FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers
Sihan WangJiayi ZhaoQingyan CaoHongbo YaoLin Shu
Aug 2026
Machine LearningNatural Language Processing
Abstract
Activation steering has emerged as a lightweight approach for modifying language model behavior without parameter updates, yet existing methods remain brittle: unstable across layers and prone to disturbing behavior unrelated to the target concept. We trace these failures to a hidden assumption shared by widely-used methods such as CAA, ActAdd, and ITI: that the intermediate activation space is Euclidean. We show this assumption is fundamentally flawed. The metric that actually governs how a hidden-state perturbation changes the output is the Fisher information metric of the softmax layer, pulled back to the intermediate layer through the Jacobian of the intervening layers. From it we derive a closed-form steering direction, applied to a hidden state at an intermediate layer, that reaches a target concept change with the least non-target distortion. The framework is sharpest in the early and middle intermediate layers, where the metric is strongly non-Euclidean and geometric correction matters most. We evaluate it on three verb-morphology concepts: third-person-singular, progressive, and past-tense inflection, following standard counterfactual-concept evaluation. On GPT-2 Small, this non-Euclidean geometry is borne out empirically, and our method lowers off-target KL divergence by median factors of 1.4--6.5x against individual steering baselines. On Llama-3-8B and Qwen3-8B, it lowers off-target KL by median factors of 1.8--3.6x against individual baselines at the early and middle layers. These results show that geometric correction retains its advantage on larger models with more complex internal structure.
This work introduces a pioneering exploration of Self-Supervised Learning (SSL) within the SNN, and proposes a novel Spiking Self-Attention (SSA) and Spiking Transformer (Spikformer) that achieves 80+% accuracy on ImageNet.
Zhaokun Zhou, Kaiwei Che, Wei Fang et al.· arXiv.org· 69 citations· ⚡10
EquiPocket is proposed, an E(3)-equivariant Graph Neural Network for binding site prediction, which comprises three modules: the first one to extract local geometric information for each surface atom, the second one to model both the chemical and spatial structure of protein and the last one to capture the geometry of the surface via equivariant message passing over the surface atoms.
Yang Zhang, Wenbing Huang, Zhewei Wei et al.· International Conference on...· 43 citations· ⚡4
It is shown that the maximum hypergraph density of any multiclass hypothesis class is upper-bounded by its DS dimension, which proves a longstanding conjecture of Daniely and Shalev-Shwartz (2014) and determines the optimal dependence of the sample complexity on the DS dimension for multiclass as well as list learning.
Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct conclusion. Mathematically, a measurement operator is Hermitian with eigenvalues in [0,1]. By noticing that this constraint on each eigenvalue is the same as that imposed on fermions by the Pauli exclusion principle, we interpret every eigenmode of a measurement operator as an independent effective fermionic mode. Under this perspective, various objective functions in quantum hypothesis testing can be viewed as the total expected energy associated with these fermionic occupation numbers. By instead fixing a temperature and minimizing the total expected fermionic free energy, we find that optimal measurements for these modified objective functions are Fermi-Dirac thermal measurements, wherein their eigenvalues are specified by Fermi-Dirac distributions. In the low-temperature limit, their performance closely approximates that of optimal measurements for quantum hypothesis testing, and we show that their parameters can be learned by classical or hybrid quantum-classical optimization algorithms. This leads to a new quantum machine-learning model, termed Fermi-Dirac machines, consisting of parameterized Fermi-Dirac thermal measurements-an alternative to quantum Boltzmann machines based on thermal states. Beyond hypothesis testing, we show how general semidefinite optimization problems can be solved using this approach, leading to a novel paradigm for semidefinite optimization on quantum computers, in which the goal is to implement thermal measurements rather than prepare thermal states. Finally, we propose quantum algorithms for implementing Fermi-Dirac thermal measurements, and we also propose second-order hybrid quantum-classical optimization algorithms.
This systematic review evaluates 55 studies from 2017 to 2023 on the application of machine learning techniques to ASD, highlighting key challenges and opportunities, particularly the need for models that can integrate complex data to improve diagnostic accuracy and treatment outcomes.
Rafael Muñoz-Terol, Jesús Peral, Sandra Amador et al.· Heliyon· 4 citations· ⚡1
This paper identifies two different routes through which models can acquire geometrically separable features: they can learn them from complementary co-occurrence signals in general language data, including text-number co-occurrence and cross-number interaction, or from multi-token addition problems.
New MIT research could lead to better materials for a fossil-fuel-free process for making the chemical that's essential to fertilizer and other products.
MIT News · Artificial Intelligence· news.mit.eduAug 18, 2026
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
