Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.24029

Do Knowledge and Reasoning Oriented Benchmarks Induce Stable Representation Signatures in LLMs?

Parsa Rahimi·Azim Dehghani Amirabad
View original source ↗Read source document ↗Export metadata ↓

Abstract

Internal signatures could support monitoring, adaptive computation, and mechanistic analysis, but benchmark prompts can be separable without any shared computational distinction. We test whether a prespecified knowledge/reasoning label defines a reusable internal signature in five contemporary 7B to 31B models. We treat the \textbf{task} as the unit of inference probes hold out complete tasks, labels are permuted across tasks, and the best layer and stream are reselected for every permutation. Raw probes recover an eight-versus-eight-subject MMLU partition in all five models (macro-F1 $0.78$--$0.81$), but prompt text predicts it nearly as well: under an identical probe configuration, the activation advantage is only $0.017$--$0.070$ macro-F1 and is not significant. At the prespecified $0.01$ level, lexical adjustment removes significance while the adjusted states still identify individual subjects, and the selected site changes across task panels and selection rules. Additionally, two released base-training trajectories show no common direction. These pooled layerwise measures recover the task label but identify no transferable knowledge/reasoning signature at the tested sensitivity, which cannot exclude moderate effects. The resulting protocol gives future internal monitors and intervention studies a sequence of tests to pass. Project page: \url{https://parsa-ra.github.io/lmbehave/}.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Parsa Rahimi, Azim Dehghani Amirabad. 2026-10-16. Do Knowledge and Reasoning Oriented Benchmarks Induce Stable Representation Signatures in LLMs?. https://arxiv.org/abs/2610.24029

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

KEEP EXPLORING

Related papers

arXiv2026

Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing work that combines DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior and the empirical distribution of the generated samples can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods. Our code is available at the following Github repository~\url{https://github.com/HaoxuanSteveC00/AFDPS-TMLR}.

cs.LG↗
arXiv2026

Optimal hypersurface decision trees

Optimal decision trees have attracted increasing attention in recent years, yet existing algorithms face two closely related challenges. First, the trees they construct have limited expressivity because their splitting rules are typically restricted to axis-parallel splits or binary features. Second, these algorithms generally scale poorly to large datasets. These challenges compound one another: more expressive splitting rules increase the combinatorial complexity of the search space, making the resulting optimal decision tree (ODT) problem even more difficult to solve. Building on the proper decision tree framework of \citet{he2025odt}, we propose, to the best of our knowledge, the first algorithm for constructing optimal decision trees with hypersurface splits. The algorithm has worst-case work complexity $O\left(K!K N^{KG+1}\right)$ when $N\geq K$ and fixed-dimensional feasibility tests are treated as constant-cost operations, where $G=\binom{D+M}{M}-1$ depends on the hypersurface polynomial degree $M$ and the data dimension $D$. Its structure is naturally amenable to vectorization and parallelization, enabling efficient execution on GPUs, and the generic algorithm design can be used to accelerate other ODT variants, such as axis-parallel decision (ADT) trees. We further develop a safe pruning strategy that substantially reduces the number of candidate configurations and an incremental generation procedure that reduces the associated feasibility-checking cost from $O(K^2)$ to $O(K)$.

cs.LG↗
arXiv2026

SPRINT: Stochastic Performative Prediction With Variance Reduction

Performative prediction (PP) is an algorithmic framework for optimizing machine learning (ML) models where the model's deployment affects the distribution of the data it is trained on. Compared to traditional ML with fixed data, designing algorithms in PP converging to a stable point -- known as a stationary performative stable (SPS) solution -- is more challenging than the counterpart in conventional ML tasks due to the model-induced distribution shifts. While considerable efforts have been made to find SPS solutions using methods such as repeated gradient descent (RGD) and greedy stochastic gradient descent (SGD-GD), most prior studies assumed a strongly convex loss until a recent work established $O(1/\sqrt{T})$ convergence of SGD-GD to SPS solutions under smooth, non-convex losses. However, this latest progress is still based on the restricted bounded variance assumption in stochastic gradient estimates and yields convergence bounds with a non-vanishing error neighborhood that scales with the variance. This limitation motivates us to improve convergence rates and reduce error in stochastic optimization for PP, particularly in non-convex settings. Thus, we propose a new algorithm called stochastic performative prediction with variance reduction (SPRINT) and establish its convergence to an SPS solution at a rate of $O(1/T)$. Notably, the resulting error neighborhood is independent of the variance of the stochastic gradients. Experiments on multiple real datasets with non-convex models demonstrate that SPRINT outperforms SGD-GD in both convergence rate and stability.

cs.LG↗