Introduction

Activation functions are a component of neural networks they introduce non-linearity into the model, enabling it to learn complex patterns. Without activation functions, a neural network would essentially act as a linear model, regardless of its depth.

Key Properties of Activation Functions

• Non-linearity: Enables the model to learn complex relationships.
• Differentiability: Allows backpropagation to optimize weights.
• Range: Defines the output range, impacting gradient flow.

In this post I will outline each of the most common activation functions how they are calculated and when they should be used.

Summary

In this post I will implement a Support Vector Machine (SVM) in python. Then describe what it does how it does it and some applications of the instrument.

What Are Support Vector Machines (SVM)?

Support Vector Machines (SVM) are supervised learning algorithms used for classification and regression tasks. Their strength lies in handling both linear and non-linear problems effectively. By finding the optimal hyperplane that separates classes, SVMs maximize the margin between data points of different classes, making them highly effective in high-dimensional spaces.

Summary

This post is about color wars: a grid containing dynamic automata at war until one dominates.

Implementation

The implementation consists of two core components: the Grid and the CellularAutomaton.

1️⃣ CellularAutomaton Class

The CellularAutomaton class represents individual entities in the grid. Each automaton has:

• Attributes: ID, strength, age, position.
• Behavior: Updates itself by aging, reproducing, or dying based on simple rules.

2️⃣ Grid Class

The Grid manages a collection of automata. It:

44. What does it mean to Fit a Model?

Answer
Fitting a model refers to the process of adjusting the model’s internal parameters to best match the given training data. It’s like tailoring a suit – you adjust the fabric and stitching to make it fit the wearer perfectly.

Key Terms:

1. Model: A mathematical representation that captures patterns in data. Examples include linear regression, decision trees, neural networks, etc.

2. Parameters: These are the internal variables within the model that determine its behavior. For instance:

Summary

The Nagel-Schreckenberg (NaSch) model is a traffic flow model which uses used cellular automata to simulate and predict traffic on roads.

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Design of the Nagel-Schreckenberg Model

1. Discrete Space and Time:

   • The road is divided into cells, each representing a fixed length (e.g., a few meters).
   • Time advances in discrete steps.

2. Vehicle Representation:

   • Each cell is either empty or occupied by a single vehicle.
   • Each vehicle has a velocity (an integer) which determines how many cells it moves in a single time step.

Rules of the Model:

• The NaSch model uses local rules to update the state of each vehicle at every time step. These rules are:

1. Acceleration:

Summary

I started with this paper A developmentally descriptive method forquantifying shape in gastropod shells and bridged the results to a cellular automata approach.

An example of the shell we are modelling:

Steps

1️⃣ Identify the Key Biological Features

The paper outlines the logarithmic helicospiral model for shell growth, where:

• The shell grows outward and upward in a spiral shape.
• Parameters like width growth (\(g_w\)), height growth (\(g_h\)), and aperture shape dictate the final form.

These features describe how the shell expands over time in a predictable geometric pattern.

Summary

This page is the first in a series of posts about Cellular Automata.

I believe that we could get the first evidence of AI through cellular automata.

A recent paper Intelligence at the Edge of Chaos found that LLM’s trained on more complex data generate better results. Which makes sense in a human context like the harder the material is I study the smarter I get. We need to find out why this is also the case with machines. The conjecture of this paper is that creating intelligence may require only exposure to complexity.

Summary

Retrieval-Augmented Generation (RAG) is a powerful technique that enhances large language models (LLMs) by allowing them to use external knowledge sources.

An Artificial Intelligence (AI) system consists of components working together to apply knowledge learned from data. Some common components of those systems are:

• Large Language Model (LLM): Typically the core component of the system, often there is more than one. These are large models that have been trained on massive amounts of data and can make intelligent predictions based on their training.

Summary

Retrieval-Augmented Generation (RAG) has become the dominant approach for integrating external knowledge into LLMs, helping models access information beyond their training data. However, RAG comes with limitations, such as retrieval latency, document selection errors, and system complexity. Cache-Augmented Generation (CAG) presents an alternative that improves performance but does not fully address the core challenge of small context windows.

RAG has some drawbacks - There can be significant retrieval latency as it searches for and organizes the correct data.
- There can be errors in the documents/data it selects as results for a query. For example it may select the wrong document or give priority to the wrong document. - It may introduce security and data issues 2️⃣.
- It introduces complication
- an external application to manage the data (Vector Database) - a process to continually update this data when the data goes stale

LLM Agents

Agents are used enhance and extend the functionality of LLM’s.

In this tutorial, we’ll explore what LLM agents are, how they work, and how to implement them in Python.

What Are LLM Agents?

An agent is an autonomous process that may use the LLM and other tools multiple times to achieve a goal. The LLM output often controls the workflow of the agent(s).

What is the difference between Agents and LLMs or AI?

Agents are processes that may use LLM’s and other agents to achieve a task. Agents act as orchestrators or facilitators, combining various tools and logic, whereas LLMs are the underlying generative engines.