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Oct 16

Learning Physical Models that Can Respect Conservation Laws

Recent work in scientific machine learning (SciML) has focused on incorporating partial differential equation (PDE) information into the learning process. Much of this work has focused on relatively ``easy'' PDE operators (e.g., elliptic and parabolic), with less emphasis on relatively ``hard'' PDE operators (e.g., hyperbolic). Within numerical PDEs, the latter problem class requires control of a type of volume element or conservation constraint, which is known to be challenging. Delivering on the promise of SciML requires seamlessly incorporating both types of problems into the learning process. To address this issue, we propose ProbConserv, a framework for incorporating conservation constraints into a generic SciML architecture. To do so, ProbConserv combines the integral form of a conservation law with a Bayesian update. We provide a detailed analysis of ProbConserv on learning with the Generalized Porous Medium Equation (GPME), a widely-applicable parameterized family of PDEs that illustrates the qualitative properties of both easier and harder PDEs. ProbConserv is effective for easy GPME variants, performing well with state-of-the-art competitors; and for harder GPME variants it outperforms other approaches that do not guarantee volume conservation. ProbConserv seamlessly enforces physical conservation constraints, maintains probabilistic uncertainty quantification (UQ), and deals well with shocks and heteroscedasticities. In each case, it achieves superior predictive performance on downstream tasks.

  • 5 authors
·
Feb 21, 2023

On Bonart's interpretation of the Square-Root Impact Law

The square-root impact law (SRIL), I = YσQ/V, bundles two facts that a single mechanism must explain at once: a shape (impact proportional to square-root of traded volume Q) and an amplitude (Y=O(1), independent of the participation rate φ). Bonart has recently proposed an elegant solution: if realized and counterfactual prices are both diffusive, information-neutral impact must have white increments and the SRIL follows without the wart. We reformulate and simplify his argument, and foreground the ingredient he himself regards as essential --- that the market whitens the stationary stream of each participant's metaorders, not any isolated one. The Lillo--Mike--Farmer model satisfies his premises, yet gives an isolated metaorder the super-square-root impact φ^{(1-γ)/2}Q^{(1+γ)/2}, γin(0,1), because single metaorders (i.e. not part of a stream) are statistically invisible and thus priced mechanically. We then construct an explicit multi-agent propagator that realizes Bonart's whitening, and show it reproduces the clean SRIL precisely when the market can attribute trades to their issuer. But correct re-attribution of anonymous trades is a formidable task, which requires markets to behave as implausibly efficient signal processing machines. The stream hypothesis makes a sharp, falsifiable prediction --- isolated metaorders, well separated in time, should not obey the SRIL --- that does not seem agree with empirical data known to us. Independently, a volume-conservation argument singles out the square-root law and lays bare the step the diffusivity route must assume: diffusivity fixes the variance of impact --- an additive, stationary, age-blind quantity --- whereas the SRIL is a law for the mean impact, which marginally decays as 1/text{age} and therefore demands an origin of time.

  • 3 authors
·
Oct 6

New Adaptive Numerical Methods Based on Dual Formulation of Hyperbolic Conservation Laws

In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative formulations of the same system, are evolved simultaneously. Since nonconservative schemes are known to produce nonphysical weak solutions near discontinuities, we exploit the difference between these two solutions to construct a smoothness indicator (SI). In smooth regions, the difference between the conservative and nonconservative solutions is of the same order as the truncation error of the underlying discretization, whereas in nonsmooth regions, it is {cal O}(1). We apply this idea to the Euler equations of gas dynamics and define the SI using differences in the momentum and pressure variables. This choice allows us to further distinguish neighborhoods of contact discontinuities from other nonsmooth parts of the computed solution. The resulting classification is used to adaptively select numerical discretizations. In the vicinities of contact discontinuities, we employ the low-dissipation central-upwind numerical flux and a second-order piecewise linear reconstruction with the slopes computed using an overcompressive SBM limiter. Elsewhere, we use an alternative weighted essentially non-oscillatory (A-WENO) framework with the central-upwind finite-volume numerical fluxes and either unlimited (in smooth regions) or Ai-WENO-Z (in the nonsmooth regions away from contact discontinuities) fifth-order interpolation. Numerical results for the one- and two-dimensional compressible Euler equations show that the proposed adaptive method improves both the computational efficiency and resolution of complex flow features compared with the non-adaptive fifth-order A-WENO scheme.

  • 4 authors
·
Jan 27

UltraVoice: Scaling Fine-Grained Style-Controlled Speech Conversations for Spoken Dialogue Models

Spoken dialogue models currently lack the ability for fine-grained speech style control, a critical capability for human-like interaction that is often overlooked in favor of purely functional capabilities like reasoning and question answering. To address this limitation, we introduce UltraVoice, the first large-scale speech dialogue dataset engineered for multiple fine-grained speech style control. Encompassing over 830 hours of speech dialogues, UltraVoice provides instructions across six key speech stylistic dimensions: emotion, speed, volume, accent, language, and composite styles. Fine-tuning leading models such as SLAM-Omni and VocalNet on UltraVoice significantly enhances their fine-grained speech stylistic controllability without degrading core conversational abilities. Specifically, our fine-tuned models achieve improvements of 29.12-42.33% in Mean Opinion Score (MOS) and 14.61-40.09 percentage points in Instruction Following Rate (IFR) on multi-dimensional control tasks designed in the UltraVoice. Moreover, on the URO-Bench benchmark, our fine-tuned models demonstrate substantial gains in core understanding, reasoning, and conversational abilities, with average improvements of +10.84% on the Basic setting and +7.87% on the Pro setting. Furthermore, the dataset's utility extends to training controllable Text-to-Speech (TTS) models, underscoring its high quality and broad applicability for expressive speech synthesis. The complete dataset and model checkpoints are available at: https://github.com/bigai-nlco/UltraVoice.

  • 9 authors
·
Oct 26, 2025

Llama Guard: LLM-based Input-Output Safeguard for Human-AI Conversations

We introduce Llama Guard, an LLM-based input-output safeguard model geared towards Human-AI conversation use cases. Our model incorporates a safety risk taxonomy, a valuable tool for categorizing a specific set of safety risks found in LLM prompts (i.e., prompt classification). This taxonomy is also instrumental in classifying the responses generated by LLMs to these prompts, a process we refer to as response classification. For the purpose of both prompt and response classification, we have meticulously gathered a dataset of high quality. Llama Guard, a Llama2-7b model that is instruction-tuned on our collected dataset, albeit low in volume, demonstrates strong performance on existing benchmarks such as the OpenAI Moderation Evaluation dataset and ToxicChat, where its performance matches or exceeds that of currently available content moderation tools. Llama Guard functions as a language model, carrying out multi-class classification and generating binary decision scores. Furthermore, the instruction fine-tuning of Llama Guard allows for the customization of tasks and the adaptation of output formats. This feature enhances the model's capabilities, such as enabling the adjustment of taxonomy categories to align with specific use cases, and facilitating zero-shot or few-shot prompting with diverse taxonomies at the input. We are making Llama Guard model weights available and we encourage researchers to further develop and adapt them to meet the evolving needs of the community for AI safety.

  • 11 authors
·
Dec 7, 2023 1