Learning from chatting with papers

Given a paper, a topic (this needs expansion), there must be a finite set of conversation space (prompts and turns) that will maximize the learning efficiency of human such that following one of them will make a human understand to a certain extend as much and as well as he can.

I can try to frame this. “learning efficiency” here is rather more similar to a function of an entity (maybe benchmark) with respect to time. a naive way to evaluate human learning is that given a new question (needs separate construction, which is inherently hard), what is the likelihood that he outputs a good enough answer.

In short, optimizing the “conversation space” to maximize human learning efficiency. This is analogous to a constrained optimization problem in mathematics, where the objective is to find the best solution within a given set of constraints.

The Constraints

1. Content Scope: The range of topics and depth of information covered. For instance, if the conversation is about a specific scientific paper, the scope is constrained to the content and implications of that paper.
2. Time: The amount of time available for the conversation, which limits the number of prompts and turns possible.
3. Cognitive Load: The human brain’s capacity to process and retain information in a single session. This limits the complexity and volume of information that can be effectively communicated. This can probably also be approximated or found in the optimization process? some sort of $Z$.
4. Prior Knowledge: The existing understanding and skills of the learner. The conversation must be tailored to this level to be effective. This is also where the first consideration of human centric learning starts: instead of “preference learning,” neither the model nor us can tractably reduce and summarize our learning traits, it can be left to a sufficiently high-dimensional model to approximate.
5. Learning Objectives: The specific goals of the learning session, such as understanding key concepts, developing certain skills, or applying knowledge in a particular way. Another objective in the process?
6. Language and Comprehension: The language used and the clarity of communication, ensuring that it matches the learner’s proficiency and comprehension level. This is purely on the model parameter side.
7. Feedback and Adaptation: The necessity to include feedback mechanisms for adapting the conversation based on the learner’s responses and progress. From an engineering perspective, small or batch-size-one can be most of the case.

Optimization

We also have several things to optimize, it starts to feel like a system of models.

Learning Efficiency

Find objective function(s) to quantify and optimize learning efficiency. This efficiency could be measured by the improvement in a human’s ability to answer relevant questions correctly over time.

Formally, if $L(t)$ is the learning efficiency at time $t$, our goal is to maximize ${\int }_0^{T}L(t)dt$, where $T$ is the total time spent learning.

I claim that given a scientific paper or a set of them, there is no global maxima but the effects will not be pseudo-uniform either: there will be a finite number of conversations sufficiently effective.

2. Constraints: The “conversation space” is finite and convex. This implies that the set of all possible conversations (prompts and responses) is bounded and every linear combination of possible conversations is also a possible conversation. This constraint shapes the feasible region for our optimization.

3. Learning as a Function of Conversations: We can model learning efficiency $L$ as a function of the conversation vector $C$, where each component of $C$ represents different aspects of the conversation (e.g., complexity, relevance, interactivity). The function $L(C)$ is what we aim to maximize.

4. Benchmarking “Good Enough”: Define a benchmark for what constitutes a “good enough” answer. This can be based on accuracy, completeness, depth of understanding, etc. We can use this benchmark to evaluate the output of the learning process.

5. Iterative Learning and Feedback Loop: Incorporate a feedback mechanism to adjust the conversation dynamically. This can be modeled by a control system where the output (learner’s performance) is constantly monitored and used to adjust the conversation vector $C$ to improve $L$.

6. Question Construction and Evaluation: Constructing and evaluating new questions is crucial. This could involve techniques from educational psychology and adaptive learning systems. The challenge is to develop questions that accurately assess understanding and not just rote memorization.

7. Mathematical Modeling and Algorithms: Use mathematical models (e.g., Markov Decision Processes, Bayesian models) to predict the effect of different conversations on learning efficiency. Machine learning algorithms can then be employed to find the optimal conversation paths within the defined constraints.

8. Human Factors: Consider cognitive load, attention span, prior knowledge, and individual differences. These factors can significantly affect learning efficiency and should be integrated into the model.

9. Real-time Adaptation and Personalization: The system should adapt in real-time to the learner’s responses, customizing the conversation path to suit individual learning styles and paces.

10. Empirical Validation: Finally, empirical testing with real learners is essential to validate and refine the model. This involves comparing the model’s predictions with actual learning outcomes and iterating to improve accuracy.

Maximizing Learning Efficiency

${\int }_0^{T}L(t)dt$ How can I claim that maximizing ${\int }_0^{T}L(t)dt$ as our objective is measuring the learning outcome? It measures human performance after we subject human to a conversation (question) sequence which elicits their critical thinking, curiosity and learning functions. my thought is on the rate of learning, think about how, if we only maximize the integral of this function, we may overlook how by doing this, there may exist some questions or periods of time within this chain that actually make the human learn slower than optimal. going off from this, it is also likely that some parts in the question chain is more likely to jeopardize the learning process, similar to how a training run would diverge. Of course, some time in the future, this can be proven to be impossible. also, this eventually would play out nicely because we maximize the integral, but i wonder whether there are some previous techniques that address similar issues.

Maximizing ${\int }_0^{T}L(t)dt$ indeed provides a measure of cumulative learning over a period, but it might not capture the nuances of the learning process, such as periods of slower learning or potential setbacks.

Some thoughts on this concern:

1. Rate of Learning and Its Impact: The rate of learning, denoted as rac{dL}{dt}, is crucial. Ideally, we want to not only maximize the integral of learning over time but also ensure that the rate of learning is consistently optimized. This requires monitoring and adapting to the learner’s progress in real-time.

2. Local vs. Global Optimization: Maximizing ${\int }_0^{T}L(t)dt$ might lead to a globally optimal solution but could overlook local dips in learning efficiency. It’s akin to the difference between finding the highest peak (global maximum) and avoiding valleys (local minima) in a landscape.

3. Feedback and Control Theory: Applying concepts from control theory, we can model the learning process as a dynamic system where feedback is used to adjust the learning trajectory. This involves creating a feedback loop where the system (learner) is continuously monitored and the input (conversation/questions) is adjusted to maintain an optimal learning rate. This may then involve some sort of bayesian techniques, like choosing the proposal function and sampling methods.