Manifold Recovery as a Benchmark for Text Embedding Models

Lennart Finke

Inspired by recent developments in the interpretability of deep learning models and, on the other hand, by dimensionality reduction, we derive a framework to quantify the interpretability of text embedding models. Our empirical results show surprising phenomena on state-of-the-art embedding models and can be used to compare them, through the example of recovering the world map from place names. We hope that this can provide a benchmark for the interpretability of generative language models, through their internal embeddings. A look at the meta-benchmark MTEB suggest that our approach is original.

Reviewer's Comments

Reviewer's Comments

Arrow
Arrow
Arrow

Nora Petrova

Good idea and simple approach which generalises easily across embedding models and concepts. May be worth exploring more abstract concepts, as concrete concepts like places have been explored before!

Minh Nguyen

Novel approach!

Mateusz Jurewicz

Really interesting project! It investigates an important question regarding the human-interpretability of an AI model's learned representations and does so via an ML-interpretability framing. The paper provides multiple visualizations that make it very easy to grasp the core concept and the discussion shows a lot of ideas on how to extend the presented work. The author also endeavours to refer to existing scientific sources to ground their exploration. Additionally, a code repository is provided for reproducibility (although a readme or some jupyter notebooks would be lovely if you'd like to make things easier for the reader). I would be very interested to see the work extended by using other vector similarity metrics, dimensionality reduction techniques and perhaps adding an intervention, e.g. changing the country or zip code of a given address and seeing how that influences the manifold or where it moves a given entry.

Jason Hoelscher-Obermaier

Very interesting project idea and great execution!   The manifold perspective could have great potential and should be explored further. I am not entirely whether, at the current state of exploration, the proposed approach goes far beyond what’s done in “LANGUAGE MODELS REPRESENT SPACE AND TIME” by Wes Gurnee & Max Tegmark (https://arxiv.org/pdf/2310.02207). Further work should make the differences clearer.

Jacob Haimes

I have to say, I love this idea! It seems incredibly valuable to examine an intermediary output of the typical language model system flow using the many techniques that have been established in multivariate analysis and visualization. In the future work, which I most definitely want to see, I would be particularly interested in finding applications of these techniques that are motivated by AI ethics and safety; perhaps this stream can be used to analyze biases in an novel manner, or can address a specific problem relevant to regulation. As a final note, I think that it would be valuable to provide a more explicit interpretation of what various results mean throughout the paper. For example, in the map of Italy, what does clustering of color imply? What about continuity? What are the practical implications of difference between the text-embedding-3 and Jina AI V2 plots? In general, I think that you do a great job suggesting the answers to these questions, but in some cases, laying out your takeaways might be really beneficial for the reader.

Esben Kran

Utilizing real world interpretable manifolds as the baseline for the benchmark is a stroke of genius and seems to be a highly generalizable technique. I'm very very curious about interpretability benchmarks and this seems like a clear milestone. By interpreting forward passes from the residual stream as text embeddings and expanding the dataset to include non-geographic concepts, next steps can potentially make this into a useful model-agnostic benchmark. I'm highly interested in more work happening on this and hooking it up to existing work within the field of mechanistic interpretability attempting to quantify the interpretability of a model (e.g. https://arxiv.org/abs/1806.10758 on first search).

Cite this work

@misc {

title={

Manifold Recovery as a Benchmark for Text Embedding Models

},

author={

Lennart Finke

},

date={

5/26/24

},

organization={Apart Research},

note={Research submission to the research sprint hosted by Apart.},

howpublished={https://apartresearch.com}

}

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

Jul 28, 2025

Momentum–Point-Perplexity Mechanics in Large Language Models

This work analyzes the hidden states of twenty different open-source transformer language models, ranging from small to medium size and covering five major architectures. The key discovery is that these models show signs of "energy conservation" during inference—meaning a certain measure combining changes in hidden states and token unpredictability stays almost constant as the model processes text.

The authors developed a new framework inspired by physics to jointly analyze how hidden states and prediction confidence evolve over time. They propose that transformers' behavior can be understood as following certain mechanical principles, much like how physical systems follow rules like conservation of energy.

Their experiments show that this conserved quantity varies very little between tokens, especially in untrained (random-weight) models, where it's extremely stable. In pre-trained models, the average energy drops more due to training, but there are larger relative fluctuations from token to token.

They also introduce a new method, based on this framework, for controlling transformer outputs by "steering" the hidden states. This method achieves good results—producing completions rated as higher in semantic quality, while still maintaining the same kind of energy stability.

Overall, the findings suggest that viewing transformer models through the lens of physical mechanics gives new, principled ways to interpret and control their behavior. It also highlights a key difference: random models behave more like balanced systems, while trained models make quicker, more decisive state changes at the cost of less precise energy conservation.

Read More

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

Jul 28, 2025

Local Learning Coefficients Predict Developmental Milestones During Group Relative Policy Optimization

In this work, we investigate the emergence of capabilities in reinforcement learning (RL) by framing them as developmental phase transitions. We propose that the individual components of the reward function can serve as direct observables for these transitions, avoiding the need for complex, derived metrics. To test this, we trained a language model on an arithmetic task using Group Relative Policy Optimization (GRPO) and analyzed its learning trajectory with the Local Learning Coefficient (LLC) from Singular Learning Theory. Our findings show a strong qualitative correlation between spikes in the LLC—indicating a phase transition—and significant shifts in the model's behavior, as reflected by changes in specific reward components for correctness and conciseness. This demonstrates a more direct and scalable method for monitoring capability acquisition, offering a valuable proof-of-concept for developmental interpretability and AI safety. To facilitate reproducibility, we make our code available at \url{github.com/ilijalichkovski/apart-physics}.

Read More

Jul 28, 2025

AI agentic system epidemiology

As AI systems scale into decentralized, multi-agent deployments, emergent vulnerabilities challenge our ability to evaluate and manage systemic risks.

In this work, we adapt classical epidemiological modeling (specifically SEIR compartment models) to model adversarial behavior propagation in AI agents.

By solving systems of ODEs describing the systems with physics-informed neural networks (PINNs), we analyze stable and unstable equilibria, bifurcation points, and the effectiveness of interventions.

We estimate parameters from real-world data (e.g., adversarial success rates, detection latency, patching delays) and simulate attack propagation scenarios across 8 sectors (enterprise, retail, trading, development, customer service, academia, medical, and critical infrastructure AI tools).

Our results demonstrate how agent population dynamics interact with architectural and policy design interventions to stabilize the system.

This framework bridges concepts from dynamical systems and cybersecurity to offer a proactive, quantitative toolbox on AI safety.

We argue that epidemic-style monitoring and tools grounded in interpretable, physics-aligned dynamics can serve as early warning systems for cascading AI agentic failures.

Read More

This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.
This work was done during one weekend by research workshop participants and does not represent the work of Apart Research.