Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.01272

Geometry of Confabulation and Refusal in Small Language Models

Vladimir Kazei
View original source ↗Read source document ↗Export metadata ↓

Abstract

Faced with an unanswerable question, small language models can either refuse or confabulate: confidently produce a wrong answer. Can the hidden state before the first generated token provide a clue? Can we flip confabulations into refusals? I introduce ConfabQA, a 784-item benchmark whose obscure-pre-cutoff category breaks the typical correctness/knowledge-cutoff confound and map the geometry of the hidden state with linear probes, a sparse autoencoder (SAE), and direct optimization of intervention directions. On Qwen3-1.7B and Gemma 2 2B the probe separates upcoming refusals from confabulations well beyond prompt features (+7.4/+16.3 pp); on Llama 3.2 3B the ConfabQA margin is within fold-to-fold spread, but a direct refusal probe on PopQA and TriviaQA recovers +18-25 pp. On Qwen I closely inspect three candidate directions for the refusal vector: probe-recovered, Qwen-Scope SAE feature, and directly optimized. Although the three directions are pairwise 50-81 degrees apart, a push at or below the state's own norm along any of them flips most confabulations into refusal openings dominated by the "As..." family. Forcing the opener without touching the hidden state yields the same one-in-three judged-refusal rate as any push. The opposite push collapses refusals mostly into confabulations, yet leaves originally correct answers intact, so the direction gates the opening speech act rather than the knowledge behind it. Confabulations do not resolve into a concentrated feature in a dictionary or a token signature on Qwen3-1.7B. Scoring every probe on the margin over the strongest of four prompt-feature baselines extracts the hidden state's own contribution. Correctness signal is model-dependent and portable only for Llama 3.2 3B: 81% of the probe's margin over test majority survives transfer between ConfabQA, PopQA, and TriviaQA. Benchmark, judge, and code are released.

Explore related subjects

cs.LGcs.CL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vladimir Kazei. 2026-10-31. Geometry of Confabulation and Refusal in Small Language Models. https://arxiv.org/abs/2611.01272

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Subspace Node Pruning

Node pruning is the art of removing computational units such as neurons, filters, attention heads, or even entire layers to significantly reduce inference time while retaining network performance. In this work, we show that a broad family of importance measures, from activation-based to Fisher-based, share a common quadratic form. Through a lower-triangular change of basis, this form yields a pruning subspace in which entire nodes can be removed while the impact of the lost units is simultaneously recovered via linear least squares. Furthermore, the importance measures within our subspace are decoupled and additive through an orthogonalization of the layer activations, allowing multi-node pruning within layers without interference between importance scores. Our method, Subspace Node Pruning (SNP), outperforms the compared baselines on VGG-16 and ResNet-50 on ImageNet. On OPT-125M and LLaMA-2 7B, SNP matches the state-of-the-art LLM Surgeon at a 40-shot schedule and outperforms it whenever fewer shots are used, all without any retraining after pruning.

cs.LG↗
arXiv2026

On the growth of the parameters of approximating ReLU neural networks

This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal approximation properties under increasing architectures, e.g., in terms of width or depth of the networks, we are concerned with the asymptotic growth of the parameters of approximating networks. Such results are of interest, e.g., for error analysis or consistency results for neural network training. The main result of our work is that, for a ReLU architecture with state of the art approximation error, the realizing parameters grow at most polynomially. The obtained rate with respect to a normalized network size is compared to existing results and is shown to be superior in most cases, in particular for high dimensional input.

cs.LG↗
arXiv2026

Correlations Are Ruining Your Gradient Descent

Natural gradient descent, and the preconditioned optimizers which have followed from it, correct gradient descent by estimating curvature and applying its inverse to the gradient. For any single layer of a deep neural network, this correction can be shown to approximately separate into two factors: one which accounts for correlations in the gradient signal, and one which accounts for correlations in the data arriving at that layer. Herein we show that this second factor can be expressed as a change of basis rather than of curvature and, considered thus, it can be removed from the optimizer entirely and placed within the network itself. Specifically, we show that, once forward weights are corrected, right-sided natural gradient descent can be implemented in a form which has three exactly equivalent forms: a gradient preconditioner, a decorrelating linear transform in the forward pass, or a set of recurrent dynamics in which all updates are Hebbian and rely only upon locally available signals. The (recurrent) decorrelation method we discover aligns closely with proposed methods for inhibitory learning and homeostatic plasticity in the brain. Notably, our transform requires no matrix inverse, no matrix decomposition, and no information beyond that which is available at an individual synapse. It can therefore be applied in distributed and physically constrained systems, including neuromorphic hardware and nervous systems, where existing preconditioners cannot. We demonstrate its effectiveness empirically in convolutional and residual network models while significantly improving a range of approximate biologically plausible methods for credit assignment.

cs.LG↗