#01Jul 22, 2026
cs.LG
The Blessing of Dimensionality: How Near-Orthogonality in High-Dimensional Spaces Explains Temporal Portability
Abigail Woodring, Adrian Chan, Rana Muhammad Shahroz Khan and 3 more
Fine-tuning has been widely used to adapt large language models (LLMs) for domain-specific tasks. Parameter efficient fine-tuning (PEFT) methods such as low-rank adaptation (LoRA) are frequently used to reduce computational costs. PortLLM is a training-free and data-free scheme used to adapt LLMs after continual pretraining. Although the initial PortLLM results show that LoRA patches exhibit short-term temporal portability, the long-term performance of PortLLM across several updates of continual pretraining remains underexplored. Furthermore, the intriguing effectiveness of PortLLM is not well understood from a theoretical standpoint. We address these two open questions by (1) performing an extensive empirical study of the long-term temporal portability of PortLLM patches across 10 continual pretraining steps using base models Mistral, Gemma, and Qwen; and (2) offering two theoretical analyses to explain our observation that the simple PortLLM method achieves competitive performance. We find empirically that the portability persists across longer time duration, indicating that repeated fine-tuning is not required when the base model is periodically updated. We find theoretically that near-orthogonality of high-dimensional vectors is a key justification for temporal portability. Our analyses also demonstrate a geometric perspective of the loss landscape in facilitating the theoretical comparison of different adaptation options.
#02Jul 22, 2026
cs.CL
surprisal is Not a Theory
Andrés Buxó-Lugo, Aniello De Santo, Morgan Grobol and 2 more
Surprisal Theory is often characterized as a computational-level explanation per (Marr, 1982). We argue in this work that, even though a computational level narrative has been used to support "representation-agnostic research" within computational psycholinguistics, the movement toward black box systems embodied by large language models (LLMs) does not exempt modelers using the surprisal metric from the representational decisions required by computational-level characterizations. In fact, we argue that the uncritical use of LLM-surprisal obfuscates the representational and algorithmic-level commitments of different models. In three analyses, we show that the choice of algorithm and model architecture play significant roles in the computation of language model probabilities. We advise that researchers who wish to test Surprisal Theory re-evaluate the practice of treating large language model probabilities as interchangeable
#03Jul 22, 2026
cs.CL
Exposure is Optional: Learning Unlike Coordination in Language Models
Jiamu Luo, Shane Steinert-Threlkeld
Coordination, a fundamental linguistic structure, remains a subject of intense debate, and its exact nature continues to elude theoretical linguistics. A common view holds that only same-category constituents can be conjoined, which has been challenged by the many grammatical unlike coordinations found in natural language. Treating language models as a computational testbed, we investigate whether the acquisition of unlike coordination requires direct exposure in the training data, or whether it can emerge organically from general compositional abilities. Using Filtered-Corpus Training (FiCT), we train GPT-2 models on corpora from which all instances of unlike coordination have been removed. We find that direct exposure is not necessary: models trained on filtered data successfully generalize to unlike coordination, achieving perplexity and grammaticality judgments comparable to models trained on unfiltered text. Furthermore, our analyses of internal representations indicate that language models process unlike coordination by treating the conjoined elements as belonging to similar structural categories or through a mechanism akin to deletion, both of which appear learnable from exposure to alike coordination alone. This work contributes to the growing understanding of how language models internally represent linguistic structures, while also adding to the broader debate on coordination by showing how models generalize and process unlike coordination without direct exposure.
#04Jul 22, 2026
cs.LG
The Quadrilateral Loss: Additivity as a Measurable Behavior of Dense Neural Networks
Antonio Di Cecco
Additive models buy interpretability by forbidding feature interactions, a constraint that neural instantiations enforce architecturally. We introduce the quadrilateral loss, a differentiable penalty that treats additivity as a measurable behavior instead: a second-order mixed difference on pairs of training points swapping one coordinate, which vanishes if and only if the coordinate carries no interaction, remains informative for piecewise-linear networks, and equals in expectation the per-coordinate interaction mass of the interventional Shapley-GAM. The loss turns additivity into a dial - most learned interactions prove removable almost for free, and on small datasets a moderate penalty improves accuracy and additivity simultaneously - and into an online observable: its per-feature surrender curves show, across seeds and datasets, that pre-regularization interaction magnitude barely predicts what a regularized model retains, undermining post-hoc interaction rankings. Against this instrument we compare routes to exact additivity, spanning structural masks, behavioral penalties (optionally crystallized into exact structure), weight decay, backfitting, the shared-section model, and bagged boosted stumps: constraining behavior before structure dominates weight-space constraints, rankings reverse between data regimes, and converging routes agree on the shape functions themselves. Three silent failure modes we document share one anatomy: guarantees imported into settings that quietly void their preconditions.
#05Jul 22, 2026
cs.CL
Notes to Self: Can LLMs Benefit from Experiential Abstractions?
Chang Liu, Xinyu Li, Artur Dubrawski
Humans distill experience into reusable abstractions, e.g., strategies and cautionary reminders, and apply them to gradually solve problems more effectively. We study whether Large Language Models (LLMs) can similarly benefit from such experiential abstractions. From LLMs' solution traces on the MATH training set, a stronger teacher or the LLMs themselves extract natural-language abstractions into a retrievable library. We explore two usage modes: (1) inference-time retrieval and (2) reinforcement learning (RL) with abstraction-augmented training prompts. Experiential abstractions improve LLM performance on mathematical and logical reasoning benchmarks. Self-extracted abstractions match teacher-extracted ones, and our abstraction usage framework can transfer to other datasets and models. These findings suggest LLMs can extract and apply experiential abstractions much as humans leverage distilled experience.