I participated in the AGI Safety Fundamentals program recently. The program concludes with a flexible final project, with the default suggestion of “a piece of writing, roughly the length and scope of a typical blog post”, so naturally, I deleted all but the last two words and here we are.

When I previously considered machine learning as a field of study, I came away with an impression that most effort and computation power was going into training bigger, more powerful models; whereas the inner workings of the models themselves, not to mention questions like why certain architectures or design choices work better than others, remained inscrutable and understudied. This impression always bothered me, and it definitely influenced me away from going into AI as a career. Of course, there are important, objective safety concerns around developing and designing models we don’t understand, many of which we discussed in the program; but my discomfort is mostly a completely unrelated nagging feeling I get whenever I’m relying on things I don’t understand.

After the program and all the concurrent developments in AI (including AlphaCode, OpenAI’s math olympiad solver¹, SayCan, and, of course, DALL-E 2), I still had this impression about the field at a very high level, but I also became more familiar with the subfield of interpretability — designs and tools that allow us to understand and explain decisions by ML systems, rather than treating them as black-boxed mappings from inputs to outputs — and confirmed that enough people study it to make it a thing. One quote from a post on the views of Chris Olah, noted interpretability researcher, captured my feeling particularly eloquently:

interpretability is very aligned with traditional scientific virtues—which can be quite motivating for many people—even if it isn’t very aligned with the present paradigm of machine learning.

I found the whole post insightful, and it happens that the bits before that in the passage were also relevant to me. I don’t have access to lots of compute!

Inspired by that post and by a desire to actually write some code (which I figured might help me understand the inner workings of modern ML systems in a different sense), and after abandoning a few other project ideas that were far too ambitious, I decided to go through some parts of the fast.ai tutorial and riff on it to see how much progress I could make interpreting the models, and to write up the process in a blog post. I tried to capture my experience holistically, bugs and all, to serve as a data point for what it might feel like to start ML engineering (for the rare individuals with a background and inclinations just like mine²), and maybe entertain more experienced practitioners or influence their future tutorial recommendations. A much lower-priority goal was trying to produce “my version of the tutorial”, which would draw more liberally from an undergraduate math education³ and dive more deeply into technical details.

Last weekend Galhacktic Trendsetters sort of spontaneously decided to do DiceCTF 2022, months or years after most of us had done another CTF. It was a lot of fun and we placed 6th!

Back in the day the silver edition was the top of the line Texas Instruments calculator, but now the security is looking a little obsolete. Can you break it?

It’s yet another Python jail. We input a string and, after it makes it through a gauntlet of checks and processing, it gets exec’d.

#!/usr/bin/env python3
import dis
import sys

banned = ["MAKE_FUNCTION", "CALL_FUNCTION", "CALL_FUNCTION_KW", "CALL_FUNCTION_EX"]

used_gift = False

def gift(target, name, value):
    global used_gift
    if used_gift: sys.exit(1)
    used_gift = True
    setattr(target, name, value)

print("Welcome to the TI-1337 Silver Edition. Enter your calculations below:")

math = input("> ")
if len(math) > 1337:
    print("Nobody needs that much math!")
    sys.exit(1)
code = compile(math, "<math>", "exec")

bytecode = list(code.co_code)
instructions = list(dis.get_instructions(code))
for i, inst in enumerate(instructions):
    if inst.is_jump_target:
        print("Math doesn't need control flow!")
        sys.exit(1)
    nextoffset = instructions[i+1].offset if i+1 < len(instructions) else len(bytecode)
    if inst.opname in banned:
        bytecode[inst.offset:instructions[i+1].offset] = [-1]*(instructions[i+1].offset-inst.offset)

names = list(code.co_names)
for i, name in enumerate(code.co_names):
    if "__" in name: names[i] = "$INVALID$"

code = code.replace(co_code=bytes(b for b in bytecode if b >= 0), co_names=tuple(names), co_stacksize=2**20)
v = {}
exec(code, {"__builtins__": {"gift": gift}}, v)
if v: print("\n".join(f"{name} = {val}" for name, val in v.items()))
else: print("No results stored.")

More precisely, the gauntlet does the following:

Last weekend Galhacktic Trendsetters sort of spontaneously decided to do DiceCTF 2022, months or years after most of us had done another CTF. It was a lot of fun and we placed 6th!

I made a blazing fast MoCkInG CaSe converter!

blazingfast.mc.ax

We’re presented with a website that converts text to AlTeRnAtInG CaSe. The core converter is written in WASM, and also checks that its input doesn’t have any of the characters <>&". The JavaScript wrapper takes an input from the URL, converts it to uppercase, feeds it to the converter, and if the check passes, injects the output into an innerHTML. The goal is to compose a URL that, when visited by an admin bot, leaks the flag from localStorage.

The converter is compiled from this C code:

int length, ptr = 0;
char buf[1000];

void init(int size) {
    length = size;
    ptr = 0;
}

char read() {
    return buf[ptr++];
}

void write(char c) {
    buf[ptr++] = c;
}

int mock() {
    for (int i = 0; i < length; i ++) {
        if (i % 2 == 1 && buf[i] >= 65 && buf[i] <= 90) {
            buf[i] += 32;
        }

        if (buf[i] == '<' || buf[i] == '>' || buf[i] == '&' || buf[i] == '"') {
            return 1;
        }
    }

    ptr = 0;

    return 0;
}

I subscribed to Discord Nitro a month ago, but only recently did I start thinking about the full range of powers the subscription granted me. I could create my own reactions, dump them in my personal server, and use them to react anywhere.

However, when I finally started trying to create some reactions, I hit an interesting snag: Discord can be used in dark and light mode,¹ and a reaction will have the same color on both modes. If I wanted my reaction to be as clearly readable in both modes as possible, what color should I make it?

(I could, of course, just outline my reaction with a contrasting color, but let’s say that’s cheating. With the limited space in a reaction, outlining isn’t that great of a solution anyway.)

Now, one can’t really just compute the “contrast of two colors” given only their RGB components; there’s no universally agreed-on definition of contrast in vision, and even if there were one, the contrast of two given colors would depend on the color space and possibly the viewer’s biology. But, to get a concrete answer to this question, we can use the standard sRGB model and the W3C’s definitions of contrast ratio and relative luminance.² As of time of writing on my computer,³ Discord reactions have background #2f3136 on dark mode and #f2f3f5 on light mode. Reactions you’ve reacted with have background #3b405a on dark mode and #e7e9fd on light mode. Because the dark mode background gets lighter and the light mode background gets darker, we’ll use the latter colors so we’re optimizing the worst-case contrast.

There are smarter approaches, but the 256³ = 16,777,216 possible 8-bit colors are perfectly feasible to brute force, so I wrote a short Python script to check all of them, which is at the bottom of this post. Under the parameters I’ve outlined, the optimal color for a Discord reaction is rgb(255, 65, 3) or #ff4103. A demo:

That was simple enough, but this color’s worst-case contrast ratio is less than 0.0000002 better than the runner-up. Surely even very mild aesthetic considerations will outweigh that. (It’s highly doubtful that the formulae I used were intended to have this degree of precision in the first place.)

After playing with a few ways to get a spread of options, I settled on categorizing colors into six buckets of saturation and twelve buckets of hue in the simple HSV model, and then finding the optimal color within each bucket. Here is a table of my results:

This post is motivated by reasons very similar to the ones that motivated my React and Redux “tutorial”. Again, it should be more accurately but less informatively titled “How I wish SQL SELECTs were explained to me”. Again, it does not imply that this method of explanation is suitable for anybody else. One difference is that this time, I mostly only wanted to learn about SQL SELECTs to the extent it would help me perform and optimize queries in Django’s ORM, but to prevent this post from languishing forever in my drafts folder, that material has been sectioned off into a possible future post, because I figured out what I wanted, ran out of steam, and am now trying to learn TLA⁺. Just me things.

Background

The SQL standard is confusing and almost never completely implemented; there are huge inconsistencies between SQL implementations. I will focus on SQLite because it’s popular and easy to play with, but generally try to stay away from unpopular or nonstandard features. SQLite’s SELECT documentation is good reading for one particular SQL implementation.

A SQL database is a place where you store and query a bunch of data that’s organized into tables. A table is a homogeneous list of rows. A row is a heterogeneous tuple of values of various simple data types. The data types supported depend on the SQL implementation; typical examples are integers and strings of various sizes, floating point numbers, and dates/datetimes. All of these types can be nullable; NULL is a SQL value that can appear just about anywhere. (Like many of the other SQL features, NULL is handled somewhat inconsistently across SQL implementations, but as a first-order approximation it’s closer to a floating-point NaN than, say, Java’s “null”. We’ll talk more about it later.) However, note that you can’t have a variable-size list of other things in a row. And just to make sure it’s clear, all the rows in a given table must have the same data types in the same order.

A “column” is just what you’d intuitively expect it to be: it’s the homogeneous list of all values in a particular position in each row of a table, which all have the same data type. One thing I haven’t mentioned yet is that table columns all have names. This is true both for tables stored in the database and for the ephemeral tables that are the output of queries.

Since I’ll also be referring to more complex types like lists and tuples often seen in conventional programming languages, I’ll call these simple data types “scalar types” and values of those types “scalars”. This is not SQL terminology; documentation usually just calls these “data types”. Here’s SQLite’s page on data types.

To play along, install SQLite and run it. You should get dropped into a connection to an ephemeral in-memory database, which is plenty enough for our purposes. Make a table and mutter some magic incantations to make the output a little prettier for us:

CREATE TABLE a (id int);
INSERT INTO a VALUES (1), (2), (3), (4);
.headers on
.mode column

Advent of Code (briefly, “AoC”) is a series of 25 festive programming puzzles¹ released daily December 1–25. Each puzzle has two parts, which use the same text input and are related; to solve a part, you submit the right output corresponding to the input on the website.

If you’re reading this, I suspect there’s a good chance you knew that already, but in case you’re new to Advent of Code, let me try to briefly explain why I like Advent of Code, from the perspective of somebody who’s spent a lot of their life so far doing programming competitions.²

• The event has a fantastic community surrounding it. I’m the most familiar with the subreddit, which is full of helpful people, interesting discussions, non-programming community games, and the occasional wonderfully, spectacularly overengineered solution to a puzzle; but I know there are also many smaller chatrooms and subcommunities focused on, say, specific timezones or programming languages.
• Another aspect is the unique two-part format of each puzzle. Even though they use the same input, you don’t get to see the second part until after you’ve solved the first one, a feature that Eric Wastl (AoC’s creator) has taken full advantage of in designing puzzles. The second part is often a surprising twist on the first part, which keeps you on your toes and challenges you to keep your code moderately general or refactorable in a way that I think almost no other programming challenges do. This sometimes even happens between days in a calendar, when a puzzle turns out to be about some model of computation you implemented two or five or ten days ago — hope you kept your code and remember how it works!
• Finally, AoC also has some non-rigorous puzzles that force you to use your intuition and “human intelligence”, either by interpreting the problem statement heuristically or writing code to let you explore the input. There are quite a few puzzles where it’s infeasible to write code that handles every step of obtaining the output from the input. The result is that Advent of Code can feature quite a few challenges that I’ve found particularly compelling because I think they simply could not be posed on any other contest platform.³

These are the things that make AoC stand out to me, but it also does a lot of other things well — the challenges are fun, approachable, and varied even aside from their interrelations; there is a long, dramatic story tying everything together (although it’s an Excuse Plot if there ever was such a thing); and, although this is obviously subjective, I find the website’s minimalist-adjacent, terminal-esque aesthetic really charming (there is a lot of detail in 2019’s calendar… after you solve everything). I’ve only done the last two years of Advent of Code, but it really seems like a one-of-a-kind event to me.

Anyway, one particular feature Advent of Code has is a leaderboard, which you can get on by being one of the first 100 people worldwide to solve each puzzle. The competition is fierce — every year, thousands of people compete to get on the leaderboard. Near the start of AoC 2019, mcpower (reddit discussion) and Kevin Yap (reddit discussion) wrote some articles about how to do this, both of which are worth reading. I also thought about writing such an article and started a draft, but I didn’t get it anywhere close to publishable before AoC had concluded, at which point I assumed few people would be interested. But here it is now.

By a strange quirk of fate, I have started writing C++ for a living.

Learning C++ was about as complicated as I think I expected it to be. By line count, I’ve written a lot of C++ for programming competitions, but I knew that I had only ever used a small cross-section of the language: basic control flow and variables, STL containers and algorithms, structs on which you mechanically define bool operator<(const T& other) const so STL algorithms can order them, and the very occasional macro or templated helper function. There were many features I wasn’t even aware existed.

In the process of learning C++ professionally, one rabbit hole I fell into quickly was C++11’s defining feature, the rvalue reference, and how it can be used to implement move semantics and perfect forwarding. By poring over a copy of the widely recommended book Effective Modern C++, by Scott Meyers, and a few dozen StackOverflow answers and blog posts, I roughly understood it after a few days, but still had a sort of blind-men-feeling-the-elephant feeling. I was confused about what lay under some of the abstractions I had been using, unsure of the full shape of the pitfalls that some of the guides had pointed out to me, and generally uncomfortable that there were still many small variations of the code I had seen that I couldn’t predict the behavior of. It took many more days to work myself out of there, and I wished I had had a guide that explained rvalue references and their applications to a bit more depth than what might be necessary for day-to-day use. So here’s my attempt to explain rvalue references in my own fundamental I-want-to-know-how-things-work-no-really style.

(If this vision doesn’t resonate with you, there are many other posts explaining rvalue references out there that you might prefer. Feel free to just skim the executive summary and/or check out some of the linked articles in the Background section.)

Executive Summary

I got… pretty carried away when writing this post, and a lot of it is just for my own understanding, which may or may not be useful to readers. Here’s a much more concise rundown (assuming you know basic C++ already):

One thing many mathematically-inclined programmers run into when implementing mathematical algorithms, particularly number-theoretic ones, is that the modulo operation doesn’t behave how they expect or prefer.

In many languages, this operator is denoted %. Concretely, one might prefer that, if the second argument is positive, then the modulo operation would always give a nonnegative result. Under this behavior, the expression (-5) % 3 would evaluate to 1 rather than -2. This is a lot more useful for number theory because then for positive integers n, the % n operation actually maps integers to exactly the n canonical representatives for the residue classes. As a result, \(a \equiv b \mod n\) if and only if a % n == b % n. You can also do things like index into a length-n array with a % n and know that the index will be in-bounds. Finally, there are also optimization opportunities: modding by a power of 2 becomes equivalent to a simple bitwise AND, which is really fast on modern computers.

A few programming languages, notably Python, do implement % this way. However, the majority of languages today, including pretty much everything remotely descended from C, do not; instead, (-5) % 3 is -2. This post attempts to track down why.

The first thing to note is that there is a more important number-theoretic identity we’d like to have:

\[\texttt{a} = (\texttt{a / b}) \cdot \texttt{b} + (\texttt{a \% b}). \tag{1}\]

In words, the integer division and modulo operators should give a breakdown of a into a sum of some copies of b plus a remainder. Note that this equation also implies that specifying the rounding behavior of division is equivalent to specifying the sign behavior of the modulo operation, which will come up repeatedly later.

It’s also very uncontroversial that that remainder should have no copies of b, positive or negative, left over, which gives the constraint:

\[|\texttt{a \% b}| < |\texttt{b}|. \tag{2}\]

Every programming language I can think of satisfies these two constraints.¹ So far so good. However, these two constraints don’t uniquely determine the values of a % b when a isn’t divisible by b; there are two possible values for a % b, one positive and one negative. Concretely, we could express \(-5\) as either \((-1) \cdot 3 + (-2)\) or \((-2) \cdot 3 + 1\), so (-5) % 3 could be -2 or 1.

It’s still mostly uncontroversial that, if a and b are both positive, then a % b should be nonnegative as well; we could call this constraint (3).² However, if a is negative and b is positive, programming languages start to diverge in their behavior. Why?

It’s December, so it’s time for a lot of things, including Advent of Code. I will not be able to be as competitive as I was last year, and already lost a lot of points to a really silly mistake on day 1, but I’ll be playing when I can and golfing the problems when I have time (so far: 7 + 14 bytes).

As one might expect, Day 1 is not too complex, but the second part can be analyzed to some mathematical depth and was discussed a bit on Reddit; plus, it occurred to me recently that I set up KaTeX on my blog but never used it, so I was looking for an excuse to write some equations anyway.

The problem statement for part 2, in brief: We are tasked with calculating the total mass of fuel required to launch a rocket module of a given mass. For something of mass \(m\), one can compute the directly required mass of fuel by dividing \(m\) by 3, rounding down, and subtracting 2; if the result is negative, it is taken to be 0 instead. However, the directly required fuel also requires fuel itself, calculated from its own mass by the same procedure, and that required fuel requires fuel based on its own mass, and so on until you reach fuel with 0 requirement.

Call me maybe? nc rev.chal.csaw.io 1001

A rev with a nasty binary. There are so many functions. I do not like this binary.

Static Analysis

After staring at the sea of functions in IDA for a little bit, I gave up and tried dumb things instead.