Conjecture COnjecture everywhere

Conjecture  about recurring digits in Pre Algebra homework

polynomial multiplication

 polynomial multiplication · point-value swap · roots of unity · recursion · one flipped sign

prompt like a mathematician

Claude agents

 Build with Thariq

a model trained on short tasks generalizes to problems 100x longer for free

Slack monitor

Slack probe

 Here is how on-chip controllers monitor and react to degrading timing slack in real time.

1. In-Situ Slack Monitors

Instead of measuring voltage or temperature as proxies, controllers use dedicated hardware sensors embedded directly inside the critical logic paths.

• Canary Circuits: Replica logic paths that mimic the slowest paths on the chip but are intentionally designed to fail slightly earlier than the actual operational logic. [1]
• Razor Flip-Flops: Specialized latches that sample data twice—once at the normal clock edge and a second time slightly later. If the two samples disagree, it indicates the timing slack has shrunk to a dangerous level.
• Transition Detectors: Sensors that watch data lines during a "guardband" window right before the clock edge. Any signal transition inside this window triggers a warning that slack is critically low.

2. Controller-Driven Recovery Mitigation

When the on-chip telemetry controller detects that the timing slack is nearing zero, it executes rapid hardware-level interventions:

[Slack Warning Triggered] │ ├──► 1. Clock Throttling (Immediate): Stretches or skips next clock cycle to grant more time. ├──► 2. Voltage Boosting (Transient): Signals PMIC to raise Vdd to speed up transistors. └──► 3. Architectural Re-execution: Re-runs the cycle securely if a Razor flip-flop detects a late transition.

• Dynamic Frequency Scaling (DFS): The controller immediately reduces the clock frequency (stretching the cycle time) to artificially open up the timing slack.
• Adaptive Voltage Scaling (AVS): The controller commands the Power Management IC (PMIC) to step up the voltage, forcing the transistors to switch faster and restoring the timing margin.
• Instruction Re-execution: If a Razor flip-flop catches a late-arriving signal that missed the primary clock edge, the controller stalls the pipeline and replays the instruction using the correct, late-sampled data.

Predictive Failure Analysis

Controllers also log the frequency of these near-miss slack events. If a specific core or execution unit continuously triggers slack warnings under normal workloads, the controller flags it as aging or degraded (due to phenomena like Negative-Bias Temperature Instability, or NBTI). The system firmware can then permanently map out or down-clock that specific block to avoid permanent SDC risks.

TRANSPOSING INFORMATION USING SHADOW LATCHES AND ACTIVE LATCHES FOR EFFICIENT DIE AREA IN PROCESSING SYSTEM

SSD

 How to write to SSD

REO: Revisiting Erase Operation for Improving Lifetime and Performance of Modern NAND Flash-Based SSDs

negotiating in pajamas

 why you should learn RL by touching nothing but the config and watching the curve go up, and why the intelligence ceiling of a specialised open-source model now subsumes the frontier for most real tasks

systemdesign concepts

Mathematical foundations of generative AI

llm compressing language

Understanding and Answering

https://paulabartabajo.substack.com/p/how-to-pass-a-technical-interview 

Knowledge Graphs, the Missing Link in Agentic AI-based Formal Verification

Agentic AI-based Coverage Closure for Formal Verification

NY story

 After a red eye flight, our five year old was tired. We were meeting friends in the new york city during the layover of international travel.

When the city was just waking up on a holiday, our friend bought us breakfast from a food stand.As we were leaving with our food, the stand owner gave our toddler a donut. He refused money for it. Intended to make the kid happy but it made a strong impression on us. A welcome to the city!!

I have been to the city many times hauling back a suticase full of second hand books from The Strand Store, Times square visit that I rendered in a poem, but that donut!!

10 years later

Any parent with a kid needs to know, where the restrooms are!! Our fiend dropped us at an entrance. There were few levels in the building. The receptionist said that the closest restroom was at a place called Occ.. something.

We started running, from one way pointer to another. It was a miracle that so much running could be done with a full bladder. Finally, the apple store pointer helped. Later in the evening, we were being shown around the Occulus, which we had seen 10 years ago, and as we were walking through it, our eyes fell on the Apple store sign and my younger one and I gave out a big laugh of the place etched in our minds, coming full circle in many ways. 

Agentic AI

 https://www2.eecs.berkeley.edu/Pubs/TechRpts/2016/Archive/EECS-2016-143.pdf - GPU Latency

https://www.cmu-agents.com/

https://www.developing.dev/p/mit-complexity-theorist-on-leetcode

Fast AI

 https://x.com/MillieMarconnni/status/2071529847189582018

https://course.fast.ai/

https://x.com/Jolyne_AI/status/2071398251480359020 - Mathematical Foundations of Reinforcement Learning

Loop Engineering

https://x.com/YiMaTweets/status/2063078487494398037

https://ma-lab-berkeley.github.io/deep-representation-learning-book/

Hitchhiker's guide to AI

https://blog.eleuther.ai/transformer-math/ - factor of 6

https://github.com/stas00/ml-engineering/blob/master/training/performance/README.md

https://lmms-engine.readthedocs.io/en/latest/reference/mfu.html

MFU

 The iron triangle: latency, throughput, cost

Goodput

https://github.com/stas00/ml-engineering/blob/master/training/performance/README.md

Transformer math

Training Large Language Models Pretraining, Alignment, and Scaling Modern AI

Alisa job search

https://alisawuffles.github.io/blog/job-search/ 

https://alisawuffles.notion.site/alisa-s-book-of-llms

https://alisawuffles.notion.site/math-notes

Innovation by Scale

  Due to the increased wealth produced by the country, the need for currency also grew. from a translated substack.

A passing thought, expounded by chatgpt.--

From Thought to Power: How Human Coordination Shapes Civilization

Someone once interpreted what I was saying as "thought is money." 

What I was trying to describe was that human civilization evolves through increasingly powerful ways of organizing thought.

The human brain is remarkable because it can create models of reality. We think, imagine, plan, and solve problems. In many ways, artificial intelligence is humanity's attempt to replicate or extend that capability. AI is essentially an effort to scale cognition itself.

But once you have intelligence, another challenge immediately appears: how do you organize it?

A single mind can accomplish only so much. Civilization emerged when humans learned to coordinate many minds together. The next great step after thought was organization.

Throughout history, we have invented different systems to organize human activity.

Language allowed people to share ideas.

Writing allowed knowledge to survive across generations.

Politics emerged as a way to organize large groups of people whose interests were not always aligned.

As societies became largeranother invention transformed coordination: currency.

Before money, exchange was limited and inefficient. Currency created a common language of value. It enabled strangers to cooperate without needing personal relationships or direct barter. Wealth accumulation became possible on a scale never seen before.

Over time, the pursuit of wealth became a central organizing force in many societies. Entire economies, institutions, and governments began orienting themselves around growth, production, and capital.

Yet money itself was never the final goal. It was simply another coordination technology.

Seen through this lens, history can be viewed as a sequence of increasingly sophisticated coordination systems:

• Thought coordinates perception.
• Language coordinates minds.
• Writing coordinates knowledge across time.
• Politics coordinates populations.
• Currency coordinates economic value.
• Corporations coordinate labor and resources.
• Computers coordinate information.
• Networks coordinate the world.
• Artificial intelligence coordinates cognition.

Each step expands humanity's ability to act collectively.

Today, we may be entering another transition.

For centuries, intelligence was scarce. Human expertise was limited by the number of trained people available. AI changes that equation. If cognitive capability becomes abundant, then intelligence itself may no longer be the primary constraint.

The bottlenecks shift elsewhere.

Now we hear discussions about data centers, energy production, semiconductor manufacturing, electrical grids, and geopolitical influence. These are not separate from the AI story; they are the next layer of it.

When cognition becomes easier to produce, the scarce resources become the infrastructure required to support it.

In previous eras, land was power.

Then labor was power.

Then capital was power.

Today, computation, energy, and the ability to govern complex systems may become the defining sources of power.

This is why AI discussions quickly become discussions about politics, economics, energy, and global strategy. Once intelligence can be scaled, organization becomes the central challenge again.

Perhaps the history of civilization is not primarily a story of technology, money, or governments. Perhaps it is a story of coordination.

Human thought created systems of organization. Politics organized people. Currency organized incentives. Computers organized information. AI organizes cognition.

And as cognition becomes increasingly abundant, power, energy, infrastructure, and governance become the next frontiers of human coordination.

Japanese Novels

 https://x.com/DrDavidVernon/status/2065720881809092945

ML job interview

 https://silviasapora.github.io/blog/ml-interviews.html

MIT primes

 https://math.mit.edu/research/highschool/primes/program/apply.html

summer math program , such as Canada/USA MathCamp , AwesomeMath , HCSSiM , MathILy , PROMYS , Ross Program , or SUMaC 

Other programs

blooket

How to become a polymath

 How to become a polymath

What is matmul Dwarkesh & Reiner

Cognitive availability and intrinsic reward MOTIF: INTRINSIC MOTIVATION FROM ARTIFICIAL INTELLIGENCE FEEDBACK

https://www.developing.dev/p/dropboxs-former-most-senior-eng-building

https://forums.welltrainedmind.com/

GPU

Optimization

 We built a multi-tier-SLO LLM serving system that treats Tensor Parallelism as a runtime knob instead of a fixed setting.

pretraining in NVFP4

https://mlbook.explained.ai/

Kernel trick

https://x.com/RolandMemisevic/status/2055321910213312943 

Training models at Anthropic

https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy

Idea divergence

General intelligence requires rethinking

Useful memory

Mathematical Methods for Computer Vision, Robotics, and Graphics

predicting the models

How to teach rust

cientific calculator in hardware using an FPGA.

How LLMs work

objects vs relations

online emulator

Deriving Muon

searching with grep

Why is the context window limited in LLMs?

Polyglot

 https://lithub.com/on-the-particular-joys-of-etymology-and-polyglot-prose/

Operating systems textbook

Counteropinion

 Your Decision Making Is All Wrong

what is the % of optimizers vs sastisficers

do we have consistent style or are we one in some areas of life and another in the rest?

There is a quick feedback loop when it comes to selecting movies to watch.

In medical, legal and other such fields, there is a need for second opinion. But some constraints make it easier. 3 Medical Routines That Older People May Not Need 

 

Chinese Characters across Asia: How the Chinese Script Came to Write Japanese, Korean, and Vietnamese

Matteo Ricci

inscriptions on the walls

Its hard to improve in a foreign language if you can't read it easily

universal contact language - culturally neutral - math?

https://x.com/Lawfull_neutral/status/2054123260200337829 - Need those dead languages in medicine and law.

Math progress

 https://x.com/benediamond/status/2051277047700267301

Mathing

Information flow

 https://hghalebi.github.io/category_theory_transformer_rs/seven-sketches-rust.html

LLM

 Challenges and Research Directions for Large Language Model Inference Hardware Xiaoyu Ma and David Patterson, Google

https://x.com/Catchingtides/status/2048765463325254130 - Language Modeling from Scratch, Stanford

Math Roadmap for high schoolers

 Imagine a blabket/carpet in your house and raise the carpet where your pet jumps highest, there you have a 3D map.

Imagine the racks in your even as seperate blankets that change to red color where they are hotter, there you have your heat maps.

calculus for dogs growth

integrals for cheese distribution on pizza

pet walk time calculation

Awesome! Let's break those down into real-life fun math problems. These examples will show how calculus, integrals, and simple time calculations can be related to pets, cooking, and real-life scenarios. Here’s how each one might work:

---

1. Calculus for Dog Growth

Let’s say you have a puppy, and you want to track how fast it’s growing. You can use calculus to figure out the rate at which your dog is gaining weight over time.

Example:

Imagine your puppy's weight as a function of time, W(t), where t is time in months and W(t) is the weight of the dog in pounds. We can model this as a curve.

W(t) = 0.5 * t^2 + 2t + 4

This might represent a growing dog. Now, if you want to figure out how fast your puppy is gaining weight at a certain time, we use the derivative (a part of calculus that gives us the rate of change). So, we take the derivative of W(t) to find how fast it’s growing at any moment.

The derivative is:

W'(t) = 1.0 * t + 2

This means that if your puppy is 4 months old, you plug t = 4 into this equation:

W'(4) = 1.0 * 4 + 2 = 6 pounds per month

So at 4 months old, your puppy is gaining weight at a rate of 6 pounds per month. If you wanted to know how much weight your dog gains in a month, you could integrate the function, essentially adding up the rate of change over time.

---

2. Integrals for Cheese Distribution on Pizza

Let’s say you’re making a pizza and want to figure out how to distribute the cheese evenly across the pizza so every slice has the perfect amount. A pizza is circular, so we can use polar coordinates and integrals to figure this out.

Example:

If we want to distribute cheese evenly over a pizza, we treat the pizza like a disk with radius r and area A = π * r². To make sure the cheese is spread evenly, the amount of cheese at any point on the pizza depends on the distance from the center.

Let’s say the cheese distribution function is C(r), where r is the distance from the center of the pizza (in inches). To distribute cheese evenly, we use an integral to figure out how much cheese to apply at each distance.

Let’s say that the cheese distribution is proportional to the square of the distance from the center. We could write this as:

C(r) = k * r², where k is a constant (like how much cheese per inch squared).

Now, to find the total amount of cheese you need to cover the entire pizza, you would integrate C(r) over the radius of the pizza. In polar coordinates, we integrate the area of each infinitesimally thin ring from the center to the edge of the pizza:

Total Cheese = ∫(0 to r) 2π * r * C(r) dr

Substitute C(r) = k * r²:

Total Cheese = ∫(0 to r) 2π * r * k * r² dr

This simplifies to:

Total Cheese = 2π * k * ∫(0 to r) r³ dr

Which, when evaluated, gives:

Total Cheese = 2π * k * [r⁴/4] from 0 to r = 2π * k * (r⁴/4)

So, you would calculate the total amount of cheese using this formula. This way, you can ensure that the cheese is distributed evenly across the pizza, taking into account the geometry of the circular shape.

---

3. Pet Walk Time Calculation

Let’s say you need to calculate how long it will take to walk your dog based on different routes.

Example:

If you want to calculate how long it will take to walk your dog, you can use basic time calculation.

Let’s assume you take 3 walks a day and each walk is 20 minutes long. The total time for walks in one day is:

Total Walk Time (per day) = 3 * 20 minutes = 60 minutes (1 hour)

Now, if you want to know how much time you spend walking your dog in 7 days, you multiply the total time per day by 7:

Total Walk Time (7 days) = 60 minutes/day * 7 days = 420 minutes = 7 hours

It’s that simple! You could also adjust this by using different walk times. For instance, if some walks are shorter or longer, just change the 20 minutes to the appropriate time.

---

These examples show how math, from calculus to simple time calculations, can be applied to real-life scenarios like your pet’s growth, distributing cheese on a pizza, or figuring out walk times. The cool part is that it’s all practical, even if it looks complicated on paper. Math is like a secret code to understand the world around us!

Great! Let's dive into differential equations and how they can be applied to things like pet growth or pet-related activities. Differential equations are used to model how things change over time, so they're perfect for describing things like a growing puppy or the cooling of a pizza. I’ll explain them in a way that ties back to pets and real-world examples.

---

1. Differential Equation for Dog Growth

Let’s extend the idea of your puppy growing over time, but now we’ll use a differential equation to model the growth rate more realistically. Instead of just having a simple equation like we did with calculus, this time we’ll use a formula where the rate of change of the dog’s weight depends on the current weight.

Example:

We know that animals grow faster when they’re smaller and that the growth rate slows down as they approach their adult size. We can model this using a logistic growth model. The logistic model is a common differential equation used for population growth and is perfect for situations like animal growth.

The logistic growth differential equation looks like this:

$$\frac{dW}{dt} = k \cdot W \cdot (1 - \frac{W}{K})$$

Where:

• $\frac{dW}{dt}$ is the rate of change of the dog's weight (how fast it’s gaining weight at any given time),
• $W$ is the current weight of the dog,
• $k$ is a constant that determines how fast the dog grows,
• $K$ is the carrying capacity, or the maximum weight the dog will eventually reach (its adult weight).

Let’s break it down:

• The term $1 - \frac{W}{K}$ represents how much room the dog has left to grow. When $W$ is small (the dog is young), this term is close to 1, so the dog grows quickly. As $W$ approaches $K$ (the dog’s adult weight), this term gets smaller, slowing the growth rate.

Solving the Equation:

This differential equation can be solved to predict how the dog's weight changes over time. You would typically need some initial condition (like how much the dog weighs when it’s born), and then you could solve for $W(t)$, which would give you the dog’s weight at any given time. The solution of this equation shows a curve that starts fast and then slows as the dog approaches its adult weight.

---

2. Differential Equation for Cooling Pizza (Newton’s Law of Cooling)

A classic example of a differential equation in cooking is Newton’s Law of Cooling, which describes how the temperature of an object changes over time as it adjusts to the surrounding temperature.

Example:

When you bake a pizza, it’s hot when you take it out of the oven. Over time, it cools down. Newton’s Law of Cooling describes this process:

$$\frac{dT}{dt} = -k \cdot (T - T_{\text{ambient}})$$

Where:

• $\frac{dT}{dt}$ is the rate of change of the temperature of the pizza,
• $T$ is the temperature of the pizza at a given time,
• $T_{\text{ambient}}$ is the ambient temperature (like the temperature of the room or outside),
• $k$ is a constant that depends on the properties of the pizza and its environment.

What this means:

• If the pizza is very hot and the room is cooler, the rate of temperature change is large, and the pizza cools down quickly. As the pizza gets closer to room temperature, the rate of temperature change slows down. This is exactly how cooling works in real life!

Solving the Equation:

You can solve this differential equation to get an expression for the temperature of the pizza at any time. For instance, if you start with a pizza at 180°F and the room is 70°F, you could predict the temperature of the pizza after 10 minutes or 30 minutes based on the value of $k$. This is a really handy way to model how the pizza cools and when it might be just the right temperature to eat!

---

3. Differential Equation for Pet Walk Distance

Another fun example could be modeling how far your dog walks over time. The rate at which your dog walks might change as it gets tired, or based on terrain (flat ground vs uphill, etc.). We can write this as a differential equation.

Example:

Let’s say the rate at which your dog walks is influenced by how tired it is. The more the dog walks, the more tired it gets, and the slower it will go. We could model this with a simple differential equation where the rate of change of the dog's distance traveled is proportional to how tired the dog is.

$$\frac{dx}{dt} = k \cdot (1 - \frac{x}{L})$$

Where:

• $x(t)$ is the distance your dog has walked at time $t$,
• $L$ is the limit of the total distance the dog can walk before getting too tired (let's say the dog’s max distance for the day),
• $k$ is a constant that determines how fast the dog gets tired (or how fast it walks).

This equation models how the dog's walking speed decreases as it approaches the maximum distance it can travel. The closer the dog gets to its maximum distance $L$, the slower it walks, until it eventually stops.

Solving the Equation:

You can solve this equation to find out how far your dog will walk after a certain amount of time, taking into account that it gets slower as it walks more. This can help you predict when it’s time to take a break or when to stop the walk for the day!

---

Wrapping It Up:

So, we’ve gone from basic rate-of-change problems (like walking times) to advanced modeling with differential equations for things like dog growth, cooling pizza, and tired dogs on walks. The cool thing about differential equations is they can describe anything that changes over time—whether that’s your pet’s weight, a pizza cooling down, or the distance your dog walks.

Turing award winner

 Mike Stonebraker is a Turing award winner famous for his fundamental contributions to databases (e.g. Postgres, C-Store and much more).

EDA vs LLM

 

"Agent-based Systems for Automated Design Space Exploration in EDA"

"Automated Chip Design Using Machine Learning: A Review of Methods and Trends"

 "Formal Verification and AI in Semiconductor Design"

 "Reliability Challenges in AI-Driven Chip Design"

"Large Language Models for Electronic Design Automation"

"Verification in AI-Driven Design Automation: A Survey"

"Autonomous Design Agents in Engineering"

"The Evolution of Verification in Semiconductor Design"

https://www.viksnewsletter.com/p/the-cpu-bottleneck-in-agentic-ai

AI knowledge graph

sum of external angles is 360

getting-into-ai-infra

 https://timzaman.com/getting-into-ai-infra

https://x.com/cosminnegruseri/status/2012041539137257544 - making llms practical

https://x.com/reinerpope/status/2044525525646119419 -  MatX, chip design and where silicon designed for LLMs is headed

https://x.com/FabianGloeckle/status/2044791592247066702 Formally verified code

https://aleximas.substack.com/p/how-will-ai-driven-automation-actually

Chipstack uses https://wavedrom.com/images/SNUG2016_WaveDrom.pdf

https://cheekypint.substack.com/p/reiner-pope-of-matx-on-accelerating 

(8:17) Tightly coupling SRAM and HBM on one chip (14:03) More MoE FLOPS, smaller KV cache load (16:08) Numerics: from 32-bit to 4-bit (19:02) Targeting both training and inference (22:14) Chip timelines (27:15) Logic and memory scarcity (29:42) Compute costs (32:07) Latency: from 20ms to 1ms as the new table stakes (40:50) Programming the chip (43:00) Starting MatX (47:11) Codesign without seeing the models (51:57) Interconnect design (55:44) Performance modeling philosophy (1:07:02) Prefill vs. decode (1:13:47) What's next

https://pdf.isaak.net/thesis - Scaling Brain emulation

https://x.com/danielhanchen/status/1931468866279932208 - FP8 in H100

Growing with AI

https://x.com/amanrsanger/status/1668144627004903424 probably needs update

https://x.com/dwarkesh_sp/status/2032493847666659780 Space GPUs

https://www.cs.cmu.edu/~213/schedule.html

Introduction to Computer Systems