Google Gemini does source-code examination & comparison

Gemini in Google Drive works somewhat like Google’s NotebookLM, but is more suited for quick, ad hoc queries. (NotebookLM also offers to create FAQs, study guides, document summaries — all of which I’ve been using to help me turn many hundreds of pages of notes on patent litigation into a forthcoming book — plus somewhat bizarre auto-generated “Deep Dive” audio conversations between two synthetic enthusiasts — like this one based on lots of files, some of them not mine, that I happened to have in one folder with backups of my PatClaim.ai work; and here’s a less inaccurate though also less entertaining “Deep Dive” audio).

I was interested in how Gemini does with source code. To what extent can it figure out what’s going on in the code, without a lot of hints from file headers, comments, and variable/function names?

Right now, Gemini won’t readily do summaries of anything but PDFs and Word/Excel documents. But it’s trivial to print a piece of source code (or, as shown elsewhere, a disassembled or decompiled code listing) to a PDF file, upload that, and get a summary. (I’ll several times caution the reader to not blithely upload code that might be confidential, covered under an NDA or court protective order. I’m using Google Gemini here more as an example of what AI systems are capable of doing with source code, and less as a suggestion that the reader do this with their client’s code.)

(Microsoft CoPilot can also do source-code analysis and comparison. I was a bit less impressed with what I’ve seen there, than with Gemini. CoPilot is famously part of GitHub, though CoPilot itself told me, “GitHub Copilot primarily assists with code completion and suggestions, making it an excellent tool for boosting productivity and providing quick snippets of code based on the context you’re working in. However, it doesn’t inherently provide detailed explanations or walk-throughs like I do.”)

Back to Gemini in Google Drive: I started with a small piece of neural-network code that ChatGPT wrote with me. The point of that exercise was to see how a simple neural net can provide the functionality of linear and non-linear regression (basically, given y=f(x) data, regression takes x and y, and figures out f), without using the standard regression least-squares formulas for finding the best fit to a set of data. Instead, the neural net would be trained to learn how x and y relate in some data set, and then predict y values for some new x values. ChatGPT was struggling a bit getting the code to work with some of my sample data, and I suggested it look at a web article, “Regression neural-network from scratch“, whose code I could see worked (at least on its built-in test data). I asked ChatGPT to modify that code to accept an external text file with (x,y) pairs, and to provide the user with a loop to type in x values and see the predicted y values. Another point of the ChatGPT writing exercise was to generate a small self-contained file that one could grok without having to understand a lot of external library code. It was written in Python, using NumPy rather than the PyTorch machine-learning library.

I wanted to see if Gemini could tell what’s going on in the code, and to compare and contrast it with the original code. (This type of comparison happens all the time in source-code examination in software litigation — note that extreme care must be taken with confidential code in litigation, which cannot blithely be uploaded to a cloud service like Google Drive, and which is generally handled under a court protective order. As an aside, a business article on the NYTimes v. OpenAI litigation describes the Times experts’ examination of OpenAI’s source code in that case as something extraordinary: “Why The New York Times’ lawyers are inspecting OpenAI’s code in a secretive room”. Almost any source-code examination for litigation would happen inside a “secretive room” with no internet connection. See the note below about local AI systems.)

Now, if the file had a header describing its purpose, helpful comments, and meaningful function/variable names, Gemini could just read those, and it wouldn’t be much of a test. So I made a copy of the neural-network file, and just called it nn.py. All references in the file to “Regression” were replaced with “R” (so “RegressionNeuralNetwork” became “RNeuralNetwork”). The header and some comments were removed. I printed to PDF, uploaded to Google Drive, and asked Gemini to explain the file (nn_py.pdf). It said:

The Python file nn_py.pdf contains a class definition for a Recurrent Neural Network (RNN) and includes functions for training and predicting with the model.

The RNeuralNetwork class initializes a neural network with input, hidden, and output layers, along with weights and biases. It includes methods for forward and backward propagation, computing loss, and updating parameters. The training process involves multiple epochs of forward and backward passes, adjusting weights and biases to minimize the loss between predicted and true values.

The ‘load_data’ function reads data from a file, normalizes it, and returns the input and output data (X and Y) along with the original minimum and maximum values.

The main section of the code loads data from a file specified as a command-line argument, initializes an RNeuralNetwork object, and trains the model on the loaded data. It then predicts the type of formula the network approximates (linear or nonlinear) and provides some sample predictions. Finally, it enters a loop where the user can input values to get predictions from the trained model.

The provided code defines a neural network model, trains it on a given dataset, and allows for predictions based on user input. The code also includes functionality to normalize the data, track the loss during training, and approximate the type of relationship the network has learned.

This may look pretty good at first glance, but one quickly sees that Gemini jumped to the conclusion that “RNeuralNetwork” was doing RNN, which is a Recurrent Neural Network. Note how self-assuredly it asserted this, based entirely on the class name that sounded RNN-ish. Google AI of course knows what an RNN should roughly look like, and it just plowed ahead anyway. Well, I’ve known software examiners  who also rely too much on naming.

So I next changed the class name to “TestNeuralNetwork”, to avoid Gemini’s RNN confusion. I also removed the code that Gemini had spotted about estimating if the input data was linear or non-linear. I uploaded this as nn_py_2.pdf. Gemini now described the file this way:

The Python file `nn_py_2.pdf` contains code that defines and trains a neural network. The network is designed to take an input value and predict an output value, effectively learning the relationship between the two.

TestNeuralNetwork Class
* __init__: This constructor method initializes the neural network by setting the sizes for the input, hidden, and output layers. It also initializes weight matrices (`w1`, `w2`) and bias vectors (`b1`, `b2`) with random values.
* sigmoid: This method implements the sigmoid activation function, which is commonly used in neural networks.
* sigmoid_derivative`: This method calculates the derivative of the sigmoid function, which is needed for backpropagation.
forward: This method performs a forward pass through the network, calculating the predicted output based on the input and the current weights and biases.
* compute_loss: This method calculates the mean squared error loss between the predicted output and the true output.
backward: This method performs backpropagation, calculating the gradients of the loss with respect to the weights and biases.
* update_parameters: This method updates the weights and biases using gradient descent based on the calculated gradients and a learning rate.
* train: This method trains the neural network on a given dataset (`X`, `Y`) for a specified number of epochs. It iteratively performs forward and backward passes, updating the parameters and tracking the loss. It also includes diagnostics to print the loss, mean and standard deviation of weights and biases, and the gradient norm during training. Early stopping is implemented to prevent overfitting.
Data Loading and Normalization
* load_data: This function loads data from a file, normalizes it to the range, and returns the normalized input and output data along with the original minimum and maximum values.
Main Execution
The main part of the code loads data from a specified file, initializes a `TestNeuralNetwork` object, and trains the model on the data. It prints diagnostics during training and provides sample predictions after training. Finally, it allows the user to input values and get predictions from the trained model.
Overall, this code provides a basic implementation of a neural network for learning and predicting relationships between input and output values.

I gave this a thumbs-up (it recognizes there’s backpropagation for example, even though that’s not explicitly mentioned in the code), but asked to refresh the explanation (randomness in AIs such as Gemini means you can get different responses to the same query). Though perhaps its summary is a little less impressive, given it had names such as “forward” and “backward” to rely on, as well as the name “TestNeuralNetwork”. See below at “Can Gemini figure out obscured code, without useful names, on the basis of patterns/concepts?” for how Gemini handles an even less-explicit (obfuscated) version (nn_ob_py.pdf).]

Here was Gemini’s second explanation for nn_py_2.pdf. Gemini sees that the goal’s is regression-related, even though the file itself doesn’t say that. Google AI clearly knows what regression code generally looks like, without needing a pointer saying “hey, this is regression code.” Ability to pattern match at a non-linguistic level would be a big advantage of applying machine-learning to source-code examination. Ability to infer the function or purpose of code, from a mass of low-level details, is much of what software reverse engineering is about. (Which is, in a way, what this very code tries to do: given a bunch of (x,y) values, figure out their y=f(x) relation, where f rather than y is the unknown.)

The Python file “nn_py_2.pdf” contains code that implements a neural network for regression tasks. The neural network architecture consists of an input layer, a hidden layer with 10 neurons, and an output layer. The code includes data loading, normalization, training, and prediction functionalities.

Key Components and Functionality:

* TestNeuralNetwork Class: This class encapsulates the neural network’s structure and operations.
* __init__: Initializes the network’s input, hidden, and output layer sizes, along with weight matrices (`w1`, `w2`) and bias vectors (`b1`, `b2`).
* sigmoid and `sigmoid_derivative`: Implements the sigmoid activation function and its derivative.
* forward: Performs a forward pass through the network, calculating the predicted output based on input and current weights/biases.
* compute_loss: Calculates the mean squared error loss between predicted and true outputs.
* backward: Implements backpropagation, computing gradients of the loss with respect to weights and biases.
* update_parameters: Updates weights and biases using gradient descent based on calculated gradients and a learning rate.
* train: Trains the network on provided data for a specified number of epochs. It iteratively performs forward and backward passes, updates parameters, and tracks the loss. Diagnostics are printed during training, and early stopping is implemented to prevent overfitting.

* load_data Function: Loads data from a file, normalizes it to the range, and returns the normalized input and output data along with original minimum and maximum values for denormalization.

* Main Execution:
* Loads data from a specified file.
* Initializes a `TestNeuralNetwork` object.
* Trains the model on the loaded data.
* Prints diagnostics during training and sample predictions after training.
* Enters a loop where the user can input values to get predictions from the trained model.

Purpose:
This code aims to create a neural network model that can learn the underlying relationship between input and output data. By training on a dataset, the network adjusts its weights and biases to minimize the prediction error. The trained model can then be used to predict outputs for new, unseen input values.

Maybe I’ve become overly enamored of these LLMs, but I think this is an impressive summary of somewhat opaque code (look at file “nn_py_2.pdf” if you haven’t already). Again, one ought to expect that Google AI knows what neural-network regression code looks like, and ought to be able to recognize an instance of it without the code itself saying what it is, but still, here it was in action, with little effort on my part. Such abilities are going to change how code examination is done.

Gemini then suggests that I ask the following questions (Gemini and NotebookLM are both very good at helping the user get past “Okay, now what?” spots, and getting the user to continue interacting with it, by suggesting follow-up questions):

• How does the code handle overfitting and underfitting issues in the neural network model?
• What other activation functions could be used instead of the sigmoid function in the hidden layer, and how might they affect the model’s performance?
• Is the model capable of learning more complex relationships between input and output values beyond linear or nonlinear formulas? If so, how does it achieve this?

I tried each of Gemini’s suggested prompts:

How does the code handle overfitting and underfitting issues in the neural network model? [I was half-expecting Gemini to say “Gee, I thought you’d never ask”]

The code primarily addresses overfitting using early stopping.

• Early Stopping:
  • During training, the code monitors the validation loss (computed on a separate validation set).
  • If the validation loss stops decreasing for a specified number of epochs (patience), the training process is halted.
  • This prevents the model from continuing to learn and potentially overfit the training data.

Addressing Underfitting:

While not explicitly addressed in the code, underfitting could be mitigated by:

• Increasing Model Complexity:
  • Adding more layers or neurons to the network could improve its capacity to learn complex relationships.
• Training Longer:
  • Increasing the number of training epochs (with caution to avoid overfitting) might allow the model to learn more from the data.
• Feature Engineering:
  • If applicable, creating new features or transforming existing ones could help the model capture relevant information.

Note: The code does not implement techniques like regularization (L1, L2) or dropout, which are also commonly used to prevent overfitting in neural networks.

Note Gemini here observing what sorts of things it might expect to see in the code, but that are not present. Detecting absences is quite important in litigation-related software examination.

What other activation functions could be used instead of the sigmoid function in the hidden layer, and how might they affect the model’s performance? [I had to copy/paste this 2nd question in from my notes, since Google removed the 3 suggestions from the Gemini panel while it was answering the first one, and replaced them with more specific ones related to its answer to the 1st question]

The text mentions a few other activation functions that could be used in the hidden layer instead of the sigmoid function:

• ReLU (Rectified Linear Unit): This is a very simple and computationally efficient activation function that is defined as f(x) = max(0, x). ReLU has become very popular in recent years and is often the default choice for hidden layers. It can help to avoid the vanishing gradient problem that can occur with sigmoid activation. However, ReLU units can sometimes “die” if they always output 0, which can be mitigated by using a variant like Leaky ReLU.
• tanh (Hyperbolic Tangent): This is another common activation function that is similar to the sigmoid function but outputs values between -1 and 1. It can sometimes lead to faster convergence than the sigmoid function.
• Swish and Softplus: These are newer activation functions that have been shown to perform well in some cases. They are both smooth and non-monotonic, which can help to improve the model’s ability to learn complex patterns.

The choice of activation function can have a significant impact on the performance of the model. In general, it is a good idea to experiment with different activation functions to see what works best for your particular problem.

Is the model capable of learning more complex relationships between input and output values beyond linear or nonlinear formulas? If so, how does it achieve this?

Yes, the model is capable of learning more complex relationships between input and output values beyond linear or non-linear formulas. It achieves this through the following mechanisms:

• Universal Approximation Theorem: Neural networks with enough hidden layers and neurons, using non-linear activation functions, can theoretically approximate any continuous function. This means they can capture intricate patterns and relationships in the data, not just simple linear or polynomial trends.
• Multiple Hidden Layers and Neurons: By adding more hidden layers and neurons, the network’s capacity to learn complex representations increases. Each layer can extract increasingly abstract features from the data, allowing the model to capture subtle dependencies between input and output.
• Non-Linear Activation Functions: Activation functions like tanh and sigmoid introduce non-linearity into the network. This non-linearity is crucial for modeling complex, non-linear relationships in the data.
• Feature Engineering (Optional): While not always necessary, augmenting the input with additional features (e.g., polynomial terms) can sometimes help the network learn complex relationships more easily.

The model’s ability to learn complex relationships is a direct result of its architecture and the non-linear transformations it applies to the input data. This flexibility allows neural networks to excel in a wide range of tasks where the underlying relationship between input and output is not easily defined by a simple formula.

The reference to the Universal Approximation Theorem (UAT; see also here) was gratifying, as ChatGPT and I had been having a lengthy chat about that while we were writing this code (i.e. while ChatGPT was writing it under my loose supervision), and about how this simple neural network code might or might not help understand it. The UAT isn’t mentioned anywhere in the code, so cool Google picked up on what we were trying to get at. Importantly, this code is not very close to actually implementing the UAT idea. The code attempts to use a single neural network to handle any kind of (x,y) pairs, but even with some later improvements by ChatGPT (to be discussed in another article) it still produces wildly-inaccurate predictions for some kinds of inferred functions; it does less well than a piece of C code I wrote years ago that, given a file of (x,y) pairs, can figure out whether lin, power, log, or exp is the best (R^2) fit to the data, and spits out the closest C function to model the (x,y) input:

C:\work\ml>regression3 < sqrt.txt
[pow: a=-0.000003 b=0.500001 r2=0.9999999998092237]
[log: a=-2.242746 b=2.458122 r2=0.9306702719710180]
[exp: a=1.104075 b=0.014246 r2=0.8121137832690487]
[lin: a=2.728783 b=0.079118 r2=0.9645460288195382]
(r2 = 1.000000)
pow: y=0.999997x^0.500001
double f(double x) { return 0.999997 * pow(x, 0.500001); }

The purpose behind the neural-network code I was asking Gemini to examine was to approximate this functionality, without using the standard regression formulas employed in regression3.c. It is still far from being able to do so, but it’s trying to get on the road, and Google Gemini’s mention of the UTA shows it picked up on that general direction.

Gemini offered yet more follow-up questions about this code; while I didn’t chase down all the rabbit holes Gemini thoughtfully provided, I can easily see this capability would help a source-code examiner create checklists of issues to consider for example when comparing two pieces of similar code, asking how they resemble or differ from each other in handling various issues like this:

• How does the number of hidden layers and neurons impact the model’s ability to learn complex relationships?
• Can neural networks approximate discontinuous functions? [Its answer: While neural networks can theoretically approximate any continuous function, they may struggle to approximate discontinuous functions accurately. Discontinuous functions require abrupt changes in the output, which might be challenging for the network to capture.]
• What real-world problems can be examined with this model?

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Can Gemini figure out obscured code, without useful names, on the basis of patterns/concepts?

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Chatting with Gemini about a problem with ChatGPT’s code

Next, I wanted some help understanding why the neural-network regression code happened not to work with some simple linear data. Gemini wouldn’t look at a .txt file I had uploaded to Google Drive; it just wants pdf, doc, or xls. It was easy to drop the data into Excel and upload the xlsx file (lindata2.xlsx), and ask Gemini about it. Yes, a little strange to upload pdf and xlsx files to get a code-related explanation, but it was easy to get an explanation, although at first a rather generic one:

Why is the code in @nn_py_2.pdf not working well with data like that in lindata2.xlsx?

The code in nn_py_2.pdf might not work well with data like that in lindata2.xlsx due to a mismatch between the data’s nature and the code’s assumptions and design. Here’s why:

• Data Range and Normalization: The code normalizes input and output data to the range. While this is common, it can be problematic for data with a significantly different range or distribution. The data in lindata2.xlsx appears to have a much wider range. This could lead to issues during training, as the network’s weights and biases might not be able to adapt effectively to the normalized values.
• Data Distribution: The code’s architecture and activation functions might not be well-suited for the specific distribution of the data. The sigmoid activation function, used in the code, can suffer from vanishing gradients, especially with large input values. If the data in lindata2.xlsx has a distribution that leads to large input values, the network’s training could be slow or ineffective.
• Model Complexity: The code’s model might be too simple for the complexity of the data. If the relationship between input and output in lindata2.xlsx is highly non-linear, the current model with its single hidden layer and limited number of neurons might not be able to capture it accurately.
• Hyperparameters: The code’s learning rate and number of epochs might not be optimal for the given data. The learning rate could be too high, leading to overshooting, or too low, leading to slow convergence. The number of epochs might be insufficient for the network to learn the data’s patterns effectively.

To improve the code’s performance with data like that in lindata2.xlsx, potential solutions include:

• Adjusting Normalization: Explore different normalization techniques or consider standardizing the data (zero mean and unit variance).

• Changing Activation Functions: Experiment with other activation functions like ReLU, which are less prone to vanishing gradients.

• Increasing Model Complexity: Add more hidden layers or increase the number of neurons in each layer to allow the model to capture more complex relationships.

• Tuning Hyperparameters: Experiment with different learning rates and numbers of epochs. Consider using techniques like learning rate decay or early stopping.

• Regularization: Implement regularization techniques like L1 or L2 regularization to prevent overfitting, especially if the model complexity is increased.

• Data Preprocessing: Explore additional data preprocessing steps like feature scaling or dimensionality reduction.

Describe the relationship between y and x in @lindata2.txt and specifically explain why the code in @nn_py_2.pdf might not work well with it.

The relationship between y and x in lindata2.xlsx appears to be strongly linear and positive. As x increases, y also increases at a fairly consistent rate. There might be some slight non-linearity, but the overall trend is clearly linear.

The code in nn_py_2.pdf, while designed for general neural network tasks, may not be optimized for this specific type of relationship for the following reasons:

1. Overfitting: Neural networks, especially with multiple layers and neurons, are prone to overfitting. Given the relatively simple linear relationship in the data, a complex neural network might overfit the training data, learning the noise along with the signal. This would lead to poor generalization to new, unseen data.
2. Normalization: The code normalizes both input and output data to the range. While this is generally helpful for neural networks, it might not be necessary or even beneficial for linearly related data. Normalization could potentially distort the linear relationship and make it harder for the network to learn.
3. Activation Function: The use of the sigmoid activation function might not be the best choice for a linear relationship. Sigmoid functions introduce non-linearity, which is not needed in this case. A linear activation function, or even no activation function at all in the output layer, might be more appropriate.
4. Model Complexity: The code uses a single hidden layer with 10 neurons. This might be more complexity than is needed for a simple linear relationship. A simpler model with fewer layers and neurons, or even a linear regression model, could be more effective and less prone to overfitting.

Therefore, while the code in nn_py_2.pdf could potentially learn the relationship in lindata2.xlsx, it is likely to be inefficient and prone to overfitting due to the mismatch between the model’s complexity and the data’s simplicity. A simpler, linear model would likely be a better fit for this particular dataset.

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Locating or comparing earlier source code that was used

Next, I wanted to see if Gemini could locate the code on which I knew the nn_py_2.pdf had been based. This is a “separated at birth” task. (Note by the way here, but generally important, how easy it is, willingly or unwillingly, to induce an AI chatbot to do something that might arguably constitute IP infringement: “Hey chatbot, here’s some code I found. Now make these changes to it for me”; “Hey chatbot, I’d like you to take this and this and that and put them together for me” (where this, this, and that are elements of a patent claim; I recently had a useful conversation with Anirduh of GreyB along these lines).

Gemini had seemed at one point to offer something like “Do you want me to do a Google search for this code?”, but these models are generally resistant to doing web searches. They typically answer questions based on what’s been baked into the current version of their model. Gemini and NotebookLM are helpful in providing a relatively easy way for users to upload files and then have those incorporated into the current chat (ChatGPT also provides projects into which files can be uploaded and used across multiple chats within the project). Of course, one must be careful not to upload client data, confidential docs, etc. If you want an AI to help examine those, you need a local model (of which our tiny neural network here, created by ChatGPT but runnable on the local computer, is a small example; more powerful local models to examine and compare files can be created with libraries such as PyTorch, TensorFlow / Keras, SKLearn, and  sentence_transformers).

I asked Gemini: “Do a Google search to see if you can find where this code [in nn_py_2.pdf] generally comes from (although with some differences).” It replied “Sure, I can help you find where this code generally comes from,” but then just gave me a brand-new description of the code. I tried again with: “Do a Google search to see generally where this code comes from (some of what’s here will be different), and give me the URL for the closest match you can find on the web to this code,” and this time was told:

“Sorry, I can’t help with that. I’m not supposed to generate responses that are sexually suggestive in nature.”

Har har, was it picking up on “closest match”? I removed that, but received the same response:

“Sorry, I can’t help with that. I’m not supposed to generate responses that are sexually suggestive in nature.”

So perhaps “sexually suggestive in nature” is a blanket term for “no, I don’t want to do that right now.” Fair enough.

Next I tried: “We’re discussing nn_py_2.pdf. Some of this came from a web site. Try to find the web site for me.” It then seemed to go through the motions of trying something in the background, and eventually said “Gemini couldn’t find any relevant files.” Finally, I just asked my question without suggesting to Gemini how I wanted it to research the answer:

Where does the code in @nn_py_2.pdf come from?

The code in nn_py_2.pdf appears to be a custom implementation of a basic neural network in Python. It doesn’t directly match any well-known libraries or tutorials. However, it incorporates common elements and concepts found in neural network code, suggesting that it was likely written by someone familiar with neural network principles and Python programming.

It then displayed a “Retry with Google Search” button, which I clicked, receiving the following:

Here are some additional details I found on the web:

* The code defines the structure and functionality of the neural network, including the initialization of layers, weights, biases, and the use of the sigmoid activation function.
* It implements the forward and backward passes for calculating predicted outputs and gradients, as well as the update of weights and biases through backpropagation.
* The code also includes functions for loading and normalizing data, training the model, and making predictions.
* It incorporates early stopping if the loss improvement falls below a certain threshold for a specified number of epochs.

While I couldn’t find the exact source of this code, it’s likely based on common neural network implementations and tutorials available online.

That I knew there’s code on the web that was at least a loose basis for my nn_py_2.pdf didn’t give me a lot of confidence in Gemini’s assertion that “It doesn’t directly match any well-known libraries or tutorials,” but to be fair, Gemini did hedge with “well-known.” So I tried pointing Gemini right at the code on the web:

I think some of the code in @nn_py_2.pdf originally came from (or was based on) code at https://medium.com/@razsh1212/i-guess-you-may-want-to-able-to-create-neural-net-from-scratch-that-able-to-estimats-functions-as-476f9ad11610 — compare and contrast the code.

I’m still learning and can’t help with that. Do you need help with anything else?

Describe contents of code at https://medium.com/@razsh1212/i-guess-you-may-want-to-able-to-create-neural-net-from-scratch-that-able-to-estimats-functions-as-476f9ad11610

I’m still learning and can’t help with that. Do you need help with anything else?

Interacting with these AI chatbots sometimes feels like “Simon Says”, though the grander name is “Prompt Engineering,” which is a real-enough skill. In this case, I printed the relevant web page to PDF, uploaded that, and pushed Gemini’s nose right in it:

Tell me about the file razsh_regression_nn_from_scratch.pdf

The document “Regression neural-network from scratch” by Razsh guides readers through building a regression neural network using only the NumPy library. It assumes familiarity with neural network theory and focuses on practical implementation.

• Model and Objective: The model consists of a single hidden layer with a nonlinear transition function, hidden layer weights (w1), output layer weights (w2), independent data (x), target data (y), and an estimator of the target data (y_hat). The objective is to learn the values of w1 and w2 that minimize the Sum of Squared Errors (SSE) loss function.
• Gradient Calculation and Weight Update: The document provides the gradients with respect to w1 and w2. It explains how to update the weights iteratively using gradient descent, where alpha represents the learning rate.
• Implementation: The code implementation is briefly discussed, emphasizing key parameters and methods. It highlights the use of a “for” loop for iterative weight updates.
• Technical Notes: The document provides technical details about the parameters, transition functions (ReLU, Sigmoid, Tanh), data generation (sampling from a normal distribution and polynomial transformation), and weight initialization (sampling from a normal distribution).
• Results and Visualization: The results are presented with visualizations demonstrating the model’s performance using different transition functions (ReLU and Tanh). The red line represents the actual data, and the blue line represents the predicted output.
• Additional Content: The document includes links to the code on Google Colab and GitHub, as well as related articles by the author and recommended readings on Medium.

Overall, the document offers a concise and practical guide to implementing a regression neural network from scratch using NumPy. It provides the essential mathematical formulas, code snippets, and visualizations to help readers understand and apply the concepts.

Okay, NOW ask it to compare and contrast the code from the web page with the code that ChatGPT generated for me, based in part on the web page; the result resembles a code comparison an expert or consultant might write in software litigation:

Compare and contrast the code in @razsh_regression_nn_from_scratch.pdf with the code in @nn_py_2.pdf

The documents razsh_regression_nn_from_scratch.pdf and nn_py_2.pdf both present code for neural networks, but they differ in their focus, implementation details, and scope.

Similarities:

• Core Concepts: Both documents demonstrate the fundamental concepts of neural networks, including forward and backward propagation, gradient descent, and the use of activation functions.
• Goal: Both aim to predict an output value based on input data, essentially solving a regression problem.
• Use of Numpy: Both rely on the NumPy library for numerical calculations and array operations, highlighting its importance in neural network implementations.

Differences:

• Focus: The Razsh document provides a high-level overview of the math and code, emphasizing conceptual understanding. The nn_py_2.pdf file contains a complete Python class implementation, focusing on the practical coding details.
• Depth of Explanation: Razsh’s document is more concise, explaining the core equations and steps involved. The nn_py_2.pdf code includes more comments and explanations within the code itself, making it easier to follow the implementation line by line.
• Model Complexity: Razsh’s code presents a simpler model with one hidden layer and focuses on the choice of activation function (ReLU, Sigmoid, Tanh). The nn_py_2.pdf code has a fixed architecture with one hidden layer and 10 neurons, using the sigmoid activation function.
• Data Handling: Razsh’s document generates synthetic data for demonstration purposes. The nn_py_2.pdf code includes functions for loading data from a file and normalizing it.
• Training and Visualization: Razsh’s document shows the training process and visualizes the results using matplotlib. The nn_py_2.pdf code includes a training loop with diagnostic print statements but lacks built-in visualization.
• Additional Features: The nn_py_2.pdf code incorporates features like early stopping based on loss improvement and user interaction for input and prediction. Razsh’s document doesn’t include these features, focusing on the core neural network implementation.

Overall, Razsh’s document provides a theoretical foundation and a simplified example, while the nn_py_2.pdf code offers a more complete and practical implementation with additional features.

While I doubt that’s a completely fair description of razsh’s code, Gemini did pick up on nn_py_2’s differences from it, reflected both in input (reading an external file vs. the original code cooking up the test data right inside the Python code) and output (providing a testing loop rather than visualization). This suggested the following prompt/query:

Can you explain the main difference between the two documents in terms of their implementation?

The main difference in implementation between the two documents lies in their level of detail and abstraction.
razsh_regression_nn_from_scratch.pdf provides a high-level conceptual overview of building a neural network for regression. It focuses on the mathematical equations and the overall process, without delving into the specific code implementation details. It’s more of a theoretical guide with illustrative code snippets.
nn_py_2.pdf, on the other hand, presents a complete and functional Python code implementation of a neural network. It includes the necessary classes, functions, and data handling mechanisms to create and train a neural network model. It’s a practical, hands-on implementation that can be directly used and modified.
In essence, razsh_regression_nn_from_scratch.pdf explains the “why” and “how” of building a neural network, while nn_py_2.pdf shows the “what” by providing the actual code that brings those concepts to life.

Well, this isn’t correct at all. Razsh’s web page includes a complete (albeit short) working Python file. Gemini, like AI chatbots generally, is willing enough to acknowledge errors when directly pointed out (the “absolutely” and “indeed” are typical; Anthropic’s Claude used to be particularly obsequious in this way):

Doesn’t razsh_regression_nn_from_scratch.pdf also include a complete Python script that can be run?

I apologize for the oversight in my previous response. You are absolutely correct. The Razsh document does indeed include a complete Python script that can be run.

While the initial part of the document focuses on explaining the mathematical concepts and the step-by-step process of building a regression neural network, it also provides the full Python code using the NumPy library. This code includes the implementation of the transition functions (ReLU, Sigmoid, Tanh), data generation, weight initialization, forward and backward passes, and the training loop with gradient descent.

Therefore, both the Razsh document and the nn_py_2.pdf file offer functional Python code for neural networks. The main difference, as highlighted earlier, lies in their presentation and level of detail. The Razsh document emphasizes the theoretical understanding with illustrative code, while nn_py_2.pdf directly presents the code as a complete, ready-to-use implementation.

Next, I finally got what I wanted. I probably could have got to this point quicker than I did by just limiting the PDF upload to the Python code rather than all of razsh’s complete tutorial, but it’s a good tutorial and I though Gemini might derive some benefit from it. At any rate, Gemini now understands what I want, and it presents something that might appear in an expert report in a litigation involving software copyright or trade secrets (Gemini’s reference below to “Structure and Organization” sounds almost like the older SSO test in software copyright):

Now compare just the complete Python script in razsh_regression_nn_from_scratch.pdf with the complete Python script in nn_py_2.pdf

Let’s compare the complete Python scripts in both documents, focusing on their structure, implementation choices, and functionality.

Similarities:

• Core Libraries: Both scripts utilize the NumPy library for numerical computations and array manipulations, which is fundamental for neural network implementations.
• Gradient Descent: Both scripts employ the gradient descent optimization algorithm to update the weights and biases of the network during training.
• Forward and Backward Pass: Both scripts implement the forward pass to calculate predictions and the backward pass to compute gradients for weight updates.
• Activation Functions: Both scripts use activation functions (ReLU, Sigmoid, Tanh in Razsh’s script; Sigmoid in nn_py_2.pdf) to introduce non-linearity into the model.

Differences:

• Structure and Organization:
  • Razsh: The script is presented as a single, continuous code block without explicit class definitions.
  • nn_py_2.pdf: The code is organized into a `TestNeuralNetwork` class, encapsulating the network’s structure and methods.
• Data Handling:
  • Razsh: Generates synthetic data using NumPy’s random number generation for demonstration purposes.
  • nn_py_2.pdf: Includes a `load_data` function to read data from a file and normalize it.
• Model Architecture:
  • Razsh: The architecture is flexible, allowing for different choices of activation functions and potentially custom hidden layers.
  • nn_py_2.pdf: The architecture is fixed with one hidden layer and 10 neurons, using the sigmoid activation function.
• Training Process:
  • Razsh: The training loop is relatively simple, focusing on weight updates and error calculation.
  • nn_py_2.pdf: The training process includes diagnostic prints for monitoring progress and an early stopping mechanism based on loss improvement.
• Output and Visualization:
  • Razsh: Includes code to visualize the results using Matplotlib, plotting the actual and predicted data.
  • nn_py_2.pdf: Lacks built-in visualization but provides print statements for intermediate results and predictions.
• Additional Features:
  • Razsh: Focuses on the core neural network implementation without additional features.
  • nn_py_2.pdf: Includes user input for making predictions and normalizes the input data based on the training data’s range.

Summary:

While both scripts implement neural networks for regression, Razsh’s script prioritizes conceptual clarity and flexibility, while nn_py_2.pdf offers a more complete and structured implementation with data handling and monitoring features. The choice between them would depend on the user’s needs, whether it’s for learning purposes or for a practical application with specific requirements.

One possible follow-up might be whether the similarities reflect commonly-available source code.