#01Nov 5, 2026
q-fin.ST
Neural Realized Measures: Forecast-Supervised Intraday Aggregation for Volatility Forecasting
Brian Sing Fan Chan, Jennifer So Kuen Chan
High-frequency volatility forecasting typically separates measurement from prediction: intraday observations are first compressed into a daily realized measure using a fixed aggregation rule, and the resulting statistic is then passed to a forecasting model. This conventional pipeline therefore treats measure construction as forecast-agnostic preprocessing. We ask whether the aggregation stage itself can instead be learned from the downstream forecasting objective while preserving the statistical structure of established realized measures. We propose Neural Realized Measures (NRM), a primitive-preserving, forecast-supervised aggregation framework that retains the original measure-specific intraday contributions but replaces uniform aggregation with positive, mean-normalized context-dependent weights. Uniform weights exactly recover the corresponding raw realized measure (RRM), so the classical construction is nested as a special case. Because NRM remains an explicit weighted sum of established primitive contributions, it also retains direct bar-level attribution. Across SF, HAR, and MIDAS forecasting specifications, NRM is evaluated against corresponding RRM specifications under controlled comparisons. In Heston simulations, NRM reduces RMSE for both contemporaneous and next-day latent integrated variance across all evaluated primitive--regime combinations. On six cryptocurrencies using five-minute data, NRM improves QLIKE in all 54 paired out-of-sample comparisons, with mean gains of 7.23\%, 8.15\%, and 9.22\% under SF, HAR, and MIDAS, respectively. Validation-selected NRM specifications also achieve the lowest mean QLIKE across the six assets among the evaluated approaches. Ablation and SHAP analyses reveal systematic time-of-day and nonlinear local-context effects in the learned allocation.
#02Nov 5, 2026
cs.LO
Typed Knowledge over Constructive Institutions
Hans-Martin Will
Type theories designed for mathematics or program verification need only that a proposition holds; proof irrelevance in conversion erases, at the kernel level, how a claim was established. A persistent knowledge store, by contrast, must retain that record: who established a claim, by which derivation or external tool, and under which assumptions. This volume presents the theory of Eigenius---a store of typed knowledge over constructive institutions---and develops its metatheory from that requirement. The kernel theory is a dependent type theory with cumulative universes, an impredicative universe of propositions, inductive families, and an intensional identity type. Proof irrelevance is an axiom with an explicit witness rather than a conversion rule, so proofs of a proposition are provably equal yet remain distinct terms. Definitional equality is joinability under an orthogonal rewriting system---confluent, injective on type formers, and decidable by a type-free test---while a separate subsumption judgment covers universe cumulativity, codomain-covariant function types, and declared class inclusions. We prove consistency via a set-theoretic model; develop a justification logic over the kernel's propositions to track evidence and support; organize environments as an institution so that store extensions are signature morphisms and external verdicts enter via comorphisms; formulate a typed knowledge-graph theory with records, classes, and refinements; and prove the correctness of conversion, normalization by evaluation, and bidirectional type checking relative to termination. A Lean 4 formalization accompanies the volume.
#03Nov 5, 2026
cs.LG
When Scores Conflict with Preferences: Pre-Alignment Diagnosis and Adaptive Correction of Constraint Drift in DPO
Ping Liu, Yan Yan
Direct Preference Optimization (DPO) is increasingly used in settings where pairwise preferences coexist with pointwise criteria such as response length, answer correctness, or safety scores. When the two disagree, standard DPO treats pairs whose preferred output scores worse on the pointwise criterion (conflict pairs) in the same way as the remaining (matching) pairs. We characterize a systematic failure mode, constraint drift: for sufficiently small updates, conflict pairs tend to increase constraint cost while matching pairs tend to repair it, and the net change depends on their balance. This balance yields a closed-form pre-alignment diagnostic, $ρ^{*}_{\mathrm{eq}}$, computable from dataset statistics, that indicates whether a dataset is self-correcting or requires intervention. Building on this diagnostic, we propose Conflict-aware DPO (CoDPO), which down-weights conflict pairs with a strength set from $ρ^{*}_{\mathrm{eq}}$ rather than tuned, and adds an adaptive margin shift that addresses residual drift during training. Empirically, drift grows monotonically with conflict exposure on the conflict-dominated domains, and the intervention decision given by $ρ^{*}_{\mathrm{eq}}$ matches the observed drift on every domain, including one that it identifies as self-correcting. On all four domains of the main comparison, CoDPO reduces drift while largely preserving the preference learning of vanilla DPO. Compared with hard filtering and recent constrained and multi-objective baselines, CoDPO also achieves a more favorable drift-preference trade-off.
#04Nov 5, 2026
cs.LG
AtlasULP: Domain-aware Universal Link Prediction via Relation Atlas
Yujing Liu, Yixin Liu, Yu Zheng and 4 more
Link prediction (LP) is a widely applied task in graph learning. Conventional LP approaches typically follow a dataset-specific paradigm, requiring independent training for each graph and incurring high computational and maintenance costs in large-scale applications. Motivated by these limitations, recent work explores Universal Link Prediction (ULP), aiming to enable training-free inference on arbitrary unseen graphs. However, existing methods primarily rely on subgraph sampling strategies to construct universal representations, which are unable to capture higher-order information due to the exponential growth of higher-order neighborhoods. As a result, they often under-perform on graphs where long-range signals are essential, such as biological networks. Moreover, their prediction models are typically domain-agnostic and lack the ability to adapt to different graph domains, leading to limited generalization. To address these challenges, we propose an Atlas-based Universal Link Prediction framework (AtlasULP), which introduces the relation atlas to capture structural associations between node pairs from both global and local perspectives, enabling a comprehensive characterization of connectivity signals across diverse graph domains. Building upon this representation, we develop a domain-guided prompting ULP model, which generates domain-aware prompt tokens from contextual structures and performs prompt-guided in-context prediction for adaptive link inference. Extensive experiments demonstrate that AtlasULP consistently outperforms state-of-the-art methods across diverse graph domains.
#05Nov 5, 2026
math.OC
From What Is Used to What Is Missing: Rethinking Dynamic Rank in LoRA
Peng Xue, Guodong Fan, Guang-Yong Chen and 1 more
Parameter-efficient fine-tuning with LoRA is governed by rank, which controls parameter budget and locally accessible task updates. Existing dynamic-rank methods mainly focus on capacity allocation, leaving unresolved whether the current adaptation space is sufficient for the task. We characterize the first-order information boundary of standard factor gradients, showing that their unobservable subspace coincides with the normal space of the low-rank manifold. Thus, factor gradients alone cannot distinguish under-optimization within the current space from task-relevant directions beyond its first-order reach. This motivates a geometric view of rank evolution, where tangent information optimizes existing degrees of freedom and the normal spectrum quantifies the value of new ones. Under a local quadratic model, we show that leading normal singular directions yield the locally optimal rank expansion, with spectral energy determining its gain. Building on this characterization, we propose GEAR, which turns the tangent--normal decomposition into rank evolution through tangent-space optimization, matrix-free normal-spectrum estimation for rank expansion, and task-induced geometric initialization. Across language and vision benchmarks, GEAR achieves the best average performance in all evaluated settings with substantially fewer trainable parameters. On LLaMA3-8B, it raises the average commonsense score from 86.61 to 88.45 while reducing trainable parameters from 42.0M to 14.4M.