Abstract inference

Followup to: Stability of event semantics, Focus of attention, Learning rules of thumb.

Not all events in the mind have natural interpretation as indicators of events in environment, even in the context of specific focus of attention. Some of the detectors form abstract inferential circuits that allow to compute effects more complicated than immediate association between events in environment (supported by rules of thumb acting on them), such as algorithms implementing skills, translating high-level commands into low-level actions executing them in a context-sensitive way, when they can’t be traced through hierarchy of consequences in the environment. These circuits can be built using the same learning algorithms and supported using the same techniques for preserving stable inference. Event detectors (or groups of detectors) act as equivalents of logic gates in a circuit or states and transitions in a finite state machine. Computation proceeds as inference between focuses of attention, directed by context outside the circuit.

Just as with normal representation, abstract inference can be supported on multiple levels of description. Low-level circuit that computes individual actions from high-level command can be described by a simple rule that models successful performance of that action, leaving out the low-level details, which is used in the planning algorithm. Circuit is activated only when action actually needs to be performed. This is an example of reflection, when mind models an aspect of mind, and not of external environment.

There is a deep analogy between this kind of within-mind reflection and the process of building many layers of representation of the environment from low-level sensory activity. Abstract circuits themselves are learned by generalizing training sessions, so for cognitive algorithm they are no different from other fragments of low-level model of environment. Strictly speaking, structure of environment is also only a statistical regularity in the environment that has no concrete existence, so when it’s captured in representation in a mind, this representation is only a way to describe the regularity, which can as well apply to the steps of abstract inference.

Another way of seeing low-level action implemented by abstract inference is by shifting the boundary of mind. Abstract inference is regarded as part of the environment, so reflective model becomes a model of just another aspect of environment. This also allows to view learning as a kind of action applied to environment, where in this case the subject of action is a part of mind. Step by step, this approach allows to reimplement the whole intelligent agent, breaking out of constraints of initial cognitive algorithm, launching the cycle of strong self-improvement, as opposed to learning within initial algorithm.

Event detector as experimental setup

Followup to: Where map meets the territory, Levels of representation, Improving event detectors.

Uncertainty about environment is uncertainty about specific events. Experiment is a procedure for which the outcome is initially unknown, but knowledge about actual outcome (after the experiment is performed) can be used to resolve the uncertainty about environment. Experimental setup is created in such a way that its future state, after the experiment is performed, indicates the property of environment in question. This constitutes a theoretical basis or interpretation for experiment. Interpretation provides both a functional cause of experiment (the reason it’s being performed, chain of events that leads to it being performed), and a way to use its results. Interpretation also provides a criterion of optimality for experimental setup, so that a particular experiment is a good solution with respect to this criterion, configuration optimized for the task.

Event detector can assume one of the multiple possible states, and serves as a tool for resolving uncertainty. The state it assumes indicates which of the alternatives holds in reality. From this perspective, event detector can be regarded as part of experimental setup, that each moment answers a question about environment.

Two complementary interpretations can be used for event detectors. First, whole intelligent agent can be regarded as experimental setup, with this particular event detector being a readout of the experiment (global interpretation). The event detector is considered independently of other elements of mind, and interpretation relates state of the detector directly to state of environment, shows what events in environment are indicated by the readout. Structure of mind is a way of obtaining measurement with required properties. The relation between detector and environment is primary, and algorithm of the mind is a way to implement that relation. Direction of improvement for the detector is defined by the external criterion, by structure of environment.

The second way is to consider only the detector itself as experimental setup (local interpretation). Detector can be configured to answer a question specific to needs of cognitive algorithm, and not so much for a feature of environment. Interpretation of its states can be derived from interpretations of elements of mind it interacts with, which makes derivation of interpretation more tractable than in global case. Starting from input/output, where detectors indicate their own state, interpretation reaches deeper in the environment as detectors get deeper in the mind. Each detector solves a local optimization problem, efficiently indicating the state of environment following from states indicated by related detectors.

Interpretation guides learning, sets the optimization target for representation. When learning is regarded as development of new experiments in anticipation of inference, interpretation can be said to be the process of learning, chain of events that leads to particular changes in representation. Global interpretation regards intelligent agent as a whole, directing representation to indicate the goal, and to figure out the ways of indicating the goal, developing the experiments that find a way to indicate the goal more efficiently. Local interpretation optimizes the representation with regard to current cognitive algorithm, where operations are instrumental, performing small subtasks far from the goal.

Improving event detectors

Followup to: Levels of representation.

Consider a binary event detector that, say, detects the presence of tigers in a picture. This detector defines a certain set of pictures for which it activates. If this is a simple preliminary detector constructed from general description of tigers, it can be significantly improved. But what constitutes an improvement? A change in detector could make it a better tiger-detector, worse tiger-detector, or even turn it into a cloud-detector.

The original detector is a vague question, and the improved detector is an answer. The initial outline allows to identify the clusters of known events fitting the description and change the detector to includes these clusters but not stray peripheral events that come through the boundary, and also to plan for extrapolation of these clusters. Event detector is constructed to be applied in the future, so it needs to be able to recognize not only causal patterns that were never observed before, but also causal patterns that never existed but will appear in the future. In a way, learning is a self-improvement action that agent applies to its future self to process certain events better.

Predicting the subsequent events requires a probabilistic model of environment, and relying on few exemplars that a newly-fledged detector managed to observe is not sufficient. If a new detector is expressed in terms of few other existing detectors (right from the vague question stage), rather than as a classifier applied to the whole input domain, the problem becomes much simpler. Existing detectors already have a good idea about probability distribution of their states, so probability distribution for the new detector roughly derives from them, modulo dependency. The form of the new detector can then be adjusted, guided by this probability distribution and facts about dependencies observed from few exemplars.

Intermediate events allow tractable inference, their purpose is in implementing computational steps that follow the natural structure of modeled environment. An event detector needs to at least not be redundant (not repeat another available detector) and be probable enough to assume more than one state during some reasonable timeframe (if a detector isn’t ever expected to activate, there is no point in keeping it around). When detector supports multiple states, many of these states need to hold sufficient probability mass. After original form of a new event detector distributes the probability mass among its states, based on the knowledge about detectors from which it’s constructed, one of the pressures for the refinement of new detector is in shifting the boundaries of its states to even out (or, at least, keep within limits) the distribution of probability.

The form events tend to assume depends on many aspects of the cognitive algorithm, and only on crude level do they correspond to natural events of the environment. Within the joint detectors of the natural events, factoring into individual detectors may look rather unnatural, like set of floating-point numbers that have a “zero” at twentieth bit in memory. The high-level dynamic of events repeats the structure of environment, but the low-level dynamic of individual detectors may look differently. The low-level dynamic needs to be specifically designed to implement the required high-level dynamic.

The dynamics of mind

Followup to: The flow of reality.

A configuration confined within a narrow event (causal pattern) plays a role of a program in the physical world: its structure (partially) determines what will follow in which contexts, what will be the output for each input, the future for each possible past. As a part of the output, causal pattern determines its successor, the pattern that will implement the next phases of the process initiated by previous pattern.

Let’s consider the dynamics of a causal pattern that implements a mind. First, some imagery to fuel intuition with. Mind is an optimization process, a converging stream in the flow of reality. In its wake, this stream warps the environment by applying little nudges calculated for higher impact. To calculate the appropriate nudges, the stream tunes itself to react to the relevant properties of the environment. The nudges are determined by common causes to become concerted with other causal patterns, so as to direct the flow towards the target. The structure of the stream gets refined over time to become more receptive to current properties of the environment and to turn them into actions to a greater effect. The flow of causality gets captured by the stream, and, transformed by its structure, it is released to shape the future.

Knowing the environment means identification of causal patterns present in it. For the knowledge to be applied to decision-making, it needs to be reflected in the state of mind. In other words, the different possible causal patterns to be found in the environment need to cause different functional states of mind (different causal patterns in the mind). The state of mind acts as a way to disambiguate the possible states of environment. Where the environment is sparse, it is sufficient for the mind to be set so as to assume different states depending on the wide events that contain the possible causal patterns in the environment. As well as representing the long-term rules by which the environment happens to play, mind needs to represent the current state of the environment, or, in other words, the state of the environment relative to the time and place where the causal pattern implementing the mind happens to be. The structure of the environment around the mind is important, because it’s where the actions are initiated. The long-term rules are used to support a representation that robustly integrates different pieces of information that the mind comes across and allows it to run deep queries about the state of the environment that are not immediately accessible to it, or even about the states of environment in the future.

Armed with representation that reflects the structure and state of the environment, the dynamics of mind causes the actions that are predicted to lead to the goal. Goal is not necessarily very fine-tuned, it may simply consist of certain events that are targeted, although that alone could be sufficient to launch the optimization process that leads to the state of environment much more intricate than anything that could’ve been created by chance. An action, or a decision to implement a high-level plan, consists in the state of mind, a belief, in the fact that the objective will be achieved, that itself causes it to be achieved. A reliable decision acts as an indicator of the outcome in the environment, in the same way as representation of other knowledge about the environment, and so it is constructed from the representation. Amusingly, making good decisions consists in the mind dreaming up self-fulfilling prophecies foretelling good fortune.

The flow of reality

Followup to: Rules of thumb.

If we are to study the mind, the structure that drives the environment towards the target by choosing the actions that lead there, we need to look at the structure of environment, and the ways in which its overall dynamics can be predictable.

The environment develops in time, the past determines the future. Physical laws establish a relation that holds between the physical configurations in the past and in the future. Given an event (set of configurations), these laws show which configurations are allowed at different times. Literally applying laws of physics to events is no use: an object that at first looks like a door, but then grows legs and runs away is not a physical impossibility, configuration that does that is included in the event of there being a door-like object. But it’s not actually realized.

Each actual physical configuration descends from the deep causal history. A certain object can only be realized when it is preceded by the process that leads to the creation of that object. The form that a particular event takes in reality is determined by its causal past, and not just by physical restrictions that apply to it.

Events that fit together either arise by coincidence, or as a result of sharing the causal past. Complex dependencies are very unlikely to result from a coincidence, but producing or preserving dependencies also requires a special kind of process that doesn’t degenerate into random noise. Causal patterns not only establish the relationship between surface properties that are associated with them, but also act as elements in the overall flow of reality, determined by causal patterns that precede them, and determining causal pattern that follow.

There are many general kinds of causal patterns that are useful in describing the environment. One-time events result from certain combinations of patterns and dissolve afterwards, casting the ripples of their structure down the stream, in the future. Persistent physical objects are patterns that preserve their structure, generating the patterns in the future that hold the same properties as patterns in the past, forming steady streams in the flow. By far the most interesting kind of pattern is optimization process. Where stability can keep the event from dissolving away, propagating its structure over time, optimization makes a step further and drives the dynamics of environment towards a state that was never encountered before. The structure of the state that optimization process targets is implicit in the structure of the process, and as such, it can be much more intricate than the structures that can appear explicitly by coincidence. Optimization process is a knot on the stream of reality that tightens over time, ever closer to revealing the hidden structure.

Just as optimization process that arises by accident may be quite unlike the target state, other patterns may also pass through implicit stages, where the causal pattern only exists in a form of the process that eventually converges on it. Persistent patterns, such as living organisms, may pass through quite a metamorphosis before restoring the pattern in original form. Events may interact with each other using stable pathways, establishing robust dependencies even when confronted with the full richness of the real world. Patterns that repeat and persist build themselves on top of the stable processes. The actions that an intelligent agent chooses may seem to oppose its goals, or look random and irrelevant, but a reliable plan adds up to the intended outcome.