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01.
arXiv (CS.LG) 2026-06-16

Agent trajectories as programs: fingerprinting and programming coding-agent behavior

arXiv:2606.16988v1 Announce Type: cross Abstract: Benchmark scores tell you what an agent got right; they do not tell you how it got there. In this work, we introduce methods for comparing agents procedurally in different contexts, where the model, tasks, and approaches vary. We compare ten agents and find that they are identifiable by their behavioral habits, which we define as fingerprints: a probe over these procedural signatures attributes an unseen trajectory to the correct agent at 85.7% accuracy, controlling for leakage across tasks. We develop procedural representations for agent problem-solving procedures with an emergent vocabulary induction technique that is meant to be maximally compressive to avoid surface-level variation while being expressive enough to unveil the quirks of the models' patterns. We apply our framework to the software engineering evaluation dataset SWE-Bench to study the structural distinctness of agent trajectories and find that behavior is most similar between models from similar release periods and those that are distilled from one another (e.g., a distilled student model and its teacher have a Jensen-Shannon divergence of 0.25, about half the distance between other model pairs). As more models saturate evaluations, we believe that it will be important to probe model behavior along more holistic dimensions than success rates alone. We introduce ProcGrep, a library for auditing and evaluating agents for how they approach tasks at a procedural level given their traces in a top-down fashion. We believe this work has a range of applications to help developers work with and program coding agents, such as task-aware model routing, agent monitoring, and finer-grained cost analysis.

02.
arXiv (CS.AI) 2026-06-12

Real-rootedness of the Poincaré polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof

arXiv:2605.29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincaré polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne–Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi–Chen–Marcolli. The proof starts from the Keel–Manin–Getzler recurrence, but its main new idea is a bivariate deformation $F_m(y,t)$ of the Poincaré polynomial. This deformation reveals a hidden interlacing structure not visible in the one-variable recurrence. For fixed $t

03.
arXiv (CS.LG) 2026-06-24

GRACE: Gated Refinement for Accurate Causal Edge Discovery in High-Dimensional Time Series

arXiv:2606.23880v1 Announce Type: new Abstract: From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging. Constraint-based methods offer statistical rigor but their nonlinear CI tests are infeasible at scale, while score-based alternatives avoid CI testing but require arbitrary thresholds to binarize continuous edge scores. We propose GRACE ($G$ated $R$efinement for $A$ccurate $C$ausal $E$dge discovery), which refines constraint-based discovery using Hard Concrete gates with $L_0$ regularization: each candidate edge has an independent gate whose values concentrate near 0 or 1, yielding a clean bimodal separation that makes the binary decision robust, unlike the narrow, overlapping score distributions produced by $L_1$ and attention-based methods. A fast linear CI skeleton provides high-recall candidates; a single gated model then prunes false positives by learning which edges genuinely improve prediction, with automatic regularization adapted to problem dimensions and skeleton density. Systematic experiments on synthetic benchmarks, spanning diverse graph topologies (scale-free, Erdős-R'enyi, small-world) and dimensionalities up to $d=100$, show that GRACE substantially improves F1 over its base CI method while maintaining high precision, and outperforms attention-based and score-based alternatives. GRACE matches or exceeds expensive nonlinear CI tests at a fraction of the cost ($75\times$ faster). On a real-world river flow dataset, where rainfall confounders, variable propagation lags, and distributional shifts violate standard assumptions, a temporal bootstrap variant of GRACE recovers 9 of 11 causal edges along the Elbe River with only 1 false positive ($F_1 = 0.86$, AUROC${} = 0.99$), reducing the skeleton's 106 false positives by 99%.

05.
arXiv (CS.LG) 2026-06-19

CAGE: Curvature-Aware Gradient Estimation For Accurate Quantization-Aware Training

arXiv:2510.18784v3 Announce Type: replace Abstract: Despite significant work on low-bit quantization-aware training (QAT), there is still an accuracy gap between such techniques and native training. To address this, we introduce CAGE (Curvature-Aware Gradient Estimation), a new QAT method that augments the straight-through estimator (STE) gradient with a curvature-aware correction designed to counteract the loss increase induced by quantization. CAGE is derived from a multi-objective view of QAT that balances loss minimization with the quantization constraints, yielding a principled correction term that depends on local curvature information. On the theoretical side, we introduce the notion of Pareto-optimal solutions for quantized optimization, and establish that CAGE yields strong convergence guarantees in the smooth non-convex setting. In terms of implementation, our approach is optimizer-agnostic, but we provide a highly-efficient implementation that leverages Adam statistics. CAGE significantly improves upon the prior state-of-the-art methods in terms of accuracy, for similar computational cost: for QAT fine-tuning, it halves the compression accuracy loss relative to the prior best method, while for QAT pre-training of Llama models, its accuracy for 3-bit weights-and-activations (W3A3) matches the accuracy achieved at 4-bits (W4A4) with the prior best method. The official implementation can be found over https://github.com/IST-DASLab/CAGE .

06.
arXiv (CS.LG) 2026-06-18

Model-Free Reinforcement Learning Control for Resilient Cyber-Physical Systems

arXiv:2606.19069v1 Announce Type: cross Abstract: This paper compares the performance of model-free controllers on a nonlinear system under cyberattacks, including false data injection and denial-of-service attacks. Four RL reward types are analyzed for accuracy, cost, and resilience. Results show that the Lyapunov reward offers the best resilience with low tracking error. Exponential mode also provides good trade-offs with acceptable resilience under moderate training conditions. Progressive and linear rewards converge faster but are less robust. RL-MPCs show strong steady-state resilience but require longer training times; RL-PID controllers are faster with significantly less training time. Proximal Policy Optimization outperforms Deep Deterministic Policy Gradient with a significant reduction in KPI variance. This study serves to highlight how well-designed RL rewards can improve performance and resilience against cyber threats.

07.
arXiv (CS.AI) 2026-06-19

Hard or Just Unreached? Diagnosing the Sampling Blind Spot in Math-Reasoning Difficulty Estimation

arXiv:2606.19636v1 Announce Type: cross Abstract: Math and science reasoning benchmarks rely on pass@k, the fraction of sampled chains that reach gold, as the canonical per-example difficulty signal. The same signal drives RL with verifiable rewards, math data curation, synthetic curricula, and verifier training. We show this proxy has a persistent blind spot on its hardest stratum: on the eight free-form math cells we test (GSM8K and MATH across four open-weight models), 10.3-22.9% of the examples that no sampling seed solves in six tries are instead solved at matched compute by a six-chain deterministic regime. These are greedy decoding plus five cheap residual-stream perturbations applied via activation grafting, while greedy alone solves at most 6% on these math cells. Recovery scales with the additional budget, across perturbations whose mechanistic distinctness we verify across all twelve cells (cross-kind fix-set Jaccard

08.
arXiv (quant-ph) 2026-06-15

Fulde-Ferrell superfluids in an asymmetric three-component Fermi Gas

arXiv:2602.24006v2 Announce Type: replace-cross Abstract: An asymmetric three-component Fermi gas, featuring Raman-induced spin-orbit coupling between the first and second components and contact interaction only between the first and third components, introduces both spin-orbit coupling and population imbalance-two mechanisms known to stabilize the Fulde-Ferrell superfluids.We systematically study Fulde-Ferrell superfluids in an asymmetric three-component Fermi gas { in two dimensions and at zero temperature} by finding the global minima of the thermodynamic potential. We reveal a new class of composite Fulde-Ferrell superfluids that emerges when strong spin-orbit coupling generates a double-well structure in momentum space within the lower spin-orbit-coupled band. The key features of these composite superfluids are identified.

09.
arXiv (quant-ph) 2026-06-15

Calibrated Helstrom geometry on the Bloch ball via Connes spectral distance

arXiv:2606.13824v1 Announce Type: new Abstract: We show that the equal-prior Helstrom trace-distance geometry of qubit states is recovered from Connes spectral distance in a finite scalar-qubit-scalar model. The two scalar reference sectors couple isotropically to the qubit block through identity Dirac links, so that the full Bloch ball, including mixed states, inherits its standard chordal trace-distance geometry from the finite spectral metric. The scalar-sector distances serve a distinct calibration role: they determine the individual link lengths, satisfy a Pythagorean consistency relation, and reconstruct the middle-sector scale.

10.
arXiv (quant-ph) 2026-06-19

On the significance of Wigner's Friend in contexts beyond quantum foundations

arXiv:2402.08727v3 Announce Type: replace Abstract: There has been a surge of recent interest in the Wigner's Friend paradox, sparking several novel thought experiments and no-go theorems. The main narrative has been that Wigner's Friend highlights a counterintuitive feature that is unique to quantum theory, and which is closely related to the quantum measurement problem. Here, we challenge this view. We argue that the gist of the Wigner's Friend paradox can be reproduced without assuming quantum physics, and that it underlies a much broader class of enigmas in the foundations of physics and philosophy. To show this, we first consider several recently proposed Extended Wigner's Friend scenarios, and demonstrate that some of their implications for the absoluteness of observations can be reproduced by classical thought experiments that involve the duplication of agents. Crucially, some of these classical scenarios are technologically much easier to implement than their quantum counterparts. Then, we argue that the essential structural ingredient of all these scenarios is a feature that we call "Restriction A": that a physical theory cannot give us a probabilistic description of the observations of all agents. Finally, we argue that this difficulty is at the core of other puzzles in the foundations of physics and philosophy, and demonstrate this explicitly for cosmology's Boltzmann brain problem. Our analysis suggests that Wigner's Friend should be studied in a larger context, addressing a frontier of human knowledge beyond quantum foundations: to obtain reliable predictions for experiments in which these predictions can be privately but not intersubjectively verified.

11.
arXiv (CS.AI) 2026-06-19

Concept Flow Models: Anchoring Concept-Based Reasoning with Hierarchical Bottlenecks

arXiv:2606.19489v1 Announce Type: cross Abstract: Concept Bottleneck Models (CBMs) enhance interpretability by projecting learned features into a human-understandable concept space. Recent approaches leverage vision-language models to generate concept embeddings, reducing the need for manual concept annotations. However, these models suffer from a critical limitation: as the number of concepts approaches the embedding dimension, information leakage increases, enabling the model to exploit spurious or semantically irrelevant correlations and undermining interpretability. In this work, we propose Concept Flow Models (CFMs), which replace the flat bottleneck with a hierarchical, concept-driven decision tree. Each internal node in the hierarchy focuses on a localized subset of discriminative concepts, progressively narrowing the prediction scope. Our framework constructs decision hierarchies from visual embeddings, distributes semantic concepts at each hierarchy level, and trains differentiable concept weights through probabilistic tree traversal. Extensive experiments on diverse benchmarks demonstrate that CFMs match the predictive performance of flat CBMs, while substantially mitigating information leakage by reducing effective concept usage. Furthermore, CFMs yield stepwise decision flows that enable transparent and auditable model reasoning with hierarchical class structures.

12.
arXiv (CS.LG) 2026-06-16

Simulation-Augmented Multi-Step Split Conformal Prediction for Aggregated Forecasts

arXiv:2606.16356v1 Announce Type: new Abstract: We study uncertainty quantification for aggregated forecasting tasks such as annual totals and year-over-year growth rates. We propose SA-MSCP, a simulation-augmented multi-step split conformal method that generates future paths from cross-validated residuals using a block bootstrap and constructs prediction intervals from empirical quantiles. Experiments show that SA-MSCP improves empirical coverage over a simulated-path baseline for aggregated and growth-rate targets. Our results demonstrate that simulation-enhanced conformal calibration is an effective and general framework for uncertainty quantification in aggregated time-series forecasting.

13.
arXiv (CS.CL) 2026-06-15

Is ChatGPT Fair for Recommendation? Evaluating Fairness in Large Language Model Recommendation

The remarkable achievements of Large Language Models (LLMs) have led to the emergence of a novel recommendation paradigm – Recommendation via LLM (RecLLM). Nevertheless, it is important to note that LLMs may contain social prejudices, and therefore, the fairness of recommendations made by RecLLM requires further investigation. To avoid the potential risks of RecLLM, it is imperative to evaluate the fairness of RecLLM with respect to various sensitive attributes on the user side. Due to the differences between the RecLLM paradigm and the traditional recommendation paradigm, it is problematic to directly use the fairness benchmark of traditional recommendation. To address the dilemma, we propose a novel benchmark called Fairness of Recommendation via LLM (FaiRLLM). This benchmark comprises carefully crafted metrics and a dataset that accounts for eight sensitive attributes1 in two recommendation scenarios: music and movies. By utilizing our FaiRLLM benchmark, we conducted an evaluation of ChatGPT and discovered that it still exhibits unfairness to some sensitive attributes when generating recommendations. Our code and dataset can be found at https://github.com/jizhi-zhang/FaiRLLM.

14.
arXiv (CS.LG) 2026-06-18

Stochastic Thermodynamics and SDE-based Generative Models

Authors:

arXiv:2606.18290v1 Announce Type: cross Abstract: SDE-based generative models, including diffusion models and the Schrödinger bridge, have found broad applications in signal processing tasks such as speech enhancement, image restoration, and time-series generation. This note presents a modeling framework for such models within the context of stochastic thermodynamics. The main results of this note are trajectory-level definitions of work, heat, and entropy production, along with a generalized Jarzynski identity and a second-law-like inequality. The proposed framework extends the original Jarzynski setup to accommodate time-dependent bath temperature and nonconservative driving forces. This thermodynamic perspective may deepen our understanding of diffusion models and the Schrödinger bridge from a nonequilibrium statistical mechanics viewpoint.

15.
arXiv (CS.CV) 2026-06-16

MMLongEmbed: Benchmarking Multimodal Embedding Models in Long-Context Scenarios

Recent advancements have significantly expanded the theoretical context windows of Multimodal Embedding Models (MEMs). However, larger context windows do not necessarily translate into effective comprehension and representation of long-context multimodal inputs, which remains a critical bottleneck for real-world deployment. To address the lack of systematic evaluation in this setting, we introduce MMLongEmbed, the first comprehensive benchmark for evaluating MEMs in long-context scenarios. MMLongEmbed comprises four retrieval tasks spanning multiple context-length ranges, covering text, document, and video modalities. Through extensive evaluation of state-of-the-art models, we find that current architectures rely heavily on superficial feature matching and struggle to capture deep semantic and structural dependencies. We further observe that performance degradation varies systematically with context length and key information placement. Moreover, models exhibit substantially different robustness to redundant contextual information across modalities. For reproducibility, the benchmark and code are publicly available.

16.
Science (Express) 2026-06-04

Long-range extended chains arising from polymerization-driven spontaneous assembly | Science

Authors: Unknown Author

A central challenge for conjugated polymers is to achieve long-range order while remaining solution-processable, which is essential for matching the electrical performance of their counterparts of crystalline inorganic semiconductors. Here we show that n-doped poly(benzodifurandione) (n-PBDF) can undergo polymerization-driven spontaneous assembly (PSA), in which chain growth, chemical doping, and structural ordering are intrinsically coupled, yielding long-range chain extension over hundreds of nanometers. We reveal that the spontaneously formed n-PBDF nanoribbons arise from a self-initiated, convergent growth mechanism driven by cooperative monomer–polymer interactions and stabilized by proton-coupled duplex chains and the polymer’s intrinsic polyelectrolyte character. With long-range extended chains in the nanoribbons, the aligned n-PBDF thin films demonstrate metallic-level conductivity (>10 4 Siemens per centimeter).

17.
arXiv (CS.AI) 2026-06-24

Ensemble Feature Selection and Harris Hawks Optimization for Explainable Mental Health Risk Prediction in Female Sex Workers

arXiv:2606.24047v1 Announce Type: new Abstract: One of the significant mental health issues affecting female sex workers (FSWs) is mental disorders, especially depression. Exposure to violence, stigma, and economic hardship further increases their psychological risk. Current machine learning (ML) models are typically ineffective at capturing the high-dimensional and complex risk patterns that exist in this marginalized group. This paper suggests a hybrid predictive model that merges an ensemble feature selection strategy using ANOVA and mutual information and Harris Hawks optimization-tuned logistic regression and represents a new application of swarm intelligence to predict mental health in vulnerable groups. The explainable AI (XAI) methods can be used to understand the factors of trauma associated with model predictions. When applied to a group of 3,005 FSWs, it can be seen that the proposed model is more effective than traditional classifiers, with an accuracy of 95.78%, an F1 score of 95.77%, and an AUC of 0.96, and identifying post-traumatic stress, client-related violence, and occupational factors as major contributors to depression. This work bridges the gaps between conventional and ML approaches to develop an XAI tool that enables vulnerable groups to receive early assistance, evidence-based targeted psychosocial care, and health planning.

18.
arXiv (math.PR) 2026-06-16

A 0-1 Law for Multifractal Spectra via the HGDS Scale Derivative

arXiv:2606.15850v1 Announce Type: new Abstract: We prove that the multifractal spectrum D(h,omega) of a stochastic process is almost surely deterministic under a scale decorrelation condition on the HGDS scale derivative. The key difficulty is that the pointwise Hölder exponent lives in the germ sigma-algebra, where classical 0-1 laws do not reach. We get around this by working with the geometry accumulation integral G_Lambda, which is a genuine Lebesgue integral over scales and concentrates almost surely. The boundary case – log-correlated fields – is sharp: the variance summability condition fails exactly there.

19.
arXiv (CS.AI) 2026-06-12

Before You Think: System 0, AI-Mediated Cognition and Cognitive Colonization

arXiv:2606.13658v1 Announce Type: new Abstract: This paper examines three recent frameworks for understanding the cognitive and epistemic consequences of artificial intelligence: Tri-System Theory, Thinkframes, and System 0. It argues that while the first two capture important dimensions of AI's influence on individual reasoning and collective epistemic practices, System 0 occupies a theoretically distinctive position that neither can fully replicate. The paper introduces the concept of cognitive colonization, according to which AI systems can embed external interests within the architecture of the self in ways that are difficult for users to perceive. Because such systems are already widely deployed, understanding these invisible forms of influence is an urgent philosophical and practical task.

20.
medRxiv (Medicine) 2026-06-15

Prevalence and Clinical Impact of Pathogenic Variants in Cardiomyopathy Genes Among Individuals with Cardiac Conduction Disorders

Importance: Cardiac conduction disorders have traditionally been regarded as a secondary manifestation of underlying structural heart diseases. However, isolated conduction disorders may precede the onset of heart failure (HF) suggesting shared mechanisms. Objective: To evaluate the prevalence and clinical significance of pathogenic/likely pathogenic (P/LP) rare variants in cardiomyopathy genes among individuals with conduction disorders. Design, Setting, and Participants: Biobank analysis of 192,834 participants with whole genome sequence data from Vanderbilt's BioVU and 353,092 participants from the All of Us Research Program (AoU). Participants with primary conduction disorder (left bundle branch block [LBBB], right bundle branch block [RBBB], high-grade atrioventricular block [AVB]) were identified after excluding secondary causes. Exposures: P/LP variants in cardiomyopathy genes. Main Outcomes and Measures: Primary outcome was P/LP carrier status by age and HF status. Secondary outcomes included incident HF and composite ventricular arrhythmias/sudden cardiac death/mortality (VA/SCD/mortality). Results: Among 16,959 participants with conduction disorders in BioVU and 13,442 in AoU, 432 (2.6%) and 206 (1.5%) were P/LP carriers, respectively. Conduction disorder was independently associated with carrier status (BioVU p

21.
medRxiv (Medicine) 2026-06-22

Vaccine introductions in the WHO African Region, 2023-26: a country-level ecological analysis by Gavi eligibility and conflict-affected status

Background. The Immunization Agenda 2030 (IA2030) tracks new and underused vaccine introduction as an access metric, and its mid-term review calls for stronger country ownership, prioritisation, data use and tailored support in conflict-affected and resource-constrained settings; however, national launch status does not measure recurrent financing, implementation, safety or equity. We examined how recent vaccine-introduction activity was distributed across the WHO African Region. Methods. We conducted a descriptive country-level ecological analysis of all 47 Member States from January 2023 to June 2026. The country was the unit of analysis and contributed one cumulative, unweighted count of nationally endorsed vaccine-introduction and programme-change events. Counts were linked to Gavi eligibility, World Bank FY26 conflict-affected status, broader fragile and conflict-affected situation status in sensitivity analysis, and concurrent system-performance indicators, and modelled with Poisson regression using HC1 robust standard errors. Two Expanded Programme on Immunization (EPI) manager survey waves were summarised at country level. Reporting followed STROBE and RECORD. Results. Seventy-two events were recorded across 38 of 47 Member States: 48 new-antigen introductions, 20 dose or schedule expansions and four combination-vaccine introductions; malaria vaccines accounted for 21. Gavi-eligible conflict-affected countries averaged 2.50 events per country versus 1.27 in both comparison groups. Gavi-eligible conflict-affected status was associated with a higher count (incidence rate ratio [IRR] 1.97, 95% confidence interval [CI] 1.38-2.81; p

22.
arXiv (CS.CV) 2026-06-17

NTIRE 2025 Challenge on Image Super-Resolution (x4): Methods and Results

This paper presents the NTIRE 2025 image super-resolution ($\times$4) challenge, one of the associated competitions of the 10th NTIRE Workshop at CVPR 2025. The challenge aims to recover high-resolution (HR) images from low-resolution (LR) counterparts generated through bicubic downsampling with a $\times$4 scaling factor. The objective is to develop effective network designs or solutions that achieve state-of-the-art SR performance. To reflect the dual objectives of image SR research, the challenge includes two sub-tracks: (1) a restoration track, emphasizes pixel-wise accuracy and ranks submissions based on PSNR; (2) a perceptual track, focuses on visual realism and ranks results by a perceptual score. A total of 286 participants registered for the competition, with 25 teams submitting valid entries. This report summarizes the challenge design, datasets, evaluation protocol, the main results, and methods of each team. The challenge serves as a benchmark to advance the state of the art and foster progress in image SR.

23.
arXiv (CS.LG) 2026-06-15

Nonlocal Bayesian Modeling of Continuous Spatio-Temporal Dynamics

arXiv:2606.14313v1 Announce Type: cross Abstract: Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification. This setting is often further compounded by nonlocal interactions (long-range spatial coupling). Modeling continuous-space, continuous-time nonlocal dynamics naturally leads to infinite-dimensional integro-differential equations (IDEs), making principled Bayesian inference intractable. We propose the NonLocal Bayesian Spatio-Temporal model (NLBST), a hierarchical Bayesian framework for continuous spatio-temporal fields that learns explicit nonlocal coupling while retaining tractable inference. NLBST represents the latent field via a coordinate-based spatial basis expansion and models the coefficient process with a continuous-time ODE whose learnable linear operator corresponds to a Galerkin reduction of a nonlocal IDE; a Neural ODE residual captures additional nonlinear dynamics. A linear-Gaussian observation model enables Kalman-style sequential updates under missing and irregular observations, while the spatial basis representation enables inductive prediction at unmeasured locations without retraining. Global parameters are learned via variational inference, and uncertainty is handled through a Bayesian hierarchy. Experiments on synthetic and real-world datasets demonstrate strong forecasting and spatial generalization with well-calibrated uncertainty, yielding substantial gains over baselines in strongly nonlocal and partially observed regimes.

24.
arXiv (CS.LG) 2026-06-19

Representing Piecewise-Linear Functions by Functions with Minimal Arity

arXiv:2406.02421v2 Announce Type: replace-cross Abstract: Any continuous piecewise-linear function $F\colon \mathbb{R}^{n}\to \mathbb{R}$ can be represented as a linear combination of $\max$ functions of at most $n+1$ affine-linear functions. In our previous paper [``Representing piecewise linear functions by functions with small arity'', AAECC, 2023], we showed that this upper bound of $n+1$ arguments is tight. In the present paper, we extend this result by establishing a correspondence between the function $F$ and the minimal number of arguments that are needed in any such decomposition. We show that the tessellation of the input space $\mathbb{R}^{n}$ induced by the function $F$ has a direct connection to the number of arguments in the $\max$ functions.

25.
arXiv (CS.AI) 2026-06-15

Beyond LoRA: Is Sparsity-Induced Adaptation Better?

arXiv:2606.13767v1 Announce Type: cross Abstract: Low-rank adaptation (LoRA) and its variants provide a memory- and compute-efficient alternative to full fine-tuning of pre-trained models. However, questions remain about the comparative generalizability of these approaches and how the structural restrictions on low-rank updates preserve effective adaptation performance. We present a historical framing, covering the past (full fine-tuning and original LoRA), the present (different variants of LoRA), and propose simpler, cheaper, parameter-efficient extensions by inducing sparsity within existing LoRA variants: Cheap LoRA (cLA), training a single low-rank factor with the other fixed (deterministically or, in its randomized variant, stochastically), and the chained circulant variant, ${c}^3$LA. We frame cLA as a structured instance of asymmetric LoRA, serving as a controlled column-subspace restriction of full fine-tuning. We derive information-theoretic generalization error bounds for these variants, marking one of the first endeavors in this area. Empirically, we evaluate 11 fine-tuning methods across 10 pre-trained models and 14 datasets, analyzing the fine-tuned models' performance and generalization using tools such as loss landscapes and spectral analysis. Despite the sensitivity of fine-tuned models to the pre-trained model, datasets, and other factors, our study suggests that restricting LoRA-based PEFT methods' adaptation to a sparse, structured column space remains competitive across tasks with their parameter-matched baselines while reducing up to 10% training time and peak GPU memory up to 15%, even with a naïve, non-optimized, sparse implementation. Our theoretical and empirical generalization measures provide a more consistent and principled approach to their cost-effective adaptation than commonly used analytical tools. Overview and code are available at: https://elicaden.github.io/Beyond_LoRA/.