We introduce the Schrodinger Neural Network (SNN), a principled architecture for conditional density estimation and uncertainty quantification inspired by quantum mechanics. The SNN maps each input to a normalized wave function on the output domain and computes predictive probabilities via the Born rule. The SNN departs from standard parametric likelihood heads by learning complex coefficients of a spectral expansion (e . g ., Chebyshev polynomials) whose squared modulus yields the conditional density $p(y|x)=\left| ψ_x(y)\right| {}^2$ with analytic normalization. This representation confers three practical advantages: positivity and exact normalization by construction, native multimodality through interference among basis modes without explicit mixture bookkeeping, and yields closed-form (or efficiently computable) functionals$-$such as moments and several calibration diagnostics$-$as quadratic forms in coefficient space. We develop the statistical and computational foundations of the SNN, including (i) training by exact maximum-likelihood with unit-sphere coefficient parameterization, (ii) physics-inspired quadratic regularizers (kinetic and potential energies) motivated by uncertainty relations between localization and spectral complexity, (iii) scalable low-rank and separable extensions for multivariate outputs, (iv) operator-based extensions that represent observables, constraints, and weak labels as self-adjoint matrices acting on the amplitude space, and (v) a comprehensive framework for evaluating multimodal predictions. The SNN provides a coherent, tractable framework to elevate probabilistic prediction from point estimates to physically inspired amplitude-based distributions.

The growing intersection of cybersecurity and law creates a complex information space where traditional legal research tools struggle to deal with nuanced connections between cases, statutes, and technical vulnerabilities. This knowledge divide hinders collaboration between legal experts and cybersecurity professionals. To address this important gap, this work provides a first step towards intelligent systems capable of navigating the increasingly intricate cyber-legal domain. We demonstrate promising initial results on multilingual tasks.

We explore a "best-of-both" approach to modelling molecular properties by combining learned molecular descriptors from a graph neural network (GNN) with general-purpose descriptors and a mixed ensemble of machine learning (ML) models. We introduce a MetaModel framework to aggregate predictions from a diverse set of leading ML models. We present a featurisation scheme for combining task-specific GNN-derived features with conventional molecular descriptors. We demonstrate that our framework outperforms the cutting-edge ChemProp model on all regression datasets tested and 6 of 9 classification datasets. We further show that including the GNN features derived from ChemProp boosts the ensemble model's performance on several datasets where it otherwise would have underperformed. We conclude that to achieve optimal performance across a wide set of problems, it is vital to combine general-purpose descriptors with task-specific learned features and use a diverse set of ML models to make the predictions.

The increasing deployment of Machine Learning (ML) models in sensitive domains motivates the need for robust, practical privacy assessment tools. PrivacyGuard is a comprehensive tool for empirical differential privacy (DP) analysis, designed to evaluate privacy risks in ML models through state-of-the-art inference attacks and advanced privacy measurement techniques. To this end, PrivacyGuard implements a diverse suite of privacy attack -- including membership inference , extraction, and reconstruction attacks -- enabling both off-the-shelf and highly configurable privacy analyses. Its modular architecture allows for the seamless integration of new attacks, and privacy metrics, supporting rapid adaptation to emerging research advances. We make PrivacyGuard available at https://github.com/facebookresearch/PrivacyGuard.

The rapid ascent of Foundation Models (FMs), enabled by the Transformer architecture, drives the current AI ecosystem. Characterized by large-scale training and downstream adaptability, FMs (as GPT family) have achieved massive public adoption, fueling a turbulent market shaped by platform economics and intense investment. Assessing the vulnerability of this fast-evolving industry is critical yet challenging due to data limitations. This paper proposes a synthetic AI Vulnerability Index (AIVI) focusing on the upstream value chain for FM production, prioritizing publicly available data. We model FM output as a function of five inputs: Compute, Data, Talent, Capital, and Energy, hypothesizing that supply vulnerability in any input threatens the industry. Key vulnerabilities include compute concentration, data scarcity and legal risks, talent bottlenecks, capital intensity and strategic dependencies, as well as escalating energy demands. Acknowledging imperfect input substitutability, we propose a weighted geometrical average of aggregate subindexes, normalized using theoretical or empirical benchmarks. Despite limitations and room for improvement, this preliminary index aims to quantify systemic risks in AI's core production engine, and implicitly shed a light on the risks for downstream value chain.

Auto-bidding is crucial in facilitating online advertising by automatically providing bids for advertisers. While previous work has made great efforts to model bidding environments for better ad performance, it has limitations in generalizability across environments since these models are typically tailored for specific bidding scenarios. To this end, we approach the scenario-independent principles through a unified function that estimates the achieved effect under specific bids, such as budget consumption, gross merchandise volume (GMV), page views, etc. Then, we propose a bidding foundation model Bid2X to learn this fundamental function from data in various scenarios. Our Bid2X is built over uniform series embeddings that encode heterogeneous data through tailored embedding methods. To capture complex inter-variable and dynamic temporal dependencies in bidding data, we propose two attention mechanisms separately treating embeddings of different variables and embeddings at different times as attention tokens for representation learning. On top of the learned variable and temporal representations, a variable-aware fusion module is used to perform adaptive bidding outcome prediction. To model the unique bidding data distribution, we devise a zero-inflated projection module to incorporate the estimated non-zero probability into its value prediction, which makes up a joint optimization objective containing classification and regression. The objective is proven to converge to the zero-inflated distribution. Our model has been deployed on the ad platform in Taobao, one of the world's largest e-commerce platforms. Offline evaluation on eight datasets exhibits Bid2X's superiority compared to various baselines and its generality across different scenarios. Bid2X increased GMV by 4.65% and ROI by 2.44% in online A/B tests, paving the way for bidding foundation model in computational advertising.

The behaviour of neural network components must be proven correct before deployment in safety-critical systems. Unfortunately, existing neural network verification techniques cannot certify the absence of faults at the software level. In this paper, we show how to specify and verify that neural networks are safe, by explicitly reasoning about their floating-point implementation. In doing so, we construct NeuroCodeBench 2.0, a benchmark comprising 912 neural network verification examples that cover activation functions, common layers, and full neural networks of up to 170K parameters. Our verification suite is written in plain C and is compatible with the format of the International Competition on Software Verification (SV-COMP). Thanks to it, we can conduct the first rigorous evaluation of eight state-of-the-art software verifiers on neural network code. The results show that existing automated verification tools can correctly solve an average of 11% of our benchmark, while producing around 3% incorrect verdicts. At the same time, a historical analysis reveals that the release of our benchmark has already had a significantly positive impact on the latter.

We investigate a relatively underexplored class of hybrid neurosymbolic models integrating symbolic learning with neural reasoning to construct data generators meeting formal correctness criteria. In \textit{Symbolic Neural Generators} (SNGs), symbolic learners examine logical specifications of feasible data from a small set of instances -- sometimes just one. Each specification in turn constrains the conditional information supplied to a neural-based generator, which rejects any instance violating the symbolic specification. Like other neurosymbolic approaches, SNG exploits the complementary strengths of symbolic and neural methods. The outcome of an SNG is a triple $(H, X, W)$, where $H$ is a symbolic description of feasible instances constructed from data, $X$ a set of generated new instances that satisfy the description, and $W$ an associated weight. We introduce a semantics for such systems, based on the construction of appropriate \textit{base} and \textit{fibre} partially-ordered sets combined into an overall partial order, and outline a probabilistic extension relevant to practical applications. In this extension, SNGs result from searching over a weighted partial ordering. We implement an SNG combining a restricted form of Inductive Logic Programming (ILP) with a large language model (LLM) and evaluate it on early-stage drug design. Our main interest is the description and the set of potential inhibitor molecules generated by the SNG. On benchmark problems -- where drug targets are well understood -- SNG performance is statistically comparable to state-of-the-art methods. On exploratory problems with poorly understood targets, generated molecules exhibit binding affinities on par with leading clinical candidates. Experts further find the symbolic specifications useful as preliminary filters, with several generated molecules identified as viable for synthesis and wet-lab testing.

Flood susceptibility mapping (FSM) is vital for disaster prevention but remains challenging in data-scarce regions where hydrodynamic models require dense geophysical inputs. This work introduces ZeroFlood, a geospatial foundation model framework for data-efficient FSM. The approach fine-tunes Geospatial Foundation Models (GFMs) with Thinking-in-Modality (TiM) reasoning, enabling flood prediction from basic Earth observation data such as Sentinel-1 or Sentinel-2 imagery. Using paired EO and simulated flood maps from data-rich regions, ZeroFlood bridges data availability gaps through cross-modal representation learning. Experiments with TerraMind and Prithvi GFMs show that TiM enhances model robustness, with the TerraMind-Large configuration achieving an F1 score of 67.21. The results demonstrate the feasibility of foundation-model-based FSM as a scalable and data-efficient solution for flood risk management.

Artificial intelligence is reshaping labor markets, yet we lack tools to systematically forecast its effects on employment. This paper introduces a benchmark for evaluating how well large language models (LLMs) can anticipate changes in job demand, especially in occupations affected by AI. Existing research has shown that LLMs can extract sentiment, summarize economic reports, and emulate forecaster behavior, but little work has assessed their use for forward-looking labor prediction. Our benchmark combines two complementary datasets: a high-frequency index of sector-level job postings in the United States, and a global dataset of projected occupational changes due to AI adoption. We format these data into forecasting tasks with clear temporal splits, minimizing the risk of information leakage. We then evaluate LLMs using multiple prompting strategies, comparing task-scaffolded, persona-driven, and hybrid approaches across model families. We assess both quantitative accuracy and qualitative consistency over time. Results show that structured task prompts consistently improve forecast stability, while persona prompts offer advantages on short-term trends. However, performance varies significantly across sectors and horizons, highlighting the need for domain-aware prompting and rigorous evaluation protocols. By releasing our benchmark, we aim to support future research on labor forecasting, prompt design, and LLM-based economic reasoning. This work contributes to a growing body of research on how LLMs interact with real-world economic data, and provides a reproducible testbed for studying the limits and opportunities of AI as a forecasting tool in the context of labor markets.