Value Formation: An Overarching Model

Thane Ruthenis15 Nov 2022 17:16 UTC

LW: 34 AF: 17

0. Introduction

When we look inwards, upon the godshatter, how do we make sense of it? How do we sort out all the disparate urges, emotions, and preferences, and compress them into legible principles and philosophies? What mechanisms ensure our robustness to ontological crises? How do powerful agents found by a greedy selection process arrive at their morals? What is the algorithm for value reflection?

This post seeks to answer these questions, or at least provide a decent high-level starting point. It describes a simple toy model that embeds an agent in a causal graph, and follows its moral development from a bundle of heuristics to a superintelligent mesa-optimizer.

The main goal of this write-up is to serve as a gears-level model — to provide us with a detailed step-by-step understanding of why and how agents converge towards the values they do. This should hopefully allow us to spot novel pressure points — opportunities for interventions that would allow us to acquire a great deal of control over the final outcome of this process. From another angle, it should equip us with the tools to understand how different changes to the training process or model architecture would impact value reflection, and therefore, what kinds of architectures are more or less desirable.

Let’s get to it.

1. The Setup

As the starting point, I’ll be using a model broadly similar to the one from my earlier post.

Let’s assume that we have some environment $E$ represented as a causal graph. Some nodes in it represent the agent, the agent’s observations, and actions.

Every turn $t$ (which might be a new training episode or the next time-step in a RL setup), the agent (blue node) reads off information from the (green) observation nodes $O$ , sets the values for the (red) action nodes $A$ , all nodes’ values update in response to that change, then the agent receives reward based on the (purple) reward nodes $R$ . The reward is computed as some function $U : R^{t} \to R$ , where $R^{t}$ represents the reward nodes’ current values.

The agent is being optimized by some optimization/selection process — the SGD, evolution, human brain reward circuitry, whatever. What matters is that this process is non-intelligent and greedy: it only ever makes marginal improvements to the agent’s architecture, with an eye for making it perform marginally better the next turn.

As per the previous post, the agent will have naturally learned an advanced world-model, which we’ll also consider to be a causal graph, $M$ . Every turn, after the agent makes the observations, it’ll use that world-model to infer as much other information about the environment as it can (i. e., the current values of the non-observed nodes). Let’s also assume that the world-model is multi-level, making heavy use of natural abstractions: both “an atom” and “a spider” are nodes in it, even if the actual environment contains only atoms.

Let’s define $M_{s}$ and $A_{s}$ as some subsets of the world-model and the action nodes respectively. The agent will have developed a number of shallow heuristics, which are defined as follows:

h : M_{s} \to A_{s}

That is: a heuristic $h$ is some function that looks at some inferred part of the world, and recommends taking certain actions depending on what it sees. Informally, we may assume that heuristics are interpretable — that is, they’re defined over some specific world-model node or a coherent set of such nodes, perhaps representing a natural abstraction.

We’ll assume that at the starting point we’re considering, the entire suite of the heuristics $H$ is subpar but much better than random behavior according to the outer reward function. E. g., they always allow the agent to secure at least 50% of the possible reward

We’ll assume that the environment is too complex for such static heuristics to suffice. As the consequence, whatever process is shaping the agent, it has just now built General-Purpose Search into it:

GPS : M^{t} \times M_{s} \times M_{s}^{G} \to A_{s}^{G} | (A_{s}^{t} = A_{s}^{G}) \Rightarrow (| M_{s}^{t} - M_{s}^{G} | = min A^{t} (| M_{s}^{t} - M_{s}^{G} |))

Where $M^{t}$ is the current state of the world-model, and $M_{s}^{G}$ , $A_{s}^{G}$ are the “target values” for the nodes in $M_{s}$ and $A_{s}$ respectively.

That is: $GPS$ is some function that takes in a world-model and some “problem specification” — some set of nodes in the world-model and their desired values — and output the actions that, if taken in that world-model, would bring the values of these nodes as close to the desired values as possible given the actions available to the agent.

Note that it’s defined over the world-model, not over the real environment $E$ , and so its ability to optimize in the actual $E$ decreases the less accurate the world-model is.

Let’s explore the following question:

2. How Will the GPS (Not) Be Used?

Pointing the GPS at the outer objective seems like the obvious solution. Let $R^{max}$ be the values of $R$ that maximize $U$ . Then we can just wire the agent to pass $M^{t} \times R \times R^{max}$ to the GPS at the start of every training episode, and watch it achieve the maximum reward it can given the flaws in its world-model. Turn it into a proper wrapper-mind.

Would that work?

Well, this idea assumes that the world-model already has the nodes representing the reward nodes. It might not be the case, the way stone-age humans didn’t know what “genes” are for the evolution to point at them. If so, then pointing the GPS at the reward proxies is the best we can do.

But okay, let’s assume the world-model is advanced enough to represent the reward nodes. Would that work then?

Sure — but only under certain, fairly unnatural conditions.^[1]

In my previous post, I’ve noted that the very process of being subjected to a selection pressure necessarily builds certain statistical correlations into the agent.

One type of such correlations is $O \to E$ , mappings from the observations to the values of non-observed environment nodes. They’re built into the agent explicitly, as $O \to M$ correlations. Taken in sum, they’re how the agent computes the world-model.
Heuristics, however, can also be viewed this way: as statistical correlations of the type $(E \to A) \to U$ . Essentially, they’re statements of the following form: “if you take such action in such situation, this will correlate with higher reward”.

The difference between the two types, of course, is that the second type is non-explicit. Internally, the agent doesn’t act as the heuristics specify because it knows that this will increase the reward — it just has a mindless tendency to take such actions. Only the $M \to A$ mappings are internally represented — and not even as part of the world-model, they’re just procedural!

But these tendencies were put there by the selection process because the $(E \to A) \to U$ correlations are valid. In a way, they’re as much part of the structure of the $E$ environment as the explicitly represented $O \to E$ correlations. They’re “skills”, perhaps: the knowledge of how an agent like this agent needs to act to perform well at the task it’s selected for.

The problem is, if we directly hard-code the GPS to be aligned with the outer objective, we’d be cutting all the pre-established heuristics out of the loop. And since the knowledge they represent is either procedural or implicit, not part of the explicit world-model, that would effectively decrease the amount of statistical correlations the agent has at its disposal — shrink its effective world-model dramatically. Set it back in its development.

And the GPS is only as effective as the world-model it operates in.

Our selection process is greedy, so it will never choose to make such a change.

3. Interfaces

Let’s take a step back, and consider how the different parts of the agent must’ve learned to interface with each other. Are there any legible data structures?

a) The World-Model. Initially, there wouldn’t have been a unified world-model. Each individual heuristic would’ve learned some part of the environment structure it cared about, but it wouldn’t have pooled the knowledge with the other heuristics. A cat-detecting circuit would’ve learned how a cat looks like, a mouse-detecting one how mice do, but there wouldn’t have been a communally shared “here’s how different animals look” repository.

However, everything is correlated with everything else (the presence of a cat impacts the probability of the presence of a mouse), so pooling all information together would’ve resulted in improved predictive accuracy. Hence, the agent would’ve eventually converged towards an explicit world-model.

b) Cross-Heuristic Communication. As a different consideration, consider heuristics conflicts. Suppose that we have some heuristics $h_{i}$ and $h_{k}$ that both want to fire in a given training episode. However, they act at cross-purposes: the marginal increase of $U$ achieved by $h_{i}$ firing at $t$ would be decreased by letting $h_{k}$ fire at $t$ , and vice versa. Both of them would want to suppress each other. Which should win?

On a similar note, consider heuristics that want to chain their activations. Suppose that some heuristic $h_{m}$ responds to a subset of the features $h_{l}$ detects. $h_{m}$ can learn to detect them from scratch, or it can just learn to fire when $h_{l}$ does, instead of replicating its calculations.

Both problems would be addressed by some shared channel of communication between the heuristics, where each of them can dump information indicating how strongly it wants to fire this turn. To formalize this, let’s suppose that each heuristic has an associated “activation strength” function $D : M_{s} \to R$ . (Note that activation strength is not supposed to be normalized across heuristics. I. e., it’s entirely possible to have a heuristic whose strength ranges from 0 to 10, and another with a range from 30 to 500, such that the former always loses if they’re in contest.)

The actual firing pattern would be determined as some function of that channel’s state.^[2]

c) Anything Else? So far as I can tell now, that’s it. Crucially, under this model, there doesn’t seem to be any pressure for heuristics to make themselves legible in any other way. No summaries of how they work, no consistent formats, nothing. Their constituent circuits would just be… off in their own corners, doing their own things, in their own idiosyncratic ways. They need to be coordinated, but no part of the system needs to model any other part. Yet.

So those are the low-hanging fruits available to be learned by the GPS. The selection pressure doesn’t need to introduce a lot of changes to plug the GPS into the world-model and the cross-heuristics communication channel^[3], inasmuch as they both follow coherent data formats.

But that’s it. Making the mechanics of the heuristics legible — both standardizing the procedural $E \to A$ knowledge and making the implicit $(E \to A) \to U$ knowledge explicit — would involve a lot more work, and it’d need to be done for every heuristic individually. A lot of gradient steps/evolutionary generations/reinforcement events.

4. Reverse-Engineering the Heuristics

That’s very much non-ideal. The GPS still can’t access the non-explicit knowledge — it basically only gets hunches about it.

So, what does it do? Starts reverse-engineering it. It’s a general-purpose problem-solver, after all — it can understand the problem specification of this, given a sufficiently rich world-model, and then solve it. In fact, it’ll probably be encouraged to do this. The selection pressure would face the choice between:

Making the heuristics legible to the GPS over the course of many incremental steps.
Making the GPS better at reverse-engineering the rest of the system the GPS is embedded in.

The second would plausibly be faster, the same way deception is favoured relative to alignment^[4]. So the selection pressure would hard-code some tendency for the GPS to infer the mechanics of the rest of the agent’s mind, and write them down into the world-model. This is an important component of the need for self-awareness/reflectivity.

The GPS would gather statistical information about the way heuristics fire, what they seem to respond to or try to do, which of them fire together or try to suppress each other, what effects letting one heuristic or the other fire has on the world-model, and so on.

One especially powerful way to do that would be running counterfactuals on them. That is, instead of doing live-fire testing (search for a situation where heuristic $h_{i}$ wants to fire, let it, see what happens), it’d be nice to simulate different hypothetical states the world-model could be in, then see how the heuristics respond, and what happens if they’re obeyed. And there’ll likely already be a mechanism for rolling the world-model forward or generating hypotheticals, so the GPS can just co-opt it for this purpose.

What will this endeavor yield, ultimately? Well, if the natural abstractions hypothesis is true, quite a lot! As I’ve noted at the beginning, each heuristic is plausibly centered around some natural abstraction or a sensible cluster of natural abstractions^[5], and it’d be doing some local computation around them aimed at causing a locally-sensible outcome. For example, we might imagine a heuristic centered around “chess”, optimized for winning chess games. When active, it would query the world-model, extract only the data relevant to the current game of chess, and compute the appropriate move using these data only.

So we can expect heuristics to compress well, in general.

That said, we need to adjust our notation here. Suppose that you’re the GPS, trying to reverse-engineer some heuristic $h_{i}$ . You obviously don’t have access to the ground-truth of the world $E$ , only a model of it $M$ . And since $M$ might be flawed, the world-model nodes $h_{i}$ is defined over might not even correspond to anything in the actual environment!

By the same token, the best way to compress $h_{i}$ ’s relationship with $U$ might not be summarizing its relationship with the actual reward-nodes, but with some proxy node. Consider this situation:

We can imagine some heuristic $h_{i}$ which specializes in controlling the value of $x_{p}$ . Ultimately, that heuristic would’ve been created by the selection pressure because of its effect on $r_{1}$ . But $h_{i}$ ’s actual mechanical implementation would only be focused on $x_{p}$ , and the causal chain between it and the agent! It would pay no mind to $x_{1}, x_{2}, . . ., x_{5}$ , so its effect on $r_{1}$ would be subject to a lot of noise — unlike its effect on $x_{p}$ . Thus, the agent would recover $x_{p}$ as the target, not $r_{1}$ . (And, of course, it might also be because $r_{1}$ isn’t yet represented in the world-model at all.)

As an example, consider chess. The algorithms for playing it well are convergent across all agents, irrespective of the agent’s goals outside chess or its reason for trying to win at chess. Their implementations would only refer to chess-related objectives.

Thus, while an “outside-picture” view on heuristics describes them as $(E \to A) \to U$ , internally they’d be best summarized as:

(M \to A) \to P

Where $P$ is some proxy objective. For simplicity, let’s say that $P$ is a 2-tuple $⟨ x_{i}, d_{i} ⟩$ , where the first entry is a world-model node and the second is the “target value” for that node. So every “goal” is to keep the value of a node as close to the target as possible.

As another technicality, let’s say that the activation-strength function $D$ increases the farther from the target the corresponding node’s value goes.

5. The Wrapper Structure

All this time, I’ve been avoiding the subject of what the GPS will be pointed at. I’ve established that it’ll be used for self-reflection, and that it won’t be optimizing for a fixed goal aligned with the outer objective — won’t be a wrapper-mind. But what spread of goals will it actually pursue at the object-level? What would be the wrapper structure around the GPS?

5A. Assumption Re-Check

First, let’s check whether aligning it with the outer objective still doesn’t work. What if we point it at the joint task of reward maximization plus self-reflection? Make it want the target objective plus inform it that there’s some useful yet inaccessible knowledge buried in its mind. That’ll work… if it had infinite time to think, and could excavate all the procedural and implicit knowledge prior to taking any action. But what if it needs to do both in lockstep?

In addition, “point it at the X task” hides a lot of complexity. Even if the reward-nodes are already represented in the world-model, building an utility function around them is potentially a complex problem, requiring many parameter updates/generations. All the while, the GPS would be sitting there, contributing nothing. That’s not how our greedy selection process works — there just aren’t gradients from “GPS does nothing” to “GPS is inner-aligned with the target objective”.

No, we need some interim objective for the GPS — something we can immediately hook it up to and make optimize, and which would at least somewhat correlate with good performance on the target objective. Once that’s done, then we can incrementally rewrite that proxy objective to the target objective… if we’ll even want to, at that point.

5B. The Interim Objective

A few points:

In the previous section, we’ve established that every heuristic $h$ enforces some relationship between a state of a world-model subset $M_{s}$ and some subset of the actions the agent will take $A_{s}$ . Let’s call this structure contextual behavior $B : M_{s} \to A_{s}$ . (We’ll assume that the activation strength $D$ is folded into $B$ .)
Such contextual behaviors are optimized for achieving some proxy objective $P$ in the world-model subset $M_{s}$ . We’ll call this a contextual goal $G : M_{s} \to P$ . (Similarly, assume that $D$ is somehow represented in $G$ .)
The GPS can, in principle, succeed at extracting both $B$ and $G$ from a given $h$ .
At the beginning, we’ve postulated that by the time the GPS develops, the agent’s heuristics, when working in tandem, would be much-better-than-random at achieving the target objective.

This makes the combination of all contextual goals, let’s call it $G_{Σ}$ , a good proxy objective for the target objective $U$ . A combination of all contextual behaviors $B_{Σ}$ , in turn, is a proxy for $G_{Σ}$ , and a second-order proxy for $U$ .

Prior to the GPS’ appearance, the agent was figuratively pursuing $B_{Σ}$ (“figuratively” because it wasn’t an optimizer, just an optimized). So the interim objective can be at least as bad as $B_{Σ}$ . On the other hand, pursuing $G_{Σ}$ directly would probably be an improvement, as we wouldn’t have to go through two layers of proxies.

The GPS can help us with that: can help us move from $B_{Σ}$ to $G_{Σ}$ , and then continue on all the way to $U$ .

We do that by first enslaving the GPS to the heuristics, then letting it take over the agent once it’s capable enough.

5C. Looping Heuristics Back In

The obvious solution is obvious: make heuristics themselves control the GPS. The GPS’ API is pretty simple, and depending on the complexity of the cross-heuristic communication channel, it might be simple enough to re-purpose its data formats for controlling the GPS. Once that’s done, the heuristics can make it solve tasks for them, and become more effective at achieving $B_{Σ}$ (as this will give them better ability to runtime-adapt to unfamiliar circumstances, without waiting for the SGD/evolution to catch them up).

I can see it taking three forms:

Input tampering. The problem specification terms $M_{s} \times M_{s}^{G}$ that gets passed to the GPS are interfered-with or wholesale formed by heuristics.
- (“Condition X is good, so I’ll only generate plans that satisfy it.” Also: “I am in pain, so I must think only about it and find the solution to it as quickly as possible.”)
Process tampering. The heuristics can learn to interfere on the GPS process directly, biasing it towards one kind of problem-solving or the other.
- (“I’m afraid of X, so my mind is flinching away from considering plans that feature X.”)
Output tampering. The heuristics can learn to override the actions the GPS recommends to take.
- (“X is an immediate threat, so I stagger back from it.”)

The real answer is probably all of this. Indeed, as I’ve illustrated, I think we observe what looks like all three varieties in humans. Emotions, instincts, and so on.

5D. Nurturing the Mesa-Optimizer

As this is happening, we gradually increase the computational capacity allocated to the GPS’ and the breadth of its employment. We gradually figure out how to set it up to do self-reflection.

It starts translating the procedural and the implicit knowledge into a language it understands — the language of the world-model. $B$ s and $G$ s are explicated and incorporated into it, becoming just more abstractions the GPS can make use of.

At this point, it makes sense to give the GPS ability to prompt itself — to have influence over what goes into the problem specifications of its future instances. It’ll be able to know when to solve problems by engaging in contextual behaviors, even if it doesn’t understand why they work, and optimizing for contextual goals is literally what it’s best at.

This way of doing it would have an advantage over letting heuristics control the GPS directly:

It would allow the GPS to incorporate procedural knowledge into its long-term plans, and otherwise account for it, instead of being taken by surprise.
It would allow the GPS to derive better, more nuance-aware ways of achieving contextual goals, superior to those codified in the heuristics. It would greatly improve the agent’s ability to generalize to new environments.

We’ll continue to improve the GPS, improving its ability to do this sort of deliberative long-term goal pursuit. At the same time, we’ll lessen the heuristics’ hold on it, and start turning heuristics towards the GPS’ purposes — marginally improving their legibility, and ensuring that the process of reverse-engineering them aims the agent at $U$ with more and more precision.

The agent as a whole will start moving from a $B_{Σ}$ -optimizer to a $G_{Σ}$ -optimizer, and then even beyond that, towards $U$ .^[6]

5E. Putting It Together

So, what’s the wrapper structure around the GPS, at some hypothetical “halfway point” in this process?

Instincts. Heuristics pass the GPS problem specifications and interfere in its processes.
Self-reflection. The GPS tries to reverse-engineer the rest of the agent in order to piggyback off its non-explicit knowledge.
A spread of mesa-objectives. The GPS uses its explicit knowledge to figure out what it’s “meant” to do in any given context, and incorporates such conclusions in its long-term plans.

6. Value Compilation

The previous section glossed over a crucial point: how do we turn a mass of contextual behaviors and goals into a proper unitary mesa-objective $G_{Σ}$ ?

Because we want to do that. The complex wrapper structure described in the previous section is highly inefficient. At the limit of optimality, everything wants to be a wrapper-mind. There’s plenty of reasons for that:

The basic argument. We wouldn’t want our optimization process/the GPS to be haphazardly pointed in different directions moment-to-moment, as different heuristics activate and grab its reins, or bias it, or override it; even as it continues to recover more and more pieces of them. We’d be getting dutch-booked all the time, act at cross-purposes with our future and past instances. The GPS explicating this doesn’t exactly help: it’ll be able to predict its haphazard behavior, but not how to prevent it in a way that doesn’t worsen its performance.
It’s computationally inefficient. Imagine a naively-formed $G_{Σ}^{naive}$ , of the following form: $G_{1} \land G_{2} \land \dots \land G_{n}$ . It would look at the world-model, run down the list of contextual behaviors, then execute the behaviors that apply, and somehow resolve the inevitable conflicts between contradictory behaviors. Obviously, that would take a lot of time; time in which someone might brain you with a club and take all your food. Contextual behaviors sufficed when they just happened, but considering them via the GPS would take too long. (Consider how much slower conscious decision-making is, compared to knee-jerk reactions.)
It might be a hard-wired terminal objective. Remember, any given individual $G_{i}$ is not a good proxy objective — only their combination $G_{Σ}$ is. So it’s entirely probable that the selection pressure would directly task the GPS with combining and unifying them, not only with reverse-engineering them. Even if there weren’t all the other reasons to do that.
Closely related to (3): ability to generalize to unfamiliar environments. Optimizing for $G_{Σ}$ would almost always allow the agent to do a good job according to $U$ even if it were dropped in entirely off-distribution circumstances. $G_{Σ}^{naive}$ , on the other hand, would trip up the moment it fails to locate familiar low-level abstractions. (E. g., a preference utilitarian would be able to make moral judgements even in an alien civilization, whereas someone who’s only internalized some system of norms of a small human culture would be at a loss.)

So, how do we collapse $G_{Σ}^{naive}$ into a compact, coherent $G_{Σ}$ ?

(For clarity: everything in this section is happening at runtime. The SGD/evolution are not involved, only the GPS. At the limit of infinite training, $G_{Σ}$ would become explicitly represented in the agent’s parameters, with the GPS set up to single-mindedly pursue it and all the heuristics made into passive and legible pieces of the world-model. But I expect that the agent would become superintelligent and even “hyperintelligent” long before that — i. e., capable of almost arbitrary gradient-hacking — and so the late-game hard-coded $G_{Σ}$ would be chosen to by it, and therefore would likely be a copy of a $G_{Σ}$ the AI’s earlier instance compiled at runtime. So the process here is crucial.)

6A. The Basic Algorithm

Suppose we’ve recovered contextual goals $G_{1}$ and $G_{2}$ . How do we combine them?

a) Conjunction. Consider the following setup:

Suppose that we have a heuristic $h_{i}$ , which tries to keep the value of $x_{i}$ at some number, and another heuristic $h_{k}$ , which does the same for $x_{k}$ . Suppose that together, their effects keep the value of $x_{v}$ within some short range. That allows us to form a contextual goal $G_{i \land k} = G_{v}$ , which activates if $x_{v}$ ’s value strays far from the center of the range $h_{i}$ and $h_{k}$ effectively kept it in.

In a sense, this is the same algorithm we must’ve followed to go from contextual actions to contextual goals in the first place! To do that, we gathered statistical information about a heuristic’s activations, and tried to see if it consistently controlled the value of some node downstream of the action-nodes. Same here: we know that $h_{i}$ and $h_{k}$ control the values of $x_{i}$ and $x_{k}$ , we hypothesize that there’s some downstream node whose value their activations consistently control, and we conclude that this is the “purpose” of the two heuristics.

Technical note: How do we compute the activation-strength function of the new goal, $D_{p}$ ? Well, $D_{i}$ and $D_{k}$ increased as $x_{i}$ and $x_{k}$ ‘s values went farther from their target values, and this relationship kept $x_{v}$ ‘s value near some target of its own. In turn, this means that $D_{i} + D_{k}$ increased as $x_{v}$ ’s value went far from some target. From that, we can recover some function $D_{p}$ which tracks the value of $x_{v}$ directly, not through the intermediaries of $x_{i}$ and $x_{k}$ . Note the consequence: the combined goal would be approximately as strong as the sum of its “parents”.

Important note: After we compile $x_{p}$ , we stop caring about $x_{i}$ and $x_{k}$ ! For example, imagine that off-distribution, the environmental tendencies change: the values of $x_{i}$ and $x_{k}$ that kept $x_{v}$ near a certain value no longer do so. If we’d retained the original contextual goals, we’d keep $x_{i}$ and $x_{k}$ near their target values, as before, even as that stops controlling $x_{v}$ . But post-compilation, we do the opposite: we ignore the target values for $x_{i}$ and $x_{k}$ to keep $x_{v}$ near its newly-derived target.

Human example: A deontologist would instinctively shy away from the action of murder. An utilitarian might extrapolate that the real reason for this aversion is because she dislikes it when people die. She’d start optimizing for the minimal number of people killed directly, and would be able to do things she wouldn’t before, like personally kill a serial killer.

Another: Imagine a vain person who grew up enjoying a wealthy lifestyle. As a child, he’d developed preferences for expensive cars, silk pillows, and such. As he grew up, he engaged in value compilation, and ended up concluding that what he actually valued were objects that signify high status. Afterwards, he would still love expensive cars and silk pillows, but only as local instantiations of his more abstract values. Post-reflection, he would be able to exchange cars-and-pillows for yachts-and-champagne without batting an eye — even if that wouldn’t make sense to his childhood self.

This shtick is going to cause problems for us in the future.

Sidenote: In a way, this approach expands the concept of “actions”. At genesis, the agent can only control the values of its immediate action-nodes. As it learns, it develops heuristics for the control of far-away nodes. When these heuristics are sufficiently reliable, it’s as if the agent had direct access to these far-away nodes. In the example above, we can collapse everything between the agent and e. g. $x_{v}$ into an arrow! And in fact, that’s probably what the GPS would do in its computations (unless it specifically needs to zoom in on e. g. $x_{3}$ ’s state, for some reason).
As an example, consider a child trying to write, who has to carefully think about each letter she draws and the flow of words, versus an experienced author, who does all that automatically and instead directly thinks about the emotional states he wants to evoke in the reader. (Though he’s still able to focus on calligraphy if he wants to be fancy.) Chunking is again relevant here.

b) Disjunction. Consider this different setup:

Again, suppose we have two contextual goals $G_{i}$ and $G_{k}$ defined over $x_{i}$ and $x_{k}$ respectively. But there’s no obvious way to combine them here: if their causal influences meet anywhere, we haven’t discovered these parts of the world-model yet. Their contexts are entirely separate.

As such, there isn’t really a way to unify them yet: we just go $G_{i \land k} = G_{i} \land G_{k}$ , and hope that, as the world-model expands, the contexts would meet somewhere.

As an example, we might consider one’s fruit preferences versus one’s views on the necessity of the Oxford comma. They seem completely unrelated to each other. (And as a speculative abstract unification, perhaps one is entertained by ambiguity or duality-of-interpretation, and so prefers no Oxford comma and fruits with a mild bittersweet taste, as instantiations of that more abstract preferences? Though, of course, all human values don’t have to ever converge this way.)

Now let’s complicate it a bit:

Again, we have contextual goals $G_{i}$ and $G_{k}$ . We don’t see a way to combine them, yet neither are they fully separate, as their contexts are entwined. If both $x_{i}$ and $x_{k}$ assume undesirable states, there might not be a distribution of values we may assign $a_{1}$ and $a_{2}$ such that both contextual goals are achieved. How do we deal with it?

Well, the selection pressure ran into this problem a while ago, well before the GPS, and it’s already developed a solution: the cross-heuristic communication channel. Any given heuristic $h_{i}$ has an activation strength $D_{i}$ , and if two heuristics $h_{i}$ , $h_{k}$ contest, the actions taken are calculated as some function of the activation strengths $D_{i}$ , $D_{k}$ , and the recommended actions $A_{s_{i}}$ , $A_{s_{k}}$ .

The GPS can recover all of these mechanics, and then just treat the sum of all “activation strengths” as negative utility to minimize-in-expectation. The actual trade-offs seem to heavily depend on the specifics of the situation (e. g., can we “half-achieve” every goal, or we have to choose one or the other?) — I’ve unfortunately failed to come up with a general yet compact way to describe conflict-resolution here. (Though I can point to some related ideas.)

A particular degenerate case is if the two contextual goals are directly opposed to each other. That is, suppose that the actions that bring $x_{i}$ near the target almost always move $x_{k}$ ’s value outside it — like a desire to smoke interferes with one’s desire to look after their health. In this case, if $D_{k}$ always outputs higher values than $D_{i}$ , $G_{i}$ ends up fully suppressed: $G_{i \lor k} = G_{k}$ .

Suppose, however, that $G_{i}$ wasn’t a hard-coded heuristic. Rather, $G_{i}$ was produced as the result of value compilation, perhaps as a combination of contextual goals over $x_{3}$ and $x_{6}$ . In this case, we may “decompile” $G_{i}$ back into $G_{3}$ and $G_{6}$ , and try to find ways to re-compile them such that the result doesn’t interfere with $G_{k}$ . Perhaps $G_{3}$ is “have a way to relax when stressed” and $G_{6}$ is “I want to feel cool”, and we can compile them into $G_{d}$ = “carry a fabulous fidget toy”.^[7]

c) By iteratively using these techniques, we can, presumably, arrive at some $G_{Σ}$ . $G_{Σ}$ might end up fully unitary, like a perfect hedonist’s desire to wirehead, or as a not-perfectly-integrated spread of values $G_{Σ} : G_{1} \land G_{2} \dots \land G_{n}$ . But even if it’s the latter, it’ll be a much shorter list than $G_{Σ}^{naive}$ , and the more abstract goals should allow greater generalizability across environments.

One issue here is that there might be multiple $G_{Σ}$ consistent with the initial set of heuristics. As far as human value reflection goes, it’s probably fine: either of them should be a fair representation of our desires, and the specific choice has little to do with AI Notkilleveryoneism^[8]. But when considering how an AI’s process of value reflection would go, well, it might turn out that even for a well-picked suite of proto-values, only some of the final $G_{Σ}$ don’t commit omnicide.

Anyway, that was the easy part. Now let’s talk about all the complications.

6B. Path-Dependence

Suppose that you have three different contextual goals, all of equal activation strength. For example, $G_{1}$ is “I like looking at spiders, they’re interesting”, $G_{2}$ is “I like learning about spider biology, it’s interesting”, and $G_{3}$ is “I want to flee when there’s a spider near me, something about being in their vicinity physically just sets me off”.

Suppose that you live in a climate where there isn’t a lot of spiders, so $G_{3}$ almost never fires. On the other hand, you have Internet access, so you spend day after day looking at spider pictures and reading spider facts. You compile the first two proto-values into $G_{1 \land 2}$ : “I like spiders”.

Then you move countries, discover that your new home has a lot of spiders, and to your shock, realize that you fear their presence. What happens?

Perhaps you compile a new value, $G_{(1 \land 2) \land 3}$ = “I like spiders, but only from a distance”. Or you fully suppress $G_{3}$ , since it’s revealed to be at odds with $G_{1 \land 2}$ whenever it activates.

That’s not what would’ve happened if you started out in an environment where all three contextual goals had equal opportunity to fire. $G_{3}$ would’ve counterbalanced $G_{1}$ and $G_{2}$ , perhaps resulting in $G_{1 \land 2 \land 3}$ = “I guess spiders are kind of neat, but they freak me out”.

Thus, the process of value compilation is path-dependent. It matters in which order values are compiled.

6C. Ontological Crises

What happens when a concept in a world-model turns out not to correspond to a concrete object in reality — such as the revelation that things consist of parts, or that souls aren’t real? What if that happens to something you care about?

This is actually fairly easy to describe in this model. There are two main extreme cases and a continuum between them.

a) “Ontology expansion”. The first possibility is that the object we cared about was a natural abstraction. This shift roughly looks like the following:

Suppose we cared about $x_{p}$ , and it turned out to be a natural abstraction over a system of $x_{p 1}, x_{p 2}, x_{p 3}$ . That would merely mean that (1) the state of $x_{p}$ is downstream of the states of $x_{p 1}, x_{p 2}, x_{p 3}$ , and (2) we can model the impact of our actions on $x_{p}$ more precisely by modelling $x_{p 1}, x_{p 2}, x_{p 3}$ , if we so choose. Which we may not: maybe we’re indifferent to the exact distribution of values in $x_{p 1}, x_{p 2}, x_{p 3}$ , as long as the value of $x_{p}$ they compute remains the same.

And $x_{p}$ is still a reasonable object to place on our map. The same way it’s meaningful to think of and care about “humans”, even if they’re not ontologically basic; and the same way we would care about the high-level state of a human (“are they happy?”) and be indifferent towards the low-level details of that state (“okay, they’re happy, but are the gut bacteria in their stomach distributed like this or like that?”).

b) “Ontology break”. In the second case, the object we cared about turns out to flat-out not exist; not correspond to anything in the territory:

As the example, consider a spiritual person realizing that spirits don’t exist, or a religious person in the middle of a crisis of faith. We valued $x_{p}$ , but now there’s just nothing resembling it in its place. What can we do?

Do value decompilation, again. Suppose that the initial set of heuristics from which the value was compiled wasn’t defined over $x_{p}$ . Suppose we had contextual goals $G_{1}$ and $G_{2}$ defined over $x_{1}$ and $x_{2}$ respectively, which we then collapsed into $G_{p}$ . We can fall back on them: we can remember why we decided we cared about $x_{p}$ , then attempt to re-compile new downstream values from $G_{1}$ and $G_{2}$ in the new world-model. Perhaps, say, we end up noticing that $G_{1}$ and $G_{2}$ do an awful lot to control the value of $x_{7}$ …?

As a human example, perhaps an apostate would decide that they cared about God because they sought a higher purpose, or wanted to feel a sense of belonging with their community. If so, they may find ways to satisfy these urges that would work in the new ontology.

The quantitative effects of this kind of ontology break can be quite dramatic. The non-existent node might be a linchpin of the world-model, having “infected” most of the nodes in it. It would entail a lengthy process of value re-compilation, and the final utility function might end up very different. Qualitatively, though, nothing would change.

We can imagine an extreme case where the basic initial heuristics were defined over empty concepts as well. In this case, perhaps they’ll just have to be outright suppressed/ignored.

A degenerate case is if all initial heuristics are defined over empty concepts. I expect it’s unlikely in real-life systems, though: many of them would likely be associated with mental actions, which would be self-evidently real by the very functioning of the system (by analogy with cogito ergo sum).

Sidenote: “But does that mean that the final form values take depends on the structure of the environment?” Yes.
Note that this doesn’t mean that moving an adult human from Earth to an alien civilization would change their values. That wouldn’t involve any ontological crises, after all — the basic structure of the environment wouldn’t change from their perspective, it would merely extend to cover this new environ. They would need to learn a number of new low-level abstractions (the alien language, what signals correspond to what mental states, etc.), but they would likely be able to “bridge” them with the previous high-level ones eventually, and continue the process of value reflection from there (e. g., if they cared for other people before, then once they properly “grasp” the personhood of the aliens, they’d begin caring for them too, and may eventually arrive at valuing some universal eudaimonia).
On the other hand, a human in a universe with God does arrive at different values than in a godless one. I think that makes sense.^[9]

c) In practice, most of the cases will likely be somewhere between the two extremes. The world-model expansion would reveal that what the agent cared about wasn’t precisely a natural abstraction, but also not entirely a thing that didn’t exist. They might end up re-calculating the correct natural abstraction, then deciding to care for it, experiencing a slight ontology break. (Humans souls aren’t real, but human minds are, so we switch over, maybe with a bit of anguish. A more mundane example: someone you knew turned out to be a very different person from what you’d thought of them, and you have to re-evaluate your relationship.)

Or maybe they’ll end up caring about some low-level properties of the system in addition to the high-level ones, as the result of some yet-disjointed value finding something in the low-level to care about. (E. g., maybe some distributions of bacteria are aesthetically pleasing to us, and we’d enjoy knowing that one’s gut bacteria are arranged in such a fashion upon learning of their existence? Then “a human” would cause not only empathy to fire, but also the bacteria-aesthetics value.)

6D. Meta-Cognition

This is the real problem.

a) Meta-heuristics. As I’d mentioned back in 5C, there’ll likely be heuristics that directly intervene on the GPS’ process. These interventions might take the form of interfering with value compilation itself.

The GPS can notice and explicate these heuristics as well, of course. And endorse them. If endorsed, they’ll just take the form of preferences over cognition, or the world-model. A spiritualist’s refusal to change their world-view to exclude spirits. A veto on certain mental actions, like any cognitive process that concludes you must hate your friends. A choice to freeze the process of value compilation at a given point, and accept the costs to the coherency of your decisions (this is how deontologists happen).

Any heuristic that can do that would gain an asymmetric advantage over those that can’t, as far as its representation in the final compilation is concerned.

I hope the rest of this post has shown that such mechanisms are as likely to be present in AIs as they are in humans.

b) Meta-cognition itself. The core thing to understand, here, is that the GPS undergoing value compilation isn’t some arcane alien process. I suspect that, in humans, it’s done fully consciously.

So, what problems do humans doing value reflection run into?

First off, the GPS might plainly make a mistake. It doesn’t have access to the ground truth of heuristics and can’t confirm for sure when it did or did not derive a correct contextual goal or conducted a valid compilation.

Second, meta-cognitive preferences can originate externally as well. A principled stance to keep deontological principles around even if you’re an utilitarian, for example.

Third, the GPS is not shy about taking shortcuts. If it encounters some clever way to skip past the lengthy process of value compilation and get straight to the answer, it’ll go for it, the same we’d use a calculator instead of multiplying twenty-digit numbers manually. Hence: humans becoming hijacked by various ideologies and religions and philosophies, that claim to provide the ultimate answers to morality and the meaning of life.

Thus, the final compilation might not even have much to do with the actual initial spread of heuristics.

At the same time, meta-cognition might counteract the worst excesses of path-dependence. We can consciously choose to “decompile” our values if we realize we’ve become confused, look at our initial urges, then re-compile the more correct combination from them.

6E. Putting It Together

As such, the process for computing the final mesa-objective $G_{Σ}$ is a function of:

The initial set of heuristics, especially those with meta-cognitive capability.
The true environment structure.
The data the agent is exposed to.
The exact sequence in which the agent reverse-engineers various heuristics, combines various values, and is exposed to various data-points.

Is it any wonder the result doesn’t end up resembling the initial outer objective $U$ ?

I’m not sure if that’s as bad as it looks, as far as irreducible complexity/impossibility-to-predict goes. It might be.

7. Miscellanea

a) Heuristics’ Flavour. You might’ve noticed that this post has been assuming that every heuristic ends up interpreted as a proto-value that at least potentially gets a say in the final compilation. That’s… not right. Isn’t it? I’m not actually sure.

I think the Shard Theory answer would be that yes, it’s right. Every heuristic is a shard engaging in negotiation with every other shard, vying for influence. It might not be “strong” or very good at this, but an attempt will be made.

Counterpoint: Should, say, your heuristic for folding a blanket be counted as a proto-value? The GPS is reverse-engineering them to gain data on the environment, and this should really just be a “skill”, not a proto-value.

Counter-counterpoint: Imagine an agent with a lot of heuristics for winning at chess. It was clearly optimized for playing chess. If the GPS’ goal is to figure out what it was made for and then go optimize that, then “I value winning at chess” or “I value winning” should be plausible hypotheses for it to consider. It makes a certain kind of common sense, too. As to blanket-folding — sure, it’s a rudimentary proto-value too. But it’s too weak and unsophisticated to get much representation. In particular, it probably doesn’t do meta-cognitive interventions, and is therefore at an asymmetrical disadvantage compared to those that do.

… Which is basically just the Shard Theory view again.

So overall, I think I’ll bite that bullet, yes. Yes, every starting heuristic should be interpreted as a proto-value that plays a part in the overall process of value compilation. (And also as a skill that’s explicated and integrated into the world-model.)

b) Sensitivity to the Training Process. Let’s consider two different kinds of minds: humans, which are likely trained via on-line reinforcement learning, and autoregressive ML models, who can continuously cogitate forever even with frozen weights by chaining forward passes. (Suppose the latter scales to AGI.)

The internal dynamics in these minds might be quite different. The main difference is that in humans, heuristics can adapt at runtime, and new heuristics can form, while in the frozen-weights model, the initial spread of heuristics is static.

As one obvious consequence, this might make human heuristics “more agenty”, in the sense of being able to conduct more nuanced warfare and negotiation between each other. In particular, they’d have the ability to learn to understand new pieces of the world-model the GPS develops, and learn new situations when they must tamper with the GPS for self-preservation (unlike static heuristic, for whom this is inaccessible information). “Heuristic” might be a bad way to describe such things, even; “shards” might be better. Perhaps such entities are best modeled as traders rather than functions-over-nodes?

But a potentially bigger impact is on value-compilation path-dependence.

In humans, when we compile contextual goals $G_{1}$ and $G_{2}$ into $G_{1 \land 2}$ , and then stay with $G_{1 \land 2}$ for a while, we end up developing a new shard around $G_{1 \land 2}$ — a structure of the same type as the initial $G_{1}$ , $G_{2}$ . Shards for $G_{1}$ and $G_{2}$ , meanwhile, might die out as their “child” eats the reinforcement events that would’ve initially went for them. (Consider the example of the Vain Man from 6A.)

But if that initial set of heuristics is frozen, as in an ML model, perhaps the agent always ends up developing a “path-independent” generalization as described at the end of 6A? The runtime-compiled values would be of a different type to the initial heuristics: just mental constructs. And if we assume the AI to be superintelligent when it finalizes the compilation, it’s not going to be fooled by whatever it reads in the data, so the “mistaken meta-cognition” concerns don’t apply. Certainly it might make mistakes at the start of the process, but if incorrect compilations aren’t “sticky” as they are with humans, it’ll just decompile them, then re-compile them properly!

Reminder: This doesn’t mean it’ll become aligned with the outer objective. $G_{Σ}$ is still not $U$ but a proxy for $U$ , so even path-independent value compilation ends with inner misalignment.

But it does make $G_{Σ}$ derivable from just the parameters and the world-model, not the data.

c) Self-Awareness. I’ve belatedly realized that there’s a third structure the GPS can interface with: the GPS itself. This fits nicely with some of my published and yet-unpublished thoughts on self-awareness and the perception of free will.

In short, the same way it’s non-trivial to know what heuristics/instincts are built into your mind, it’s non-trivial to know what you’re currently thinking of. You need a separate feedback loop for that, a structure that summarizes the GPS’ activity and feeds it back into the GPS as input. That, I suspect, directly causes (at least in humans):

Self-awareness (in a more palatable fashion, compared to just having abstractions corresponding to “this agent” or “this agent’s mental architecture” in the world-model).
The perception of the indisputability of your own existence.
The perception of free will. (You can request a summary of your current object-level thoughts and make a decision to redirect them; or you can even request a summary of your meta-cognition, or meta-meta-cognition, and so on, and redirect any of that. Therefore, you feel like you’re freely “choosing” things. But the caveat is that every nth-level request spins up a (n+1)th-level GPS instance, and the outermost instance’s behavior isn’t perceived and “controlled” by us, but is us. As such, we do control our perceived behavior, but our outermost loop that’s doing this is always non-perceivable and non-controllable.)

But that probably ought to be its own separate post.

8. Summary

Once the GPS develops, the selection pressure needs to solve two tasks:
- Let the GPS access the procedural and implicit knowledge $(E \to A) \to U$ represented by the heuristics, even though they’re completely illegible.
- Pick some interim objective for the GPS to make object-level plans around.
The selection pressure solves the first problem by hooking the GPS up to the two coherent data structures that were already developed: the world-model, and the cross-heuristic communication channel.
The second problem is solved by teaching the heuristics to use the GPS to assist in problem-solving. In essence, the GPS starts “optimizing” for the implicit goal $B_{Σ}$ of “do whatever the agent was already doing, but better”.
As this is happening, the GPS proves more and more useful, so the amount of compute allocated to it expands. It learns to reverse-engineer heuristics, getting explicit access to the non-explicit knowledge.
The GPS is encouraged to treat heuristics as “clues” regarding its purpose, and $B_{Σ}$ as some proxy of the real goal $G_{Σ}$ that the agent is optimized to solve. (Which, in turn, is a proxy of the real target objective $U$ .)
Every heuristic, thus, is at once a piece of the world-model and a proto-value.
There’s plenty of incentives to compress these splintered proto-values into a proper utility function: it’s a way to avoid dominated strategies, the splintered goal-set is computationally unwieldy, and the GPS can probably derive a better, more generalizable approximation of $G_{Σ}$ by explicitly trying to do that.
The basic process of value compilation goes as follows:
- Hypothesize that a number of heuristics, e. g. $h_{i}$ and $h_{k}$ , are jointly optimized for achieving some single goal $G_{i \land k}$ . If such a goal is found, start optimizing it directly.
- If no goal is found, compute the appropriate trade-offs between $G_{i}$ and $G_{k}$ based on the underlying heuristics’ activation-strength functions $D_{i}$ and $D_{k}$ . If one of the goals has to be fully suppressed, try decompiling it and repeating the process.
- Iterate, with initial heuristics replaced with derived contextual goals, until arriving at $G_{Σ}$ .
That process runs into several complications:
- Path-dependence, where the order in which contextual goals are compiled changes the form the final goal takes.
- Ontological crises, where we either (1) expand our model to describe the mechanics of the natural abstraction we care about, or (2) experience an ontology break where the object we cared about turns out not to exist, which forces us to do value decompilation + re-compilation as well.
- Meta-cognition: The agent might have preferences over the value compilation process directly, biasing it in unexpected ways. In addition, the GPS implements (something like) logical reasoning, and might lift conclusions about its values from external sources, including mistaken ones.
Some considerations have to be paid to the online vs batch training: agents trained on-line might be uniquely path-dependent in a way that those with frozen weights aren’t.

9. Implications for Alignment

My main practical takeaway is that I am now much more skeptical of any ideas that plan to achieve alignment by guiding the process of value formation, or by setting up a “good-enough” starting point for it.

Take the basic Shard Theory approach as the example.^[10] It roughly goes as follows:

Real-life agents like humans don’t have static values, but a distribution over values that depends on the context.
There’s ample reason to believe that AI agents found by the SGD will be the same.
What we need to do isn’t to make an AI that’s solely obsessed with maximizing human values, but to ensure that there’s at least one powerful & metacognition-capable shard/proto-value in it that values humans: that our value distributions merely roughly overlap.
Then, as the AI does value compilation, that shard will be able to get a lot of representation in the final utility function, and the AI will naturally value humans and want to help humans (even if it will also want to tile a large swathe of the cosmos with paperclips).

A hopefully non-catastrophic value distributions divergence, according to the scheme above. *Source.*

One issue is that the value-humans shard would need to be perfectly aligned with human values, and that’s most of this approach’s promised advantage gone. That’s not much of an issue, though: I think we’d need to do that in any workable approach.

But even if we can do that, I fear this wouldn’t work out even in the path-independent scenario. The Vain Man from 6A, again: over the course of value compilation, the AI might decide that it only likes humanity as an instantiation of some more abstract principle. Which might be something nice like “all possible sapient life”… or maybe it’s more paperclips, and it trades us away like a car for a yacht.^[11]

And then we get into the actually complicated path-dependent meta-cognitive mess (which we have to be ready to deal with, since we don’t know how the last-minute AGI architecture will look), and… I don’t think this is tractable at all. We’d need to follow the AI’s explicit reasoning into superintelligence; it’d be hopeless. Would take decades to understand manually, to reverse-engineer and translate the abstractions it’ll be thinking in.

So I suspect that we won’t be able, in practice, to figure out how to set up some initial proto-values such that they’ll compile into a non-omnicidal utility function. I suspect any plan that hinges on this is doomed.^[12]

My current most promising alignment scheme is as follows:

Train an AI to the point where the GPS forms.
Find a way to distinguish heuristics/proto-value from the world-model and the GPS.
Wipe out every proto-value, eating the cost in effective world-model downgrade.
Locate human values or corrigibility in the world-model (probably corrigibility, see this discussion).
Hook the GPS up directly to it, making the AI an aligned/corrigible wrapper-mind.
Let it bootstrap itself to godhood. The GPS will be able to spin up new heuristics and re-expand the world-model.^[13]

If there are no proto-values leading the GPS astray, there’s no problem. (Those are, by the way, the “unnatural conditions” I’ve mentioned all the way back in Section 2.)

Finding a way to identify learned world-models, or to somehow train up a pure world-model, therefore seem like high-priority research avenues.

Bonus: The E-Coli Test for Alignment

Alright, so an E. coli doesn’t implement a GPS, so it can’t do value compilation on its own. As such, it’s unclear how meaningful it is to talk about its “values”. But an attempt can be made! How we may do it:

Draw a causal graph of the E. coli’s environment, all the natural abstractions included.
Scan the E. coli and back out its “heuristics”, i. e. functions that locate conceptually localized environment features and respond with specific behaviors.
Do path-independent value reflection as described in 6A, or plot out some random value-compilation path and go through it.
Whatever you end up with is the E. coli’s values. They should be highly-abstract enough to be implementable in environments alien to it, as well.

Hm, that was insightful. For one, it appears that we don’t need the agent’s own world-model for path-independent (or random-path) value compilation! We can just get the “true” world-model (if we have access to it) and the heuristics set, then directly compile the final values using it. In essence, it’s just equivalent to getting all the ontological crises out of the way at the start.

What we can do with subjective world-models is compute “impossible fantasy” values — values that the agent would have arrived at if the world really had the structure they mistakenly believe it to have; if the world’s very ontology was optimized for their preferences. (E. g., valuing “spirits” if spirits were a thing.)

10. Future Research Directions

I think this model is both robust to a lot of possible changes, sufficing to describe the dynamics within many categories of agents-generated-by-a-greedy-algorithm, and very sensitive to other kinds of interventions. For example, the existence of some additional convergent data structure, or a different point for the GPS to originate from, might change the underlying path dynamics a lot.

That said, I now suspect that the work on value compilation/goal generalization is to a large extent a dead end, or at least not straightforwardly applicable. It seems that the greedy selection algorithms and the AI itself can be trusted with approximately 0% of the alignment work, and approximately 100% of it will need to be done by hand. So there may not be much point in modeling the value-formation process in detail...

The caveat here is that building a solid theoretical framework of this process will give us data regarding what features we should expect to find in trained models, and how to find them — so that we may do surgery on them. As such, I think the questions below are still worth investigating.

I see two ways to go from here: expanding this model, and concretizing it. Expansion-wise, we have:

Are there any other consistently-formatted internal data structures that agents trained by a greedy algorithm form, in addition to the world-model and the cross-heuristic communication channel? What are they? What changes to the training process would encourage/discourage them?
What causes meta-cognitive heuristics to appear? Are there any convergently-learned meta-heuristics?
Is there any difference between “goals” and “values”? I’ve used the terms basically interchangeably in this post, but it might make sense to assign them to things of different types. (E. g., maybe a “goal” is the local instantiation of a value that the agent is currently pursuing? Like a yacht is for a high-status item.)
Is there a sense in which values become “ever more abstract” as value-compilation goes on? What precisely does this mean?
Where in the agent does the GPS form? (I see three possibilities: either as part of the heuristic conflict-resolution mechanism, within one of the heuristics, or within the world-model (as part of, e. g., the model of a human).)
What’s the minimal wrapper structure and/or set of world-model features necessary to let the GPS “handle itself”, i. e. figure out how to solve the problem of automatically pointing itself at the right problems, no heuristical support necessary?

On the concretization side:

A proof that the world-model would converge towards holisticity. Does it always hold, past some level of environment complexity?
- The “Crud” Factor is probably a good starting point.
A proof that “heuristics” is a meaningful abstraction to talk about.
- Presumably uses the Natural Abstraction Hypothesis as the starting point. Might be fairly straightforward under some environment structure assumptions, like there being mostly-isolated contexts such that you can optimize in them without taking the rest of the world-model into consideration.
- (There’s interesting tension between this and the Crud Factor thing, but it’s probably not an actual contradiction: mapping from observations to the world-model and optimizing in the world-model are very different processes.)
A proof that heuristics aren’t under pressure to become internally intelligible.
Some proofs about the necessary structure of the cross-heuristic communication channel.
Exact specification of the environment structure that can’t be solved without the GPS.
A more formal description of the basic value-formation algorithm.
A more formal description of meta-cognitive heuristics. What does it mean to “bias” the value-compilation process?

^
We’ll return to them in Section 9.
^
This function can be arbitrarily complex, too — maybe even implementing some complex “negotiations” between heuristics-as-shards. Indeed, this is plausibly the feature from which the GPS would originate in the first place! But this analysis tries to be agnostic as to the exact origins of the GPS, so I’ll leave that out for now.
^
And plausibly some shared observation pre-processing system, but I’ll just count it as part of the world-model.
^
Though this is potentially subject to the specifics of the training scheme. E. g., if the training episodes are long, or we’re chaining a lot of forward passes together like in a RNN, that would make runtime-computations more effective at this than the SGD updates. That doesn’t mean the speed prior is going to save us/reduce the path-dependence I’ll go on to argue for here, because there’ll still be some point at which the GPS-based at-runtime reverse-engineering outperforms selection-pressure-induced legibility. But it’s something we’d want fine-grained data on.
^
Second-order natural abstraction?
^
Naively, this process would continue until the agent turns into a proper $U$ -optimizer. But it won’t, because of gradient starvation + the deception attractor. There are other posts talking about this, but in short:
Once $G_{Σ}$ agrees with $U$ in 95% of cases, the selection pressure faces a choice between continuing to align $G_{Σ}$ , and improving the agent’s ability to achieve $G_{Σ}$ . And it surely chooses the latter most of the time, because unless the agent is already superintelligently good at optimization, it probably can’t actually optimize for $G_{Σ}$ so hard it decouples from $U$ .
Then, once the agent is smart enough, it probably has strategic awareness, wants to protect $G_{Σ}$ from the selection pressure, and starts trying to do deceptive alignment. And then it’s in the deception attractor: its performance on the target objective rises sharper as its general capabilities improve (since that improves both the ability to achieve $U$ and the ability to figure out what it should be pretending to want), compared to improving its alignment.
^
Note: This isn’t a precisely realistic example of value compilation, for a… few reasons, but mainly the phrasing. Rather than “smoking” and “using a fabulous fidget toy”, it should really say “an activity which evokes a particularly satisfying mixture of relaxation and self-affirmation”.
There seems to be some tendency for values to increase in abstractness as the process of compilation goes on: earlier values are revealed to be mere “instantiations” of later values, such that we become indifferent to the exact way they’re instantiated (see the cars vs. yachts example). It works if “relax” and “feel cool” are just an instantiation of “feel an emotion that’s a greater-than-its-parts mix of both”, such that we’re indifferent to the exact mix. But they’re not an instantiation of “smoke a cigar”: if smoking ceased to help the person relax and feel cool, they’d stop smoking and find other ways to satisfy those desires.
^
Although I imagine some interesting philosophy out of it.
^
Or maybe not. Something about this feels a bit off.
^
Note that this isn’t the same as my disagreeing with the Shard Theory itself. No, I still think it’s basically correct.
^
You might argue that we can set up a meta-cognition shard that implacably forbids the AI’s GPS from folding humanity away like this, the way something prevents deontologists from turning into utilitarians, or the way we wouldn’t kill-and-replace a loved one with a “better” loved one. I’m not sure one way or another whether that’ll work, but I’m skeptical. I think it’ll increase the problem difficulty dramatically: that it’d require the sort of global robust control over the AI’s mind that we can use to just perfect-align it.
^
One idea here would be to wait until the AI does value compilation on its own, then hot-switch the $G_{Σ}$ it derives. That won’t work: by the point the AI is able to do that, it’d be superintelligent, and it’ll hack through anything we’ll try to touch it with. We need to align it just after it becomes a GPS-capable mesa-optimizer, and ideally not a moment later.
^
One issue I don’t address here is that in order to do so, the GPS would need some basic meta-cognitive wrapper-structure and/or a world-model that contains self-referencing concepts — in order to know how to solve the problem of giving its future instances good follow-up tasks. I’ve not yet assessed the tractability of this. We might need some way to distinguish such structures from other heuristics, or figure out how to hand-code them.

What links here?