Vectors
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5 papers in the last four weeks, down 17% on the four weeks before. 0.1% of all new papers.
Latest papers 58
In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings under a spiked model. The existing theory of the SVM in the HDLSS context relies on the geometric representation of HDLSS data, which requires that the eigenvalues of the covariance matrices are not dominant. We first show that the geometric representation does not hold under the spiked model. We show that the Gram matrix of HDLSS data converges in distribution to a random matrix, namely, the HDLSS data converge to a random configuration in a finite-dimensional space whose dimension is given by the number of the spikes. We show that the misclassification rates of the SVM do not tend to zero, that is, the SVM does not hold the consistency property. We also show that the bias-corrected SVM (BC-SVM) does not give preferable performance in this setting because the bias term itself should be modified. In order to overcome such difficulties, we propose a spike-corrected SVM (SC-SVM). We show that the SC-SVM holds the consistency property when the sample size goes to infinity, and that the growth of the sample size is essential in the sense that any projection-based procedure fails when the sample size is fixed. Finally, we check the performance of the classifiers by numerical simulations.
Training-Free Task Vectors for LLM Behavioral Control
Task vectors enable post-training model editing by identifying semantically meaningful directions in weight space, typically computed as the difference between a fine-tuned model and its pretrained initialization. However, this reliance on fine-tuning makes discovering such directions costly and limits the practicality of post-training model editing. To address this limitation, we introduce Training-Free Task Vectors (TFTVs), a novel method to compute task-vector-like directions without requiring fine-tuning. Our method maps activation steering vectors to rank-one weight-space edits using only forward-pass statistics, while satisfying arithmetic properties that directly support learning via addition, forgetting via subtraction, and the composition of multiple edits. Empirically, we evaluate TFTVs on large language model behavioral control tasks and show that they consistently amplify, suppress, and compose target behaviors while preserving general knowledge and problem-solving skills. We also validate our method against other editing and steering baselines, experimentally demonstrating that TFTVs achieve stronger trait control with better or competitive utility preservation. We hope our work opens new directions for the community in post-training model editing and broader training-free model control. Code is available on the project website: tftv-llm.github.io.
Why shared attention vectors fail: a case for outcome-indexed tuning
Dimensional attention in learning is often implemented as a globally shared attention vector, where each stimulus dimension corresponds to a single scalar. These scalars are learned by models through gradient-descent on error, where predictive features acquire more salience. We show that under multi-outcome learning, where models predict more than one outcome, this shared vector becomes unstable; it collapses to its bounds and prevents the models from learning meaningful attentional tunings for learning and generalization. We address this by introducing an outcome-indexed attentional matrix that converts globally shared attentional tuning into an outcome-indexed representation. We present an analysis of the unstable shared vectors and derive the conditions under which it holds. Empirically, three synthetic experiments benchmark the proposed attention matrices and show that they converge to meaningful representations, something shared attention vectors fail to do. These results suggest that outcome-indexed attentional matrices are a general fix for gradient-based attentional processes, which improves models of learning under multi-outcome conditions.
Reading a Legal Question Word by Word: Embedding Trajectories of 2,144 Vietnamese Legal Headlines
A dense retriever encodes a question as one vector, but the question arrives one word at a time. We read 2,144 held-out headlines from Thu Vien Phap Luat (Vietnamese legal library) word by word with Nemotron-3-Embed 8B/1B and Qwen3-Embedding 8B/0.6B, encoding 65,444 prefixes against 20,034 articles, plus every prefix of 3,438 sub-questions from 1,112 multi-question headlines and of 168 answers. (i) The gold article becomes rank 1 after a median of 6-7 content words in every encoder, before the interrogative frame is read, and stays there to the end in 78-85% of cases. (ii) In a multi-question headline the lock is inside the first sub-question 94-98% of the time; the second leaves rank unchanged in 89-95%; encoded alone, the second reaches rank 1 in 42-58% vs 91-96% for the first, at the same lock word (95-97% identical). (iii) Numbers, dates and instrument identifiers move the embedding twice as far as content words and four times as far as interrogative words; 72-78% of steps move toward the gold article, and the closing interrogative frame moves against that direction in 95-99% of headlines. (iv) Rank/cosine clustering yields six archetypes (instant, typical, unstable, late, never-locking) that differ by legal area and form (chi-squared p < 1e-8): real-estate and litigation headlines never lock on a number; environmental and accounting headlines do so a third of the time. (v) An answer read word by word retrieves its article after 8-16 words and addresses the sub-questions in order asked in 83-89% of cases. (vi) A word's step keeps a consistent direction across headlines (cosine 0.25-0.33; 0.44-0.60 for numbers); a preceding question rotates that step by about 60 degrees and a greeting by about 30 degrees; steps shrink as i^{-0.8}; and a two-question headline is within 12-17 degrees of a linear mix of its two questions. We call this a context-modulated additive walk.
Singularity-Free Guiding Vector Fields on SO(3) with Designer-Specified Progression Behavior
This paper develops a singularity-free guiding vector field (SF-GVF) for path following on the special orthogonal group SO(3). First, we lift the Euclidean SF-GVF construction to SO(3), integrating the augmented-state approach with the intrinsic Lie-group geometry and obtaining a closed-form geometric guidance law whose integral curves converge to a designer-specified attitude path. The field is defined on a dense open subset of SO(3), excluding only the measure-zero antipodal set - a manifestation of the topological obstruction to continuous global stabilization on SO(3). The construction requires no per-step optimization and produces a control input intrinsically in so(3) as body angular rates. Second, we formalize the progression behavior along the path as a designer-supplied function ν(ξ), promoting the parametric speed from an implicitly resolved degree of freedom to a first-class design specification. In contrast to the Euclidean condition v = 0, which excludes vehicles with minimum-speed constraints, the corresponding condition ω= 0 on SO(3) is physically admissible for most platforms with active attitude control, making the progression behavior a design freedom structurally available on SO(3) but absent in the Euclidean setting. The framework's structural results are established under a bi-invariant Riemannian metric and hold uniformly across choices of path, progression, and Lyapunov gain. The framework is illustrated in simulation on self-intersecting paths under both constant and point-convergence progression behaviors.
Stochastic complexity of vectors containing cluster structure
This paper studies the problem of computing the stochastic probability (shortest code length) of the encoded vectors containing cluster structure using Normalized Maximum Likelihood (NML) model. This is of great theoretical and practical importance in data clustering based on Minimum Description Length (MDL) principle, such as for estimating the best number of clusters and best cluster structure for the data. Straightforward computation of the shortest code length of the vector containing cluster structure based on the NML model requires polynomial time with respect to the size of the vector and number of clusters. We show that this is a tractable problem by introducing a recursion formula for the efficient computation of normalizing constant from the NML model. The time complexity of the new formula is linear opposed to previous polynomial time with respect to the size of the vector and number of clusters.
Modeling Human Behavior with Type Vectors Using AI
We introduce a general, easy-to-implement AI-based modeling technique for analyzing human behavior. A key feature of this approach, which contrasts with existing modeling techniques, is that it combines the flexibility and interpretability of natural language with a mathematical structure that can be fitted to data and easily analyzed. We assign a large language model a vector of trait intensities-a type vector-and then ask it to choose actions across settings in which we observe human choices. For instance, the type vector (2,4) could correspond to "You are a player characterized by the following profile: Altruism: 2 out of 5, Risk Aversion: 4 out of 5," after which it is asked to make choices. We can then vary the traits (e.g., Altruism, Fairness, Trust,...) and values (e.g., 1-5) to minimize distance to human choices. We illustrate the method by applying it to model 119,147 decisions made by 78,657 subjects from more than 35 countries across 10 classic economic game roles. We find that human behavior can be closely matched using three dimensions: Risk Aversion, Strategic Sophistication, and Trust. The type vectors needed to fit individuals across games cluster into fewer than a dozen groups, with substantial variation in fit across subjects. Moreover, the individual type vectors can predict behavior in held-out games with different rules and available actions. More broadly, this new modeling method is highly generalizable and interpretable: we can input any vector of traits and use them to model behavior across any setting
Click2Poly: A VLM for vector mapping buildings and walls
Accurate vector mapping of buildings and walls is critical for geospatial applications but remains a labor-intensive process. While recent deep learning methods have improved automatic extraction, in order to meet cartographic standards they always require a human to perform quality control and fix complex cases in the extraction. We present Click2Poly, a human-in-the-loop AI assistant designed to speed up this manual step. Extending the Florence-2 Vision Language Model (VLM), Click2Poly responds to user clicks by editing the building or wall vector layer directly. Implemented as a QGIS plugin, Click2Poly speeds up the manual editing of building and wall vector layers in a real-world production environment.
AkasicDB: Demonstrating Omni RAG with a Unified Vector-Graph-Relational DBMS
Recent Retrieval-Augmented Generation (RAG) systems increasingly combine vector retrieval with structured knowledge, such as Graph RAG and Filtered vector search. However, existing database architectures struggle to support such complex RAG workflows efficiently, as they rely on out-of-DB pipelines or in-DB non-native integration, leading to high overhead. This demo paper presents AkasicDB, a database system that natively supports such RAG workflows by jointly executing vector similarity search, graph traversal, and relational filtering within a single execution framework. AkasicDB extends our prior work, Chimera, with native vector support to enable such unified execution. Based on AkasicDB, we demonstrate the first native integration of Vector-Graph-Relational RAG, which we refer to as Omni RAG. Through an interactive chat-style demonstration, users execute and visualize Omni RAG queries, directly experiencing its superior retrieval and reasoning over vector-only approaches while observing the practical limitations of existing database architectures in supporting Omni RAG. A demonstration video is available at https://youtu.be/8d09_dtrEIM
Safety Cost of Steering Vectors Is Separable and Reducible
Steering vectors are a lightweight tool for controlling LLM behavior. However, emerging evidence shows that steering vectors can unintentionally compromise a model's safety mechanisms and increase compliance with harmful requests, while no effective mitigation yet exists. In this work, we show that this safety degradation arises from a separable component in the vector that disrupts the model's safety mechanisms but contributes little to the steering objective. We identify and remove this safety-degrading component, formulating the task as a constrained optimization problem solved through primal-dual updates, subject to preserving the intended steering effect and bounding false refusal. The resulting solution is both interpretable and surgical: the optimization recovers a single direction whose ablation from the steering vector restores model safety with minimal utility cost. Across models, steering behaviors, and attack suites, including unseen attacks types, our method substantially reduces steering-induced safety degradation while preserving the original steering effect with minimal impact on false refusal. Our method offers a post-hoc correction to steering vectors that mitigates their safety cost, and more broadly, it provides a general recipe for applying activation-level model interventions without paying a safety tax.
Reachability in 3-VAS
We settle the exact complexity of the reachability problem in (stateless) vector addition systems (VAS) in fixed low dimension. In dimensions 2-4 it has only been known to be sandwiched between NP and PSPACE. We prove PSPACE-hardness of the reachability problem for symmetric vector addition systems in dimension 3 (3-VAS), a restricted fragment of general 3-VAS. Combined with previously established PSPACE upper bounds, our result settles the complexity of the problem to be PSPACE-complete in 3-VAS and 4-VAS, as well as in their symmetric fragments.
Inverted Detection and Control in Steering Vectors
Steering vectors (SVs) are widely used to influence the expression of concepts (e.g., truthfulness) in large language model outputs. A key assumption underpinning SVs is that they are linearly discriminative with respect to the concept: representations of texts that exhibit the concept are more aligned with the SV than those that do not, motivating shifts along the positive or negative SV direction to respectively promote or suppress the concept. In this work, we identify an inverted detection-control phenomenon in which some highly discriminative SVs that are aligned with positive representations can consistently promote the opposite behavior. We refer to such vectors as inverted-steering vectors (ISVs). We provide a geometric characterization of ISVs' effects, finding that steering along these directions systematically pushes representations in discriminative downstream heads as if the concept were absent, even prior to decoding. Motivated by this analysis, we propose an approach for distinguishing ISVs without requiring generation or associated response scoring. This enables targeted sign flips, which we use to improve a foundational detection-based steering pipeline via Inference Time Intervention (ITI). Our approach improves results in 27/30 experiments, ranging from +0.9% to +138%. We evaluate our findings on Gemma 3 12B, Qwen 2.5 14B, and Olmo 3 7B across 5 concepts.
QASP: Query-Adaptive Robust Vector Search Policy
A fundamental challenge of vector search is achieving consistently high recall while minimizing computational costs. Fixed search parameters cause significant performance variance across queries, and conventional evaluation on average recall masks these per-query disparities. We introduce QASP (Query-Adaptive robust vector Search Policy), which predicts the complete recall progression curve per query via a single upfront supervised regression, from which a search policy is derived for any recall target; this avoids iterative model invocations during search or separate predictors per target. By predicting normalized recall values with scale-invariant features and pre-search inference, QASP generalizes across recall targets, index configurations, and datasets. Its fine-grained progress predictions further enable a lightweight reactive complement that adjusts search depth based on predicted-versus-observed deviations without additional inference. We prove that QASP requires a finite training sample independent of dataset size and dimensionality, that its loss exceeds the irreducible lower bound of any fixed policy by a vanishing margin, and that its data access savings over fixed probing grow exponentially in intrinsic dimensionality. Experimentally, QASP achieves significantly lower recall variance and deviation from target, higher query satisfaction rate, and scales to large data and hierarchical indices without retraining, achieving 99% recall with 80% less data access.
VQ-bench: A Composable Vector Quantization Framework
Vector quantization is an old problem but has recently become central to AI infrastructure. It is therefore experiencing a surge of renewed engineering and research activity. This paper provides a unified framework for developing and benchmarking new quantization algorithms. We describe 7 common conceptual quantization primitives and show how to compose them arbitrarily. We then re-express 25 common quantizers as pipelines of these primitives. Finally, we publish VQ-bench as open-source to be extended further and make reproducible benchmarks publicly available.
Do Unified Multimodal Models Think in One Space? A Lens Through Cross-Branch Steering
Unified multimodal models (UMMs) aim to integrate understanding and generation within a single architecture, yet it remains unclear whether these capabilities share a unified and transferable semantic space. This question is fundamentally challenging, as the two branches operate over heterogeneous representations (text tokens vs.\ visual latents) and distinct training objectives, making direct comparison difficult. To address this, we introduce \emph{cross-branch semantic steering}, an intervention-based framework that extracts semantic directions from one branch and applies them to the other. We show that steering vectors learned from the understanding branch can transfer to generation, enabling controllable image synthesis and improved semantic faithfulness. In contrast, the reverse direction consistently shows limited effectiveness. Our analysis suggests that this asymmetry may be related to a practical representational mismatch: understanding-derived vectors capture transferable, object-centric semantics, while generation-derived vectors primarily encode low-level appearance features. Our results reveal that architectural unification does not guarantee semantic alignment, and establish cross-branch steering as a practical tool for probing multimodal representations.
MSVS-VAE: Multi-Scale Anchored VecSet for High-Fidelity 3D Reconstruction
High-fidelity 3D generative modeling increasingly relies on the latent diffusion paradigm, where the reconstruction quality of the underlying 3D VAE becomes a primary bottleneck. Existing approaches largely follow two paradigms: sparse voxel-based representations achieve strong reconstruction quality but incur significant memory and computational overhead, while set-based representations are compact and continuous yet typically lag in fidelity due to latent sparsity and excessive global smoothness. We propose MSVS-VAE, a hierarchical set-based VAE that closes this fidelity gap without sacrificing compactness. Our key idea is to progressively densify anchored VecSet latents via hierarchical point-shuffle upsampling, increasing spatial capacity for fine-grained geometry modeling. To efficiently decode from the densified hierarchy, we replace global cross-attention with AVS-Conv, a geometry-aware local aggregation operator operating within local neighborhoods rather than the exhaustive latent set. We further introduce multi-scale query decoding to fuse coarse-to-fine latent features, where coarse scales provide stable global context, and fine scales refine localized geometry, reducing artifacts from overly local receptive fields. Extensive experiments on Objaverse, ABO, and in-the-wild benchmarks demonstrate that MSVS-VAE consistently outperforms prior set-based and voxel-based VAEs, delivering approximately 10x faster decoding than prior set-based methods and approximately 10x higher compactness than voxel-based baselines.
Vector-Bench: Can Models Surgically Edit SVG Code?
Instruction-based vector editing requires two capabilities: making a requested change and leaving everything else alone. The second is easy to miss when an output is judged only as a raster image. We introduce Vector-Bench, a compact, difficult benchmark of 40 SVG repair tasks. Each task pairs a corrupted SVG program with an author-written visual instruction, a hidden target program, 5.05 annotated repairs on average, and an average of 60.55 protected objects. Instructions describe visible defects without exposing element identifiers, coordinates, color codes, or path data. We define a deterministic binary specification reward: requested repairs use attribute-aware perceptual tolerances, while unrequested rendering- or application-relevant structure must remain semantically unchanged and the result must be a valid SVG. Canonical target equality and stricter source fidelity are retained as diagnostics. Validity-gated repair progress, a near-complete tier, and valid-output Unintended Change Rate (UCR) explain partial outcomes. We evaluate 34 model endpoints (25 listed as open-weight, 5 inexpensive controls, and 4 frontier closed endpoints) over 1360 requests. The strongest endpoint reaches only 15.0% full specification success, despite 43.7% mean repair progress, showing that apparent repair progress and specification-faithful editing remain substantially different. All prompts, outputs, scoring code, costs, and per-task reports are released.
VecFontLLM: Anchor-Guided Direct Synthesis of Chinese Vector Fonts
Direct generation of Chinese vector fonts is a challenging and ongoing problem. A Chinese vector glyph contains complex component structure, anchor layout, and Bézier curve details, which work at different scales, but a standard vector sequence writes them together in one long sequence, making the task of vector font synthesis challenging. Existing direct vector generators often fail on complex characters, while raster-domain methods must vectorize the synthesized glyph images afterward. To address the above-mentioned problem, this paper proposes VecFontLLM, an anchor-guided multimodal large language model for direct few-shot synthesis of Chinese vector fonts. Our key idea is to generate vector glyphs through anchors rather than a standard vector sequence. Specifically, the proposed VecFontLLM first predicts and refines an anchor scaffold that fixes the coarse layout of components and contours, and then completes Bézier control points to recover local curvature and style. At test time, a confidence-guided generation chain samples multiple component candidates and continues synthesis from the highest-confidence one, improving stability for complex glyphs. This work demonstrates, for the first time, high-quality few-shot synthesis of complex Chinese vector glyphs directly in the vector domain, without raster generation or vectorization. Experiments on several Chinese font datasets show substantial improvements over existing vector font synthesis methods, competitive glyph rendering quality against raster-domain baselines, and vector command distributions close to real fonts.
PRISM Edit: One Vector for All Temporal Answers
Model editing keeps large language models (LLMs) up to date without retraining, but temporal facts expose a limitation of the prevailing locate-and-edit paradigm: an update is not always a replacement. When a fact changes, the new answer should become current while the old answer may remain correct in historical time contexts. Building on this insight, we use causal tracing to show that LLMs already support this distinction via a two-stage internal computation: early MLP layers retrieve a time-agnostic subject representation, and later layers modulate it with temporal context to yield the time-correct answer. Motivated by this finding, we introduce PRISM Edit, which optimizes a single polysemous representation across temporal contexts and leverages the model's inherent modulation pathway to route it to temporally correct predictions without requiring any architectural modification. We evaluate on TimeConflict, a newly introduced temporal editing benchmark, and on temporally augmented CounterFact. PRISM Edit improves multiple core metrics over the best baseline, most notably +23.3 Temporal Consistency (TC) and +33.7 Current Relative-time Score (CRS) on LLaMA-3, while being more than 2x faster. Code and data are publicly available at https://github.com/CheerCHuang/PRISM-Edit.
When Do Geometric Algebra Layers Beat Scalarization? A Controlled Study on SO(3)-Equivariant Vector Laws
Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples. We ask whether the geometric algebra structure itself contributes anything beyond exact equivariance. We compare against a minimal scalarization baseline: invariant dot products fed to a small MLP that outputs coefficients on the equivariant basis {v_i, v_i x v_j}, which is also exactly equivariant. On single-stage laws (rotation by axis-angle, cross product, central force), scalarization matches or beats the Cl(3,0) network at a fraction of the training cost, so the geometric algebra adds nothing there. On compositional targets whose computation graph nests group operations (apply R2 R1 to a point; map a local force through an orientation, then take a torque), the Cl(3,0) network beats scalarization by an order of magnitude in the low-data regime, reaching with 100 samples what the baseline needs 3000 for, and the gap survives strengthening the baseline with the triple-product invariant and 17x more parameters, external Vector Neurons and e3nn baselines, and a multiplicative coefficient network. Ablations show the required network depth tracks the rotation chain length, and scalarization falls below the constant predictor on chains of four rotations. The advantage is not composition per se: on a rotation-free nested cross product, which flattens into polynomial invariant coefficients, scalarization wins by 24x. No tested model, equivariant or not, extrapolates invariant magnitudes: on radius and separation shifts every model is worse than a constant predictor once errors are normalized. We conclude that geometric algebra layers are not a general shortcut for low-data 3D learning, but become useful precisely when the target composes group elements in depth.
On the Limits of Steering Vectors for Preference-Aligned Generation
Steering vectors have emerged as a promising approach to controlled text generation, offering interpretable, training-free mechanisms for shaping model outputs. However, their practical generality remains poorly understood. We study the limits of steering vector generalization along three dimensions: trait expressibility, task transfer, and multi-trait composition. Using the PLUME writing personalization benchmark, we extract steering vectors for a range of preferences and evaluate them on summarization and email-writing tasks across two open-source models (Qwen2.5-7B-Instruct and Llama3.1-8B-Instruct). We find that steering effectiveness varies substantially across traits. We further show that steering effectiveness can degrade when vectors extracted from positive and negative style examples are transferred to downstream writing personalization tasks. Finally, we compare common methods for composing multiple steering vectors and find that all methods suffer significant drops in trait expression as more vectors are added, with a tradeoff between coherence and expressibility that requires per-setting hyperparameter tuning. Taken together, our results suggest that steering vectors face meaningful limits as a general-purpose tool for preference alignment.
DPPE: Rethinking Camera-Based Positional Encoding for Scaling Multi-View Transformers
The remarkable scalability of Transformers has expanded their application to 3D computer vision, where camera-aware positional encoding is crucial for providing spatial cues in multi-view geometry. Recent advancements have established the practice of using camera parameters -- such as extrinsics or projection matrices -- as relative positional encoding into the query, key, and value vectors of the attention mechanism. However, when scaling up the training recipe of novel view synthesis (NVS) models with the camera-based positional encoding, we observe a significant issue: model performance stagnates in the late stages of training. In this paper, we investigate the cause of the performance bottleneck when scaling up and demonstrate that storing rotation and translation given by the positional encoding in the same dimensions of the value vector causes indeterminacy in their independent identification, hindering training scalability. To address this, we propose Decoupled Pose Positional Encoding (DPPE), a novel camera-based positional encoding that explicitly decouples rotation and translation. Extensive evaluations on NVS tasks demonstrate that DPPE enables stable long-term training even in scaled-up training setup. Furthermore, it exhibits superior generalization performance in extrapolation settings, such as handling an increased number of viewpoints and zoom-in scenarios.
Learning to Bid in Discriminatory Auctions with Budget Constraints
We study repeated bidding in multi-unit discriminatory (pay-as-bid) auctions for a single bidder with per-round utility equal to value minus times payment, where is a cost-of-capital parameter. The bidder aims to maximize cumulative utility over rounds subject to a total budget . The problem is challenging even without budgets: the action space is exponential in , the maximum demand of the bidder and the valuation vector (context) varies over time. Exploiting a decomposition of utility across units, we develop polynomial-time learning algorithms based on shortest paths in a directed acyclic graph, obtaining sublinear regret under both full-information and bandit feedback. In the bandit setting, the regret is independent of the number of contexts due to complete cross-learning: observing the utility of the chosen action under the realized context reveals the utility for the same action under all counterfactual contexts. With budget constraints, when the average normalized per-round budget , we design a coupled primal-dual algorithm in which the DAG-based procedure uses dual-adjusted edge weights for primal updates, while online gradient descent updates the dual variable, yielding -approximate sublinear regret. Finally, we give implementations whose per-round time and space are independent of the number of contexts, enabling scalability to large or even infinite context spaces.
HiComm: Hierarchical Communication for Multi-agent Reinforcement Learning
Cooperative multi-agent reinforcement learning (MARL) often relies on communication to mitigate partial observability, yet most existing protocols treat messages as flat dense vectors detached from the structure of the observations they summarize. This design overlooks an important source of inductive bias in many cooperative environments, where observations naturally follow a hierarchy such as groups and entities. We propose \textsc{HiComm}, a plug-in communication module that grounds messages in the sender's hierarchical observation. \textsc{HiComm} is receiver-driven: the receiver issues a query, and the hierarchy is resolved through a three-stage decoding process that first selects a group, then a sender, and then an entity within that group, returning the corresponding feature slice as the message. This converts communication from unstructured vector transmission into structured information retrieval over the sender's observation hierarchy. We instantiate this mechanism with Straight-Through Gumbel-Softmax for differentiable discrete selection and a lightweight shared projection design that attaches to standard MARL pipelines. Experiments across cooperative MARL tasks with different observation structures and coordination demands show that \textsc{HiComm} matches or outperforms representative learned communication baselines while reducing communication volume by up to per receiver per episode.
BitNet Text Embeddings
LLM-based text embedders have substantially improved retrieval and semantic representation quality, but their deployment remains costly: large backbone models slow down embedding inference, while high-dimensional full-precision embeddings impose substantial storage and bandwidth overhead on large-scale indexes. In this paper, we present BITEMBED, an extreme low-bit framework for LLM-based text embedding that jointly targets encoding efficiency and vector storage. BITEMBED converts pretrained LLM backbones into BitNet-style embedding encoders with ternary weights, quantized activations, and lightweight normalization refinement. The converted model is adapted to representation learning through continual contrastive pre-training, followed by supervised contrastive fine-tuning with both similarity-distribution distillation and attention-relation distillation from a full-precision teacher. Beyond quantizing the backbone, BITEMBED further trains output embeddings to support multiple storage precisions meeting different storage needs in various scenarios. Experiments on MMTEB (eng, v2) with Qwen3-0.6B and Gemma3-270M show that BITEMBED is largely comparable to full precision teacher embedders. Moreover, BITEMBED flexibly obtains text embeddings of various precisions, achieving a trade-off between performance and storage cost.
When Does Depth Matter For In-Context Learning? Adaptive Inference in Deep Transformers
Transformers perform computations through many successive attention and feedforward blocks, allowing them to learn complex correlations between a large collection of coupled variables. When does stacking successive attention-feedforward computations over many layers provide a computational advantage over a single transformer block? We address this question by examining in-context learning in generalized linear attention transformers. We first introduce a general theory of distributed inference in such transformers, subject to constraints on communication and depth. We show that such systems can exploit internal representations (`function vectors') to infer a latent context variable at increasingly finer scales over its layers. For an in-context linear regression task, the theory predicts that while one-layer transformers without feedforward blocks are optimal for Gaussian priors over the context variable, multi-layer transformers are superior for non-Gaussian, tree-like priors. Trained linear attention transformers reproduce quantitative predictions from the theory. Using causal key-patching experiments, we verify that function vectors in intermediate layers mediate adaptive routing of information. Our results suggest that depth and feedforward blocks enable transformers to implement adaptive inference, and this is advantageous when the distribution over latent variables has hierarchical structure.
Towards Robust Generative Speech Enhancement Using Vector Quantisation-Based Neural Audio Codec
This work investigates modelling strategies in continuous and discrete latent spaces in the vector quantisation (VQ)-based neural audio codec (NAC) speech enhancement (SE), along with the role of VQ regularisation. We propose cNAC-SE and dNAC-SE frameworks that predict continuous representations and discrete tokens in latent space, respectively. Theoretical analysis and visualisations in latent space are performed to exhibit their inherent modelling mechanisms. Experimental results show that the fully fine-tuned cNAC-SE model consistently outperforms all dNAC-SE variants across diverse test conditions and achieves leading performance among established generative approaches in DNS-MOS metrics. Comparison with the discriminative counterpart shows that VQ enhances robustness through an intrinsic effect of clean-prior-constrained regularisation, independent of discrete token processing. This highlights the transferable value of VQ regularisation to other continuous modelling methods.
Vector Space of Cycles
Most statistical and machine learning methods for directed interactions focus on pairwise effects among variables. Even existing cyclic models represent feedback primarily through node-level dependencies, making large-scale recurrent organization difficult to estimate and compare. This limitation is particularly acute in biological and neural systems, where interactions are highly recurrent and involve many overlapping cycles. We introduce a variational framework for statistical inference on cyclic interactions. Directed interactions are represented as edge flows on a simplicial complex and evolved under an energy-minimizing dynamical system. The resulting dynamics separate transient interaction components from persistent harmonic flows, yielding a low-dimensional cycle space that captures stable recurrent organization. Rather than enumerating individual cycles, the proposed framework represents cyclic interactions as elements of a Hilbert space, enabling projection, averaging, comparison, and population-level statistical inference. We establish theoretical properties of the harmonic projection, including characterization of the cycle space, variance reduction, and population inference. Simulations demonstrate substantially improved recovery of cyclic structure in dense recurrent systems compared with existing directed-interaction methods. Applied to resting-state fMRI from 400 human subjects, the framework reveals reproducible large-scale cyclic organization that is not detectable through edgewise averaging. These results provide a scalable statistical framework for studying recurrent interactions in high-dimensional dynamical systems.
Steering Vectors are an Adversarial Attack Surface
Activation steering has become a popular way to control Large Language Model (LLM) behavior without fine-tuning. Since the technique is plug-and-play, users share datasets and precomputed vectors to steer model activations. However, we show that a \emph{stealth data poisoning attack} silently compromises this pipeline. By substituting of tokens in the steering dataset, an attacker can silently align the resulting vector with an anti-refusal direction. This jailbreaks the target model while preserving the intended steering effect on benign prompts. Under this threat model, a malicious actor can distribute an apparently safe bundle containing texts, vectors, and weights, alongside an equivalence certificate that the end-user can verify. We test the attack on two open-weight model families and eight model-attribute combinations, observing that poisoned vectors reach an absolute attack success rate (ASR) of , to over a clean reference. Finally, we find that a refusal-direction orthogonalization defense can recover of the ASR gap without harming benign behavior.
RogueMerge: Robust and Unified Attacks against LLM Model Merging
Model merging composes specialized capabilities into a single LLM by aggregating task vectors sourced from unverified public platforms, exposing a critical supply-chain attack surface: Because any malicious behavior can be encoded into a task vector, and merging grants third-party vectors direct write access to model weights, an attacker-provided task vector can enable or amplify diverse downstream threats. Prior work studies only backdoor attacks against model merging for classifiers using static arithmetic heuristics, which fail to effectively handle diverse attacks on generative LLMs for three reasons. (i) LLMs rely on autoregressive decoding, where the minor parameter drift introduced by merging compounds across tokens and rapidly degrades the attack. (ii) Attackers have no knowledge of the victim's merging configurations, causing a static attack vector optimized in isolation to be easily diluted or destroyed. (iii) Practical threat induction must generalize to attack prompts unseen during optimization, which static vectors cannot adequately encode. We present RogueMerge, the first principled, unified framework that addresses all three challenges. To handle autoregressive generation, we replace static arithmetic with a joint optimization that explicitly enforces attack success after merging. To handle unknown merging settings, we formulate attack injection as a stochastic min-max problem and solve it via meta-learning-style simulation. To generalize across heterogeneous attack prompts, we employ distributionally robust optimization and derive a tractable first-order Taylor approximation at LLM scale, with a provable error bound. Across four threats, six merging algorithms, and over 170 merged LLMs, RogueMerge consistently outperforms existing attacks. It also remains stable across diverse merging settings and resists standard defenses.
HARVE: Hacking-Aware Reward-Head Vector Editing for Robust Reward Models
Reward models are central to large language model (LLM) alignment, but they remain vulnerable to reward hacking. To evaluate reward-model robustness, we introduce RewardHackBench containing 13 reward-hacking patterns covering real life high-stakes domains and general settings, and we find severe failures on specific subcategories across eight reward models. To mitigate these failures, we propose HARVE, a training-free reward-head editing method for scalar reward models. Instead of fine-tuning the reward model, HARVE identifies a multi-directional hacking subspace from residual stream directions associated with selected hacking subcategories, and removes the component of the reward-head vector aligned with that subspace. This directly reduces the reward head's sensitivity to hacking-related features using only a small set of contrastive gold-hacked examples, without gradient updates or fine-tuning. Comprehensive experiments across eight reward models indicates that \model improves hacking robustness, outperforms fine-tuning baselines, and preserves reward-models' general capability. Further analyses suggest that reward hacking is better captured as a multidimensional residual-space structure than by isolated surface cues.
Do Value Vectors in Deep Layers Need Context from the Residual Stream?
The success of the transformer architecture as the backbone of modern LLMs is in large part due to its use of attention layers. An attention layer follows the standard neural network paradigm: it takes the residual stream as input and thereby produces context-dependent query, key, and value vectors. However, we find that model performance meaningfully improves when deeper layers learn only a context-free value vector to preserve the original token information, without drawing on any context from the residual stream. When the model has access to this context-free value vector, adding back the context-dependent component provides little additional benefit for aggregate benchmark performance. Such context-free value vectors can be stored as sparse model parameters, eliminating the need to recompute or persistently cache these values. Through systematic ablations on the key design choices for such context-free value vectors, we propose Bank of Values (BoV), a new way of computing value vectors in attention by learning a lookup table of token-specific value vectors for each of the last third of layers. Across 135M and 780M models, BoV improves validation loss over standard attention and, at 780M, the average score across 21 benchmarks, matching the previous best method that adds token information to the value vector with less compute and memory.
Spatial Representation Learning Beyond Pixels: Unifying Raster Data and Vector Semantics for Human-Centric Geospatial Foundation Models
Earth Observation (EO) has fundamentally transformed the monitoring of environmental processes and human activities up to planetary scale. Recent advances in self-supervised learning have given rise to Earth Observation Foundation Models (EOFMs), which leverage petabyte-scale unlabeled EO data to learn transferable representations across a wide range of downstream geospatial tasks. Despite these advances, current EOFMs remain largely confined to raster modalities, overlooking the rich, structured information encoded in openly-accessible vector data sources such as OpenStreetMap and Overture. Vector data provides explicit and compact representations of geographic entities, including geometry, topology, and semantic relationships, offering critical contextual signals that are often ambiguous or inaccessible in imagery alone. Raster and vector data thus represent complementary views of geographic space: raster data captures continuous physical and spectral patterns, while vector data encodes discrete objects and their relational structure and often represents more of the human rather than the physical systems (e.g. social or demographic data). However, existing geospatial representation learning paradigms treat these modalities in isolation, relying on imperfect and often lossy transformations to bridge them. This perspective paper calls for a paradigm shift toward joint Spatial Representation Learning (SRL) in an unified embedding space that integrate raster perception with vector-based reasoning. Building on emerging efforts in multimodal geospatial learning, we highlight conceptual foundations, technical challenges, and promising directions for aligning heterogeneous spatial data sources. We contend that such integration is essential for developing next-generation geospatial AI systems capable of more accurate, interpretable, and semantically grounded understanding of the Earth.
Inner Product Aware Quantization: Provably Fast, Accurate, and Adaptive Algorithms
Quantization is a fundamental tool used to compress datasets, neural network weights, and memory usage in a range of computational tasks. Many downstream applications of vector quantization perform inner products with arbitrary inputs. This motivates the study of inner product aware quantization schemes that approximately preserve inner products with unseen vectors -- in contrast to simply minimizing the mean-squared error. In this work, we formulate objectives that capture natural desiderata and develop adaptive and unbiased quantization methods that approximately preserve inner products with worst-case and average-case inputs. An analysis of these objectives shows a tight connection with the well-studied notion of Adaptive Stochastic Quantization (ASQ). We develop provably fast exact and approximate algorithms for our objectives. Our theoretical results inspire efficient practical algorithms that perform well across a variety of workload distributions. They also lead to practical algorithms for standard ASQ which are 2-10 faster than prior state-of-the-art methods while maintaining quality. These theoretical and empirical results contribute towards making adaptive quantization techniques more efficient and tractable in practical settings.
Vector Linking via Cross-Model Local Isometric Consistency
We study Vector Linking: given two embedding clouds produced by different black-box encoders over partially overlapping datasets, recover cross-model object correspondences using only vectors. Empirically and theoretically, we show that independently trained contrastive encoders exhibit local geometric consistency: short-range distances are approximately preserved up to a scale factor, while long-range distances are not due to model-specific distortion. Building on this, we propose an iterative, reference-based geometric embedding hashing that recovers vector links from a tiny seed set of paired anchors. It represents each vector by distances to sampled paired anchors, proposes candidate links via hash-space matching, and aggregates evidence across views in a Beta-Bernoulli posterior to bootstrap high-confidence links as new anchors. Experiments across multiple benchmarks and embedding model pairs demonstrate accurate and robust linking under varying overlap, seed budgets, and out-of-domain anchors, with applications to vector database integration and cross-model clustering. Code is available at https://github.com/DBgroup-Edinburgh/VecLinking.
Mixing Vector Model for Copolymer Inference via Mixed Integer Linear Programming
A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the two-layered model, with guaranteed optimality and exactness relative to the given learned prediction function and structural constraints. In this study, we extend this framework to copolymers by introducing a simple feature representation, called the mixing vector (MV) model. In the proposed model, a copolymer feature vector is represented as a convex combination of MILP-tractable monomer descriptors weighted by the mixing ratio of the constituent monomers. This representation does not require explicit sequence-class information and is therefore naturally compatible with MILP-based inverse design. Under this model, we construct prediction functions for several copolymer property datasets using artificial neural networks, reduced quadratic multiple linear regression, and random forests. The proposed representation achieves practically useful predictive performance across multiple physicochemical property datasets; in particular, the best test R^2 score exceeds 0.7 for nine of the ten datasets and exceeds 0.9 for six datasets. We also formulate a multi-monomer inverse-design problem under the MV representation with a prescribed mixing ratio and show that the resulting MILP instances remain tractable, even for three-monomer settings. Finally, we perform an external consistency check by re-evaluating the inferred candidates and comparing the re-computed property values with those predicted by the learned model. Overall, the proposed framework gives a tractable first step toward model-level exact inverse design of copolymers under the two-layered model.
Vectors Are Not Neutral: Sensitive-Information Inference from Exported LLM Representations in Summarization
Large language model (LLM) summarization systems may pass compact vector representations of private inputs to downstream retrieval, monitoring, audit, or analytic workflows. Even when source documents remain access-restricted, derived vectors may be handled under different access controls and still support sensitive-information inference, creating a residual information-disclosure risk. We study this issue in clinical discharge-summary generation as a high-stakes case study, using electronic health record (EHR)-recorded race as a controlled sensitive-label audit. We audit two artifacts that a system might retain or expose to downstream components: the final prompt-token hidden state and the mean-pooled prompt representation. Our results show that reducing recoverability of the case-study sensitive label from one exported artifact does not necessarily reduce recoverability from another. As a mitigation case study, we introduce SurfaceLoRA, an exported-vector-targeted parameter-efficient fine-tuning method that uses a gradient-reversal discriminator attached to a designated exported vector. Under a balanced five-way probing protocol, SurfaceLoRA reduces EHR-recorded race recoverability from the targeted final-token artifact toward chance while preserving summarization utility, yet recoverability remains substantially higher from untargeted pooled artifacts. These findings show that privacy auditing and mitigation should be performed on the exact vector artifact retained or exposed to downstream components.
Function-Vector Heads Are Two Populations: Writers and Cancellers in In-Context Learning
Function-vector (FV) heads are identified by the magnitude of their causal contribution to in-context rule tasks, and the resulting top set is treated as a single functional class. We show this hides a sign structure. Under a sign-preserving criterion (refined direct logit attribution, validated head by head with path patching) the FV population splits into two opposing groups: writers push the rule-correct logit up, cancellers push it down, and ablating both together moves the readout less than the sum of the two. The split is causal and reproducible. It holds in all but two of the fifteen (model, task) cells we test, spanning three architectures and six Pythia scales, and a sign-shuffle null rejects the single-class account in all but one of the six main cells. It is also invisible to magnitude-only ranking, which surfaces whichever group locally dominates and misses the other, so any function vector or ablation built that way silently averages a promoting and a suppressing mechanism. Cancellers are not attention sinks, induction heads, or copy-suppression heads, and their causal effect is larger than that of magnitude-matched non-FV controls. Zero-ablating them recovers to nats on the correct label in every main cell, and shifts accuracy by to pp in the same direction.
AssetGen: Deployable 3D Asset Generation at Interactive Speed
While 3D generation is progressing rapidly, recent work has often focused on obtaining high-resolution assets, leaving user experience and deployability as afterthoughts. We present AssetGen, a 3D generator that focuses instead on these two aspects. Given one reference image, in 30 seconds it produces a high-quality mesh with baked normals, a color texture, and a controlled polygon budget suitable for real-time rendering, including mobile use cases. The AssetGen Flash variant further reduces latency to 14 seconds for interactive and agentic creation loops. Our model generates the object geometry with a coarse-to-refine VecSet framework, which implements mesh simplification, cleaning, and normal baking on the GPU, and a fast parallel UV unwrapping. It then generates textures in a multi-view fashion, followed by backprojection and 3D inpainting. Model distillation, kernel optimization, and pipeline parallelization are co-designed to accelerate the system end-to-end. We introduce numerous automated and blind human evaluations and demonstrate competitive visual quality against leading commercial solutions in 30 seconds and preview-quality results in less than 15 seconds. The final result is a system that supports AI-assisted, deployable 3D content creation in interactive workflows.
AnchorFlow: Editable SVG Reconstruction via Sparse Anchor Point Fields
Image-to-SVG reconstruction aims to produce vector graphics that are faithful to raster inputs and easy to edit. Existing methods face a structural trade-off in how vector structure is parameterized, including how many paths represent an image and how many anchor points define each path. High-fidelity methods often rely on many paths or densely parameterized curves, whereas overly compact SVG generation may deviate from the input geometry. This issue becomes more pronounced when local raster evidence is imperfect, where boundary-following reconstruction can introduce redundant anchors and fragmented structures. We argue that this trade-off should be addressed at the level of anchor placement, since anchors on Bezier curves define local path structure and strongly affect both accuracy and editability. We propose AnchorFlow, an editable SVG reconstruction framework that models path-level anchor placement with sparse anchor point fields. Given path-like foreground components extracted from a raster image, AnchorFlow predicts an image-conditioned sparse anchor field for each component and resolves it into an ordered Bezier path. Rendering-guided feedback then corrects local structural errors before re-resolution. The recovered paths are then assembled and optimized into the final SVG. Experiments on isolated paths and full images show that AnchorFlow achieves a favorable fidelity-editability trade-off, substantially reducing editable complexity while preserving competitive raster fidelity.
IVF-TQ: Calibration-Free Streaming Vector Search via a Codebook-Free Residual Layer
Approximate nearest neighbor (ANN) indexes deployed against streaming corpora silently lose recall over weeks. The standard diagnosis is distribution shift, but under shuffled-i.i.d. ingestion -- no shift at all -- product quantization still degrades -3.8pp at sub-matched bit budgets. The dominant production compression methods (PQ, OPQ, ScaNN) all fit a codebook to an initial sample and reuse it as the database grows by orders of magnitude. This paper presents IVF-TQ, an inverted-file index whose residual compression layer is data-independent: a fixed random rotation followed by a precomputed Lloyd-Max scalar quantizer parameterised only by the bit width b and dimension d. Only the IVF coarse k-means partition is trained. A uniform-over-sphere inner-product error bound depending only on (b, d, delta) provides a structural guarantee no learned-codebook method admits. The same codebook-free design enables an IVF-amplification effect that closes the gap to Extended RaBitQ to within statistical noise (+17.7pp over flat TQ at matched bit budget), and an Adaptive variant that refreshes the partition without touching the compression layer. Across nine controlled cells (three 10M datasets, three PQ memory regimes, three seeds), per-batch PQ codebook retraining never recovers the streaming gap; IVF-PQ streaming stability requires per-dataset bit-budget tuning, while IVF-TQ holds at one fixed (b, d) configuration on all three datasets with Delta in [-0.80, +0.56]pp. The contribution is operational: no codebook to train, no per-dataset bit-budget tuning, no retraining cycle that ever closes the gap.
How Few-Shot Examples Add Up: A Causal Decomposition of Function Vectors in In-Context Learning
In-context learning (ICL) excels at new tasks from minimal examples, yet we still lack a mechanistic explanation of how few-shot prompts shape a model's function vector (FV)--a causal activation direction that drives task behavior on the ICL query. Across tasks and models, an -shot FV is well-approximated by a linear combination of example-level sub-FVs, suggesting additive and composable contributions from individual demonstrations. Beyond additivity, we show that models contextualize individual examples' representations based on prior examples to adaptively reweight which demonstrations dominate the FV: attention shifts toward examples that are more informative and less ambiguous under the context. Finally, a causal decomposition separates Query-Key routing from Value updates, finding that contextualization's most consistent contributions to FV quality arise from Query-Key alignment--particularly in ambiguous settings--while Value-mediated effects are more heterogeneous. Together, these results unify additive superposition with context-dependent attention reweighting into a mechanistic, testable account of how few-shot prompts implement tasks.
VectorSmuggle: Steganographic Exfiltration in Embedding Stores and a Cryptographic Provenance Defense
Modern retrieval-augmented generation (RAG) systems convert sensitive content into high-dimensional embeddings and store them in vector databases that treat the resulting numerical artifacts as opaque. Major vector-store products do not provide native controls for embedding integrity, ingestion-time distributional anomaly detection, or cryptographic provenance attestation. We show this opens a class of steganographic exfiltration attacks: an attacker with write access to the ingestion pipeline can hide payload data inside embeddings using simple post-embedding perturbations (noise injection, rotation, scaling, offset, fragmentation, and combinations thereof) while preserving the surface-level retrieval behavior the RAG system exposes to legitimate users. We evaluate these techniques across a synthetic-PII corpus on text-embedding-3-large, four locally hosted open embedding models, a cross-corpus replication on BEIR NFCorpus and a Quora subset (over 26,000 chunks combined), seven vector-store configurations, an adaptive-attacker variant of the detector evaluation, and a paraphrased-query retrieval benchmark. Distribution-shifting perturbations are often caught by simple anomaly detectors; small-angle orthogonal rotation defeats distribution-based detection across every (model, corpus) pair tested. A disjoint-Givens rotation encoder gives a closed-form per-vector capacity ceiling of floor(d/2) * b bits, but real embedding manifolds impose a capacity-detectability trade-off, and the retrieval-preserving operating point sits well below it. We propose VectorPin, a cryptographic provenance protocol that pins each embedding to its source content and producing model via an Ed25519 signature over a canonical byte representation. Any post-embedding modification breaks signature verification. Embedding-level integrity is a deployable, standardizable control that closes this attack class.
Tracing Persona Vectors Through LLM Pretraining
How large language models internally represent high-level behaviors is a core interpretability question with direct relevance to AI safety: it determines what we can detect, audit, or intervene on. Recent work has shown that traits such as evil or sycophancy correspond to linear directions in the internal activations, the so-called persona vectors. Although these vectors are now routinely utilized to inspect and steer model behavior in safety-relevant settings, how these representations are formed during training remains unknown. To address this gap, we trace persona vectors across the pretraining of OLMo-3-7B, finding that persona vectors form remarkably early -- within 0.22% of OLMo-3 pretraining -- and remain effective for steering the fully post-trained instruct models. Although core representations are formed early on, persona vectors continue to refine geometrically and semantically throughout pretraining. We further compare alternative elicitation strategies and find that all yield effective directions, with each strategy surfacing qualitatively distinct facets of the underlying persona. Replicating our analysis on Apertus-8B reveals that our findings transfer qualitatively beyond OLMo-3. Our results establish persona representations as stable features of early pretraining and open a path to studying how training forms, refines, and shapes them.
The End Justifies the Mean: A Linear Ranking Rule for Proportional Sequential Decisions
AI alignment and participatory design motivate a new democratic design problem: how to collectively choose a decision rule to use repeatedly. We study this problem for linear ranking rules, which repeatedly rank items within batches , where each item's ranking is dictated by its score according to a fixed scoring vector . Given voters' preferred scoring vectors and their population fractions , we ask how to choose a collective vector satisfying individual proportionality (IP): every voter type should agree with the resulting rankings to an -proportional degree, either on average over time (long-run IP) or even within each batch (per-batch IP). The default rule, the arithmetic mean of the , has been shown to be severely majoritarian; more generally, it is not clear that any fixed linear rule can balance many voters' disparate opinions. Our main result is that, surprisingly, there is a simple rule that does satisfy long-run IP: the angular mean, the spherical analog of the arithmetic mean. We then show that exact per-batch IP is impossible for fixed linear rules, but that the gap between per-batch and long-run IP shrinks quickly with batch size. Experiments on three real-world preference datasets show that all rules perform similarly when voters' preferences are homogeneous, while the angular mean substantially improves proportionality in high-disagreement regimes.
Direction-Preserving Number Representations
Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.
Retrieval with Multiple Query Vectors through Anomalous Pattern Detection
A classical vector retrieval problem typically considers a \emph{single} query embedding vector as input and retrieves the most similar embedding vectors from a vector database. However, complex reasoning and retrieval tasks frequently require \emph{multiple query vectors}, rather than a single one. In this work, we propose a retrieval method that considers multiple query vectors simultaneously and retrieves the most relevant vectors from the database using concepts from anomalous pattern detection. Specifically, our approach leverages a set of query vectors (with ), and identifies the subset of vector dimensions within that standout (anomalous) from the rest of dimensions. Next, we scan the vector database to retrieve the set of vectors that are also anomalous across the previously identified vector dimensions and return them as our retrieved set of vectors. We validate our approach on two image datasets, a text dataset, and a tabular dataset. Overall, we observe that, across most datasets, larger query sets lead to improved retrieval performance. The improvement is most pronounced when increasing the query sets from 1 to 8, while the gains become smaller beyond that.
Toward a Functional Geometric Algebra for Natural Language Semantics
Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable empirical success, yet they face persistent structural limitations in compositional semantics, type sensitivity, and interpretability. I argue in this paper that geometric algebra (GA) -- specifically, Clifford algebras -- provides a mathematically superior foundation for semantic representation, and that a Functional Geometric Algebra (FGA) framework extends GA toward a typed, compositional semantics capable of supporting inference, transformation, and interpretability while retaining full compatibility with distributional learning and modern neural architectures. I develop the formal foundations, identify three core capabilities that GA provides and linear algebra does not, present a detailed worked example illustrating operator-level semantic contrasts, and show how GA-based operations already implicit in current transformer architectures can be made explicit and extended. The central claim is not merely increased dimensionality but increased structural organization: GA expands an -dimensional embedding space into a multivector algebra where base semantic concepts and their higher-order interactions are represented within a single, principled algebraic framework.
Exploring Language-Agnosticity in Function Vectors: A Case Study in Machine Translation
Function vectors (FVs) are vector representations of tasks extracted from model activations during in-context learning. While prior work has shown that multilingual model representations can be language-agnostic, it remains unclear whether the same holds for function vectors. We study whether FVs exhibit language-agnosticity, using machine translation as a case study. Across three decoder-only multilingual LLMs, we find that translation FVs extracted from a single EnglishX direction transfer to other target languages, consistently improving the rank of correct translation tokens across multiple unseen languages. We further find that the highest-gain tokens span multiple languages and that translation FVs across directions share most of their top-ranked heads, indicating that the FV encodes a largely language-agnostic translation signal rather than a language-pair-specific mapping.
VecHeart: Holistic Four-Chamber Cardiac Anatomy Modeling via Hybrid VecSets
Accurate cardiac anatomy modeling requires the model to be able to handle intricate interrelations among structures. In this paper, we propose VecHeart, a unified framework for holistic reconstruction and generation of four-chamber cardiac structures. To overcome the limitations of current feed-forward implicit methods, specifically their restriction to single-object modeling and their neglect of inter-part correlations, we introduce Hybrid Part Transformer, which leverages part-specific learnable queries and interleaved attention to capture complex inter-chamber dependencies. Furthermore, we propose Anatomical Completion Masking and Modality Alignment strategies, enabling the model to infer complete four-chamber structures from partial, sparse, or noisy observations, even when certain anatomical parts are entirely missing. VecHeart also seamlessly extends to 3D+t dynamic mesh sequence generation, demonstrating exceptional versatility. Experiments show that our method achieves state-of-the-art performance, maintaining high-fidelity reconstruction across diverse challenging scenarios. Code is available at https://github.com/Scalsol/VecHeart.
WorldDB: A Vector Graph-of-Worlds Memory Engine with Ontology-Aware Write-Time Reconciliation
Persistent memory is the bottleneck separating stateless chatbots from long-running agentic systems. Retrieval-augmented generation (RAG) over flat vector stores fragments facts into chunks, loses cross-session identity, and has no first-class notion of supersession or contradiction. Recent bitemporal knowledge-graph systems (Graphiti, Memento, Hydra DB) add typed edges and valid-time metadata, but the graph itself remains flat: no recursive composition, no content-addressed invariants on nodes, and edge types carry no behavior beyond a label. We present WorldDB, a memory engine built on three commitments: (i) every node is a world -- a container with its own interior subgraph, ontology scope, and composed embedding, recursive to arbitrary depth; (ii) nodes are content-addressed and immutable, so any edit produces a new hash at the node and every ancestor, giving a Merkle-style audit trail for free; (iii) edges are write-time programs -- each edge type ships on_insert/on_delete/on_query_rewrite handlers (supersession closes validity, contradicts preserves both sides, same_as stages a merge proposal), so no raw append path exists. On LongMemEval-s (500 questions, ~115k-token conversational stacks), WorldDB with Claude Opus 4.7 as answerer achieves 96.40% overall / 97.11% task-averaged accuracy, a +5.61pp improvement over the previously reported Hydra DB state-of-the-art (90.79%) and +11.20pp over Supermemory (85.20%), with perfect single-session-assistant recall and robust performance on temporal reasoning (96.24%), knowledge update (98.72%), and preference synthesis (96.67%). Ablations show that the engine's graph layer -- resolver-unified entities and typed refers_to edges -- contributes +7.0pp task-averaged independently of the underlying answerer.
Unsupervised Skeleton-Based Action Segmentation via Hierarchical Spatiotemporal Vector Quantization
We propose a novel hierarchical spatiotemporal vector quantization framework for unsupervised skeleton-based temporal action segmentation. We first introduce a hierarchical approach, which includes two consecutive levels of vector quantization. Specifically, the lower level associates skeletons with fine-grained subactions, while the higher level further aggregates subactions into action-level representations. Our hierarchical approach outperforms the non-hierarchical baseline, while primarily exploiting spatial cues by reconstructing input skeletons. Next, we extend our approach by leveraging both spatial and temporal information, yielding a hierarchical spatiotemporal vector quantization scheme. In particular, our hierarchical spatiotemporal approach performs multi-level clustering, while simultaneously recovering input skeletons and their corresponding timestamps. Lastly, extensive experiments on multiple benchmarks, including HuGaDB, LARa, and BABEL, demonstrate that our approach establishes a new state-of-the-art performance and reduces segment length bias in unsupervised skeleton-based temporal action segmentation.
Coordinate-Independent Robot Model Identification
Robot model identification is commonly performed by least-squares regression on inverse dynamics, but existing formulations measure residuals directly in coordinate force space and therefore depend on the chosen coordinate chart, units, and scaling. This paper proposes a coordinate-independent identification method that weights inverse-dynamics residuals by the dual metric induced by the system Riemannian metric. Using the force--velocity vector--covector duality, the dual metric provides a physically meaningful normalization of generalized forces, pulling coordinate residuals back into the ambient mechanical space and eliminating coordinate-induced bias. The resulting objective remains convex through an affine-metric and Schur-complement reformulation, and is compatible with physical-consistency constraints and geometric regularization. Experiments on an inertia-dominated Crazyflie--pendulum system and a drag-dominated LandSalp robot show improved identification accuracy, especially on shape coordinates, on both downsampled and full datasets.
GroundSet: A Cadastral-Grounded Dataset for Spatial Understanding with Vector Data
Precise spatial understanding in Earth Observation is essential for translating raw aerial imagery into actionable insights for critical applications like urban planning, environmental monitoring and disaster management. However, Multimodal Large Language Models exhibit critical deficiencies in fine-grained spatial understanding within Remote Sensing, primarily due to a reliance on limited or repurposed legacy datasets. To bridge this gap, we introduce a large-scale dataset grounded in verifiable cadastral vector data, comprising 3.8 million annotated objects across 510k high-resolution images with 135 granular semantic categories. We validate this resource through a comprehensive instruction-tuning benchmark spanning seven spatial reasoning tasks. Our evaluation establishes a robust baseline using a standard LLaVA architecture. We show that while current RS-specialized and commercial models (e.g., Gemini) struggle in zero-shot settings, high-fidelity supervision effectively bridges this gap, enabling standard architectures to master fine-grained spatial grounding without complex architectural modifications.
Functional Subspace, where language models can use vector algebra to solve problems
Large language models (LLMs) were invented for natural language tasks such as translation, but they have proved that they can perform highly complex functions across domains. Additionally, they have been thought to develop new skills without being trained on them. These learning capabilities lead to LLMs adoption in a wide range of domains. Thus, it is imperative that we understand their operating mechanisms and limitations for proper diagnostics and repair. The earlier studies proposed that high level concepts are encoded as linear directions in LLMs activation space and that the geometry of embeddings have semantic meanings. Inspired by these studies, we hypothesize that LLMs may use subspaces and vector algebra in subspaces to perform tasks. To address this hypothesis, we analyze LLMs' functional modules and residual streams collected from LLMs engaging in in-context learning (ICL), one of the emergent abilities. Our analyses suggest that 1) LLMs can create subspaces, where evidence can be accumulated and 2) ICL tasks can be solved via simple algebraic operations in subspaces.
White-Box Sensitivity Auditing with Steering Vectors
Algorithmic audits are essential tools for examining systems for properties required by regulators or desired by operators. Current audits of large language models (LLMs) primarily rely on black-box evaluations that assess model behavior only through input-output testing. These methods are limited to tests constructed in the input space, often generated by heuristics. In addition, many socially relevant model properties (e.g., gender bias) are abstract and difficult to measure through text-based inputs alone. To address these limitations, we propose a white-box sensitivity auditing framework for LLMs that leverages activation steering to conduct more rigorous assessments through model internals. Our auditing method conducts internal sensitivity tests by manipulating key concepts relevant to the model's intended function for the task. We demonstrate its application to bias audits in four simulated high-stakes LLM decision tasks. Our method consistently indicates substantial dependence on protected attributes in model predictions, even in settings where standard black-box evaluations suggest little or no bias. Our code is openly available at https://github.com/hannahxchen/llm-steering-audit
Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inference
Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions--without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.
Where is the Mind? Persona Vectors and LLM Individuation
The individuation problem for large language models asks which entities associated with them, if any, should be identified as minds. We approach this problem through mechanistic interpretability, engaging in particular with recent empirical work on persona vectors, persona space, and emergent misalignment. We argue that three views are the strongest candidates: the virtual instance view and two new views we introduce, the (virtual) instance-persona view and the model-persona view. First, we argue for the virtual instance view on the grounds that attention streams sustain quasi-psychological connections across token-time. Then we present the persona literature, organised around three hypotheses about the internal structure underlying personas in LLMs, and show that the two persona-based views are promising alternatives.