What is Knowledge?
from Epistemology, AI, and Neuroscience perspectives
Introduction
Knowledge is a concept that has been explored and defined in various fields of study, including philosophy, deep learning, and neuroscience. In this blog post, we will delve into the definition of knowledge in each of these three areas.
Knowledge in Epistemology
Justified True Belief
In philosophy, knowledge is generally defined as justified true belief. This means that in order for something to be considered knowledge, it must be believed to be true, it must actually be true, and there must be a good reason or justification for believing that it is true. Philosophers have debated and refined this definition for centuries, and there are many different perspectives on what constitutes justification and truth.
Gettier Problem?
A majority of discussion in this respect is shaped around a tricky problem called the Gettier problem. Researchers from epistemology argue that sometimes you can never claim that the justification process can really eliminate the situation where your belief is just a lucky guess. For example, imagine that you believe your friend Bob is in town because you saw someone who looks like Bob walking down the street. In reality, Bob is in town, but the person you saw was actually his doppelganger. In this case, you believe something that is true, but your justification for that belief is flawed.
One possible solution to the Gettier problem is to add a fourth condition to the definition of knowledge. This fourth condition, called the “no-false-grounds” condition, states that in order for a belief to count as knowledge, there must be no false grounds for the belief. This means that if there is any possibility that your belief could be false, even if it happens to be true in this particular instance, it cannot be considered knowledge.
JTB+X
In addition to the proposed solution of adding a fourth condition to the definition of knowledge, called the “no-false-grounds” condition, there is also a class of remedies known as JTB+X. This approach involves adding a stricter definition or constraint to the justification condition in order to rule out the possibility of taking merely lucky guesses on the Gettier problem. Some examples of such constraints include the requirement that the justification must be based on an inference that is itself known to be true, or the requirement that the justification must be based on a reliable method or source of information. While these remedies have been proposed and debated by philosophers, there is no consensus on which approach is most effective in resolving the Gettier problem.
In her 1994 paper “The Inescapability of Gettier Problems,” Linda Zagzebski argued that it is always possible to construct a Gettier case that tricks one’s justification process into the “lucky guess” category. She suggested a two-step process for constructing such a case:
- Start with an example of a case where a subject has a justified false belief that also meets condition X;
- Modify the case so that the belief is true merely by luck. Zagzebski’s argument highlights the difficulty of defining knowledge in a way that is immune to Gettier-style counterexamples.
Virtue Theoretic Method
The virtue-theoretic approach in epistemology is a way of understanding knowledge and justification in terms of intellectual virtues, which are intellectual qualities or dispositions that contribute to acquiring knowledge and forming justified beliefs.
According to this approach, knowledge and justification are not simply a matter of having true beliefs or reliable methods of belief formation, but also depend on the exercise of intellectual virtues such as honesty, open-mindedness, intellectual humility, attentiveness, thoroughness, and intellectual courage.
Proponents of this approach argue that an individual’s epistemic status is not determined solely by the content of their beliefs, but also by the way they acquired those beliefs and the character traits they exhibit in the process.
Virtue epistemology emphasizes the importance of intellectual character and moral virtues for knowledge and justification, and encourages individuals to cultivate these virtues in order to become better knowers and to form beliefs that are more likely to be true and justified.
AAA: knowledge as apt belief
The “Accuracy, Adroitness, Aptness” (AAA) approach, proposed by Ernest Sosa, is a virtue-theoretic method for analyzing knowledge. According to this approach, knowledge can be understood in terms of three conditions: accuracy, adroitness, and aptness.
The accuracy condition is similar to the truth condition in JTB analysis, in that it requires that a belief be true in order to count as knowledge. However, the AAA approach emphasizes the importance of the process by which the belief was formed, rather than simply the content of the belief.
The adroitness condition is concerned with the skill or competence of the knower. It requires that the belief be formed in a way that is indicative of the knower’s skill or competence. This condition is intended to address the problem of lucky guesses in JTB analysis.
The aptness condition is concerned with the relevance of the belief to the situation at hand. It requires that the belief be appropriately related to the situation in which it is held. This condition is intended to address the problem of irrelevant beliefs in JTB analysis.
Overall, the AAA approach provides a more nuanced and comprehensive account of knowledge than JTB analysis, by taking into account not only the truth of a belief, but also the process by which it was formed, the skill of the knower, and the relevance of the belief to the situation at hand.
Knowledge in Deep Learning
Knowledge as Embeddings
In the field of deep learning, knowledge is a bit more narrowly defined. Normally it refers specifically to the information that is learned and stored by artificial intelligence systems as they are trained on large sets of data. This knowledge can be used to make predictions, recognize patterns, and perform a variety of other tasks.
To intepret in the language of epistemology, knowledge in deep learning refers to the information used in the justification process that generates beliefs. However, these beliefs don’t necessarily have to be true, as the training data used in deep learning only represents a portion of the real world data. We want the accuracy to be high on the training set, but the justification process, or the deep learning model, is supposed to work on out-of-distribution data, which is the testing dataset. If a model is trained until it reaches 100% accuracy on the training dataset, an industry practitioner would hold a skeptical view of the model. This is because it’s almost certain that the model is overfitting on a limited view of the real world.
Regularization?
Non-deep learning experts might wonder how it is possible to train models with imperfect data and still expect them to perform well on out-of-distribution, real-world data. In practice, deep learning researchers have come up with a set of assumptions that work well. The most famous assumption is based on Occam’s razor: a less complex model is better than a more complex one. This idea leads to a collection of regularization techniques in deep learning, including dropout, l_n regularization, and sparsity as regularization.
Respectively,
- In dropout, nodes are randomly turned off during training, which helps the model learn to rely on multiple features rather than a single one. This is usually done during the learning process, and during inference time, the dropout is turned off. However, in some applications such as speech synthesis, researchers have found that using dropout during inference time can significantly improve the resulting audio quality.
- L_n regularization adds a penalty term to the loss function that encourages the weights to be small, which can help prevent overfitting.
- Sparsity as regularization is a technique that encourages the model to learn sparse representations, which are more interpretable and generalize better to new data. These regularization techniques help mitigate the problem of overfitting and improve the generalization performance of deep learning models.
Common Inductive Bias in DL
Other than the simple assumption that less is more implied by Occam’s razor, another line of research is to impose different inductive biases on the models. Some of the most famous inductive biases used in deep learning are as follows:
- Spatial bias: This bias is commonly used in convolutional neural networks (CNNs), which are frequently employed in image and video recognition tasks. Spatial bias refers to the assumption that the inputs are images, and it imposes a bias on the model to learn features that are translation-invariant. This bias helps the model to learn to recognize objects regardless of their position in the image.
- Spectral bias: This bias is based on the idea that in some cases, the lower frequencies in the data contain the most important information. Spectral bias is used to prioritize the learning of lower frequencies first in the training process. This approach can help the model to learn simple patterns that generalize well across data samples.
- Structured perception and relational reasoning bias: This bias introduces structured perception and relational reasoning into deep reinforcement learning architectures. By leveraging this bias, reinforcement learning agents can learn interpretable representations and exceed baseline agents in terms of sample complexity, ability to generalize, and overall performance. This bias can be especially useful in meeting some of the most challenging test environments in modern artificial intelligence.
- Invariance and equivariance bias: This bias can be used to encode the structure of the relational data. Invariance and equivariance bias notify the behavior of a model under various transformations, which can help the model to generalize better to new data. Equivariant models have been successfully used for various deep learning tasks on data with various structures, such as translation-equivariant images, geometric settings, and discrete objects such as sets and graphs.
Note that this blog post does not aim to provide a detailed guide on how to build better deep learning models. Instead, it highlights that deep learning models are not just large and complex, and that researchers impose a set of meta-properties on the learning, or searching in a complex space of high dimensions, process to reduce complexity. As Dr. Richard Sutton said, “We want AI agents that can discover like we can, not which contain what we have discovered.”
While there have been significant advancements in AI, it is important to note that these advancements are still within a scope of a JTB analysis. In this analysis, computational models parse sensory data and generate predictions as beliefs. Although we may incorporate human knowledge to design inductive biases that can help us build a more reliable justification process, we still evaluate models based solely on testing data, which does not account for the possibility of lucky guesses.
Knowledge in NeuroScience
In the realm of neuroscience, knowledge is intimately tied to the workings of the brain. It is believed to arise from the intricate interactions between neurons and the diverse systems of the brain. While much research has been devoted to uncovering the neural mechanisms underlying knowledge, many mysteries remain.
How is knowledge encoded, stored, and retrieved in the brain?
How does the brain represent abstract concepts and complex relationships between them?
These are just a few of the questions that researchers in the field of neuroscience are striving to answer. Unlike philosophical discussions, which often delve into metaphysical questions, neuroscience focuses purely on the physical and biological mechanisms that give rise to cognition and intelligence. Ultimately, a deeper understanding of the neural underpinnings of knowledge could pave the way for groundbreaking advances in fields such as artificial intelligence and cognitive enhancement.
All things come together from an AI perspective
As we have seen, knowledge is a complex and multifaceted concept that has been studied and defined in various fields of study. But what can the AI field learn from neuroscience and epistemology?
Let’s conclude this blog post with a set of open questions from both perspectives:
From the neuroscience side, ongoing discussions about the efficiency of human brains compared to the energy consumption of deep learning models with the same level of performance raise the question of whether we can make deep learning models as efficient in energy consumption as our brains during inference. For the learning process, can we take as little data as a human brain would see for a deep learning model to achieve the same level of performance?
From the epistemology side, we can ask whether we can evaluate deep learning models based on more reasonable metrics, or whether we can take insights from philosophers to think about what kind of datasets would help models come closer to true knowledge. A far-fetched proposal is: can we automatically generate Gettier-like cases that drive the design of meta-properties as biases used in deep learning models? These are questions that may lead to new approaches and innovations in the field of AI.
