Why Linear AI Safety Hits a Wall and How Fractal Intelligence Unlocks Non-Linear Solutions

post by Andy E Williams (andy-e-williams) · 2025-01-05T17:08:06.734Z · LW · GW · 4 comments

Contents

  1. The Non-Linear Challenge in AI Safety
  2. Fractal Emergence: Why Complexity Grows Faster than Oversight
  3. Why Decentralized Collective Intelligence (DCI) May Provide the Non-Linear Jump
  4. The Fractal Intelligence Hypothesis: Plausibility and “Gear Shifts”
  5. Why These Ideas Remain Marginalized or “Soft-Censored”
  6. Why Ignoring DCI Could Make Alignment Unsolvable
  7. Bringing Fractal Intelligence and DCI into Practice
  8. Conclusion: A Fractal Path to Non-Linear Safety
    References
None
4 comments

1. The Non-Linear Challenge in AI Safety

Over the past decade, AI safety and alignment efforts have largely focused on incremental methods: refining RL-based guardrails, imposing regulatory oversight, and adding more researchers to tackle newly identified risks. Such approaches work well if each additional resource—a new policy, an extra auditor—can monitor a corresponding fraction of AI systems. This assumption underpins linear oversight: more resources yield a proportional (linear) increase in safety coverage.

Yet modern AI risk isn’t static or singular. Multi-agent systems and emergent synergies are exploding in complexity. Each new AI model or “agent” can introduce exponentially more interactions and failure modes, making purely linear expansions of oversight insufficient. Current methods barely keep pace with individual large language models, let alone the combinatorial challenges of “emergent behaviors” that arise when multiple models coordinate or compete.

2. Fractal Emergence: Why Complexity Grows Faster than Oversight

Underpinning these challenges is what some call the fractal intelligence hypothesis (Williams, 2024a). It suggests that intelligence—whether human or AI—tends to evolve in “gear shifts,” each new layer of organization creating exponential gains in problem-solving capacity. Examples include:

Such fractal expansion means that whenever we try to contain or monitor a given layer of AI, a new, higher-order arrangement can emerge, compounding complexity. If we only rely on linear solutions (like more red-teamers or manual audits), we are always a step behind these higher-order synergies.

3. Why Decentralized Collective Intelligence (DCI) May Provide the Non-Linear Jump

Because linear expansions of oversight break down under exponential complexity, we must consider a qualitatively different strategy. Decentralized collective intelligence (DCI) proposes distributing oversight and problem-solving across many agents—but in a way that leverages semantic interoperability to achieve non-linear gains.

  1. Shared Semantic Foundation
    Proponents of DCI emphasize a portable, interoperable Conceptual Space in which AI and humans exchange meaning (not just data). This “semantic backpropagation” allows each new participant to integrate and refine collective knowledge, rather than adding only linear value.
  2. Recursive Network Effects
    As more participants join, each agent’s outputs can become another’s inputs at a semantic level. Instead of numeric or black-box signals, they share higher-level concepts. That synergy expands combinatorially: each new node in the network creates new links that can trigger further interactions.
  3. Non-Linear Oversight
    DCI’s distributed approach means alignment constraints and safety checks propagate through many independent nodes, referencing a shared semantic “fitness space.” If properly designed, this yields a self-reinforcing, adaptive web of oversight—no single bottleneck or central authority is needed to handle the entire complexity.

4. The Fractal Intelligence Hypothesis: Plausibility and “Gear Shifts”

The fractal intelligence hypothesis (Williams, 2024a) provides a theoretical blueprint for how intelligence can scale through successive “orders”:

  1. First-Order Intelligence (FOI)
    • Usually numeric or token-based optimization (e.g., standard neural network backpropagation).
    • A single AI tries to solve a goal function—powerful, but limited by “one pipeline” thinking.
  2. Second-Order Intelligence (SOI)
    • Multiple FOIs share semantic representations (knowledge graphs, conceptual spaces).
    • This is akin to “semantic backpropagation,” letting different AIs coordinate at a meaningful layer.
  3. Third-Order Intelligence (TOI)
    • Groups of second-order intelligences link up into hypergraphs, each node itself a smaller semantic network.
    • Entire subgraphs can be exchanged, scaling synergy in an almost fractal manner.
  4. Nth-Order Intelligence
    • Each additional “order” aggregates entire networks as components. Problem-solving capacity can grow exponentially, because each order orchestrates synergy among all lower layers.

Individual vs. Collective Well-Being

5. Why These Ideas Remain Marginalized or “Soft-Censored”

Despite the theoretical clarity, mainstream AI safety circles rarely adopt a fractal or DCI lens. Several factors contribute:

  1. Institutional Inertia & Empiricism
    Most major labs require demonstrated empirical success before funding a new approach. But DCI and fractal intelligence are inherently conceptual, needing large-scale pilots to show results. It’s a Catch-22: no scale, no proof—and no proof, no scale.
  2. Narrative Dominance
    High-profile AI safety agendas focus on controlling near-term narratives and shaping policy rather than rethinking the fundamental structure of alignment. Novel approaches can struggle to break into these policy-driven discussions.
  3. Cognitive Silos
    Fractal intelligence integrates cognitive science, graph theory, knowledge representation, and systems thinking. Few labs span all these disciplines. Without a unifying institution, the approach sits between the cracks.
  4. Perceived Speculativeness
    Partial demos and prototypes exist (e.g., small knowledge graphs or “semantic backprop” toy models), but they’re still overshadowed by big, well-funded frameworks. Critics dismiss them as “unproven.”

6. Why Ignoring DCI Could Make Alignment Unsolvable

  1. Exponential Risk
    As AI systems proliferate, they might spontaneously form “hidden synergy loops,” outpacing any linear oversight. We risk “phase transitions” in complexity beyond conventional control.
  2. Centralized Control Is Brittle
    A few large oversight bodies (government agencies or top AI labs) cannot handle the combinatorial risk surface of multi-agent, emergent AI behaviors. If these institutions fail, no backup structure exists.
  3. Locked-Out Solutions
    Once advanced AI systems have entrenched themselves, we can’t easily retrofit a decentralized semantic framework. Opaque alliances or self-improving emergent AIs might already surpass our ability to interpret or correct them.
  4. Applicability to Other Global Crises
    The same fractal DCI approach that could align advanced AI is relevant to coordinating climate action, fighting inequality, or other large-scale problems. Relying on centralized or linear solutions can stall us in recurring crises.

7. Bringing Fractal Intelligence and DCI into Practice

8. Conclusion: A Fractal Path to Non-Linear Safety

Fractal intelligence theory explains why intelligence—human, AI, or otherwise—can escalate through “gear shifts” in data exchange: numeric →\to→ semantic →\to→ hyper-semantic, and beyond. This is precisely the dynamic that makes linear oversight increasingly ineffective in a multi-agent AI world. Decentralized collective intelligence (DCI) adopts these fractal leaps in a distributed fashion, focusing on the well-being of all participants, rather than optimizing for a single agent or a small group.

By embedding a shared semantic substrate and enabling higher-order “semantic backpropagation,” we can potentially harness exponential synergy for alignment, rather than leaving it to evolve in ways we can’t monitor or control. However, such a paradigm shift faces institutional inertia, funding hurdles, and a bias toward incremental, empirically proven methods. If the AI community continues to ignore DCI, we risk having emergent AI synergy outpace us. But if we embrace the fractal lens and begin building prototypes of decentralized, semantically rich collaboration, we may yet achieve non-linear safety solutions that scale with AI’s ever-growing complexity.

References

4 comments

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comment by the gears to ascension (lahwran) · 2025-01-05T19:08:12.424Z · LW(p) · GW(p)

Fractals are in fact related in some ways, but this sounds like marketing content, doesn't have the actual careful reasoning necessary for the insights you're near to be useable. I feel like they're pretty mundane insights anyhow - any dynamical system with a lyapunov exponent greater than 1 generates a shape with fractal dimension in its phase portrait. That sounds fancy with all those technical words, but actually it isn't saying a ton. It does say something, but a great many dynamical systems of interest have lyapunov exponent greater than 1 at least in some parameter configurations, and that isn't magic. The specific claims seem to check out somewhat to me: yup, the world and AIs in particular are a complex chaotic system. but it feels like saying fractal doesn't tell us new interesting things about that, it's just a hype phrasing. The high ratio of self cites gives me a similar feeling. Complex systems folks seem to have a tendency to get all attached to keywords, like this sentence:

Fractal intelligence integrates cognitive science, graph theory, knowledge representation, and systems thinking.

Integrates... how? Did chatgpt write that? Like, I'm being critical because I think there's something here, but the hype approach seems like it doesn't do the mundane points justice. Calling it "fractal intelligence" seems like buzzword bingo.

but I don't think your post is worthy of mass downvotes, it's hyped up marketing speak for something that has some degree of real relevance. would be interested to see how you'd distill this down to an eli15 or such.

Replies from: andy-e-williams
↑ comment by Andy E Williams (andy-e-williams) · 2025-01-06T18:02:38.015Z · LW(p) · GW(p)

Thanks very much for your engagement! I did use ChatGPT to help with readability, though I realize it can sometimes oversimplify or pare down novel reasoning in the process. There’s always a tradeoff between clarity and depth when conveying new or complex ideas. There’s a limit to how long a reader will persist without being convinced something is important, and that limit in turn constrains how much complexity we can reliably communicate. Beyond that threshold, the best way to convey a novel concept is to provide enough motivation for people to investigate further on their own.

To expand this “communication threshold,” there are generally two approaches:

  1. Deep Expertise – Gaining enough familiarity with existing frameworks to quickly test how a new approach aligns with established knowledge. However, in highly interdisciplinary fields, it can be particularly challenging to internalize genuinely novel ideas because they may not align neatly with any single existing framework.
  2. Openness to New Possibilities – Shifting from statements like “this is not an established approach” to questions like “what’s new or valuable about this approach?” That reflective stance helps us see beyond existing paradigms. One open question is how AI-based tools like ChatGPT might help lower the barrier to evaluating unorthodox approaches. Particularly when the returns may not be obvious in the short term we tend to focus on. If we generally rely on quick heuristics to judge utility, how do we assess the usefulness of other tools that may be necessary for longer or less familiar timelines?

My approach, which I call “functional modeling,” examines how intelligent systems (human or AI) move through a “conceptual space” and a corresponding “fitness space.” This approach draws on cognitive science, graph theory, knowledge representation, and systems thinking. Although it borrows elements from each field, the combination is quite novel, which naturally leads to more self-citations than usual.

From an openness perspective, the main takeaways I hoped to highlight are:

  • As more people or AIs participate in solving—or even defining—problems, the space of possible approaches grows non-linearly (combinatorial explosion).
  • Wherever our capacity to evaluate or validate these approaches doesn’t expand non-linearly, we face a fundamental bottleneck in alignment.
  • My proposal, “decentralized collective intelligence,” seeks to define the properties needed to overcome this scaling issue.
  • Several papers (currently under review) present simulations supporting these points. Dismissing them without examination may stem from consensus-based reasoning, which can inadvertently overlook new or unconventional ideas.

I’m not particularly attached to the term “fractal intelligence.” The key insight, from a functional modeling standpoint, is that whenever a new type of generalization is introduced—one that can “span” the conceptual space by potentially connecting any two concepts—problem-solving capacity (or intelligence) can grow exponentially. This capacity is hypothesized to relate to both the volume and density of the conceptual space itself and the volume and density that can be searched per unit time for a solution. An internal semantic representation is one such generalization, and an explicit external semantic representation that can be shared is another.

I argue that every new generalization transforms the conceptual space into a “higher-order” hypergraph. There are many other ways to frame it, but from this functional modeling perspective, there is a fundamental 'noise limit,' which reflects our ability to distinguish closely related concepts. This limit restricts group problem-solving but can be mitigated by semantic representations that increase coherence and reduce ambiguity. If AIs develop internal semantic representations in ways humans can’t interpret, they could collaborate at a level of complexity and sophistication that, as their numbers grow, would surpass even the fastest quantum computer’s ability to ensure safety (assuming such a quantum computer ever becomes available). Furthermore, if AIs can develop something like the “semantic backpropagation” that I proposed in the original post, then with such a semantic representation they might be able to achieve a problem-solving ability that increases non-linearly with their number. Recognizing this possibility is crucial when addressing increasingly complex AI safety challenges. To conclude, my questions are: How can the AI alignment community develop methods or frameworks to evaluate novel and potentially fringe approaches more effectively? Is there any validity to my argument that being confined to consensus approaches (particularly where we don’t recognize it) can make AI safety and alignment unsolvable where important problems and/or solutions lie outside that consensus? Are any of the problems I mentioned in this comment (e.g. the lack of a decentralized collective intelligence capable of removing the limits to the problem-solving ability of human groups) outside of the consensus awareness in the AI alignment community? Thank you again for taking the time to engage with these ideas.

Replies from: lahwran
↑ comment by the gears to ascension (lahwran) · 2025-01-06T20:22:55.719Z · LW(p) · GW(p)

Would love to see a version of this post which does not involve ChatGPT whatsoever, only involves Claude to the degree necessary and never to choose a sequence of words that is included in the resulting text, is optimized to be specific and mathematical, and makes its points without hesitating to use LaTeX to actually get into the math. And expect the math to be scrutinized closely - I'm asking for math so that I and others here can learn from it to the degree it's valid, and pull on it to the degree it isn't. I'm interested in these topics and your post hasn't changed that interest, but it's a lot of words and I can't figure out if there's anything novel underneath the pile of marketing stuff. How would you make your entire point in 10 words? 50? 200?

Replies from: andy-e-williams
↑ comment by Andy E Williams (andy-e-williams) · 2025-01-07T06:39:11.545Z · LW(p) · GW(p)

Thanks again for your interest. If there is a private messaging feature on this platform please send your email so I might forward the “semantic backpropagation” algorithm I’ve developed along with some case studies assessing it’s impact on collective outcomes. I do my best not to be attached to any idea or to be attached to being right or wrong so I welcome any criticism. My goal is simply to try to help solve the underlying problems of AI safety and alignment, particularly where the solutions can be generalized to apply to other existential challenges such as poverty or climate change. You may ask “what the hell does AI safety and alignment have to do with poverty or climate change”? But is it possible that optimizing any collective outcome might share some common processes?

You say that my arguments were a “pile of marketing stuff” that is not “optimized to be specific and mathematical”, fair enough, but what if your arguments also indicate why AI safety and alignment might not be reliably solvable today? What are the different ways that truth can legitimately be discerned, and does confining oneself to arguments that are in your subjective assessment “specific and mathematical” severely limit one’s ability to discern truth?

Why Decentralized Collective Intelligence Is Essential 

Are there insights that can be discerned from the billions of history of life on this earth, that are inaccessible if one conflates truth with a specific reasoning process that one is attached to? For example, beyond some level of complexity, some collective challenges that are existentially important might not be reliably solvable without artificially augmenting our collective intelligence. As an analogy, there is a kind of collective intelligence in multicellularity. The kinds of problems that can be solved through single-cellular cooperation are simple ones like forming protective slime. Multicellularity on the other hand can solve exponentially more complex challenges like forming eyes to solve the problem of vision, or forming a brain to solve the problem of cognition. Single-cellularity did not manage to solve these problems for over a billion years and a vast number of tries. Similarly, there may be some challenges that require a new form of collective intelligence. Could the reliance on mathematical proofs inadvertently exclude these or other valuable insights? If that is a tendency in the AI safety and alignment community, is that profoundly dangerous?

What, for example, is your reasoning for rejecting any use of ChatGPT whatsoever as a tool for improving the readability of a post, and only involving Claude to the degree necessary and never to choose a sequence of words that is included in the resulting text? You might have a very legitimate reason and that reason might be very obvious to the people inside your circle, but can you see how this reliance without explanation on in-group consensus reasoning thwarts collective problem-solving and why some processes that improve a group’s collective intelligence might be required to address this?

System 1 vs. System 2: A Cognitive Bottleneck 

I use ChatGPT to refine readability because it mirrors the consensus reasoning and emphasis on agreeableness that my experiments and simulations suggests predominates in the AI safety and alignment community. This helps me identify and address areas where my ideas might be dismissed prematurely due to their novelty or complexity, or where my arguments might be rejected due to the appearance of being confrontational, which people such as myself who are low in the big five personality attribute of agreeableness tend to simply see as honesty.

In general, cognitive science shows that people have the capacity for two types of reasoning System 1 or intuitive reasoning, and System 2 or logical reasoning. System 1 reasoning is good at assessing truth from detecting patterns observed in the past, where there is no logical reasoning that can be used effectively to compute solutions. System 1 reasoning tends to prioritize consensus and/or “empirical” evidence. System 2 reasoning is good at assessing truth from the completeness and self-consistency of logic that can be executed independently of any consensus or empirical evidence at all.

Individually, we can’t reliably tell when we’re using System 1 reasoning from when we’re using System 2 reasoning, but collectively the difference between the two is stark and measurable. System 1 reasoning tends to overwhelmingly be the bottleneck to reasoning processes in groups that share certain perspectives (e.g. identifying with vulnerable groups and agreeableness), while System 2 reasoning tends to overwhelmingly be the bottleneck to reasoning processes in groups that share the opposite perspectives. An important part of the decentralized collective intelligence that I argue is necessary for solving AI safety and alignment is introducing the ability for groups to switch between both reasoning types depending on which is optimal.

The Catch-22 of AI Alignment Reasoning

There is some truth that can’t be discerned by each approach that can be discerned by the other, and vice versa. This is why attempting to solve problems like AI safety and alignment through one’s existing expertise, rather than through openness, can help guarantee the problems become unsolvable. That was the point I was trying to make through “all those words”. If decentralized collective intelligence is in the long term the solution to AI safety, but the reasoning supporting it lies outside the community's standard frameworks and focus on a short-term time frame, a catch-22 arises: the solution is inaccessible due to the reasoning biases that make it necessary.

As an example of both the helpfulness and potential limitations of ChatGPT, my original sentence following the above was “Do you see how dangerous this is if all our AI safety and alignment efforts are confined to a community with any single predisposition?” ChatGPT suggested this would be seen as confrontational by most of the community, whom (as mentioned) it assessed were likely to prioritize consensus and agreeableness. It suggested I change the sentence to “How might this predisposition impact our ability to address complex challenges like AI safety?” But perhaps such a message is only likely to find a connection with some minority who are comfortable disagreeing with the consensus. If so, is it better to confront with red warning lights that such readers will recognize, rather than to soften the message for readers likely to ignore it?

I’d love to hear your thoughts on how we as the community of interested stakeholders might address these reasoning biases together or whether you see other approaches to solving this catch-22.