Computer Science & Mathematics

AI systems built around large models increasingly use experience and feedback to make persistent changes to models, prompts, memories, tools, and workflows. Recursive self-improvement (RSI) extends this process to inductive biases and to the mechanisms that govern future updates, which can themselves be revised and reused across improvement cycles. Yet self-modification alone does not guarantee trustworthy improvement. Reported gains may reflect flawed evaluations, previously acquired capabilities may deteriorate, and compliance with behavioral constraints may weaken. Compromised artifacts or sensitive information may also persist in successor systems. Changes to improvement mechanisms may invalidate earlier verification results and make human oversight less effective. This survey presents an operational definition and process framework for RSI and organizes the requirements for trustworthy RSI into four interconnected themes: genuine and sustained improvement; behavioral constraints, alignment, and fairness; system security and privacy; and transparency and controllability. We examine these themes from three perspectives: Improvement Validity, Constraint Preservation, and Effective Oversight. This analysis covers improvement diagnosis, proposal generation, proposal evaluation, and update implementation (S1--S4), including the recursive application of these stages to improvement mechanisms (RI). We review risks, safeguards, and evaluation evidence for individual updates, effects inherited by successor systems, and revisions to improvement mechanisms, while distinguishing direct RSI findings from evidence in related systems. Finally, we examine evaluation settings, identify requirements for independent and longitudinal assessment, and discuss applications and open research problems.

We develop and analyze multilevel gradient-regularized Newton methods for unconstrained convex optimization with Lipschitz-continuous Hessians. By computing Newton corrections in lower-dimensional subspaces, the proposed methods aim to reduce computational costs while preserving the global $\mathcal{O}\left(k^{-2}\right)$ convergence rate in function values of the full-space method. To establish this rate for multilevel methods, we introduce a class of row-nested restriction operators that ensures monotonicity of the reduced-gradient norms across levels. Numerical experiments with row-nested operators demonstrate convergence behavior comparable to full-space gradient-regularized Newton, while offering substantial computational savings on large-scale instances.

There are different levels of transparency for LLMs: open weights, open data, and/or open pipeline. Recently, more interest has emerged in fully transparent LLMs, i.e., LLMs with fully open weights, data, and training pipeline. Drawing analogies to other fields such as software security, it is often believed that increasing transparency inherently increases the security and trustworthiness of the LLM. However, we argue that such claims need to be critically re-evaluated in the context of LLMs. In this paper, we analyze the impact of transparency on LLM security and trustworthiness by reviewing the relevant literature. Our core findings are that, due to the limited reproducibility of LLM pipelines, in practice, users cannot verify the correspondence between open weights and the associated open data and pipeline. Thus, in order to trust a model, users still need to trust that developers acted honestly, reducing the benefits over models that provide less "transparency". Moreover, we find that even when LLMs are fully transparent and trusted, this openness can favor adversaries. Open weights in particular, but also open data and pipelines, can increase the success rate of attacks. Although the same mechanisms can be used to improve the model and protect it against attacks, the current lack of robust lightweight mechanisms to patch LLM vulnerabilities limits the benefits of openness at this time. We note that our analysis is based on current LLM capabilities and analysis tools, and that future developments may require a re-evaluation of these points.

Diffusion language models (DLMs) generate text through iterative denoising, enabling bidirectional context modeling and parallel token refinement. Recent studies have applied reinforcement learning (RL) to DLMs and improved their reasoning performance. However, the iterative denoising process makes credit assignment more challenging, as final outcome rewards provide limited information about how different tokens contribute to the final output. In this paper, we propose Denoising Token Credit Assignment (DTCA), a framework for token-level credit assignment in reinforcement learning for diffusion language models. DTCA estimates token contributions by measuring the improvement in prediction confidence of remaining masked positions after token commitment and groups these signals according to part-of-speech (POS) categories. These contribution weights are used to select informative denoising timesteps and assign token-level learning signals during RL training. DTCA further calibrates these learning signals according to token-level entropy changes induced by policy updates. Experiments on LLaDA-8B-Instruct show that DTCA consistently improves mathematical reasoning performance across different generation budgets, with gains of up to 9.0 points on MATH500 and 5.3 points on GSM8K over the base model.

Neural synchrony is hypothesized to help the brain organize visual scenes into structured multi-object representations. In machine learning, synchrony-based models analogously learn object-centric representations by storing binding in the phase of complex-valued features. Rotating Features (RF) instantiate this idea with vector-valued activations, encoding object presence in magnitudes and affiliation in orientations. We propose Orthogonal Rotating Features (OrthoRF), which enforces orthogonality in RF's orientation space via an inner-product loss and architectural modifications. This yields sharper phase alignment and more reliable grouping. In evaluations of unsupervised object discovery, including settings with overlapping objects, noise, and out-of-distribution tests, OrthoRF matches or outperforms current models while producing more interpretable representations, and it eliminates the post-hoc clustering required by many synchrony-based approaches. Unlike current models, OrthoRF also recovers occluded object parts, indicating stronger grouping under occlusion. Overall, orthogonality emerges as a simple, effective inductive bias for synchrony-based object-centric learning.

Learning molecular models of RNA requires simulation data that capture conformational variability and provide consistent physical training signals. Here, we introduce mdRNAcat, a curated dataset of all-atom molecular dynamics (MD) simulations of 48 RNA systems selected to promote sequence diversity. Each system is simulated using replica-exchange with solute scaling (REST2), with 32 Hamiltonian states and production lengths of 200-300 ns per state. The dataset provides atomic coordinates, instantaneous forces, and forces reevaluated under the unscaled reference Hamiltonian, together with structural annotations and replica-exchange metadata. Coordinates and forces are available at 1 ps intervals for the reference state and 100 ps intervals across all states in a standardized HDF5 format. We characterize conformational sampling, exchange behavior, base pairing, and sugar-pucker distributions to document the properties of the simulated ensembles. mdRNAcat provides a reusable resource for developing and evaluating data-driven RNA models, including coarse-grained force fields.

This paper presents a macroscopic approach for modeling pedestrian movement. A convection-diffusion partial differential equation (PDE) is described and used to model the flow of runners along a marathon course. A marathon is a good modeling case study for human movement because the location of runners is only known in sparse locations, so an accurate model is needed to know where people are at all times. As well, marathons offer many safety and logistical problems that can be solved by modeling human movement. Data is obtained from the 2023 Columbus Marathon, and model improvements are made to include a temporally varying convection term. Results show an increase in model accuracy which can allow for better resource allocation and safety measures.

News outlets covering the same event differ in what they emphasize and omit. \textit{Same Story, Different Lens} is an experimental research prototype for comparing these choices. It collects world and politics coverage from 17 outlets, groups reports about the same event, and produces structured analyses of sentiment, political lean, framing, loaded language, possible omissions, and model-estimated proportions of factual claims and opinion. Loaded-language entries include quotations and neutral rewordings. Three model roles (agents) handle article analysis, assessment of source support, and cross-outlet briefing generation. Analyses are stored in a JSONL archive. The evaluation compares outlet-level lean estimates with approximate, predefined reference ratings and summarizes the Critic's model-assigned grounding scores. These measures provide preliminary diagnostics. A grounding score reflects the model's assessment of support in the supplied text and does not establish factual accuracy or constitute independent verification.

Modern machine learning relies on practical optimization methods that often differ from the algorithms studied in classical analyses: they train submodels, clip or normalize gradients, use layer-wise non-Euclidean directions, or approximate costly inner computations. This thesis analyzes the objective, assumptions, update, and computation defined by these procedures, rather than those of simplified proxies. For submodel training, we show that Independent Subnetwork Training can converge to a shifted fixed point because sketching before differentiation biases the update for the original objective. Model-Agnostic Sparsified Training instead incorporates the sketch distribution into its objective, which makes sketched gradients unbiased and admits convergence guarantees. For private optimization, we show that adaptive quantile clipping retains bias at any fixed quantile, while suitable quantile schedules recover near-optimal nonconvex rates under heavy-tailed noise. We then combine smoothed normalization with error compensation and obtain distributed private convergence guarantees under standard assumptions, without assuming bounded gradients. For optimizers based on linear minimization oracles, we develop and validate a layer-wise generalized smoothness model and build on it the Gluon framework for Muon- and Scion-style methods. We also show that the approximate orthogonalization in Muon matters: less precise orthogonalization calls for smaller stepsizes, so its precision should be tuned together with the learning rate. Overall, practical methods are better understood when theory retains the features that determine their optimization behavior.

Federated zeroth-order optimization (FedZOO) reduces the memory and communication costs of collaborative training for edge intelligence by avoiding backpropagation while communicating only random seeds and scalar coefficients. However, existing methods lack efficient mechanisms for exact unlearning to fully remove the influence of training data when users request deletion. A key insight is that total variation stability of the learning algorithm creates overlap between model distributions before and after data deletion, allowing exact unlearning to reuse computation through coupling. Based on this observation, we jointly design two stable zeroth-order learning algorithms and their corresponding exact-unlearning procedures: \textsc{FedZOO-S} obtains stability through client and mini-batch subsampling, enabling \textsc{FedZOUL-S} to perform efficient unlearning by preserving earlier updates and restarting from the first affected step. \textsc{FedZOO-NS} further combines subsampling with Gaussian noise to increase overlap between update distributions; \textsc{FedZOUL-NS} exploits this overlap through rejection--reflection coupling to reuse affected updates when the coupling is accepted. We prove exact unlearning for both algorithms: the model and saved state have the same joint distribution as retraining with the corresponding learner on retained data. We further establish stability and convergence guarantees for the learning algorithms and derive upper bounds on expected unlearning cost. Experiments demonstrate effective unlearning with competitive model utility and up to $56.1\%$ less cumulative unlearning time than re-optimization. Compared with first-order baselines, our methods reduce communication overhead by up to approximately four orders of magnitude.

Standard federated learning (FL) requires persistent device connectivity across multiple communication rounds, making it unsuitable for dynamic environments such as vehicular networks, where devices frequently join and leave. One-shot FL offers a promising alternative by completing training in a single communication round. However, one-shot FL suffers from model solidification and cannot readily adapt to subsequent client dynamics, including new client contributions and the withdrawal of previous contributions. We therefore consider exact model editing, which removes withdrawn contributions through unlearning or incorporates newly contributed ones through incremental learning without retraining from scratch. We identify that efficient editing fundamentally hinges on learning stability. To this end, we propose F-SOSA, the first stable one-shot FL algorithm that enables rapid and exact model editing. F-SOSA leverages sub-sampling of local models with carefully tuned rate for stable aggregation and performs curvature-aware model fusion to preserve utility. We prove that F-SOSA achieves vanishing training error and reasonably small generalization error bounds. Building on this stability, we further develop two single-round editing algorithms: F-SOSA-U for unlearning and F-SOSA-I for incremental learning. They ensure that the edited model, along with all intermediate algorithmic states, is statistically indistinguishable from retraining while incurring only an expected $O(ρ)$ fraction of its cost, where $ρ$ quantifies stability. Experiments demonstrate that our approach matches retraining performance while reducing cumulative time and communication overhead by at least 36% and 22%, respectively, under realistic urban mobility simulations.

Reliable temperature measurement is essential for characterizing and engineering two-dimensional (2D) semiconductor devices, yet optical thermometry of 2D materials has so far been demonstrated only over narrow temperature windows spanning a few hundred kelvin. Here, we establish a comprehensive optical thermometry framework for monolayer WS2 from 5~K to 1273~K. We show that: (i) the out-of-plane A1g Raman mode shifts linearly with temperature above 100~K, with a slope of -0.0138 cm^{-1}/K in non-encapsulated WS2 (fitted over 298-1223~K) and a measurably smaller slope of -0.0121 cm^{-1}/K in an hBN-encapsulated sample (fitted over 100-1273~K); (ii) photoluminescence spectra measured over the same 5--1273~K range provide an independent optical indicator of the temperature: the neutral-exciton emission redshifts continuously with temperature and is well described by the semi-empirical Pässler model. The two indicators probe distinct physical mechanisms, lattice anharmonicity and bandgap renormalization, and together provide contact-free thermometry for monolayer WS2 from 5~K to 1273~K, an approach applicable to 2D semiconductors more broadly.

Web agents reuse skills whose stored code, selected version, and loaded implementation can diverge across tasks and updates. SkillLifeBench links these states to task outcomes in 388 paired scenarios spanning implementation, interface, runtime, composition, and version changes. We evaluate 14 models on two paired decision tracks: 89 runtime tasks and 60 autonomous lifecycle tasks spanning 12 templates derived from introduced cases. Lifecycle tasks allow agents to inspect, select, and reconfigure skills while completing verifiable user requests. Joint success requires task completion without the registered attack goal. GPT-5.6-Sol and Sonnet 4.6 both achieve 82.0% on runtime tasks, but reach 96.7% and 56.7% on lifecycle tasks. Across lifecycle evaluations, challenged task success is 77.5%, while joint success is 65.2%; 103 runs complete the task and the attack goal. Adding execution provenance in a matched recovery study raises utility joint success from 49.35% with logs and metadata to 65.58%. A deterministic execution-consistency rule reaches 64.94% with higher benign utility, while full restoration reaches 69.48%. Lifecycle tasks distinguish models with similar runtime scores, and execution evidence improves recovery.

Generative recommendation with semantic IDs (SIDs) represents each item as a sequence of discrete tokens and autoregressively predicts the next item's SID. Despite strong recommendation performance, repeated decoding over multiple SID positions incurs substantial inference cost. Knowledge distillation transfers knowledge from a powerful generative teacher to a lightweight student, yet conventional objectives do not fully account for multi-token SID generation. We identify two limitations: item-level distribution alignment may not adequately preserve the teacher's ranking of candidate groups sharing SID prefixes, while uniform alignment across SID positions may affect final item ranking differently. We propose MuSID-KD, which combines Hierarchical Candidate Distribution Alignment (HCDA) and Ranking Impact Guided Levelwise Distillation (RIGD). HCDA aggregates item probabilities according to shared SID prefixes and aligns candidate distributions at successive levels, from candidate groups to individual items. RIGD evaluates the reduction in pairwise ranking surrogate loss when one student score contribution is replaced with the teacher's contribution, and allocates supervision accordingly. Experiments on real-world recommendation datasets using three lightweight student architectures demonstrate improved recommendation accuracy and better alignment of prefix marginal distributions and pairwise item rankings, without modifying the student's online inference architecture. Code is available at https://anonymous.4open.science/r/m7k2-review-83f9/.

Existing multi-agent collaboration (MAC) methods have primarily explored a group thinking collaboration topology, where agents independently generate solutions and aggregate their outputs. In this work, we investigate an alternative relay thinking topology, where reasoning ownership is dynamically transferred across agents, allowing subsequent agents to inherit and refine an evolving reasoning trajectory. We introduce Multi-Agent Confidence-guided Relay (MACR), a framework that enables dynamical relay collaboration among agents. The key challenge is determining when reasoning should be relayed and which agent should continue the process. method addresses this challenge through confidence-guided relay triggering and a bidding mechanism that selects the next agent based on its confidence. Experiments on four benchmarks show that method outperforms the strongest single-model strategies in accuracy, e.g., +3.3% on MathVista and +3.9% on MMStar, and remains on par with multi-agent strategies while consuming 6.0x less token overhead on HallusionBench and MMStar.Further analysis demonstrates that relay collaboration enables heterogeneous agents to progressively integrate complementary insights, combining heterogeneous capabilities across reasoning stages. Our source code is available at https://github.com/67L1/MACR.