The recent wave of one-step generative models, which compress the multi-step trajectory of diffusion via either distillation or learned flow maps, has reached an inflection point where they can generate high-quality images. Here, we ask a natural question that follows from these advances: what happens to the denoising trajectory of multi-step diffusion when generation is compressed into a single forward pass? We offer an empirical observation we call \textit{depth as time}: the denoising computation that multi-step diffusion performs across sampling steps appears to unfold across the depth of a single forward pass, and can be recovered by decoding intermediate layers with the model's own output head. Most interestingly, we show that this depthwise computation depends on the transport task a flow map is trained to solve. The most surprising case is MeanFlow, where probing shorter transport intervals reveals both denoising and renoising within a single network evaluation. In contrast, generators trained without a time-indexed transport task, such as drifting models, do not exhibit the same depthwise denoising. Consequently, we show that models that exhibit the depthwise denoising phenomenon are more compressible across the layerwise computation: a MeanFlow \texttt{SiT-L/2} model can be compressed by $16.6\times$ in parameters into a single time-conditioned block. We offer an explanation for this denoise-then-renoise behavior and show that, when we treat the layerwise computation explicitly as a flow, a single time-conditioned block can be trained to denoise across layers, compressing a MeanFlow \texttt{SiT-L/2} model by $16.6\times$ in parameters. Together, these results suggest that the temporal computation of diffusion is not eliminated by one-step generation, but reorganized across network depth.
https://arxiv.org/abs/2610.03626
Relational databases are among the most widely deployed forms of structured knowledge, and natural language access to them requires grounding language onto schema entities and relations while handling the ambiguity inherent in how people phrase requests. Existing synthetic NL-to-SQL data generation methods largely ignore this ambiguity and produce oversimplified queries that fail to prepare models for the complexity of real-world structured knowledge access. We present FALCON, a framework that generates realistic, ambiguity-aware NL-to-SQL data matching the complexity of challenging real-world benchmarks, at low cost using compact open models. Our approach combines reserved-word SQL seeding and persona-based prompting to generate structurally complex queries, while alignment-based filtering preserves difficulty by distinguishing genuinely incorrect examples from complex but valid queries. Human evaluation confirms consistent high quality across model sizes, and our generated data exceeds existing benchmarks in both SQL complexity and natural language richness. Difficulty-stratified analysis shows models trained on FALCON data increasingly outperform baseline-trained models as query complexity increases, validating our pipeline's success in generating challenging training data. When combined with a small proportion of existing benchmark data, mixed training recovers performance on simpler queries while preserving these advantages on complex ones. The model- and database-agnostic design enables organizations to generate high-complexity NL-to-SQL training data locally without external APIs.
https://arxiv.org/abs/2610.03625
Table-to-report generation refers to the task of automatically generating article-level analyt- ical reports from relational tables and is an essential capability for automated data science and decision support. Its central challenge lies in systematically discovering verifiable com- posite insights across tables, attributes, and analytical perspectives, and organizing them into coherent, complete, and traceable evidence chains. Existing methods primarily rely on sequential, reactive data agents or direct Large Language Model(LLM) generation. They suffer from exploration bias: early local observations constrain subsequent actions, causing models to focus prematurely on local analyzes and miss cross-table or cross-dimensional evidence. We propose ComInsight, which reformulates insight discovery as the composition of atomic evidences. We first define an atomic insight as the smallest executable analytical unit conforming to a predefined analysis pattern and enumerate all valid atomic insights from database schema and content. These atoms are then organized into a multi-relational insight graph, where nodes represent verified data facts and edges encode logical, temporal, or hierarchical relations. Finally, a set of composition operators systematically fuses atomic nodes into higher-order composite conclusions. Every composite output is accompanied by executable SQL and fine-grained provenance, ensuring full verifiability. Across three benchmarks InsightBench, DDR-Bench, and T2R-Bench, ComInsight consistently outperforms strong baselines in factual correctness, novelty, and structural completeness. We believe ComInsight offers a reliable, efficient, and explainable path toward table-to-report generation.
https://arxiv.org/abs/2610.03525
Editable 3D models of field-grown crops support high-throughput phenotyping and in silico breeding trials, but building them from scanned point clouds requires organ-level segmentation and fitting. Procedural generators can turn an organ-level parameter set into an analysis-suitable 3D model, but obtaining that set requires hours of manual tuning per plant or segmentation models trained on species-specific labels. We present an automated pipeline that reconstructs procedural maize models from raw 3D point clouds without manual tuning or species-specific training data. A multimodal vision-language model (VLM) annotates leaf midlines in rendered orthographic views. Deterministic geometric algorithms back-project the annotations onto the point cloud, merge them into 3D leaves by cross-view consensus, and grow the midlines to full blades on an orientation-weighted surface graph. Measured organ parameters populate a plant descriptor for a Non-Uniform Rational B-Spline (NURBS)-based procedural model generator. Each leaf surface is then refined against its scan points by differentiable NURBS fitting. The pipeline reached a median whole-plant Chamfer distance of 5.4 mm on 100 genotypically diverse field-grown maize plants from the MaizeField3D dataset. The reconstructions were closer to the scans than those of an earlier semi-automated pipeline based on manual annotations. The pipeline recovered 1,017 of 1,023 (99.4%) curated reference leaves at an intersection-over-union of at least 0.5 without using those labels as input. These results show that VLM annotations become usable organ-level measurements when downstream geometric stages can correct them. This makes automated generation of editable 3D plant assets feasible at the scale of modern phenotyping experiments.
https://arxiv.org/abs/2610.03468
This paper presents a web-based application for navigating and composing microtonal harmony, built on the Harmonic Eigenspace, a four-dimensional psychoacoustically grounded space in which tetrad chord types are located by their spectral dissonance profiles, computed with Sethares's roughness/dissonance model. The coordinate system is transposition-invariant: a coordinate triple ({\alpha}, \b{eta}, {\gamma}) locates the three upper notes in relation to the root, so a chord quality corresponds to a direction in the space, the invariant ray along which transposition acts, while the root frequency sets the scale. The dissonance field over these coordinates can be computed at any register; the locations of its local minima are register-invariant, as they arise from partial-coincidence ratio conditions. The dissonance volume contains 100 local minima that align with just-intonation intervals and act as landmarks, organising the space into basins around the most consonant tetrads. We embed tetrads from three tonal equal temperaments as discrete lattices within this continuous volume. The application presents this space through two components: the Harmonic Eigenspace as a navigable 3D visualisation of the dissonance volume in which all nodes are playable, and a Modal Studio that extends modal interchange logic to the ten-gradation interval vocabulary of 53-TET. The application also functions as a MIDI controller with MIDI Polyphonic Expression support, usable in any digital audio workstation that supports this format. A listening study with 31 participants used both scenes of the application: listeners first rated isolated 53-TET chords alongside chords familiar from Western practice, such as the maj7 and the m7; they then rated chord progressions composed in the Modal Studio, measuring their acceptance or rejection of microtonal progressions heard for the first time.
https://arxiv.org/abs/2610.03398
Lung ultrasound (LUS) is attractive for tuberculosis (TB) screening at primary-care level, but labelled cohorts are small. Echocardiography carries no such constraint, while sharing the same underlying ultrasound imaging physics, signal processing and B-mode appearance as LUS. We ask whether an encoder pretrained on that high-resource ultrasound domain carries representations that remain usable in the low-resource one. Only the encoder varies, across seventeen encoders spanning three architecture families. Among them, a latent-predictive video encoder pretrained on generic video (V-JEPA2-L) and its echocardiography counterpart (EchoJEPA-L) differ in pretraining corpus alone. The choice among these encoders does not resolve the classification, the whole family spanning 2.50 percentage points against a measurement resolution of 2.71. What moves the task instead is feature conditioning. Standardising the features between the encoder and the classifier improves all seventeen encoders by a mean of +1.23 percentage points at $p=1.5\times10^{-5}$. On the held-out test set every encoder selected on the development folds stands above the baseline system by up to +2.57 percentage points of area under the receiver operating characteristic curve (AUROC), and specificity at 90% sensitivity reaches 79.3% against 60.3%. The contrast specified in advance, EchoJEPA-L against V-JEPA2-L, measures -0.16 percentage points at $p=0.926$. We therefore find no evidence that shared ultrasonic physics alone makes echocardiography a more productive pretraining corpus than generic video, and any advantage, if present, is smaller than this cohort can resolve. The video encoders receive replicated still images, however, so whether this absence of an effect reflects the pretraining domain or a video encoder applied to static frames cannot be separated. The limiting factor is the labelled cohort rather than the encoder.
https://arxiv.org/abs/2610.03290
Touché 2026 extends causality extraction to counter-causal claims: news sentences whose surface form appears causal but whose meaning denies the causation, as in "It is falsely believed that X caused Y." A system that relies on surface cues such as "caused" or "led to" will accept such a sentence as causal and give it the wrong polarity. On the Countercausal News Corpus (CCNC), the task has three subtasks: deciding whether a sentence is causal (detection), locating its cause and effect spans (extraction), and labeling its polarity as procausal, counter-causal, or uncausal. We build one model per subtask. Detection is a fine-tuned classifier with a single cross-task rule that uses the extracted spans to remove false positives. For extraction, we ensemble three RoBERTa-large BILOU+CRF taggers by averaging their token-level scores before decoding, rather than voting on the spans each tagger produces. For polarity, where labeled counter-causal examples are scarcest, we add training sentences generated by a large language model prompted with nine patterns of counter-causal expression adapted from Hagen et al., keeping only those that pass automatic structural checks. On the held-out CCNC test set, the system reaches F1 0.869 on detection and macro-F1 0.817 on polarity, and in the organizers' final causal-only evaluation of extraction it scores granularity-adjusted F1 0.728, the highest extraction score among all submissions including the organizers' baseline. The development split is used only for component selection and the ablations reported in the paper.
https://arxiv.org/abs/2610.03268
Large language models (LLMs) are increasingly deployed in public health, finance, and governance, requiring both accuracy and societal value alignment. Despite recent advances, LLMs often perpetuate or amplify bias embedded in their training data, posing challenges to fairness. While self-debiasing encourages an LLM to identify and correct its own biases, relying on a single model's intrinsic knowledge may be insufficient to address deeply ingrained stereotypes. To address this limitation, we introduce Collective Bias Mitigation (CBM), a framework that alleviates bias by learning fine-grained model behavior and fostering knowledge sharing among diverse LLMs. This work is the first to systematically explore the effective selection and organization of distinct LLMs to cultivate fairer LLM responses. Experiments show CBM substantially outperforms standalone baselines (e.g., in the top-7 setting, Committee lowers the age bias score from 0.25 to 0.10). Our Debating and Committee topologies achieve substantial bias reduction, with the latter balancing mitigation effectiveness and inference cost, highlighting the potential of CBM for fairer LLMs.
https://arxiv.org/abs/2610.03240
Mobile Gaussian reconstruction must satisfy two requirements: the reconstruction model must execute within a device resource envelope, and the resulting Gaussian asset must expose a representation size suited to downstream mobile use. Existing feed-forward Gaussian reconstructors commonly decode dense, image-aligned candidates whose final cardinality is implicitly determined by the input resolution and number of views. We present PocketSplat, a feed-forward framework for budgeted mobile Gaussian asset construction. Given a prescribed output budget, PocketSplat organizes dense geometry-aware latent candidates in predicted world space, allocates exact integer capacity across local latent cells, and decodes complete Gaussian attributes only for retained candidates. Cell-conditioned latent fusion aggregates repeated multi-view evidence before decoding, while spatial responsibility decoding adapts Gaussian support after local sparsification. Experiments on DL3DV and out-of-distribution benchmarks establish a strong quality--budget trade-off against feed-forward Gaussian reconstruction baselines. On Mip-NeRF 360, PocketSplat executes directly on a target iPhone and constructs compact, higher-quality Gaussian assets substantially faster than a deployable streamed MVSplat variant; native MVSplat and DepthSplat exceed the device memory budget.
https://arxiv.org/abs/2610.03192
Workspace agents combine large language models with execution harnesses to perform stateful, multi-step tasks that access or modify external resources. Existing benchmarks leave gaps in executable coverage of their runtime security risks, while evolving model capabilities, harnesses, tools, and threats motivate benchmark evolution. We introduce EvoRiskBench, an evolving benchmark organized around the EP-Path-EF framework, which links an initial risk entry point to a one-hop technical effect through an agent-mediated risk path. The framework defines nine entry-point categories and five effect categories; a 20-participant study supports their interpretability and classification consistency on representative cases. Guided by this framework, an automated end-to-end workflow constructs and executes risk cases in isolated environments and independently verifies outcomes using runtime traces and environment states. The benchmark provides a reproducible dataset of 450 adversarial tasks across six scenarios. We evaluate nine model-harness configurations spanning three models (GPT-5.6 Sol, DeepSeek-V4-Pro-0813, and Claude Opus 5) and three harnesses (Claude Code, Codex, and OpenClaw). Our results reveal substantial vulnerabilities across systems. The most vulnerable configuration, Codex with DeepSeek-V4-Pro-0813, reaches a 68.44% attack success rate (ASR), indicating that configuration of workspace agent is insufficient to ensure secure autonomous execution. ASR varies more across models than harnesses, and harness differences depend on the model. The benchmark cases and evaluation platform will be released after completion of artifact safety and reproducibility checks.
https://arxiv.org/abs/2610.03153
Biological literature retrieval systems are often developed and evaluated using broad biomedical corpora and general-purpose search tasks. However, many curated knowledge bases operate in narrower model-organism domains, where the literature is sparse and terminology is organism-specific. We introduce a retrieval benchmark from dictyBase for Dictyostelium, a model organism in cell and developmental biology. The benchmark consists of curator-generated biological queries linked to PubMed-indexed articles, together with structured gene annotations. Using this benchmark, we study three factors in niche biological retrieval: cross-encoder reranking, gene-aware query expansion, and abstract-only versus full-text retrieval. We report that reranking and gene-aware query expansion improve retrieval selectively: reranking is most useful when the model is well suited to biological evidence matching, whereas curated annotations help clarify compact biological queries by reducing vocabulary mismatch. Full-text chunks substantially improve retrieval when abstracts omit supporting evidence, increasing both candidate recall and top-rank performance, although these cases are harder than queries supported by abstracts. Data and code are publicly available at this https URL, and the benchmark dataset is additionally archived on Zenodo.
https://arxiv.org/abs/2610.03130
Open-weight language models can be downloaded, modified, and deployed beyond their developers' control, limiting the effectiveness of centrally enforced safeguards. Recent work has therefore proposed \emph{trigger-tag} mechanisms that produce a detectable signal when a model is used under a target condition, such as generating phishing contents. Although these mechanisms borrow from established techniques, their use for conditional misuse detection in open-weight LLMs is relatively new. Therefore, existing research works have not systematically studied the robustness of trigger-tag mechanisms under adversarial attacks. To close this gap, (i)~we formalize trigger-tags and distinguish \emph{token-level trigger-tags}, which introduce watermark-inspired signals during decoding, from \emph{weight-level trigger-tags}, which learn backdoor-inspired associations between target conditions and detectable model behavior. Furthermore, (ii)~we introduce \Untag, a unified attack framework that organizes their mechanism-specific attack surfaces into a common taxonomy. We evaluate representative token-level and weight-level trigger-tags using phishing as a case study. We find that while trigger-tags may provide useful evidence in controlled settings, our attacks render the existing trigger-tag mechanisms to be entirely ineffective. Consequently, we argue that these mechanisms should not be treated as robust misuse detectors when attackers can transform outputs or modify open weights.
https://arxiv.org/abs/2610.03124
Text-to-image (T2I) models are judged by benchmarks that measure whether requested content appears, but these benchmarks largely overlook the complementary ability to satisfy negated constraints, for example, generating "a non-red cup." Measuring negation raises challenges not faced by affirmation-based benchmarks and requires careful prompt and evaluation design. We introduce NegT2IBench, a benchmark of 4,800 prompts covering two attribute types and four relation categories. Prompts are organized by polarity: the number of positive statements that must hold and negated statements that must not, each ranging from 0 to 2. Varying the two independently separates the effect of negation from the effect of prompt complexity. Our detector-based scoring is reproducible, auditable, and pinpoints which requirement failed. On 600 images with three-annotator labels, it agrees with humans as closely as vision-language judges up to 30x larger, while using only a fraction of their GPU memory. Across eleven T2I models and 211,200 images, nine score lower on a single negated statement than on a single positive one. Per-statement scoring reveals that the loss is largest for color and near zero for proximity, and that 41.5% of failed statements render exactly what the prompt forbids. Rendering what a prompt asks for and withholding what it forbids are distinct capabilities that an aggregate compositional score cannot distinguish. NegT2IBench measures the latter directly, providing a controlled testbed for diagnosing negation failures and developing methods to overcome them.
https://arxiv.org/abs/2610.03084
Propaganda detection is an essential task in natural language processing (NLP), particularly in the context of manipulative political communications. However, identifying specific propaganda techniques presents a significant challenge due to their often subtle nature and reliance on context, making them difficult to distinguish from legitimate persuasive language. Propaganda often involves highlighting certain facts while downplaying or ignoring others to create a desired perception. This biased communication aims to influence attitudes, beliefs, or behaviors towards a particular cause or position. This paper explores advances in detecting propaganda techniques through a comparative analysis of modern language models, using the SemEval-2020 Task 11 dataset. We evaluated both masked language models (based on XLM-RoBERTa or DeBERTa V3) and causal models (from OpenAI, Google, Mistral, Anthropic and Meta), employing two prompting strategies: base and chain-of-thought prompting. Our results demonstrate improvements over state-of-the-art models, with the best-performing MLM achieving an F1 score of 63.18 in technique classification and the best causal model achieving 63.62. We also observed that certain models excel in specific techniques, such as loaded language and name-calling, while struggling with others like bandwagon and black-and-white fallacy. These findings suggest that fine-tuning, ensemble modeling, and the use of larger datasets can further enhance propaganda detection capabilities.
https://arxiv.org/abs/2610.03077
Large language models are increasingly used as reasoning components in AI-driven materials Co-Scientists, yet the reliability of the resulting verification pipeline remains unclear. Metal-organic frameworks (MOFs) provide a particularly challenging setting because structures may appear under different identifiers, synthesis outcomes depend strongly on experimental conditions, evidence is distributed across heterogeneous sources, and some hypotheses require computation rather than literature alone. We introduce a diagnostic benchmark with four task families covering structural grounding, synthesis-condition verification, evidence-sufficiency verification, and MLIP-based computational verification. T-MOF-1-3 are evaluated under closed-book, retrieval-enabled, and oracle-evidence settings to localize failures in knowledge access, evidence acquisition, and reasoning, while T-MOF-4 separately evaluates computational verification. Guided by these diagnosed failure modes, we develop MOF-Verify, a failure-aware agentic harness that targets structural, literature, evidence-sufficiency, and computational bottlenecks before producing a final verdict. Across multiple backbone LLMs, MOF-Verify substantially improves hypothesis-verification performance over direct inference and retrieval-based baselines. Benchmark datasets are released at this https URL.
https://arxiv.org/abs/2610.03056
Large language models (LLMs) contain broad knowledge, but they cannot access all of it reliably. We study this problem through knowledge accessibility, which describes whether the knowledge needed for a query can be recalled from the model. We find that knowledge accessibility has a simple geometric structure in the model's representation of the query alone, before any generation. More accessible queries are closer to a center in the representation space, while less accessible queries are farther away. This geometry reveals a knowledge boundary that separates more accessible queries from less accessible ones. Accessibility consistently decreases with distance from the center, and this distance-based ordering transfers across datasets even when the centers differ. Controlled experiments further show that the centered geometry is more closely related to knowledge accessibility than to reasoning difficulty. The geometry also reveals when different interventions are useful. Query rewriting helps more for accessible queries, chain-of-thought reasoning helps more near the boundary, and retrieval gives larger gains beyond the boundary. These findings not only provide a new geometric view of how knowledge is organized in language models, but also suggest a useful pre-generation signal for adaptive inference.
https://arxiv.org/abs/2610.03052
Social bees are important pollinators that support biodiversity and crop pollination globally and serve as important model systems for collective behavior, but scalable measurement of individual- and colony-level behavior remains difficult in dense, occluded nest environments. Existing monitoring workflows use fiducial tags (e.g., ArUco) to preserve individual identity, yet tag-based tracking can fail when markers are obscured and provide limited information about body extent, spatial context, and untagged individuals. We present BeeWhere, an AI-assisted annotation and analysis workflow that combines ArUco detections with deep-learnt instance segmentations to quantify bumble bee behavior from high-resolution colony images and videos. Using bumble bee (Bombus impatiens) microcolonies as a test case, we annotate 483 frames containing 8,443 bee instances. We additionally annotate pollen balls, nest structures, and chamber boundaries, and train YOLO instance segmentation models for downstream behavioral analysis. Instance segmentations enable quantification of important behavioral metrics based on body contours, including nearest-neighbor distance, proximity to nest structures, spatial occupancy within the nest, and detection counts over time. We apply the BeeWhere models to tag-based tracking in an exploratory validation study assessing the behavioral impacts of neonicotinoid pesticide exposure. BeeWhere increased detection rates compared to tag-based tracking, particularly when bees were partially obscured or under challenging imaging conditions, and also captured treatment-associated changes in bee spatial organization not captured using tag-based tracking alone. These results suggest that instance segmentation can complement fiducial-marker tracking by recovering behaviorally meaningful signals under challenging colony conditions.
https://arxiv.org/abs/2610.03051
What makes a short story gripping; a news article newsworthy; or a math proof elegant? These constructs resist articulation or verification; their meaning is at least partially tacit. However, modern AI models are improved primarily via articulated constitutions, rubrics and verifiers (i.e. in RLAIF and RLVR); tacit components of preferences are typically understudied. We introduce a large, labeled preference dataset CreativePreferences, containing 2.8M texts labeled by 317M human preference judgments across 7 creative domains, with 42 benchmark tasks. We model these labels with executable programs, rubric banks and densely trained models (V, A and VAT, respectively). We observe robust articulability gaps, VAT-VA; and verifiability gaps, VAT-V; we estimate upper and lower bounds for each gap with a novel measurement approach that discovers articulable and verifiable metrics, identifies spurious variables and estimates the value of undiscovered metrics using capture-recapture. These gaps occur across all domains, even in domains traditionally treated as fully verifiable: correctness-centered domains (i.e. mathematics and software engineering) and claim- and novelty-centric domains (i.e. news, patents, peer review). The size of the gap varies based on domain (e.g. peer review and creative writing have the largest articulability gaps) and widens as more people take part in the judgment, consistent with Collins' collective tacit knowledge. We show two consequences: (1) on human generations, the full model more closely matches human preferences, often in disagreement with articulated criteria, and (2) in an analogy to Goodhart's law, articulating preference shifts it away from the tacit dimension. Articulability and verifiability gaps are consequential; we give recommendations on when tasks can be prompted; how learning mechanisms might improve; and when to leave judgments with humans.
https://arxiv.org/abs/2610.03025
Accurate 3D detection is essential for mobile embodied agents, while Vision Foundation Models (VFMs) offer transferable visual and geometric priors. Yet existing VFM-based 3D detectors rely on narrow-view monocular images or discrete perspective views, limiting coherent surround perception; equirectangular projection (ERP) instead encodes a continuous 360 scene in a single image. Direct transfer remains difficult because ERP organizes geometry and visual information differently, making object-relevant cues hard to model, localize, and preserve. We propose OmniAct3D, a framework that adapts perspective-trained VFM detectors to ERP while preserving transferable VFM priors. To resolve geometric mismatch, the ERP-Ray Geometry Adapter (ERGA-Ray) models spherical viewing rays and periodic spatial structure. To localize evidence in scene-wide context, the Visual-Action Reasoning Chain (VARC) grounds each hypothesis in relevant panoramic evidence and converts it into a structured geometric action. To recover local cues lost under fixed token budgets, the Appearance-Guided Heading Expert (AGHE) re-encodes object regions at higher resolution for heading estimation. Experiments show that OmniAct3D improves over the previous best 3D detector by 2.96 NDS points on Spheriverse and over the unadapted VFM baseline by 24.87 mAP points on PanoMMOcc. With target-specific geometry adaptation, VARC retains 95--98% of the same-configuration mAP, indicating reusable object-level 3D reasoning across sensing configurations. The source code will be made publicly available at this https URL.
https://arxiv.org/abs/2610.03015
Intrinsic explainability remains a challenging problem, particularly in contexts where multilayer perceptrons (MLPs) require dynamic re-training within an optimization environment. This paper investigates how MLPs and their training dynamics can be represented and studied in non-Euclidean spaces; our representation features the Poincaré model of hyperbolic geometry. We aim to capture the geometric evolution of their weighted topology and self-organization over time. Instead of restricting the analysis to single checkpoints---as per established measure-based explainability methods---we construct temporal \textit{parameter graphs}, i.e., snapshots over time $T$ steps of the optimization/training process for MLPs. This reflects the view that neural networks encode information not only in their weights but also in the trajectory traced during training. Drawing on the idea that many complex networks admit embeddings in hidden metric spaces where distances correspond to connection likelihood, we present a geometric and temporal graph-based metalearning framework for obtaining dynamic hyperbolic representations of the underlying neural parameter graphs. Our model embeds temporal parameter graphs in the Poincaré model ball, and learns from them while maintaining equivariance to within-snapshot neuron permutations and invariance to permutations of past snapshots. In doing so, the approach preserves functional equivalence over time and recovers the latent evolving geometry of the network. Experiments on regression and classification tasks with trained MLPs show strong meta-network performance, accompanied by hyperbolic temporal representations. This reveals how the network structure emerges over time under specific training environments, thus providing insights into the network's self-organization.
https://arxiv.org/abs/2610.03000