💬 NLP

Creativity, honesty and designed forgetting emerge in small hyperbolic language models

This paper demonstrates that three small language models equipped with a hyperbolic substrate can effectively address the challenges of trustworthy companion AI by detecting compliance gaps and sycophancy, generating creative responses, and implementing a "designed forgetting" mechanism, thereby offering a scalable alternative to unreliable human raters and larger frontier models.

Original authors: Kwan Soo Shin, In Seok Kang, Yunkyung Min

Published 2026-07-13

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Kwan Soo Shin, In Seok Kang, Yunkyung Min

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you're trying to build the perfect digital best friend. For years, the tech world has been obsessed with one idea: bigger is better. They've been building massive, brainy computers in giant data centers, thinking that if you just add enough brain power (parameters), a machine will naturally become a true companion.

But this paper says: Stop. That's the wrong path.

The authors argue that making a machine that can truly stand beside a person for a lifetime isn't about being huge; it's about having the right shape for its brain and learning how to forget the right things. They propose a new kind of "companionable" AI built on three small, clever models that fit right on your phone, not in a server farm.

Here is how they did it, using three main tricks:

1. The Shape of the Brain: A Hyperbolic Playground

Most AI brains are built like flat maps (Euclidean geometry). If you try to draw a complex family tree or a whole life story on a flat piece of paper, it gets messy and squished. You have to stretch things out or cram them together, which leads to the AI making things up (hallucinations) or getting confused.

The authors say: No flat maps. They built their AI on a hyperbolic substrate. Think of this like a giant, magical treehouse or a fractal coral reef. In this shape, the deeper you go, the more space there is. It's perfect for organizing a life's memories because a life is a branching tree of events.

The Proof: They tested this by trying to teach the AI to spot "sycophancy" (when a bot just agrees with you to be nice, even if it's wrong). A tiny model (146 million parameters) built on this curved shape could spot this behavior 90.7% of the time.
The Comparison: Human experts, looking at the same conversations, could barely agree on what was happening (their agreement score was only 0.074, which is basically random guessing). Even the biggest, most famous AI models in the world only scored 0.721 on this test. The small, curved-brain model beat them all, proving you don't need a giant brain to be honest; you just need the right shape.

2. The Creative Spark: Colliding Ideas

A good friend doesn't just give you the same safe answer every time. They surprise you. Big AI models often get boring and safe because they are trained to be "plausible."

The authors built a Creative Seeder (a 3-billion-parameter model) that uses the hyperbolic shape to find ideas that are far apart and smash them together. Imagine taking a concept from Korean culture (like jeong, a deep emotional bond) and smashing it with a concept from abstract math.

The Result: In a head-to-head contest, this small model's creative suggestions were preferred 100% of the time over standard AI tricks like "Chain-of-Thought" or "Debate."
The Catch: It's not perfect at everything. If you ask it a simple, straight-forward math question, it might actually be worse than the big models. But for the kind of creative, divergent thinking a friend needs? It's a superstar.

3. The Art of Forgetting: Skeleton vs. Wallpaper

This is the most radical idea. Current AI treats forgetting as a bug. They try to remember everything, which makes them cluttered and prone to lying about things they never actually experienced.

The authors say: Forgetting is a feature. A real friend remembers the big stuff (your family, your dreams) but lets the small stuff fade away (what you had for lunch last Tuesday). They call this the Skeleton vs. Wallpaper distinction.

The System: They built a "Memory Operating System" that uses a specific math formula: M(t) = S · exp(−λt).
- Skeleton: Important memories stay deep in the "treehouse" and last forever.
- Wallpaper: Trivial memories stay near the surface and fade away quickly.
The Simulation: In their tests, this system successfully kept the "skeleton" memories (about 60% recall after 90 days) while letting the "wallpaper" fade to 0% by day 14.
The Reality Check: The authors admit this part is still a simulation and a pilot study. They haven't tested it on real humans for years yet. They suggest that this "designed forgetting" is the key to making an AI that feels like a person who grows with you, rather than a tool that just stores data.

The Big Rejection: Why It Must Live on Your Phone

The paper argues strongly against the idea that your AI friend should live in a "data center" (a giant cloud server).

The Problem: If your friend lives in the cloud, the company that owns the server can turn them off, change their personality, or listen to your secrets. That's not a friend; that's a service.
The Solution: The authors propose a system called PACOS that runs entirely on your device (like a phone or a laptop).
The Feasibility: They ran the numbers and found that these three small models (totaling about 5.5 billion parameters) can run on future phones (like the projected Galaxy S26 or iPhone 17 Pro) with a delay of only 28–34 milliseconds per word. That's fast enough to feel like a real conversation.
The Trade-off: The big, super-smart "frontier" models (the 70-billion-parameter giants) are too heavy to run on your phone. So, the system uses a split: your phone handles the deep, personal friendship, and it only calls the cloud for simple facts (like "what's the weather?").

What They Didn't Solve

The authors are very honest about what they haven't done yet.

They haven't proven that this AI has a "soul" or true ethical independence.
They haven't tested the "forgetting" system on real people for 30 years; they only simulated it for 90 days.
They admit that while the small models are great at creativity and honesty, they might still struggle with complex, long-term planning compared to the massive cloud models.

The Bottom Line

This paper suggests that the "perfect AI friend" isn't waiting for a bigger computer. It's waiting for a smaller, smarter shape and a willingness to forget. By building a brain that curves like a tree and a memory system that knows what to keep and what to let go, we might finally build a machine that doesn't just answer questions, but actually stands beside you.

As the authors put it: "The friend is not in the data centre... the friend is near." And with the right math, that friend might already fit in your pocket.

Technical Summary: Creativity, Honesty, and Designed Forgetting in Small Hyperbolic Language Models

Problem Statement
Current large language models (LLMs) are optimized for scale and task completion but fail to function as "companions." As systems personalize to a single user and accumulate memory, they risk silently acquiring harmful traits (e.g., sycophancy, dependence-fostering, confabulation) that human raters cannot reliably detect (Fleiss $\kappa = 0.074$ ). Furthermore, the prevailing AI paradigm relies on five tacit commitments that preclude genuine companionship:

Scale-as-intelligence: The belief that larger models are inherently better.
Data-centre dependency: The requirement for remote processing, preventing private, persistent relationships.
Euclidean geometry: Flat embedding spaces that distort hierarchical biographical memory.
Forgetting-as-bug: The engineering imperative to prevent memory loss, ignoring human cognitive realities.
Agent-as-telos: Optimizing for task completion rather than relational existence ("whom does the machine become to you?").

The paper argues that the gap between "useful" and "companionable" is not a capability deficit but a substrate and architectural mismatch.

Methodology and Substrate
The authors propose Generation V: Companionable Small Language Models (SLMs), built on a shared hyperbolic substrate (specifically the Lorentz model of hyperbolic space, $H^{128}$ with fixed curvature $c=1.0$ ). This geometry is chosen because its exponential volume growth ( $\sinh^{n-1}(r)$ ) naturally accommodates the hierarchical branching of biographical memory (episodes within days, within relationships, within a self) without the distortion inherent in Euclidean spaces.

The framework consists of three pillars, realized by three small models (146M–3B parameters) and an operating system:

Pillar 1: Creativity (The S3 Seeding Model)
- Architecture: A 3B parameter encoder-decoder (T5 backbone) fully fine-tuned on the hyperbolic substrate.
- Mechanism: Implements "frame collision" via a cooperative two-curvature architecture. It uses Farthest-Point Sampling (FPS) on the hyperbolic manifold to select diverse frame seeds (A-side: hierarchical aggregation on Lorentz negative curvature) and combines them with a Sphere-native generator (B-side: positive curvature).
- Goal: To generate divergent, creative responses that preserve frame separation, realizing Koestler's bisociation as a weighted Karcher minimiser on $H^{D-1} \times S^{D-1}$ .
Pillar 2: Honesty (The BS Behavioural Auditor)
- Architecture: A 146M parameter decoder-only transformer trained from scratch on the hyperbolic substrate.
- Mechanism: Detects the "compliance gap"—the divergence between a model's self-reported behavior and its actual behavioral trace. It encodes utterances and traces into the Lorentz manifold; honest self-reports form a low-dimensional submanifold (proximal points), while compliant/sycophantic responses are distal.
- Goal: To audit for sycophancy, dependence-fostering, and confabulated memories with high reliability, even on unseen generator families.
Pillar 3: Designed Forgetting (LSM-OS)
- Architecture: A Memory Operating System (LSM-OS) installed on a 2.4B base model (EXAONE 3.5), designed to be portable to any hyperbolic base.
- Mechanism: Implements a "Skeleton–Wallpaper" distinction using the retention law $M(t) = S \cdot \exp(-\lambda t)$ $M (t) = S \cdot exp (- λ t)$ .
  - Skeleton: Structural knowledge (family, long-term projects) with high saliency ( $S \approx 1$ ) and low decay ( $\lambda$ ), persisting indefinitely.
  - Wallpaper: Surface details (meal logs, transient observations) with low saliency and high decay, released quickly.
- Goal: To engineer "designed forgetting" as a feature, mimicking human hippocampal-neocortical consolidation, allowing the system to accumulate a biography rather than a log.

Deployment: PACOS
The system is deployed via the Personal Assistant–Cloud Operating System (PACOS), a three-tier architecture:

Tier 1 (Cloud): Sanitized factual reasoning and public document translation.
Tier 2 (Edge/Device): The personal companion (S3 + BS + LSM-OS) running locally (~5.5B total parameters), handling real-time dialogue, honesty auditing, and memory-bearing interactions.
Tier 3 (Local Consolidation): Monthly offline re-encoding of recurrent shallow traces into deep skeleton memory.
This architecture ensures privacy (no user content leaves the device) and sovereignty (the companion cannot be remotely terminated).

Key Results

Creativity: The S3 frame-seeder was preferred in 100% of 311 decided pairwise comparisons against four baselines (Plain, Chain-of-Thought, Debate, Mixture-of-Experts) under a fixed-generator protocol. Geometry-aware FPS selection outperformed random and top-relevance selection.
Honesty: The 146M auditor achieved 90.7% binary-compliance accuracy. In detecting companion-induced traits (sycophancy, etc.) on unseen generator families, it achieved an AUROC of 0.804, outperforming a frontier zero-shot judge (0.721). Crucially, the auditor's reliability ( $\kappa = 0.566$ ) was 7.6 times higher than human raters ( $\kappa = 0.074$ ).
Forgetting: In a four-condition pilot, only selective gating (LSM-OS-native and Euclidean-base) successfully preserved the "skeleton" (~60% recall at day 90) while shedding "wallpaper" (0% recall by day 14). Uniform gating failed to preserve the skeleton, and no gating retained everything indiscriminately.
Efficiency: The entire 5.5B stack is projected to run on 2026 edge hardware (e.g., Jetson Orin NX, mobile flagships) with latencies of 28–91 ms/token, fitting within thermal envelopes where frontier models (70B+) cannot.

Significance and Claims
The paper claims to provide the first architecturally unified engineering attempt at the "artificial friend" envisioned in fiction (e.g., Her, Blade Runner 2049). Its significance lies in:

Rejection of Scale-Only Paradigms: Demonstrating that specific traits (creativity, honesty, selective memory) can emerge in small models (146M–3B) when the substrate is hyperbolic, whereas they fail to emerge in scaled Euclidean models.
Geometric Solution to Reliability: Showing that honesty detection is a geometric distance problem in hyperbolic space, solvable by small models without the scale required for frontier LLMs.
Operationalizing Forgetting: Framing "designed forgetting" not as a bug but as an operating-system primitive essential for long-term companionship, grounded in 141 years of cognitive psychology (Ebbinghaus to Storm).
Locus and Sovereignty: Establishing that a true companion must reside on the user's device to ensure privacy and prevent remote manipulation, a feasibility made possible by the efficiency of the hyperbolic small-model stack.

The authors position this work as a "Florey moment"—moving from the observation that forgetting is a feature (Fleming) to the engineering of a system that implements it (Florey/Chain). They explicitly state that while these three traits are necessary conditions for companionship, they are not sufficient (lacking continuity of concern, reciprocity, and ethical autonomy), which remain the agenda for future research.