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版本更新 · v3arXiv:2610.20108

Exhaustive Canonical Skeletons Generation: A Formal Dataset for Decomposable Symbolic Regression

Giorgio Morales, Anikó Ekárt

原文摘要

Neural symbolic regression (SR) models require diverse datasets of mathematical expressions for robust training. However, existing datasets rely predominantly on stochastic sampling methods, which suffer from high structural redundancy and incomplete functional coverage. To address this, we introduce an exhaustive dataset of univariate canonical skeletons generated via a deterministic constrained context-free grammar. A canonical skeleton acts as a generic structural representation that subsumes more specific functional forms, eliminating redundant expressions and avoiding repeated computational efforts. Although our dataset consists of univariate skeletons, it is designed to support the decomposable SR paradigm to solve multivariate SR problems without assuming linear separability. Furthermore, we pair this dataset with a sampling strategy that generates clean numerical data without triggering numerical instabilities or relying on artificial protected operators. Canonicalizing two existing neural SR datasets reveals that our dataset is substantially more compact, eliminates structural repetitions, and achieves a uniform operator distribution free of simplicity bias. Finally, we establish a benchmark of 150 SR problems across three tiers, on which state-of-the-art SR methods are shown to struggle significantly.

cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.10521

TimeHF 2.0: Multimodal, Multivariate, and Multi-Region Collaborative Forecasting for Large-Scale Retail Supply Chains

Zhongxuan Han, Zhengxin Shi, Kunxiu Chen, Xiaolin Huang, Yulin Huang, Anni Zhang, Xiaoming Lin, Zhengyu Chen 等 33 位作者

原文摘要

Large-scale retail supply chains need sales forecasts for specified products, future dates or planning windows, and regions under the conditions available at the forecast origin. Regional sparsity, changing environments, volatile sales, and unfamiliar business situations make these dimensions difficult to model together. We introduce TimeHF 2.0, a multimodal, multivariate, and multi-region collaborative forecasting framework that makes flexibly expressed business knowledge usable in numerical prediction. A coverage-aware directed encoder integrates regional sales and applicable covariates. A semantic alignment module transfers language-model hidden representations of natural-language plans and domain experience into target-specific forecasting context. Learning against sales observations connects these meanings to numerical evidence, allowing business users to supply experience, future plans, and changing circumstances without defining a new numerical feature for each description. Text-conditioned future queries and shared/routed experts adapt prediction to the supplied context. An ordered-distribution head allocates fine resolution to routine fluctuations and coarse resolution to extreme sales movements, while daily/window learning connects forecasts to cumulative planning quantities. Online parallel forecasting at JD yields relative accuracy improvements of 18.25% and 17.94% for national daily and planning-window sales, and 19.44% and 18.99% for DC daily and planning-window sales, over the original production deep learning baseline. Component comparisons, loss-design results, and product-type analyses examine the roles of regional information, covariates, business knowledge, context-dependent processing, and robust planning-oriented learning.

cs.AI · cs.LG

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arXiv ↗PDF ↗
版本更新 · v5arXiv:2410.22729

Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots

Vincent Guan, Joseph Janssen, Hossein Rahmani, Andrew Warren, Stephen Zhang, Elina Robeva, Geoffrey Schiebinger

原文摘要

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE from data is a challenging task, especially if individual trajectories are not observable. Motivated by burgeoning research in single-cell datasets, we present the first comprehensive approach for jointly identifying the drift and diffusion of an SDE from its temporal marginals. Assuming linear drift and additive diffusion, we show that non-identifiability can only arise if the initial distribution possesses generalized rotational symmetries. We further prove that even if this condition holds, the drift and diffusion can almost always be recovered from the marginals. Additionally, we show that the causal graph of any SDE with additive diffusion can be recovered from the identified SDE parameters. To complement this theory, we adapt entropy-regularized optimal transport to handle anisotropic diffusion and introduce APPEX (Alternating Projection Parameter Estimation from $X_0$), an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals, and demonstrate its effectiveness on simulated data from linear additive noise SDEs.

stat.ML · cs.LG · math.ST

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arXiv ↗PDF ↗