The sky was in the transition state between light and dark. I stepped into the room. The voidness of the room holds a trauma that will never fade. The room is where my grandmother sat, facing north, lastly without her soul. And I shed my tears for hours, days, weeks, until I fainted. But that day had something surreal for me in the room.

What was that? A huge, dark, yellow, countless-legged giant centipede. I was taken aback at the sight of it. The centipede made a harsh sound and moved fast between my legs. I felt the segments in its body thrashing against my legs as it moved fast. That bunch of grotesquely arranged legs was just crossing my legs, touching them.

I wanted to trace it. Because I hadn't seen the full body of the centipede. It appeared mysterious to me. I wanted to kill it. I started chasing it, and it crawled faster. It started to crawl onto the wall. I, with a panicked heart, threw the old chisel at it. And half of the body of the centipede fell down. I saw a hand from the big upper body, letting the short bottom part fall down. And the part fell down. It was motionless. I thought it was meaningless to chase the fallen-down part.
![fell-down-part](https://qbghhenrxoupaykgnxyj.supabase.co/storage/v1/object/public/ariverse/arizone/posts/me-and-the-centepede/images/fell-down-part.webp?v=1788632076374)
I wanted to know the mystery of the upper part. I chased it again. It went higher into the margosa tree, climbing up like the coiled snake of the Garden of Eden, or the Caduceus, or Kundalini, or as in the abdomen of Baphomet. When it went up into the leaves, I wanted a view of it from the ground. So, I moved apart. Then I saw my house, which is half-built and half-complete. Yet, the centipede was not visible. I couldn't believe that I had let it go somewhere. I really wanted to kill it. The sound it made, the touch it gave to my legs, those brushy legs didn't deserve a life, I thought.
![into-sky](https://qbghhenrxoupaykgnxyj.supabase.co/storage/v1/object/public/ariverse/arizone/posts/me-and-the-centepede/images/into-sky.webp?v=1788632099677)
When I came back to the room, I saw the fallen-down part, motionless. When I took it in my hand, it suddenly gained movement and injured my hands. I felt a sharp kind of pain. I saw my hands turning reddish around the bite mark. The portion was moving around the room without a brain controlling it; it couldn't find death. It wanted to shake its hands with the remaining real part, which had gone into the world and was yet to be found.

And I woke up suddenly. With slight eye irritation and redness, I checked my phone. It was around 9:45 pm. I had lain down on the bed around 6:30 pm. But it's not my habit. What made me sleep early and get a dream like this? The day and the continuous grinding in my mind!

Some days ago, I created a mastery plan for learning unseen AI concepts and gaining real-world expertise in those untouched parts. But looking at the continuous advent of technologies, the so-called mind in me doesn't accept anything as a canonical source of material. You can console it using a thousand philosophical angles, but what I've got inside is stubborn. It has to be fooled in an appropriate way. It has to be fed the dopamine drink, which is holier than the bread and wine of Catholics, more intoxicating than the toddy of the South, the mead of honey, the wines upper varnas offer to devas in the Rig Veda, and whatnot.

I got vexed. I loved the solitude in the office, and that's why I visit the office all the days, including WFH days. But Friday hit differently.
![office-alone](https://qbghhenrxoupaykgnxyj.supabase.co/storage/v1/object/public/ariverse/arizone/posts/me-and-the-centepede/images/office-alone.webp?v=1788632148802)
It's an absence of words indeed, but also that of activeness. Mental dilution is common, but it could affect me heavily. I saw the release of Astra and started reading the usual hype and some early startups' early adoption of it. In the Discord group, where I saw a lot of researchers posting stuff, I felt too dark, as I am not into any of it. I also looked into my past works and past versions, the past me, the past works. Of course, I've made big, big, big progress. Yet, it's not enough for the stubborn internal chief.

I put my AI curriculum away. I stopped looking into it. Am I slightly hating my passion? Yes! Call it so! But love indeed entails hatred. But not today! No love today! I've lost all my vril thinking about it. As a result, I couldn't even wear my fake smile when my inter-company friends came near the door. I felt dizziness and then a one-sided headache.

I wanted rest. But, in the meantime, is someone releasing an unprecedented paper? Someone receiving recognition? At a time when someone is spending time on the startup they've built? Everybody's bowl is being filled with something productive. Mine? Of course, yes! From the outer world's perspective, but the stubborn internal has unique standards.

It was almost 5:30 pm. I came back to Besant Nagar, where I stay, with a headache and dull eyes. The mind controls the body, and it controlled mine. I laid my body onto the bed and closed my eyes.

I saw the things I have to learn as a giant centipede. For some reason, it is tied to my grandmother, because the life I am living is because of her prayers, as per her opinion, and because of her sacrifices for me, as per my opinion.

I also saw the path I've come so far as the part that fell down from the giant centipede. The part felt deadish. No movement. No activeness. When I chased the things I had to learn, it constantly rose into the sky. It was continuously evolving and becoming a mystery. I wanted to pursue it forever, till my last breath.

I saw my house half-built in between the chase. Yes! This passion, which became my profession, filled my bowl enough to build this half-house. The other half has to come from the endless part I am chasing and learning, and that spits out a version of me.

The fallen-down part really stung me. What I already have is really painful when I digest it. I am longing badly for the next version. I wanted the full centipede.

So, that's the meaning of my dream. But why should it be a centipede and this symbolic? Because I am more into these animals and symbolism. Among all the dreams I have had, this one is the masterpiece. Sorry, a monster-piece!

When I confessed this to my human friend, his advice was to take a break from these ridiculous learnings and show-offs. But would it be enough to convince the stubborn internal? That part of me is not demanding rest, but proof that I am not falling behind.

arizone/posts/me-and-the-centepede/content.md

Me and The Centepede

<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*apStXJ7fdXr2Ru3k3FFD9g.png</image>
We mostly talk about two broad tasks in machine learning, which are Classification and Regression. Classification forms the basis of many tasks we perform, from recognizing images to being the backbone of large language model training. Yes! Even in LLM training, classification happens at multiple levels, typically optimized using the well-known classification loss: Cross Entropy.

Let’s take one example. How will I classify an image into a particular class?
A CNN just gives me the feature vector of the image. What is my next step so that the classification actually works and does not suck?
<imageCaption>
<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*qbJZisU90c8ReBWRVb4poQ.png</image>
<caption>Say ARI when it is ARI</caption>
</imageCaption>

## Binary Cross Entropy
When we have only two classes of data, say images of Ari and Octopus, we can use Binary Cross Entropy Loss.
<imageCaption>
<image>https://miro.medium.com/v2/resize:fit:720/format:webp/1*hwiEgdmmx4mGQwwfWKgUcw.png</image>
<caption>Octopus vs Ari</caption>
</imageCaption>

And the loss is,
<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*Fkip9RqoAbAu76kvY3teDA.png</image>

To understand this loss, we need to understand -log(p) first!

We want our model to give high probability to the correct class. If the image is Ari, the probabilty should be high for the class of Ari.
<imageCaption>
<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*9ZmJDxGCzrLpyQ6KzGMKng.png</image>
<caption>Amazing Model1 and Awful Model2</caption>
</imageCaption>
Since it is binary classification, we can simply assign numbers 0 and 1 to the classes. So if the true label is Ari (Let’s say y = 1), we want p = probability(model says “Ari”) to be as close to 1 as possible.

In other words, the model should be trained in such a way. If the model says p=0.98, that’s amazing! If it says p=0.1, that’s terrible.

Let’s see what happens when we plug in different p values.
<imageCaption>
<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*Is287tDjh3ZeWDo2xJYyPg.png</image>
<caption>Higher the p, lower the log(p)</caption>
</imageCaption>
We take negative of log(p) just to make it positive.
If the model is confident and correct (p ≈ 1), -log(p)≈ 0.
If it’s wrong and gives a small probability to the true class (p ≈ 0), the loss shoots up.

Now, we know what -log(p) does. Let’s just fit this understanding into the Binary Cross Entropy Loss Function.
<img>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*Fkip9RqoAbAu76kvY3teDA.png</img>
As we said, we have two classes (1 and 0).

If the true label is 1 (Ari), then only the first term matters: −log(p) and the second term becomes zero. So, the loss punishes low p values, the model must make p → 1.

If the true label is 0 (Octopus), then only the second term matters: −log(1−p) and the first term disappears. Now, the loss punishes high p values, the model must make p → 0.

We add both terms because we don’t know in advance whether the label will be 0 or 1. It is just a smart way to combine both cases into one single equation. Depending on whether y=1 or y=0, one term automatically becomes active, and the other goes to zero.

That’s BCE Loss!

## Cross Entropy
Alright, Binary Cross Entropy worked great when we had only two classes: Ari and Octopus. But what if we now have Ari, Octopus, and StarFish?
<imageCaption>
<image>https://miro.medium.com/v2/resize:fit:614/format:webp/1*g_UNBZ54LcqNTRX72e0I7Q.png</image>
<caption>Octopus vs Ari vs StarFish</caption>
</imageCaption>
Now it’s multi-class classification and here comes Cross Entropy Loss. When we have more than two classes, the model doesn’t just give us one probability. Instead, it gives a probability distribution over all classes.
<imageCaption>
<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*J8-6v1bxSnBWmuA8D9dRCA.png</image>
<caption>Probability Distribution over the classes: Ari, Octopus, StarFish, seems like a good model</caption>
</imageCaption>
The formula is nothing when you already know BCE Loss.
<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*T_eDSFkxaRzCPGWQ5RHs7Q.png</image>
If we expand this, it’s just y₁log(p₁) + y₂log(p₂) + y₃log(p₃) + … + y꜀log(p꜀). Now, if the class is Ari, how are we going to zero out Octopus and StarFish?

Well! We have something called One-Hot Encoding.
For each class, we have a vector filled with zeros except for a 1 at the index of the correct class. That means:

If it’s Ari, the vector is [1 0 0]ᵀ
If it’s Octopus, it’s [0 1 0]ᵀ
If it’s StarFish, it’s [0 0 1]ᵀ

When we multiply y₁, y₂, y₃ with their respective log(p) values, only the true class’s term survives, the rest all become zero.

For example, if the true class is Ari, the one-hot vector is [1 0 0]ᵀ. Substituting:

Loss = -(1·log(p₁) + 0·log(p₂) + 0·log(p₃))
Loss = -log(p₁)

Only the term corresponding to the true class survives, the rest become zero. That’s how Cross Entropy automatically focuses on the correct class without us manually handling the others.

After training with Cross Entropy Loss, the model learns to assign high probability to the correct class and very low probabilities to all other classes. In other words, for a given input, the output probability distribution becomes sharp and confident, with the true class close to 1 and the rest close to 0. This is the result of the model learning from the loss function over many examples.
<imageCaption>
<image>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*rdyeE7mXRYgA-i-34HhHbQ.png</image>
<caption>Correct Probability Distribution: The Fruition of Cross Entropy</caption>
</imageCaption>

Note: The model won’t give probability values itself; we use a softmax over the logits the model gives us.

arizone/posts/classification-losses-bce-and-ce/content.md

Classification Losses: BCE and CE

Sound waves are analog signals, meaning they are continuous. To understand this, we can use a sine wave as a simple example, since it is also a continuous signal.
<imageWithCaption>
    <img>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*I3aLKf99aY-SZsl8gyJylw.png</img>
    <caption>SINE WAVE | y = sin(2πx)</caption>
</imageWithCaption>
When we say a signal is continuous, it means there are infinitely many values between any two points on the wave. No matter how close two points are, there are always more (infinite) values in between. We can’t store all these values in a computer.
<imageWithCaption>
    <img>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*n2oAHwG13pkzy-nquToNKw.gif</img>
    <caption>Infinite Values In Between Two Points in A Wave</caption>
</imageWithCaption>
So, we record only some values, which are called samples, and they are enough to represent the entire wave. In simple words, we use a few points to represent the entire signal.
<imageWithCaption>
    <img>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*PVgyT7GBWW7EZ5TLtenF6w.png</img>
    <caption>Only Few Points</caption>
</imageWithCaption>
<imageWithCaption>
    <img>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*qgfLJo3fpM5d1Kw6jsl-cw.png</img>
    <caption>Reconstructing Wave: Possibility 1: The Good Reconstruction</caption>
</imageWithCaption>
<imageWithCaption>
    <img>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*GJjqYT7Cm-N-FIdwAuH1xQ.png</img>
    <caption>Reconstructing Wave: Possibility 2: The Bad Reconstruction</caption>
</imageWithCaption>

So, the next question would be: how many samples are required? 30 samples per second? 40 samples per second? Or what’s the number? Let it be whatever, but this number of samples recorded per second is called the sample rate.

Now, to answer this question correctly, understand that there are many frequency components in a sound wave. That means, per second, there could be an irregular number of complete cycles. One particular instance may have a frequency of 2 Hz, and another may have 4 Hz. That’s what a wave signal is like in the natural world.

We need to pick the highest frequency component of all, and our sampling rate should be at least twice the highest frequency value. This number helps in reconstructing the signal perfectly, and this is the so-called Nyquist–Shannon Sampling Theorem. If the highest frequency component in the wave is 3 Hz, the sampling rate should be at least 2*3 Hz = 6 Hz.
 <img>https://miro.medium.com/v2/resize:fit:1100/format:webp/1*_IfS8jxJN9IaQiwFTF0oyg.jpeg</img>
Before we answer how this number is enough to represent the complete signal, we have to discuss what happens if we don’t follow the proper sampling rate. Let’s say we have a sampling rate that is lower than the highest frequency component. In such case, If there are 10 complete cycles per second (10 Hz), our sampling rate would represent only 5 complete cycles, making the computer think that the wave is a lower-frequency one. This phenomenon is called Aliasing and it brings us some fake tones, distortion and beating effect in the audio.

Waves from the natural world contain many high-frequency components, often higher than what our sampling system can handle. To avoid problems, we use a low-pass filter to remove those high frequencies before sampling. This ensures that aliasing-causing frequencies are removed.

You might wonder: “Won’t we lose some audio by filtering these frequencies?” The answer is: yes, but that’s okay. Humans can only hear roughly from 20 Hz to 20 kHz. CD audio uses a sampling rate of 44.1 kHz, which means the Nyquist frequency is 22.05 kHz. Any frequency above ~22 kHz is removed, but we cannot hear those frequencies anyway. So there is no audible loss at all.

Once we have enough sampling points and we remove high frequencies, the wave is forced to be smooth. Given these points, there is only one smooth wave that can pass through them. Any other wave would require sharp changes, which are not allowed by the filter.

Sampling gives us dots, and filtering forces smoothness. Together, they force the original wave to come back.

arizone/posts/the-perfect-wave/content.md

AriZone

Me and The Centepede

Classification Losses: BCE and CE

The Perfect Wave