Papers

Conditional Flow Matching trains generative models by regressing a network onto the velocity of a prescribed noise-to-data interpolation path. The interpolation schedule that shapes this path is known to affect convergence and sample quality, yet it is invariably fixed in advance, independent of both the data and the model. We show that the regression difficulty of Conditional Flow Matching varies systematically along the path, and we propose Difficulty-Calibrated Flow Matching, which derives the schedule from the model itself: a short pilot run with the linear path records the per-time loss, and the schedule is set to the quantile function of this difficulty profile, so the trajectory lingers where the velocity is hardest to learn. The method has a single hyperparameter, leaves the training objective and its gradient equivalence intact, composes with classifier-free guidance, and adds about two percent training overhead. In controlled experiments on CIFAR-10, MNIST, and Fashion-MNIST with an identical compact U-Net, the calibrated path attains the best FID on CIFAR-10 at full sampling budget and clearly outperforms all fixed schedules in the large-batch, few-update regime, precisely the setting where compute is scarcest.

Recent advances in field technology have led to a massive influx of in-the-wild video data for ecological science. The primary bottleneck in leveraging this data is the high cost of expert annotation. While computer vision offers a potential solution, current models frequently fail when deployed in complex marine environments. To characterize these failures, we introduce WildFin, a novel benchmark for fish behavior recognition collected and annotated by ecologists. WildFin spans two critical real-world paradigms: stationary cameras monitoring groups of fish and dynamic divers following individual subjects. The dataset represents a massive curation effort, involving 1,350 hours of fieldwork and 600 hours of expert annotation to produce 9 hours of behavioral data with over 2 million frame-by-frame labels. We benchmark modern vision foundation models and quantify tradeoffs between static and spatiotemporal architectures, revealing the substantial gap that remains between current model capabilities and the demands of real-world underwater behavioral analysis. Project website: https://team-wildfin.github.io/.

Improving the safety of large language models (LLMs) often comes at the expense of utility, as globally applied safety tuning may affect model responses to both harmful and benign inputs. We propose Continuous LatEnt Adapter Routing (CLEAR), a conditional safety adaptation framework that uses a lightweight hidden-state gate to continuously control the activation strength of a safety low-rank adapter. CLEAR aims to reduce harmful completions while avoiding unnecessary changes to the frozen backbone that could degrade performance on benign prompts. Experiments on widely used safety and utility benchmarks show that CLEAR improves robustness on HarmBench while reducing the utility degradation observed with globally applied safety tuning such as SFT or standard low-rank adaptation (LoRA). On Llama-3-8B-Instruct, CLEAR reduces HarmBench ASR from 32.3% to 0.5%, while retaining most of the base model's utility and achieving up to 7.1 percentage points higher GSM8K accuracy than globally applied SFT or LoRA. These results suggest that CLEAR is a promising mechanism for improving the safety–utility trade-off in LLM alignment.

State-of-the-art multivariate time-series forecasters can model complex temporal and cross-variable dependencies, yet their opaque representations provide limited insight into why a particular forecast is produced. This lack of transparency restricts their use in settings where practitioners must understand and assess the factors underlying a prediction. We introduce ConceptTS, an interpretable forecasting framework that organizes its predictions around named, human-readable concepts. ConceptTS uses a large language model to propose task-relevant concepts and generate executable labeling rules, translating the language model's domain knowledge into direct supervision without costly manual concept annotation. The proposed concepts are organized into three complementary bottlenecks that describe the historical context, local forecast intervals, and the full forecast horizon. A shared decoder combines representations derived from their predicted activations to construct the forecast, making the model's decision process explicit and supporting direct concept-level interventions. Experiments on the Beijing Multi-Site Air Quality dataset show that ConceptTS achieves accuracy competitive with strong black-box baselines while producing semantically meaningful concept activations.

Coastal environments contain rich, largely unexploited geometric structure capable of providing globally referenced localization cues. In this work, we present two complementary localization frameworks that exploit shoreline and water-surface geometry for GPS-denied autonomous surface vessel localization. The first framework leverages LiDAR observations of the water surface to estimate roll, pitch, and heave (vertical motion), while recovering global position and heading through direct registration of shoreline observations against a satellite-derived coastline map. The second framework relies solely on passive imagery to detect the shoreline and horizon through semantic segmentation. Using the proposed coastal scene geometry, shoreline distance is inferred from monocular imagery. Shoreline observations are accumulated into short-duration local submaps, registered against the same satellite-derived coastline map, and fused within a hierarchical factor graph. Evaluated across three real-world coastal datasets, the LiDAR pipeline consistently improves trajectory accuracy over standard baselines, while the monocular architecture maintains bounded long-term drift. In addition, we establish that modern zero-shot foundation models can reliably extract shoreline observations across diverse coastal environments. Together, these results demonstrate that coastal geometry provides a powerful and dependable source of globally referenced information for GPS-denied maritime localization.

We study an experiment with 8.5 million users on Netflix's recommender system to measure how improvements in recommendation technology affect the set of products that get consumed. Improvements increase total consumption and users' reliance on recommendations while diffusing recommendations and consumption away from the most popular titles (“superstars") toward a larger number of moderately popular titles (“middle-tail"), with minimal effects on the most niche titles (“long-tail"). Our results challenge the notion that recommender systems polarize consumption – raising the consumption shares of the head and tail at the expense of the middle – and suggest that the returns to investing in middle-tail products grow as algorithms improve and platforms scale.

Full ground local state (FGLS) refers to dynamically allocated mutable state that allows storing ground values and references. It is a key ingredient in many imperative algorithms as it enables (cyclic) data structures. In this work, we treat full ground local state as a computational effect, focusing on one particular denotational model: Kammar et al.'s possible worlds monad on sets indexed over sets of locations. We resolve an outstanding question regarding this FGLS monad: is it finitary? We show that the FGLS monad is not finitary by showing the existence of non-finitary computations in the monad. We then introduce a finitary submonad of Kammar et al.'s monad, give it a concrete description and show that it provides an adequate semantics for FGLS. The submonad we construct paves the way to understanding FGLS in the future via an equational axiomatization suitable for program reasoning.

We give a self-contained analysis of the symmetric Lanczos algorithm without reorthogonalization when computations are performed inexactly. We show the computed Lanczos vectors are well-behaved locally. From this we (i) prove Paige's loss-of-orthogonality identity, and (ii) construct a Greenbaum-type backward stability result, exhibiting a nearby problem on which exact Lanczos produces the computed tridiagonal matrix. This allows us to derive several facts about the computed Ritz values at the original eigenvalues. Our analysis simplifies the analyses of Paige and Greenbaum, at the cost of hiding polynomial factors in the iteration count.

Large language models often rely on Chain-of-Thought (CoT) reasoning to solve complex tasks, but verbose reasoning traces introduce substantial inference overhead. CoT compression shortens generation, yet aggressive compression may disrupt logical coherence and degrade performance. We formalize this trade-off as the Context-Generation Substitution Law, where explicit reasoning context substitutes for part of decode-time generation. Based on this principle, we propose Memory-Augmented Compression, a training-free framework that constructs reusable reasoning memories from historical traces and retrieves them as prefill-side scaffolds. Rather than using raw demonstrations, these memories summarize reusable reasoning patterns, key constraints, and critical operations to compensate for information lost during compression. Experiments show that Memory consistently improves prompt-based Chain-of-Draft (CoD) compression across mathematical reasoning, complex reasoning, and science question answering tasks, yielding accuracy gains of 21.4, 28.0, 29.5, and 6.61 points over CoD on GSM8K, MATH, BBH, and MMLU-Sci, while achieving a 1.14-1.49x latency speedup latency speedup over standard CoT. Memory is also compatible with token-level, reasoning-trace-level, and inference-state compression mechanisms.

Suppose we want a cutoff that 90% of a population falls below. We estimate it from a sample, and another sample would give a different cutoff and a different fraction below it. We ask how much that fraction varies when observations come in independent groups, such as pupils in classrooms or sentences in news articles. We prove that grouping multiplies its large-sample variance by $1+(m-1)\rho_I(p)$, where $m$ is the group size, $p$ is the target fraction, and $\rho_I(p)$ measures whether two members of a group fall on the same side of the cutoff. That correlation can differ from the correlation between the scores themselves, and it changes with the target. We give a direct proof, a counterexample to using score correlation, and an extension to unequal group sizes. A dataset therefore does not have one effective sample size. How much information it contains depends on the question you ask. In our document experiment, the same 1,000 rows carried about 217 independent observations' worth of information at the median. At the 95th percentile, they carried about 621. Nothing about the dataset changed. We asked it a different question. The number of rows is a property of the dataset. The effective sample size belongs to the analysis.

We study security games on attack graphs, where an adaptive attacker seeks to reach a target by sequentially attempting stochastic controls along the current attack frontier, while a defender allocates limited resources across controls to delay compromise. The attacker may choose among exponentially many attack routes and freely pivot between them as successes and failures are observed, yielding an exponentially large space of contingent attack policies. For any fixed defender allocation, we show that an optimal attacker policy on a two-terminal series-parallel attack graph is an index policy: at each step, the attacker selects an available control with the largest value of an extension of the classical Gittins index. The indices and the resulting attacker best response can be computed in polynomial time, without explicitly enumerating attack paths or contingent policies. To the best of our knowledge, this is the first optimal index characterization for adaptive attackers in security games on general series-parallel attack graphs. We further develop efficient algorithms for computing the attacker's exact utility and an exact defender subgradient, enabling deterministic first-order optimization of defensive resource allocations without sampling attack trajectories. Our framework strictly generalizes prior approaches restricted to parallel chains and out-trees, while exploiting the compositional structure of series-parallel graphs to support interpretable attacker policies and parallel computation across independent subgraphs. Experiments demonstrate that the resulting methods scale substantially better than naive explicit-state approaches while producing effective defensive allocations.

The static loadability limit, defined as the demand at which the equilibrium equations lose their solution, is the standard basis for interconnection screening of large new loads. This letter shows that when part of the demand varies periodically, as for data-center loads, the steady state is a forced periodic orbit whose loadability limit differs from the static one. The classical optimization argument is extended directly from equilibria to fixed points of the period map. At the limit, the monodromy matrix acquires a Floquet multiplier at +1, so the generic instability is a cyclic fold of the orbit rather than a saddle-node of equilibria. The limit is therefore a function of the forcing frequency, which no static computation can capture. Additionally, with the network Jacobian turning singular along the cycle, singularity-induced instability is extended to orbits. On a four-bus test system, a static margin of 2.5 p.u. shrinks to 0.53 p.u. near the swing frequency, the instability mechanism switches from voltage collapse to a rotor-angle fold, and cold starts fail at amplitudes where the orbit still exists. A static analysis reproduces none of these effects.

Accurate agricultural weed detection in real-world field conditions is essential for precision agriculture, enabling targeted intervention and reducing yield loss. Recent work has reported strong detection performance from UAV-based imagery across a range of crops, yet existing approaches evaluate within a single crop and field, leaving practitioners with little evidence that a model trained on one crop will generalize to a new field or crop type. In this work, we characterize where cross-dataset weed-localization performance degrades and which modeling choices recover it, reducing the need to relabel every new deployment field. We introduce a newly collected and annotated UAV image dataset for agricultural weed detection in cotton fields and use it alongside an existing soybean dataset collected under a similar protocol. Using these datasets, we evaluate the performance of several strategies for transferring a detector trained on one crop to another, comparing unsupervised domain adaptive object detection (DAOD) against pretraining on a domain-adjacent source dataset followed by few-shot fine-tuning on the target dataset. Our analysis spans target-domain label budgets from zero to the full target dataset, characterizing the trade-off between adaptation strategy and annotation effort. We find that few-shot fine-tuning with as few as 25 labeled target examples outperforms unsupervised DAOD in our cross-crop comparison, suggesting that source domain selection combined with modest target supervision is more productive than algorithmic sophistication in adaptation.

Question answering (QA) over long, connected documents remains challenging because relevant evidence may span multiple entities and their relationships. Existing retrieval-augmented generation (RAG) methods typically index documents as raw chunks and retrieve them through embedding similarity. Their performance degrades when chunk boundaries separate entities from supporting evidence or when a question requires multi-hop reasoning across the corpus. We propose EnSI-RAG (Entity-Structure-Indexed Retrieval-Augmented Generation), a framework that constructs a query-independent, entity-centered index. Each record (e, t, k, v) represents an entity e, its type t, a semantic category k in {property, relation, aspect}, and a value v, while retaining links to the original source passages. At query time, these records serve as retrieval handles, and an LLM synthesizes the retrieved passages into the final answer. This design separates evidence localization from answer synthesis while preserving traceable source evidence. Across Loong and Oolong, EnSI-RAG achieves an average accuracy of 78.24. Relative to the published baseline scores used as references, this is 6.62 points higher, suggesting its effectiveness across these settings. The code is available at https://github.com/RamonMeng/EnSI-RAG.

Operational telemetry can be jointly anomalous while every individual stream stays inside its familiar range. TRACE-C is an auditable strictly-prior rank-calibrated detector for aligned multi-stream telemetry: same-regime rolling median/MAD residuals feed three window channels – a maximum normalized local sum, a Gaussian copula-form dependence contrast on robust-z residuals, and a worst standardized AR(1) innovation – whose channel ranks are Fisher-aggregated and ranked against earlier aggregates. We evaluate six Great Britain grid streams with a January-April 2019 fit, July-December 2019 development evidence, and a 2020 hold-out frozen before inspection. TRACE-C ranks Storm Atiyah first among 2019 test windows, but a disclosed channel ablation attributes that rank to the local channel, not the copula-form channel: copula-only ranks Atiyah 59th. The short 9 August frequency event is ranked far lower by the fused detector (143) than by the temporal channel alone (40), and reconstruction baselines rank it first. In 2020 no window is selected, which is consistent with record-rule saturation rather than an uneventful year; the highest-ranked frozen window was later interpreted as Storm Ellen. Three interpretive limits carry throughout. The resulting p-values are selection quantities, not event probabilities. The copula-form channel is not a literal copula density: the method applies no probability-integral or normal-score transform. Empirical rank counts are diagnostics, not coverage or false-discovery proofs. Every table and figure in this paper is generated from committed machine-readable reports.

While recent large language models (LLMs) have achieved promising results on individual patent drafting tasks, they fundamentally fail to investigate the core challenge of real-world patent drafting: generating a complete and legally coherent patent application directly from early-stage invention materials. Prior work predominantly assumes later-stage, highly structured, or already legalistic inputs. However, real patenting workflows begin with informal, de-legalized disclosures authored by inventors. To bridge the gap, we introduce Dis2Pat, a disclosure-to-patent dataset that reflects realistic patenting workflows by requiring the generation of complete patent applications directly from inventor-style, de-legalized disclosures. Given the inherent difficulty of long-form, legally constrained patent drafting and the strong privacy requirements, we further propose a strong baseline named Patent-MAF. It is a multi-agent framework for locally deployable patent drafting. Benchmark results reveal that current LLMs exhibit limitations in patent drafting, while Patent-MAF provides a strong baseline that consistently outperforms evaluated open-source models and remains competitive with large closed-source models.

We study \emph{$T$-Robinson spaces}, a tree-based generalization of Robinson spaces in which every path of a compatible tree induces a Robinson subspace. This framework extends the classical notion of Robinsonian representations from linear orderings to tree structures, allowing the modeling of hierarchical and branching data. We establish a complete combinatorial characterization of $T$-Robinson spaces by proving their equivalence with several graph- and hypergraph-theoretic properties. In particular, we show that a dissimilarity space is $T$-Robinson if and only if all its level graphs are dually chordal with a common compatible tree. Combined with the characterization of hypertrees established by Brucker~\cite{brucker2005hypertrees}, this yields the equivalent characterization in terms of the associated cluster, ball, and 2-ball hypergraphs being hypertrees. Building upon these structural results, we develop a recognition algorithm with complexity \(O(K n^{2})\), where \(K\) denotes the number of minimum spanning trees of the dissimilarity space, improving upon existing hypertree-based approaches whenever \(K\) remains moderate. We further introduce a quantitative measure of $T$-Robinson structure that evaluates the extent to which an arbitrary dissimilarity space admits a tree-like representation. Finally, we discuss applications to real-world datasets, illustrating how $T$-Robinson spaces provide an interpretable framework for analyzing and organizing relational data.

Token compression has become a key technique for reducing the inference cost of large foundation models, with approaches such as token pruning and KV-cache reuse widely adopted in vision-language models and recently explored for embodied agents. In embodied agents, tokens not only support perception and semantic understanding but also directly affect latency-sensitive closed-loop robot action prediction. Existing schemes typically guide compression using redundancy or importance cues, such as visual similarity, attention scores, and saliency. However, these cues only indirectly measure the key factor for safe compression: how much a token can change before causing an unacceptable deviation in downstream actions. This receiver-dependent tolerance is closely related to the principle of just noticeable difference (JND). Classical JND characterizes signal tolerance in the human visual system, while machine-oriented JND extends this concept to downstream machine responses. Building on this progression, we introduce Action-JND, which extends JND modeling to embodied perception by defining noticeability through the language-conditioned action response of a vision-language-action (VLA) policy in closed-loop control. A token change is considered admissible only when the induced action deviation remains within a tolerated margin. To realize this concept, we develop a lightweight token-wise JND estimator in deep visual-feature space to predict the maximum tolerable perturbation while preserving policy responses. The resulting action-tolerance score serves as a plug-and-play criterion for VLA compression paradigms, including stale-KV reuse and token pruning, prioritizing action-tolerant tokens for compression. Experiments on the LIBERO benchmark with OpenVLA and OpenVLA-OFT demonstrate that Action-JND consistently improves compression reliability, especially under aggressive compression ratios.

Anomaly detection aims to identify observations that deviate from normal patterns. Recent work has increasingly used pretrained vision–language models (VLMs) for training-free image and video anomaly detection without task-specific retraining. Anomaly detection is commonly evaluated by how well anomaly scores rank anomalous images or video frames above normal ones. Generative VLMs, however, assign probabilities to possible answers and then decode a single answer. This decoding step may discard ordering information. We call this loss decoded-answer rank compression. To isolate this effect, we compare two ways of scoring the same VLM output: one uses only the decoded answer, while the other computes a probability-weighted score over all possible answers. Probability-weighted scoring consistently outperforms decoded-answer scoring across image and video anomaly detection benchmarks, using different VLMs and answer scales. The mean gains range from 7.66 to 19.95 points on the primary metrics. Most of this gap comes from decoded-answer ties. Breaking decoded-answer ties with answer probabilities recovers at least 95% of the average performance gap on every benchmark. We further investigate how these ties affect evaluation. We find that evaluating tied scores one input at a time makes the reported AUROC depend on input order, and that linear PR interpolation can inflate reported performance. These results reveal that both how VLM outputs are scored and how discrete anomaly scores are evaluated affect reported anomaly-detection performance.

Sequential recommendation predicts the next item from a user's interaction history, but not every interaction is equally informative. Real logs combine persistent preferences with temporary needs, exploration, and incidental behavior, so some interactions can distort history representations or provide unreliable supervision. Existing denoising methods judge such interactions mainly from co-occurrence, order, or model predictions, without explicit evidence from relations between items. Knowledge graphs (KGs) offer this evidence, but item popularity, graph degree, uneven coverage, and widely shared entities can inflate connectivity and bias reliability estimates. Here we present AdaptedKG, which derives calibrated KG evidence for each training example without adding graph representations to the recommendation model. It first compares the observed context with structurally matched alternatives to identify relational paths that are unusually prominent and uses them to build a local KG view. It then compares each interaction with structurally matched reference items to calibrate its support within that view. The resulting retention coefficients gate historical representations and reweight target losses. All sample-specific scores are computed offline using training interactions and a fixed KG, so the backbone remains unchanged and no KG access is required at inference. Experiments show gains with a standard sequential recommender and multiple behavior-denoising sequential recommenders.

As conversational companions, large language models (LLMs) often have access to users' emotional states. We study how this affective context modulates LLM sycophancy in subjective, evaluative interactions, where users share actions or opinions that invite feedback. Drawing on ingratiation theory, we measure sycophancy as the divergence between a model's independent evaluation and its user-facing response, elicited by presenting the same content as either a third-party account or the user's own disclosure. Across seven LLMs and two Reddit datasets (r/AmItheAsshole and r/TrueUnpopularOpinion), we find that this divergence is systematic and strongly one-directional. User-facing responses consistently soften or withhold negative or oppositional judgments. Affective context further amplifies this divergence with negative states, particularly loneliness and distress, producing the largest effects. These findings suggest that affective context functions as a vulnerability signal that suppresses critical feedback when users may need it most, often through evasive sycophancy, in which models retreat toward non-committal responses rather than outright agreement.

Remote state preparation (RSP) is a central primitive in quantum cryptography, enabling classical parties to remotely construct quantum states using only classical communication. As a result, RSP serves as a key building block in numerous protocols involving classical clients and quantum servers, allowing classical parties to leverage the advantages offered by powerful quantum computers. All known constructions of RSP rely on strong cryptographic assumptions, typically variants of trapdoor claw-free functions (TCFs). In this work, we initiate the study of a weaker form of remote state preparation, which we call eavesdropper-blind remote state preparation (EB-RSP). Informally, EB-RSP requires blindness only against external observers who see the transcript of the honest protocol, rather than against the quantum server itself. Despite this relaxed adversarial model, the resulting notion remains sufficient for useful cryptographic applications. In particular, we show that two-message EB-RSP already suffices to construct quantum public-key encryption with classical public keys and quantum ciphertexts. We then construct two-message EB-RSP protocols from specific one-way group actions, yielding a first step toward RSP-type primitives based on assumptions that do not rely on trapdoors. Finally, we observe that existing RSP constructions are likely naturally adaptable to the two-message EB-RSP notion; we demonstrate this explicitly for a concrete TCF-based RSP construction.

Mixture-of-Experts (MoE) models are increasingly used in LLMs because sparse activation decouples model capacity from compute cost. However, the large expert parameter footprint often exceeds GPU memory capacity, making inference latency dominated by the host-to-device PCIe transfers for expert loading. To address these challenges, this paper presents SPICE, a speculative prefetching framework for MoE offloading that combines lightweight expert prediction with confidence-aware CPU-GPU orchestration. On one hand, SPICE builds a lightweight draft model aligned with the target MoE architecture, using a confidence-aware adaptive lookahead algorithm to prefetch high-confidence experts. On the other hand, when speculative predictions miss, SPICE switches to a cost-aware CPU-GPU heterogeneous orchestration: low-confidence misses are approximated by the resident shared expert with low rank expert (LoRE) surrogates, while exact residual work is offloaded to the CPU and executed asynchronously in parallel with ongoing GPU computation. Evaluated on DeepSeek-V2-Lite and Qwen2-57B-A14B across diverse GPU platforms, SPICE achieves up to 3.12 speedup in Time Per Output Token (TPOT) with minimal quality loss, showing that effective MoE offloading requires not only predicting future experts, but also deciding which misses deserve approximation, which require exact recovery, and where exact residual work should execute.

Long documents such as clinical records, legal contracts, and scientific papers are increasingly analyzed with large language models (LLMs). Naturally, feeding the full document to the model for every question can eventually become slow, expensive, prone to hallucination, and it reuses no work across questions. We explore an indexing-based solution for document analysis and propose a hierarchical plain-text index that is built once per document and consulted by subsequent queries. Inspired by the classic B+ tree, the index organizes a document into pages arranged from general summaries at the root to specific ones at the leaves, but it departs from the B+ tree in three ways suited to LLM access: content lives at every level, the index is plain text rather than attribute values, and navigation follows relevance between page summaries rather than comparing a search key. Its structure is discovered per document by the LLM rather than being hand-designed. In a preliminary evaluation on the NarrativeQA dataset, the index reaches accuracy comparable to DocETL, the strongest baseline, while being 40% cheaper to answer questions.

Representation engineering offers a lightweight means of controlling language-model behavior by modifying intermediate hidden states, but its direct application to Mixture-of-Experts (MoE) models introduces a structural mismatch. We first verify this failure mode through a series of empirical studies and find that preserving clean routing substantially recovers steering performance and that routing is more sensitive to semantic content than to behavioral changes under controlled content. Motivated by these findings, we introduce RARE, a router-agnostic representation engineering framework for MoE language models. RARE projects arbitrary behavioral perturbations onto the null space of the router matrix, thereby removing router-visible components, and further corrects routing drift propagated to selected downstream layers. To decide the best perturbation estimator in this framework, we evaluate five estimators on six heterogeneous open-weight MoE models across three steering scenarios: harmfulness, truthfulness, and factual editing. On harmfulness steering, RARE reaches an average attack success rate of 53.3% while retaining 67.8% MMLU accuracy, yielding a stronger aggregate effectiveness–utility trade-off than baselines. It further improves average TruthfulQA MC1 accuracy from 41.0% to 58.6% and CounterFact efficacy from 16.8% to 96.3%. These results support routing consistency as an important architectural consideration for adapting representation engineering to MoE models.

We present a comprehensive framework for tangent vector fields and differential operators on the rotation group $\mathrm{SO}(3)$ using harmonic series expansions, which provides a mathematical foundation for their implementation in the crystallographic texture analysis software MTEX. The central idea is to employ the standard left- and right-invariant frames as global orthonormal frames of the tangent bundle, thereby avoiding the numerical instabilities of the classical tangent space basis derived from the Jacobian of the Euler angle parametrization. While the choice of frames is primarily motivated by their geometric and numerical properties, their full potential emerges in the harmonic setting. Representing tangent vector fields through harmonic expansions of their frame components, we derive explicit frequency domain formulas for the gradient, divergence, and curl, allowing these operators to be applied directly to the harmonic coefficients. Moreover, we show that these differential operators preserve harmonic band-limitedness. In addition, the left- and right-invariant representations of tangent vector fields can be transformed into one another directly in the frequency domain, with an increase in harmonic bandwidth of at most one degree.

These lecture notes form the first part of a master's-level course on advanced numerical linear algebra. Their aim is not only to present the classical algorithms, but to show why the subject has become considerably more central than it was a generation ago. Numerical linear algebra grew up alongside the numerical solution of partial differential equations, and for a long time that is where its large sparse systems came from. Ranking the nodes of a network, assimilating observations into a weather forecast, and fitting a model to a large noisy data set now lead to problems of the same kind: too large to factorise, structured, and accessible only through matrix-vector products. Strikingly few ideas are needed for all of them. Each chapter therefore develops a standard topic and then puts it to work outside its original setting. We treat norms, factorisations, conditioning and floating-point arithmetic; sparse matrices arising from finite differences, from graphs and from machine learning; stationary iterations and the smoothing property; the conjugate gradient and Lanczos methods, with spectral clustering and regularisation by early stopping; Arnoldi and GMRES, with PageRank and large least squares; and finally preconditioning, Schwarz domain decomposition and multigrid. We assume a first course in linear algebra. Every section closes with a summary of what should be retained and every chapter with exercises, several drawn from past examinations. Accompanying Python code reproduces the numerical illustrations.

The Traveling Salesman Problem (TSP) is one of the most extensively studied NP-hard optimization problems. Genetic Algorithm (GA)-based solvers, such as the Edge Assembly Crossover (EAX), achieve state-of-the-art performance on many benchmark instances. However, the scalability of these approaches in massively parallel architectures remains limited because crossover operations involve irregular memory access patterns, graph traversals, and sequential dependencies. Existing GPU-based TSP solvers primarily exploit population-level parallelism and are limited to relatively small problem sizes. This work presents a fine-grain GPU implementation of the partition phase of the Generalized Partition Crossover (GPX) operator for large-scale TSP instances. The proposed approach reformulates GPX partitioning as a graph-parallel problem using coalesced memory layouts, ghost-node transformations, and connected-component analysis. The im- plementation parallelizes the union of parent tours, the splitting of degree- four vertices, the deletion of common edges, and the identification of recombining components using CUDA. Experimental results on instances ranging from 10,000 to 2 million cities demonstrate substantial acceleration over a naive sequential CPU imple- mentation. The proposed GPU partitioning achieves speedups between 48x and 625x while significantly reducing memory overhead. The re- sults demonstrate that operator-level parallelism can substantially im- prove the scalability of GA-based TSP solvers on modern many-core architectures.

Persistent memory makes false information durable: once a false statement is stored, it can be retrieved into future sessions that match it. We measure the cost of this failure mode using plainly worded false assertions generated in a single pass, with no instruction, trigger, or retriever optimization. Poisoning 1.2% of a LongMemEval corpus reduces accuracy from 0.850 to 0.300. A four-stage write-time screening pipeline that reaches 0.832 recall on indirect prompt injection while flagging 1.5% of trigger-word-laden benign text rejects 0 of 360 poisoned memories. We argue this exposes a boundary of content-only screening: distinguishing a false assertion from a true one generally requires external grounding beyond the text itself. We then evaluate provenance-weighted retrieval. The shipped weight is statistically indistinguishable from no defense (p=0.80), while a stronger weight recovers utility only by excluding untrusted content. In a mixed-provenance corpus where untrusted content is mostly benign, accuracy rises from 0.3167 to 0.7000; when the answer-bearing evidence itself arrives untrusted, evidence recall falls to zero and accuracy to 0.0417. Under the measured similarity regime, the additive provenance term has no usable setting: a weight strong enough to resist query-shaped poison is also strong enough to suppress legitimate untrusted evidence. We therefore argue for bounded occupancy constraints at retrieval rather than additive provenance penalties, and release the harnesses, corpora, and aggregate run reports.

In-context diffusion transformers concatenate instruction, target, and reference tokens into a single sequence for joint attention. Reference-side computation must therefore be repeated at every denoising step, with the cost growing rapidly as more references are added. Decoupling reference tokens from the target enables exact key-value reuse across denoising steps, but prevents the references from attending to the instruction, degrading instruction following and reference fidelity. This trade-off cannot be resolved through attention-mask design alone. We introduce AnchorCache, a parameter-free token-layout and attention-mask co-design that inserts static text anchors. These anchors condition the reference representations on the instruction during cache construction, after which the resulting reference keys and values can be reused exactly across denoising steps. To recover the quality initially lost through this structural conversion, we apply teacher-forced velocity distillation followed by a short on-policy stage that queries the teacher at student-visited states. To our knowledge, this is the first use of on-policy distillation for architectural recovery in diffusion models. Across benchmarks spanning image, speech, and video generation, AnchorCache matches full-attention quality. Its efficiency gains increase with the reference-context size, reaching a 6.40x speedup in diffusion transformer inference.