Paper: Generalized Convergence Analysis of Tsetlin Machines: A Probabilistic Approach to Concept Learning (ICLR-2024)

Reviewer comment (Writing):
The main weakness of the paper is in the wording of some claims. For example, already in the abstract, the authors write: "Despite this, the convergence proof for the TMs, ... remains an open problem. This paper aims to fill this gap by presenting a comprehensive convergence analysis of Tseitin automaton-based Machine learning algorithms". This is an extremely unclear way of formulating your contributions.

Author response:
Thank you for your constructive feedback. As mentioned in our general response, Tsetlin Automatons serve as foundational components for both PCL and the original Tsetlin Machine (TM), but they should not be mistaken for the Tsetlin Machine approach detailed in Section 2. It is important to note that our proof is the first of its kind for approaches utilizing Tsetlin Automatons, such as TM and PCL, but it does not apply to the original Tsetlin Machine model itself.
We have updated the title, the abstract and added a sentence at the end of the introduction to remove any confusion.
We thank the reviewer again for pointing this our.

Reviewer comment (Writing):
The wording in the abstract gives the impression that you are solving the open problem that remained open about the convergence of Tsetlin machines in the general case, whereas the convergence claims that you explicitly mention are with respect to another model (PCL).

Author response:
Thank you for your constructive feedback. As mentioned in our general response, Tsetlin Automatons serve as foundational components for both PCL and the original Tsetlin Machine (TM), but they should not be mistaken for the Tsetlin Machine approach detailed in Section 2. It is important to note that our proof is the first of its kind for approaches utilizing Tsetlin Automatons, such as TM and PCL, but it does not apply to the original Tsetlin Machine model itself.
We have updated the title, the abstract and added a sentence at the end of the introduction to remove any confusion.
We thank the reviewer again for pointing this our.

Reviewer comment (Theory):
Does the proof of convergence for your model PCL imply a proof of convergence for the original TA model in the general case?

Author response:
Thank you for your constructive feedback. As mentioned in our general response, Tsetlin Automatons serve as foundational components for both PCL and the original Tsetlin Machine (TM), but they should not be mistaken for the Tsetlin Machine approach detailed in Section 2. It is important to note that our proof is the first of its kind for approaches utilizing Tsetlin Automatons, such as TM and PCL, but it does not apply to the original Tsetlin Machine model itself.
We have updated the title, the abstract and added a sentence at the end of the introduction to remove any confusion.
We thank the reviewer again for pointing this our.

Reviewer comment (Writing):
If no, please state this very explicitly in the abstract and introduction. Something like: "We note that the original problem about the convergence of TA's remains widely open for the case of number of bits greater than 2."

Author response:
Thank you for your constructive feedback. As mentioned in our general response, Tsetlin Automatons serve as foundational components for both PCL and the original Tsetlin Machine (TM), but they should not be mistaken for the Tsetlin Machine approach detailed in Section 2. It is important to note that our proof is the first of its kind for approaches utilizing Tsetlin Automatons, such as TM and PCL, but it does not apply to the original Tsetlin Machine model itself.
We have updated the title, the abstract and added a sentence at the end of the introduction to remove any confusion.
We thank the reviewer again for pointing this our.

Reviewer comment (Writing):
For non-experts in TMs, the paper is hardly accessible. I am having an hard time understanding the background (see detailed feedback).

Author response:
Thank you for your constructive feedback. Section 2 of our paper provides a description of the original Tsetlin Machine, which should not be confused with the Tsetlin Automaton. It is true that some concepts introduced there are exclusive to the original Tsetlin Machine and do not apply to the basic framework of PCL. The reviewer's concern about the unclear description of sampling has been resolved by removing the relevant content from the paper. The parameters involved in sampling, including the vote sum ($v$), the voting error ($\epsilon$), and the margin ($T$), are not employed in either the PCL method or its proof. These parameters are specifically used in vanilla TM for differentiating between various sub-patterns. To prevent confusion, we have decided to omit certain notations that are irrelevant to PCL and will focus only on defining the key aspects of the original Tsetlin Machine (check our updated Section 2). We thank the reviewer for pointing this out.

For information on the practical implications, results, and the generalization of the PCL proof, please refer to the answer provided in the general response section.

Reviewer comment (Writing):
The background assumes that the reader knows what a Tsetlin Automata is.

Author response:
Thank you for your constructive feedback. Section 2 of our paper provides a description of the original Tsetlin Machine, which should not be confused with the Tsetlin Automaton. It is true that some concepts introduced there are exclusive to the original Tsetlin Machine and do not apply to the basic framework of PCL. The reviewer's concern about the unclear description of sampling has been resolved by removing the relevant content from the paper. The parameters involved in sampling, including the vote sum ($v$), the voting error ($\epsilon$), and the margin ($T$), are not employed in either the PCL method or its proof. These parameters are specifically used in vanilla TM for differentiating between various sub-patterns. To prevent confusion, we have decided to omit certain notations that are irrelevant to PCL and will focus only on defining the key aspects of the original Tsetlin Machine (check our updated Section 2). We thank the reviewer for pointing this out.

For information on the practical implications, results, and the generalization of the PCL proof, please refer to the answer provided in the general response section.

Reviewer comment (Writing):
The sentence "Clause updating probability depends on vote sum, v, and the voting error, ε, uses a margin T to produce an ensemble effect" is the first time a sentence implies that feedback might be disregarded. Vote sum, vote error and the margin are mentioned for the first and only time.

Author response:
Thank you for your constructive feedback. Section 2 of our paper provides a description of the original Tsetlin Machine, which should not be confused with the Tsetlin Automaton. It is true that some concepts introduced there are exclusive to the original Tsetlin Machine and do not apply to the basic framework of PCL. The reviewer's concern about the unclear description of sampling has been resolved by removing the relevant content from the paper. The parameters involved in sampling, including the vote sum ($v$), the voting error ($\epsilon$), and the margin ($T$), are not employed in either the PCL method or its proof. These parameters are specifically used in vanilla TM for differentiating between various sub-patterns. To prevent confusion, we have decided to omit certain notations that are irrelevant to PCL and will focus only on defining the key aspects of the original Tsetlin Machine (check our updated Section 2). We thank the reviewer for pointing this out.

For information on the practical implications, results, and the generalization of the PCL proof, please refer to the answer provided in the general response section.

Reviewer comment (Writing):
The sentence "Upon sampling from P(Feedback), TA state adjustments are computed" lacks clarity on how the sampling works. Input pairs (x,y) are sampled according to P(Feedback), which in turn depends on the prediction of the current TM state. This should be clarified.

Author response:
Thank you for your constructive feedback. Section 2 of our paper provides a description of the original Tsetlin Machine, which should not be confused with the Tsetlin Automaton. It is true that some concepts introduced there are exclusive to the original Tsetlin Machine and do not apply to the basic framework of PCL. The reviewer's concern about the unclear description of sampling has been resolved by removing the relevant content from the paper. The parameters involved in sampling, including the vote sum ($v$), the voting error ($\epsilon$), and the margin ($T$), are not employed in either the PCL method or its proof. These parameters are specifically used in vanilla TM for differentiating between various sub-patterns. To prevent confusion, we have decided to omit certain notations that are irrelevant to PCL and will focus only on defining the key aspects of the original Tsetlin Machine (check our updated Section 2). We thank the reviewer for pointing this out.

For information on the practical implications, results, and the generalization of the PCL proof, please refer to the answer provided in the general response section.

Reviewer comment (Theory):
Is PCL a strict generalization of TM? Do the theoretical guarantees hold for TMs in general?

Author response:
We express our gratitude to the reviewer for the insightful comment. 

Emphasizing the significance of the convergence proof, we underscore its role in offering **valuable guidelines and essential elements** for proving convergence in approaches using Tsetlin Automatons as foundational components.

Our contribution ensures that future analyses of convergence in Tsetlin Automaton-based machine learning approaches need not to start from scratch, instead, researchers can leverage the insights provided in our proof.

Furthermore, our proof holds potential utility in the convergence analysis of the original Tsetlin Machine model. 
A best practice in tackling a complex problem (the convergence analysis of the Tsetlin Machine in this case) is to initiate the inquiry with a less complex, but similar, problem (the convergence proof of PCL). 
We are optimistic that **our proof will serve as a valuable resource for the Tsetlin machine community**, aiding in the examination of convergence across various variants.

We extend our gratitude once again to the reviewer for his thoughtful consideration and time. We kindly request a reconsideration of the evaluation, confident that our work will contribute to the advancement of knowledge in this domain.

Reviewer comment (Novelty):
Sec 2: this is a nice short intro to the Tsetln machines. I would have liked more state-of-the-art, and namely examples justifying the need for convergence (some algs such as loopy message passing often work well without providing guarantees they converge).

Author response:
We concur that proving the convergence of a machine learning model is essential, as it affirms the model's reliability and stability, ensuring consistent and dependable solutions. This proof not only aids in the development and evaluation of algorithms but also serves as a theoretical benchmark for assessing performance and comprehending the limitations of the model. It is true that some algorithms may perform effectively in practical applications even without a formal proof of convergence. Nonetheless, providing such proof undeniably enhances the robustness of the approach. To support this, we have included relevant references in the second paragraph of our introduction.

Reviewer comment (Experiments):
sec5: why not compare with std Tsetln?

Author response:
For additional experiments, please  
refer to the experimental results in our updated paper and the general response section.