[Paper] Abstract Activation Spaces for Content-Invariant Reasoning in Large Language Models

Source: arXiv

Source: arXiv:2602.02462v1

Overview

Large Language Models (LLMs) excel at generating fluent text, yet they often falter on pure logical deduction, mixing “what sounds right” with “what is logically valid.”

The paper Abstract Activation Spaces for Content‑Invariant Reasoning in Large Language Models proposes a novel approach: insulating the reasoning component of an LLM from the semantic baggage of the input by leveraging the model’s own hidden activations.

Key Contributions

• Abstract Reasoning Space – Introduces a dedicated activation sub‑space that captures structural inference, built from model responses to deliberately “abstract” (content‑free) syllogisms.
• Lightweight Abstractor Modules – Trains tiny feed‑forward networks that map the LLM’s residual‑stream states (the hidden vectors during generation) onto the abstract reasoning space, without fine‑tuning the whole model.
• Multi‑layer Intervention Mechanism – Injects the Abstractor’s predictions back into the forward pass at several layers, steering the model toward content‑invariant reasoning while preserving its language abilities.
• Cross‑lingual Transfer Demonstration – Shows that the same abstractor trained on English syllogisms improves logical performance on French and German test sets, indicating language‑agnostic abstraction.
• Empirical Gains on Validity‑Sensitive Benchmarks – Reduces the classic “content effect” error rate by up to 18 % and raises overall logical accuracy on a standard syllogistic reasoning suite.

Methodology

1. Data Construction – The authors create paired datasets:

   • Content‑laden syllogisms (e.g., “All birds can fly; Penguins are birds; Therefore, penguins can fly”).
   • Abstract syllogisms where the lexical items are replaced by placeholders (e.g., “All X can Y; Z are X; Therefore, Z can Y”).

2. Defining the Abstract Space – They run the LLM on the abstract pairs and collect the residual‑stream activations (the hidden vectors that travel through the transformer). By applying a simple linear projection (PCA/CCA), they isolate a sub‑space that consistently encodes the logical structure regardless of the actual words.

3. Training Abstractors – Small MLPs (≈ 2 M parameters) are trained to predict the abstract‑space representation from the model’s activations on content‑laden inputs. The loss is the distance between the predicted vector and the true abstract vector obtained from the placeholder version.

4. Intervention During Generation – At selected transformer layers, the predicted abstract vector is blended (via a learned gating factor) with the original hidden state before the next layer processes it. This “steering” nudges the model toward reasoning that follows the abstract structure.

5. Evaluation – The system is tested on a benchmark of syllogistic problems in multiple languages, measuring two metrics:

   • Validity Accuracy – Does the answer follow formal logic?
   • Content Effect Ratio – How often does semantic plausibility override logical validity?

Results & Findings

• Content‑invariant reasoning improves dramatically without sacrificing the model’s natural‑language generation quality.
• Cross‑lingual transfer works: an abstractor trained only on English abstract syllogisms still yields sizable gains on French and German, confirming that the abstract space captures language‑agnostic logical structure.
• Lightweight interventions are enough—the full LLM remains untouched, meaning the approach scales to any existing transformer model.

Practical Implications

Developers can integrate the abstractor as a plug‑in layer in existing transformer inference pipelines (e.g., via Hugging Face’s transformers callbacks), enabling logic‑first mode for any downstream task that demands rigorous deduction.

Limitations

• Scope limited to syllogistic reasoning – The current abstraction is built around a narrow logical form; extending it to richer first‑order logic or probabilistic reasoning remains open.
• Dependence on well‑crafted abstract prompts – The quality of the abstract space hinges on the placeholder dataset; noisy or poorly designed abstractions could degrade performance.
• Intervention granularity – Experiments use a fixed set of layers; adaptive selection (e.g., based on attention patterns) could yield further gains.
• Scalability to massive LLMs – Although the Abstractor itself is lightweight, the extra forward‑pass interventions add latency; optimizing for high‑throughput serving is a next step.

Future Work

• Learn abstract spaces jointly with the main model (instead of post‑hoc).
• Apply the method to chain‑of‑thought prompting.
• Explore abstraction for other reasoning modalities such as mathematical problem solving or code synthesis.

Authors

• Fabio Massimo Zanzotto
• Gabriele Maraia
• Leonardo Ranaldi
• Marco Valentino

Paper Information