🧬 biology

An entropic explanation of insistence on sameness in autism

This paper proposes an information theory-based framework that defines autism as a cognitive limitation in processing environmental properties, explaining the insistence on sameness as a strategy to minimize entropy by restricting unpredictable stimuli to known memories, thereby offering quantifiable metrics and algorithmic guidelines for therapies and robotic caregivers.

Original authors: Przemysław Śliwiński

Published 2026-08-06

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Przemysław Śliwiński

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The Brain's Quest for a Quiet Room

Imagine your brain is like a super-fast video game console that is constantly trying to predict what will happen next. In the world of science, this is often called "minimizing surprise." Think of it like walking through a dark forest: if you know the path, you aren't scared. But if a branch snaps in a spot you didn't expect, your heart races because your brain has to scramble to figure out what's going on. This feeling of "Oh no, I didn't see that coming!" is what scientists call surprise or uncertainty.

Now, imagine a special kind of "distance" between what you see in the real world and what you remember. If what you see matches your memory perfectly, the distance is zero, and you feel calm. If what you see is totally new and your memory has no clue what to do, the distance is huge, and you feel overwhelmed. This paper, written by Przemysław Śliwiński, dives into a specific corner of science where information theory (the math of how we store and send data) meets autism. It asks a big question: Why do some people with autism insist so strongly on things staying exactly the same? The paper suggests that for some, the "distance" between the real world and their memory is so hard to bridge that the only way to feel safe is to make the real world look exactly like what they already know.

The Paper's Big Idea: A Math Map for "Sameness"

This paper proposes a new way to look at autism, specifically focusing on the behavior known as "insistence on sameness"—the need for routines, repetitive actions, and strict order. Instead of just describing these behaviors with words, the author uses a mathematical formula to explain them. The core idea is that the brain of a person with autism (specifically those who are non-verbal and have severe support needs) is trying to solve a very difficult puzzle: how to keep the "entropy distance" as low as possible.

In plain English, the author suggests that for these individuals, the brain's "memory" (let's call it M) and the "real world" (let's call it R) are having a hard time talking to each other. The paper uses a formula, $D_H(R, M) = H(R|M) + H(M|R)$ , which basically measures how much "surprise" and "uncertainty" exists between the two.

$H(R|M)$ is the surprise: "I saw something new, and my memory didn't know what it was."
$H(M|R)$ is the uncertainty: "I saw something, but my memory has too many guesses about what it means."

The paper argues that to stop the feeling of being overwhelmed (which can lead to anxiety or "meltdowns"), the brain tries to minimize this distance. It has two main strategies:

Learn everything: Memorize the whole world so nothing is ever new.
Control the world: Make the world stay exactly the same as what is already in the memory.

The paper suggests that "insistence on sameness" is actually the second strategy in action. It's not just a random quirk; it's a survival tactic. By keeping the environment rigid and predictable, the person ensures that the "surprise" level stays at zero.

The "Nearest Neighbor" Brain

To explain why this happens, the paper builds a model with a few key assumptions about how the brain works in this specific context. Imagine the brain is like a very strict librarian who only uses a "nearest neighbor" rule. When a new book (a stimulus from the world) comes in, the librarian doesn't understand the story or the meaning. They only look at the cover and find the book in the library that looks most similar.

Here is where the paper gets interesting:

No Abstract Meaning: The model assumes the brain doesn't understand abstract ideas like "love," "friendship," or "time." It only understands tangible, physical things. You can't have a memory of "nothing" because "nothing" isn't a physical object you can touch.
The "Snapshot" Memory: Every moment is just a snapshot. The brain doesn't connect dots to make a story; it just stores the snapshot. If you change the order of events, even slightly, it looks like a totally new, scary snapshot because the "nearest neighbor" rule can't find a match.
The Danger of Choices: If you give a person two different paths to walk, the brain gets confused. It doesn't know which one to pick, and that confusion creates "uncertainty." The paper suggests that rigid routines are a way to remove choices entirely, turning a confusing fork in the road into a single, straight path.

What This Means for Therapy and Care

The paper doesn't just stop at theory; it uses this math to create a set of "rules" for how to help. If the goal is to lower the "surprise distance," then therapy shouldn't be about teaching abstract concepts or forcing flexibility immediately. Instead, the paper suggests:

Stick to the Tangible: Use real objects, not pictures or words, because the brain might not connect the picture to the object.
No Shortcuts: If a routine is learned as a long chain of steps, you can't skip a step. Skipping a step makes the whole chain look like a new, scary thing.
Predictable Choices: If you must offer a choice, make the options very distinct so the brain doesn't get stuck guessing.
Self-Stimulation as a Safety Valve: The paper offers a fascinating guess about "stimming" (like hand-flapping or rocking). It suggests these might be a way for the person to generate their own "known" signals. If the outside world is too noisy and unpredictable, making your own predictable movements creates a "comfort zone" where the surprise level is low.

The "Robot" and the "Digital Twin"

One of the most creative parts of the paper is how it suggests we test these ideas. The author admits that testing this on real people is hard and slow. So, they propose a "Turing test-like" approach. Imagine building a "digital twin"—a computer avatar that acts exactly like the person with autism based on these mathematical rules. You could put this avatar in a virtual world and see if it starts insisting on sameness when things get too random. If the robot behaves like the human, it suggests the math model is correct.

The paper also imagines a future where "robotized live-in caregivers" could be programmed with these optimization algorithms. Instead of a human guessing what to do, the robot would calculate the perfect sequence of events to keep the "surprise distance" low, helping the person learn new skills without getting overwhelmed.

What the Paper Says It Doesn't Know

It is important to note what this paper doesn't claim. It doesn't say this is the only reason for autism, nor does it claim to have found a cure. The author is very clear that this is a "functional model," meaning it describes what the brain is doing, not how the biology works under the hood. It focuses specifically on non-verbal individuals with severe needs, so it might not apply to everyone on the spectrum.

The paper suggests that "insistence on sameness" is actually a special case of a general human behavior: everyone tries to minimize surprise. But for people with this specific type of cognitive limitation, the brain is so restricted to tangible, memorized patterns that the only way to minimize surprise is to freeze the world in place.

The Final Takeaway

In the end, this paper offers a new definition of autism: a condition where the brain's cognitive tools are limited to sorting, remembering, and predicting physical things, but cannot handle abstract meanings or flexible changes. When the world gets too chaotic, the brain doesn't have the tools to understand it, so it demands the world stay the same.

The author concludes that if we accept this math-based view, we can design better therapies. Instead of forcing people to be flexible, we can build environments and robots that gently guide them, step-by-step, expanding their "known world" without ever spiking their surprise levels too high. It's a shift from seeing these behaviors as "problems to fix" to seeing them as "smart strategies for survival" in a confusing world.

Technical Summary: An Entropic Explanation of Insistence on Sameness in Autism

Problem Statement
The paper addresses the lack of a precise, mathematically rigorous definition for Autism Spectrum Disorder (ASD), particularly regarding the phenomenon of "insistence on sameness" (stereotyped, repetitive behaviors). Current definitions rely heavily on verbal descriptions and behavioral checklists (e.g., DSM-5), which the author argues are arbitrary and lack a unified theoretical framework. The specific focus is on non-verbal, low-functioning individuals (Level 3 ASD), where the inability to process abstract concepts and the drive to minimize surprise and uncertainty manifest as rigid behaviors. The paper seeks to explain this insistence on sameness not as a primary symptom, but as a consequence of specific cognitive restrictions within an information-theoretic framework.

Methodology
The proposed framework models the cognitive process of an individual with autism using information theory, specifically entropy metrics. The core methodology involves three components:

Entropy Metric: The uncertainty between the environment ( $R$ , a sequence of random stimuli) and the individual's memory ( $M$ ) is quantified by the entropy distance metric:
$D_H(R, M) = H(R|M) + H(M|R)$
Here, $H(R|M)$ represents surprise (the unpredictability of the environment given current memory), and $H(M|R)$ represents uncertainty (the unpredictability of the memory given a new stimulus). The goal of the system is to minimize this metric.
Stimuli Processing Loop: The cognitive process is modeled as a loop with two phases:
- Perception: The individual observes a stimulus $r_n$ . If the surprise $H(R|M)$ exceeds a threshold $T_{so}$ , sensory overload occurs.
- Prediction: The individual predicts the next state based on the stimulus. If the uncertainty $H(M|R)$ exceeds a threshold $T_a$ , anxiety occurs.
- Classification: Stimuli are processed via a nearest-neighbor algorithm ( $m_n = \rho(r_n)$ ), meaning new stimuli are classified only by their similarity to existing memory items.
Cognitive Assumptions (A1–A4): The model operates under strict constraints specific to the target population:
- Stimuli are raw, random signals without abstract semantics (e.g., "nothing" or "trust" cannot be represented).
- Memory is limited to storing and retrieving tangible sequences; inference is restricted to replication of memorized patterns.
- Classification relies solely on perceptible properties, ignoring hierarchy, importance, or abstract relations.
- Thresholds for overload and anxiety are random variables, varying by individual and time.

Key Contributions
The paper offers both theoretical and practical contributions:

Theoretical: It redefines autism as an impairment where cognitive functions are restricted to the discrimination, memorization, and prediction of tangible properties of the environment. It posits that "insistence on sameness" is a behavioral strategy to minimize the entropy distance $D_H(R, M)$ by constraining the environment ( $R$ ) to match the known memory ( $M$ ), rather than learning new environmental patterns.
Practical: It translates these cognitive constraints into a set of design guidelines (G1–G5) for learning therapies and daily care. These guidelines treat therapy as a constrained optimization problem, allowing for the formulation of algorithms for robotic live-in caregivers.
Validation Strategy: It proposes a "Turing test-like" approach (V2) for validation. Instead of direct clinical trials with individuals (which are difficult to standardize), the framework suggests creating "digital twins" (avatars) in virtual environments to simulate and validate the behavioral predictions against therapist observations.

Results and Analysis
The analysis demonstrates how minimizing the entropy metric explains specific autistic behaviors:

Pedantry and Routine: Strict adherence to known sequences reduces $H(R|M)$ to zero, eliminating surprise.
Ritualistic Behavior: Stemming from the inability to ignore irrelevant items (due to the nearest-neighbor classification), leading to a focus on all tangible details.
Rigidity and Aversion to Learning: New stimuli introduce high uncertainty ( $H(M|R) = H(M)$ ). To avoid anxiety, the individual restricts $R$ to the known set $M$ , rejecting new options.
Self-Stimulation: The paper conjectures that self-stimulatory behaviors (e.g., hand flapping) generate low-entropy, predictable internal stimuli, keeping surprise and uncertainty within a "comfort zone" when external stimuli are too chaotic.
Optimization Formulation: Learning therapy is formulated as finding a sequence of stimuli $R$ that maximizes mutual information $I(R; M)$ (learning new vital activities) while strictly satisfying the constraints $H(R|M) < T_{so}$ and $H(M|R) < T_a$ .

Significance and Claims
The paper claims that if validated, this framework provides a formal foundation for understanding autism that moves beyond descriptive language.

Unified Explanation: It unifies concepts such as sensory overload, anxiety, comfort zones, and rigidness under a single principle: the minimization of surprise and uncertainty via entropy reduction.
Therapeutic Design: It enables the creation of "optimization algorithms" for therapy, specifically for robotic caregivers, ensuring that new activities are introduced only when the entropy constraints are met.
Definition of Disorder: It proposes a new definition: Autism is an impairment where cognitive functions are restricted to tangible properties, making the "insistence on sameness" a rational response to cognitive limitations rather than a pathological deviation.
Modesty: The author acknowledges limitations, noting that the model is functional and does not define biological implementation. It explicitly limits its scope to non-verbal, low-functioning individuals to maintain formal accuracy and avoids applying the model to higher-functioning individuals who may process abstract concepts. The framework requires further validation through the proposed digital twin experiments.