculate lengths of arcs using (x2 - x1) % n for east and (x1 - x2) % n for west directions

And that is it!

def go_best(dr, dl, nr, nl):
  d, s = [(dr, nr), (dl, nl)][dl<dr]
  for _ in range(s):
    move(d)

def nav(x2, y2):
  n = get_world_size()
  x1, y1 = get_pos_x(), get_pos_y()
  go_best(East, West, (x2 - x1) % n, (x1 - x2) %n)
  go_best(North, South, (y2 - y1) % n, (y1 - y2) %n)

P.S.

Here I use "boolean as index" trick because there is no (v1 if cond else v2) construction in the TFWR dialect.
Note that (x2 - x1) % n is Pythonic expression is important because, for example, in C++ operator % works in a little bit different way and there you are to write something like (r%n+n)%n to have the same result.

Liquid Nitrogen Station

An attentive reader of one of my previous posts about the diamond plate in an electron microscope could notice a repetitive note: let's pour liquid nitrogen here, let's pour liquid nitrogen there. Sounds like a lot of liquid nitrogen. And it is. When I worked at the Physical Institute of the Russian Academy of Sciences, it was an everyday workout—to go with a special Dewar bowl and bring 17 liters of liquid nitrogen to the laboratory. Like 13 liters went to pump the air out of the microscope and cool down the specimen during the measurement. The remaining 4 liters evaporated during the night.

It's quite an interesting liquid and, when you have it in abundance, you can have a lot of fun. I heard that our colleagues froze ice cream with it. I myself conducted all the well-known experiments: freeze and cleave a piece of rubber. Dip your hand into it. The most amazing thing was to put a porous plastic which was widespread in the Soviet Union for packing scientific equipment. In normal conditions it's a springy material that you can compress and then it restores its original shape. But when you put it into liquid nitrogen, it becomes extremely brittle, and when you squeeze it, it becomes just a small heap of thin powder.

One more experiment I conducted inadvertently. When I was pouring liquid nitrogen into the photodetector bowl, a narrow stream escaped and soaked my jeans. So, when I unbent my leg, my jeans cracked. Jeans. Cracked. It was fun.