Perspectives on machine-learned intelligence

These are just some of my thoughts on machined-learned intelligence, formed by reading a bunch of papers and watching a few talks here and there.

Intelligence, tasks, representations and learning

Taking inspiration from Wikipedia, intelligence or intelligent behavior may be decomposed into these capabilities

1. Perceive or infer information
2. Retain that information into knowledge for easy reuse (store and factorize experience)
3. Apply this knowledge towards adaptive and preferred behaviors within an environment or context
4. Ability to measure success and learn from decisions by exploring opportunities to improve the steps above

In Legg2007, a quantitative definition of intelligence is proposed, where the objective (referred to as Universal Intelligence) is essentially maximized when for each task, the agent tries to minimize the computational complexity of learning and inference of agent policies for each task. In essence, to solve each task efficiently.

A task is making a decision (or sequence of decisions) based on the data. Decisions could be classifications, predictions and actions. A representation is a function of the data which is useful for a task. Usually the input data dimension is very large (pixel space, sampled waveforms, etc.) and the target space (classifications) are in a much lower dimensional space. Learning is the process of using data (or experience) to figure out good representations to solve the task.

What are good representations?

Let $x$ denote the input data, $f(x)$ be a function that maps the input to a representation $z = f(x)$ which is designed so that the task, denoted by decision (random variable) $y$ can be solved effectively. The mapping $f(x)$ is learned via data and tasks. We would like that the features or representations learned help efficient future task learning and ideally have the following attributes

1. Invariant to nuisances
2. Disentangled, independent, composable, reusable, interpretable
3. Compressed, minimal, sparse
4. Hierarchical, multilevel
5. Task agnostic
6. Dynamically added via life-long learning

We would like the representation to be invariant to nuisances, such as translation, rotation, change of scale or lighting, noise, that are not relevant to predicting $y$

Disentangled or independent representations allow composition of factors of variation to create new unseen concepts (imagination) and allow abstract reasoning. These factors correspond to finding invariants and independently transformable aspects of the world. Tasks are defined in terms of these invariant entities. New concepts can be formed from logical combination of old concepts. For example, a blue orange. Disentangled factors of variation can be used for one-shot or zero-shot learning. New factors can be discovered and added in a life-long learning setting.

In order to reason about concepts or imagine scenarios, it is essential to have a representation which is also sparse. We don’t want to reason about things that are irrelevant to the task at hand. We need to be really good at discerning irrelevant information and throwing it away. Sometimes the previously trained representations may need to be adapted to provide this property.

As we get more abstract and form higher-level concepts, it is necessary to throw away information and only model things about the objects in the input that are crucial for the task. This not only makes it more robust, but also allows reasoning at this higher level of abstraction. It is likely easier to model the world (physics) at this level as well. We would like the representation $f(x)$ to have enough information to solve the task and simultaneously minimize information about the data that is not relevant for the task $y$. Stated mathematically using the concept of mutual information and referred to as the Information Bottleneck

We should note that one task’s nuisance is probably another task’s discriminative data. I’m thinking of a speech recognizer and an environment (noise) sound classifier, for example. There is some interesting work Jacobsen2018 about invertible neural networks where they show that compression (throwing away information, except at the last classifier layer) is not required for achieving high classification performance. Based on this we are speculating representations to have some sort of hierarchy:

1. Invertible task-agnostic features: no information loss
2. Intermediate task group features: information loss via gating, masking or attention mechanisms
3. Task-level features: high-level disentangled abstract latent space

As an example of hierarchical representations, we can have at highest level (deepest layer) the concept of living organism, then at the next lower level, the concept of bird and then the level below that the concept of crow and bluebird and then beaks, wings, legs and so forth. We could ask, what are similarities between different examples of a class and these could be color, size, shape differences. As we go deeper into the hierarchy we lose details about the input that aren’t relevant. So if we are interested in cat detection, all information about the background could be thrown away by the time we reach the cat concept.

Learning and prediction

Deep learning has been successful in various tasks. The model parameters that are the weights of the layers of the neural network are learned via backpropagation using stochastic gradient descent (SGD). If we have good hyperparameters (initial weights and learning rates) and sufficient training data, SGD can often provide good representations that generalize. Transfer learning via fine tuning the final layer and/or representations is a practical method of taking a network trained on one task (for its representations) and then applying it on another where the data is not as plentiful. Meta learning addresses the problem of how to efficiently learn a new task, given experience learning various tasks. In life-long learning we need to detect shifts in data distribution. We need to prevent catastrophic forgetting. We need to allocate spare representation capacity to learn new concepts and share or consolidate latents where appropriate.

The concept of compute adaptive prediction, in order to effectively focus on the right information for the task, there may be parts in the prediction or representation that are not fixed steps and may be iterative for complicated inputs. This could be a sequential process driven by RL-based policy. Humans take more time when trying to find an object that is camouflaged or speech in low SNR, for example. In an environment with a time aspect, we want to predict multiple outputs for a single input and learn when the actual observation is divergent from our predicted future. Having a concept of prediction with constraints allows to produce outputs that satisfies certain task-dependent constraints, such as a linguistically correct sentence. We can use energy/barrier functions for prediction with constraints

As an example of learning disentangled factors from data, we have independent generative factors like position, size, shape, rotation and color. Then the generated image is an example of entangled data. In Higgins2017 a model called BetaVAE was proposed to learn the disentangled representations. The BetaVAE model is able to learn disentangled representations by modifying the loss function with additional terms that encourage independence of the latent representations. A key concept in learning good representations is constructing objective and loss functions. These representations allow to traverse across the latent dimensions.

Curriculum learning is a well-designed sequence of tasks that enables reuse and good representation learning. Open question is how to design these automatically.

Final thoughts

For now, we will superficially list a bunch of concepts or buzzwords that seem to be relevant to the design of intelligent systems, this is the TL;DR version if at all

• Gradient-based learning are learning algorithms that use the gradient of the objective function or loss function with respect to the differentiable model parameters to nudge the model towards a better performance on the task
• Continual or life-long learning: is the idea of the model being capable of learning to do new tasks and avoid the problem of catastrophic forgetting, where the model forgets about tasks it learnt in the past. Controlled forgetting is when the model purposefully forgets what has been learned in order to learn something new in a new situation faster, perhaps a more compact factorization of knowledge.
• Self-supervised learning: learning representations without the labels is termed unsupervised learning. Recent work in NLP and Vision have shown that good low level features can be learned from even a single representative example using augmentation and appropriate self-supervised tasks
• Specialized modeling: For particular instances in a set of tasks, it may be beneficial to route it to a more specialized model to provide higher capacity. It helps to understand the environment in which we are in to figure out best modeling options for the downstream task. Alternately, this could be a special preprocessing step on the instance to adapt its domain
• Memorization: special case handing for useful concepts and exceptions (OOD) to enable faster adaptation when domains switch. Clustering and exemplars.
• Multilevel features: global vs. local perspective, using attention to dynamically focus on different aspects sequentially
• Metalearning: figuring out whether transfer learning (final stage linear classifier), rapid learning, good initializations, adding spare capacity (new representations), decide what representations to share, those to modify in a proper way are needed to learn new tasks efficiently
• Disentangled representations: to enable wider generalizations beyond interpolation to nearest example, there needs to be high level semantic features that are sparse, independent, disentangled, where notions of similarities, new combinations are easily performed
• Generative modeling: models learned in the abstract disentangled latent space will allow simulation of futures and allow high-level action planning. These could be trained via self-supervised predictive coding.