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arXiv

Neurosymbolic Discovery of Algebraic Graph Constructions

David Seka, Stefan Szeider

There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators. These methods return the result as raw data: an adjacency matrix or a string encoding. The raw data certifies that the graph exists, but it does not reveal any structural properties of the graph. We ask whether one can automatically discover a short algebraic description if only this raw data is provided. We look for a description such as a Cayley graph $\mathrm{Cay}(Γ, S)$ or a lexicographic product $C_5[K_3]$. We address this question with a neurosymbolic approach. We propose an agent that runs on a general-purpose large language model with no fine-tuning or per-target training. The model interleaves reasoning with calls to the computer algebra system SageMath: it analyzes the target graph, proposes and tests candidate constructions, and revises them until the output matches the target. The agent communicates with SageMath through a Model Context Protocol (MCP) server, which we release as a general-purpose bridge. Whether a construction matches the target is checked by a single exact isomorphism test, and therefore rests on the symbolic side and not on the model. We test the approach on a benchmark of 100 highly symmetric graphs, namely two-orbit graphs on up to 25 vertices; the benchmark was fixed in advance. Our agent could find verified algebraic constructions for all of them, without falling back to raw encodings. A strong template-enumeration baseline reaches only about $20\%$, and a catalog lookup could not identify any of these graphs. However, construction quality declines when symmetry is removed. As a concrete application, we identify the smallest known counterexample to the Bernhart-Kainen dispersability conjecture, a $16$-vertex graph that enumeration found as raw data. For this graph, our agent found an explicit algebraic construction.

arXiv

Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains

Jeeeun Lee, Denis Korolev, Miro Duhovic, Seong Su Kim

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

arXiv

Hierarchical Multi-Task Federated Learning in VANETs

M. Saeid HaghighiFard, Sinem Coleri

Vehicular Ad hoc Networks (VANETs) increasingly rely on federated learning (FL) to enable collaborative intelligence without sharing raw sensory data. However, most existing vehicular FL frameworks assume that all vehicles train a single global model for a common task, which limits their applicability in practical vehicular environments where vehicles may perform heterogeneous learning tasks under non-independent and identically distributed (non-IID) data, intermittent connectivity, and high mobility. To address these challenges, this paper proposes an AutoEncoder-based Reliability-Optimized Hierarchical Multi-Task Federated Learning (AERO-HMTFL) framework for dynamic multi-hop clustered VANETs. The proposed framework introduces a tri-weighted clustering metric that jointly considers vehicular mobility, shared-model similarity, and task affinity to produce mobility-stable, semantically aligned clusters. Each vehicle employs a split-model architecture comprising a shared autoencoder-based representation module and multiple task-specific heads, with only the shared autoencoder parameters exchanged while the task heads remain local. To improve robustness, cluster heads perform reliability-aware aggregation based on historical validation performance and participation frequency, while the Evolved Packet Core (EPC) conducts global shared-autoencoder fusion across clusters. Extensive simulations demonstrate that, compared with the multi-task federated learning benchmarks, AERO-HMTFL achieves up to 13% higher sustained EPC-level accuracy, exhibits more stable learning dynamics, and reduces EPC-level packet transmissions by approximately 87-97%. Under short-range connectivity, it also requires approximately 13-29% fewer communication rounds to converge.

arXiv

Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates

Rui Wu, Zongyuan Chen, Hong Xie

Smooth acyclicity constraints answer whether a weighted support is a DAG, whereas structure learning asks which support change should be made. Existing analyses establish degeneracy for particular constraint formulas but do not isolate what follows from smooth exactness itself. At a DAG boundary, we show that minimal cycle completions generate a squarefree monomial ideal containing every restricted Taylor jet of an exact representation. If the smallest completion has $q$ edges, the first possible response has order $q$ for a vector residual and $2q$ for a nonnegative scalar. Exponentially many constant-scale cyclic manifolds exhibit the same lack of ranking away from the boundary for NOTEARS and DAGMA. We derive the exact selection time for an isolated cycle. When $Ψ'(h)\asymp h^ν$, the feasibility-only time is $T_0(\varepsilon)=Θ(\varepsilon^{-(2ν+1)})$; a score margin changes the leading dynamics at scale $T_0^{-1}$ for $ν>0$, while $ν=0$ has a logarithmic boundary layer requiring $γT_0\log(1/\varepsilon)\to0$. Experiments verify this law, and a truth-free separation statistic predicts selection time on 320 official NOTEARS/DAGMA trajectories (Spearman $-0.52$ and $-0.66$, permutation $p<10^{-4}$). For finite samples, a parent-set confidence family and forced-opposite queries certify skeleton and unshielded-collider labels shared by every population optimum of a frozen score. Across 320 runs, every regret bound covers an independent oracle-score audit. None of 3,042 certified skeleton or 2,396 collider labels disagrees with the oracle-score optimum, although 4.4% and 5.5%, respectively, disagree with the generating graph. These results separate DAG feasibility, score-based support selection, and causal identification.

arXiv

Defending Retrieval-Augmented Intrusion Detection Against Knowledge Poisoning and Prompt Injection

Kaysarul Anas Apurba, Md. Hasibul Hasan, Mahedee Zaman Moon, Sk. Md. Mizanur Rahman, Atsuo Inomata

Retrieval-Augmented Generation (RAG) enables large language models to classify network flows and generate human-readable incident reports by retrieving semantically similar historical traffic from a vector knowledge base. However, the retrieval layer introduces vulnerabilities to knowledge poisoning and prompt-injection attacks. We present RAG-IDS, a three-tier multi-agent intrusion detection framework with a retrieval-boundary defense combining soft trust scoring, label-embedding consistency checking (LECC), and prompt sanitization, designed to recover classification quality under retrieval-layer attack. Experiments on CIC-UNSW-NB15 show recovery relative to clean undefended performance ranging from R=1.0 at 1% poisoning to R=0.57 at 30%, with negligible clean-performance overhead. Under prompt injection, multi-document retrieval limits label-flip success to 0.6-2.4%, compared with 35-55% for single-document retrieval. Ablation results show that LECC is the primary contributor to robustness, while soft trust-based demotion outperforms hard filtering. The defended RAG pipeline offers an explainable, attack-resilient foundation for intrusion detection, well suited for hybrid deployment alongside high-throughput classifiers.

arXiv

RotaryQuant: Fitting 120B MoE Models on Consumer Hardware via Fused Compressed-Space Attention

Anthony. Lui, Mohamed. Elsaied, N. P. Savani

Large mixture-of-experts (MoE) language models with 26--120 billion parameters exceed the memory capacity of consumer devices through three simultaneous pressures: resident weight matrices, key-value (KV) cache state that grows linearly with context, and dozens of expert sublayers that must be paged on demand. We present RotaryQuant, a three-axis compression system that addresses all three. Mixed-precision weight quantization assigns bit-widths by architectural role: 4-bit for dense layers, 2-bit for routed experts, and 8-bit for the shared expert whose high activation kurtosis resists aggressive compression. LRU expert offloading pages non-resident experts to disk under genuine memory pressure. The novel axis is IsoQuant, a KV cache compression method that applies a Walsh--Hadamard transform followed by block-diagonal SO(4) rotations to isotropize activation distributions before 3-bit scalar quantization, requiring $O(d \log d)$ operations and 256 stored parameters per head versus $O(d^2)$ and 16{,}384 for dense rotation methods. A fused four-kernel Metal GPU pipeline performs attention directly on packed 3-bit tensors without materializing full-precision KV state---a different execution model, not just a quantization scheme. The combined system fits Gemma 4-26B-A4B and Qwen3-30B-A3B within a 16\,GB budget and Nemotron-H 120B within 32\,GB, running interactively at 9--19 tok/s with near-zero perplexity degradation ($Δ$PPL $\leq +0.0012$) and 100\% retrieval accuracy at 32K context.

arXiv

PATH: Next-Interval Prediction via Autoregressive Tree Hierarchy on Tabular Data

Pengxiang Cai, Wanchen Lian, Chenyang Liu, Xiaohan Li, Qingyuan Zeng, Jinhong Wang, Jintai Chen

Interval prediction aims to achieve a target coverage level while producing intervals that are as short as possible. Many conformal regression pipelines first predict an uncertainty surrogate and then convert it into an interval through calibration or selection. This separation supports coverage calibration, but post hoc rules largely determine the final interval and do not fully use the learned output distribution. We observe that the resulting intervals have inherently hierarchical geometry: an interval can be recursively refined into nested subintervals, and binary trees naturally represent this structure. We formulate this hierarchy as next-interval prediction and propose PATH, which learns how probability mass flows from each interval to its next nested subintervals. PATH predicts a base leaf distribution and uses an autoregressive decoder to refine branch probabilities. Matching the distribution to the interval hierarchy aligns learning with extraction: PATH accumulates probability over adjacent output intervals and returns the shortest contiguous range reaching a selected mass. We compare PATH with 24 baselines for interval prediction on PATHBench, comprising 56 OpenML regression datasets. PATH substantially shortens the resulting intervals, achieving the lowest mean normalized length, 0.1473, while maintaining mean coverage of 0.9144. These results establish hierarchical output modeling as an effective approach for compact interval prediction on tabular data. Code is publicly available at https://github.com/pxcai/PATH.

arXiv

CLAM: Causal Spatial Disaggregation to Infer Local Effects From Coarse Data

Gerrit Großmann, Sumantrak Mukherjee, Sebastian J. Vollmer

Learning fine-grained spatial patterns from coarse-resolution data is challenging, especially in causal settings where high-resolution effects must be inferred from aggregated interventions and outcomes. We introduce CLAM, a method for estimating localized causal effects from coarse observations by exploiting high-resolution contextual covariates that modulate these effects. By jointly learning the causal mechanism and a disaggregation mapping, CLAM captures interactions that are missed when addressing these problems independently. The method supports localized effect estimation, counterfactual reasoning, and principled outcome disaggregation, and reliably captures spatially varying causal effects across diverse settings. This is particularly relevant for applications such as public health and environmental policy, where decisions are made at broad scales despite substantial local heterogeneity. Code is available at https://github.com/gerritgr/clam

arXiv

A cylindrical neural approximation theorem for conditional laws of McKean-Vlasov equations with common noise

Nacira Agram, Reda Hmioui, Jan Rems

We introduce conditional cylindrical neural networks for approximating functionals of conditional laws in McKean-Vlasov equations with common noise. Fourier moments of the initial law and truncated signatures of the time augmented common noise are mapped by a mixture density network to a Gaussian mixture approximation of the conditional law. A cylindrical neural network then evaluates the target functional through analytic integrals against this predicted measure. Rough path well posedness and stability provide a conditional law map that is continuous in the initial distribution and the rough driver and agrees almost surely with the classical conditional law at the Itô Brownian lift. Combining this continuity with Fourier separation, signature uniqueness, Wasserstein density of Gaussian mixtures, and neural universal approximation, we prove an $L^2$ universal approximation theorem for continuous square integrable functionals. The numerical study implements the resulting two stage procedure on six examples, including non Gaussian initial laws, nonlinear drift, multiplicative common noise, and a two dimensional state. Independent particle references are used when no closed form law is available. The learned conditional law and functional approximations consistently improve on the empirical particle plug in, and additional experiments examine feature sensitivity, training from one terminal observation per common noise scenario, and Itô--Stratonovich consistency.

arXiv

Do All LLMs Know When They're Being Harmful? A Reproducibility Study of Latent-Space Safety Probes Across Model Families

Alizishaan Khatri, Dun Li Chan

Khatri et al. (2026) [DOI: 10.1109/DSN-W70714.2026.00027] show that lightweight MLP probes on final-layer activations of a single 8B model (LLaMA-3.1-8B) detect harmful prompts at F1 competitive with guard models 1000x larger, using one probe per benchmark. We reproduce this pipeline end-to-end and extend it along two axes the original study leaves open. First, we test whether the result generalizes across other model architecture and scale by training identical probes on activations from models like Gemma-4-E4B, Mistral-7B-v0.3, and Qwen2-7B, using the three benchmarks (WildJailbreak, BeaverTails, AEGIS 2.0). Second, we test how much of the reported performance is affected by non-determinism during inference by repeating extraction under five random seeds and measuring the variance of F1 scores. Our results reproduce the original LLaMA model benchmarks within 0.37 percentage points of the original F1 scores (and within 0.2 points on BeaverTails). We find that the original MLP probe architecture extends to other model families with F1 scores within a point of the values reported for LLaMA-3.1-8B. Our experiments varying seed values reveal an interesting observation: final token latent vectors remained the same for all tested architectures irrespective of the seed values used.

arXiv

BASIS: Breach-Aware Selective Prompt Injection Shielding with Prefill Attention Probes

Laiqiao Qin, Tianqing Zhu, Longxiang Gao, Wanlei Zhou

Prompt injection is a critical security threat in large language model (LLM) applications, where attackers hijack model behavior by embedding malicious instructions in user or external data. Existing detection methods only detect the presence of injection and refuse to respond upon detection, overlooking the fact that for many modern aligned models, well-crafted instructions can resist most injection attacks. This means that the injection robustness varies significantly across instructions and models. This leads to widespread unnecessary over-refusal: inputs containing injections that the model could have handled correctly are rejected incorrectly. To deal with this over-refusal issue, we propose BASIS (Robustness-Aware Prompt Injection Defense). This defense method uses the Attention Competition Ratio ($ρ$) as features to train two sparse linear probes: an existence probe and a breach probe. Both probes make defense decisions through cascaded gating, which does not require additional LLM inference. BASIS comprises three stages: injection existence detection, per-sample breach prediction, and instruction robustness assessment; the online cascade refuses only when the model would actually be compromised and thus avoids over-refusal on robust instructions. Experiments across four tasks and six open-source LLMs show that BASIS maintains near-perfect injection detection while substantially reducing over-refusal on safe attack samples, especially under robust instruction templates.

arXiv

Ground-Truth Neighborhood Regularization for Reinforcement Learning Post-Training of Time Series Foundation Models

Jianqi Zhang, Xingyu Zhang, Zeen Song, Changwen Zheng, Fanjiang Xu, Wenwen Qiang

Time series forecasting (TSF) plays an important role in a wide range of real-world applications. Recently, time series foundation models (TSFMs), pretrained on large-scale datasets, have demonstrated strong generalization capabilities and emerged as an important paradigm for TSF. Reinforcement learning (RL) post-training has consequently attracted growing attention as a means of further improving their performance on downstream tasks. However, we find that, in certain forecast regions, RL post-training may gradually shift the output distributions of TSFMs away from the ground truth, thereby limiting their performance. We refer to this phenomenon as \textbf{suboptimal collapse}. Our analysis suggests that difficulty in initially sampling high-quality trajectories near the ground truth is an important contributing factor to suboptimal collapse. To address this issue, we propose Ground-Truth Neighborhood Regularization (GTN-R) for RL post-training of TSFMs. GTN-R uses the ground truth as a reference for locating high-quality regions and guides the model's probability mass toward the ground-truth neighborhood. This increases the probability of sampling high-quality trajectories, mitigates suboptimal collapse, and improves performance. Moreover, GTN-R can be flexibly integrated into various RL methods for TSFMs. Extensive experiments show its effectiveness.

arXiv

Quality-Diversity Stress Tests for Process Reward Models:What Archive Coverage Can and Cannot Certify

Ibne Farabi Shihab, Fariya Afrin

Process reward models (PRMs) score intermediate reasoning steps and are widely used for search, ranking, and training, but optimization can exploit these learned proxies by increasing reward while turning correct reasoning into incorrect reasoning. We formulate PRM stress testing as a quality-diversity search problem using MAP-Elites, retaining the most severe correctness-flipping edit in each behavior-space region while separating search coverage from exploit coverage. We characterize what such archives certify: finite-cell repair bounds covered-cell tail risk and average residual severity but cannot bound the worst remaining cell from covered fraction alone; under Lipschitz post-repair loss and metric-cover auditing, the residual is bounded by archive fitting error plus the Lipschitz constant times the covering radius. A controlled landscape validates this certificate and the impossibility of any fraction-only worst-case guarantee. On real PRMs, the search reveals an aggregation-dependent vulnerability in Qwen2.5-Math-PRM-7B: padding yields 44 strict exploits with maximum gain 0.294 under mean pooling versus one exploit under minimum readout; a matched syntactic control isolates the mechanism, and an RLHFlow value-head model shows the same qualitative effect with maximum gain 0.005. A predeclared paired LoRA repair protocol reduces exploit rates from 0.148 to 0.037 to 0.074, lowers the worst attack from 0.333 to 0.177 to 0.212, improves ranking AUROC without degrading best-of-4 accuracy, attributes gains to adversarial fine-tuning rather than archive diversity, and is confirmed by independent unpaired replications (44 to 1, clean-split worst gain 0.0092, MATH-500 41 to 0, clean ranking 40/40).

arXiv

Evaluator Ensembles Under Reward Hacking: Covariance Geometry and Finite-Search Guarantees

Fariya Afrin, Ibne Farabi Shihab

Language-model judges and reward models enable scalable supervision, but finite optimization can exploit evaluator errors rather than improve response quality. We characterize this failure through the covariance geometry of evaluator ensembles. For calibrated judges, the ensemble mean retains common-mode error along the all-ones direction, whereas cross-judge disagreement captures only orthogonal error. Consequently, disagreement can be high despite robust aggregation, or low while shared response-dependent errors persist. We prove that common-mode error is not identifiable from internal judge scores alone. Under a joint sub-Gaussian model, we bound best-of-K selection overstatement and target-quality regret, extending the guarantees to predictably adaptive search under conditional calibration. The resulting search terms scale as the square root of log K and are asymptotically tight for Gaussian projected errors. We further show that noisy quality proxies introduce artificial rank-one covariance without changing disagreement, and propose a bounded two-anchor Bernstein certificate for finite-search error and regret. Fixed-seed Gaussian stress tests over 120 (J, rho, K) configurations and real-model audits validate the theory while revealing the limits of disagreement-based diagnostics under increasing search pressure.

arXiv

ZeroLock: Concurrent Memory-Efficient LLM Training via Modular Update Decoupling

Wentao Dai, Xuanran Li, Yuxiang Zhang, Ming Tang, Chao Huang

Large language model (LLM) fine-tuning at the edge adapts the model to scenario-specific data while preserving privacy. Although existing studies proposed pipeline parallelism to address the limited memory and computing resources of edge devices, they commonly rely on backpropagation (BP) training, which has a fundamental limitation of update locking and could experience severe throughput and memory bottlenecks. In this work, we propose a BP-free algorithm, called ZeroLock, that decouples the model updates into independent chunk updates by local objective construction. It breaks the update locking of BP and hence can improve throughput at the algorithm level and lower memory usage by reducing activation storage. To the best of our knowledge, we provide the first theoretical framework for such local objective construction-based approaches under general model chunk division by mapping local objectives to the global objective. We prove that ZeroLock has a convergence rate of $\tilde{\mathcal{O}}(1/\sqrt{T})$, which differs from BP only by polylogarithmic factors. We design a system for ZeroLock and build real-world prototypes, incorporating techniques such as early forwarding and failure recovery for efficient and robust implementation. Experiments on the prototype show that compared to BP-based baselines, ZeroLock reduces the memory by 26.5% and improves throughput by 4.9%.

arXiv

From Uncertainty to Failure Attribution: Self-Diagnosing Models for Failure Attribution under Distribution Shift

Yiyao Yang

Distribution shift poses a significant challenge to the robustness of machine learning models, but the current solutions only aim to detect out-of-distribution (OOD) samples and predict uncertainty levels. We introduce a problem setting for failure attribution under distribution shift, which enables the models not only to detect OOD samples, but also to find out the reason for their failure. The solution we propose is called self-diagnosing models, which are capable of jointly learning predictive output, predictive uncertainty, and a failure attribution signal. In particular, we use the failure attribution vector, produced by a neural network, which provides a structured representation of predictive unreliability by distinguishing four different types of failures: covariance shift, semantic shift, noise corruption, and adversarial perturbation. In other words, we move from scalar uncertainty towards failure identification. For training the model, we introduce a consistency regularizer that encourages consistency between uncertainty and failure attribution predictions. Moreover, to be able to evaluate the model on its ability to find the reasons for failure, we construct several distribution shift benchmarks with predefined mechanisms for generating distribution shifts.

arXiv

Persistent Semantic Entities in Tool-Augmented LLM Systems

Zhaohui Wang

Tool-augmented LLM agents can harbor implicit state that persists across sessions, activates through events, and propagates across agent boundaries---largely invisible to standard debugging. We formalize this as Persistent Semantic Entities (PSEs): constructs defined by name binding, event triggering, and cross-boundary propagation, and evaluate them across 24 models from 11 families (1.5B--1T parameters). First, every tested model is susceptible (20--100% on the 20-model susceptibility panel), with name binding as the necessary and dominant mechanism: without it, contamination is 0%. Second, persistence depends on contamination type rather than scale or deployment: preference contamination persists undecayed on every model probed (100% at t=10) and instruction contamination persists wherever adopted, persona-style injection decays partially (90%$\to$10%), while factual injection is model-dependent---self-corrected on Llama-3.1-8B and GPT-4o-mini but held at ceiling on both Qwen2.5-coder variants, so we do not claim it self-corrects in general. The preference and instruction results hold across providers in our controlled setting. Third, context-isolated self-verification achieves 20--79% reduction (median 36.5%) without oracle references while keyword-based detection produces systematic false positives, and contamination compounds 1.9$\times$ along a four-stage agent pipeline (40%$\to$75%). Preference and instruction contamination---persistent, lacking self-correction, and poorly captured by standard monitoring---represent a particularly concerning attack surface for deployed agent systems.

arXiv

Agentic AI for Clustering, Relationship Discovery, and Semantic Trading in Prediction Markets

Agostino Capponi, Alfio Gliozzo, Brian Zhu

Prediction markets allow users to trade on outcomes of real-world events, but are prone to fragmentation with overlapping questions, implicit equivalences, and hidden contradictions across markets. We present an agentic AI (AAI) pipeline that autonomously recovers cross-market structure from contract text before prices enter the analysis. The workflow first clusters markets into coherent topical groups using natural-language understanding over contract text and metadata, and then identifies contracts within each cluster, but from different event markets, that exhibit strong dependence or leader--follower relationships. We evaluate this system, along with a natural language inference (NLI) benchmark, on a large prediction market dataset from early 2026. Using resolved outcomes to evaluate identified relations, we find that AAI-identified relations are 62.8\% consistent with exchange-recorded settlements, whereas the NLI benchmark only achieves 40.6\% accuracy. Within clusters, the AAI output is sparse and also remarkably compatible as a signed graph with a frustration rate of 0.324\%. As an application, we show how discovered relations inform semantics-based trading strategies on prediction markets. One such strategy yields 14.12\% net ROI after fees in a two-month period in 2026. Overall, we demonstrate the potential for agentic AI as a structural discovery layer for prediction markets.

arXiv

Second Order Drifting Models

Drake Brown, Yuhao Huang, Shih-Hsin Wang, Bao Wang

Drifting models are a recent class of one-step generative models that evolve the model distribution during training using a predefined sample-based drift field. Although they avoid iterative inference, their kernel-based drift fields induce frequency-dependent training dynamics: In the linearized regime, each Fourier mode of the density residual decays at a rate determined by the kernel spectrum, leading to slow recovery of fine-scale structure. We propose Second-Order Drifting Models, which lift drifting dynamics into phase space by augmenting generated samples with artificial velocity variables. We show that the resulting density perturbations obey accelerated second-order dynamics in Fourier space, connecting drifting models to the celebrated Nesterov acceleration from optimization theory. This provides a principled mechanism for mitigating the spectral stiffness of first-order drifting while preserving one-step inference. We derive a practical semi-implicit training algorithm and evaluate it on synthetic distribution matching, sequential data generation, and robotic control. Across these settings, the second-order drifting model improves convergence behavior and achieves competitive or superior performance over first-order drifting baselines.

arXiv

Information Routing across Batch Boundaries: Memory--Batch Tradeoffs in Lipschitz Bandits

Zicheng Lyu, Zengfeng Huang

Adaptive learning needs both a state that preserves what observations imply and opportunities to act on that state. We study this width--depth tradeoff in stochastic Lipschitz bandits. After each pull, the learner retains at most $W$ bits of live reward-dependent state and organizes its pulls into at most $B$ committed batches. For $W\gtrsim_d\log(eT)$, we characterize minimax expected pseudo-regret up to logarithmic factors; the lower bounds hold for every $W$. Besides the classical sequential and unrestricted-memory batch costs, the frontier contains the new penalty \[ T^{\frac{d+2}{d+3}} \bigl(1+(B-1)W\bigr)^{-\frac1{d(d+3)}}, \] proving that state width and update depth are not interchangeable. The interaction is an information-routing constraint: at regional scale $s$, low regret forces the committed action transcript to encode $Θ_d(s^{-d})$ regional decisions, while the collected boundary states carry at most $(B-1)W$ bits of entropy. Matching policies stream and erase verification statistics while retaining a mask of a safe active set, either in memory or fragment by fragment. The theorem recovers the full-dimensional worst-case batch-only frontier and logarithmic-memory achievability in the fully sequential specialization; static batch boundaries match predictable adaptive ones.

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