This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale (KSS) random field on the sphere, and applies it to two problems: Spiked Tensor PCA and the landscape of the spherical $k$-spin model. For Tensor PCA, we study the non-asymptotic statistical limits of estimating a rank-$R$ symmetric signal tensor of order~$k\ge 3$ and dimension~$d\ge 3$ from a single Gaussian observation at signal-to-noise ratio~$λ$, through the \emph{profile maximum likelihood estimator}, the MLE restricted to normalized rank-$R$ tensors of coherence at least~$κ$. Our analysis uses a single reduction: a deterministic geometric inequality (the Tube Method) and a rank-reduction step bound the estimation error by the supremum of the canonical KSS field, which the Kac--Rice formula turns into a Gaussian integral against the expected absolute characteristic polynomial of a shifted Gaussian Orthogonal Ensemble, controlled in turn by the four explicit tail bounds of our hierarchy (three from a Mehta--Fyodorov representation, one from a Ben Arous--Dembo--Guionnet large deviation). The same reduction yields two results, each with explicit constants. For estimation, a finite-$(k,d)$ error bound recovers the asymptotically optimal rate~$\sqrt{d\log k}$ of Perry, Wein and Bandeira, with explicit dependence on the rank~$R$ and the coherence~$κ$. For the landscape, a two-sided non-asymptotic bracketing of the annealed complexity of the spherical $k$-spin Hamiltonian recovers the Auffinger--Ben Arous--Černý complexity function in the high-dimensional limit.

The Schrödinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds.

Georgieva said that AI would wipe out many roles traditionally taken up by younger workers. Georgieva said that AI would wipe out many roles traditionally taken up by younger workers. Young will suffer most when AI'tsunami' hits jobs, says head of IMF Artificial intelligence will be a "tsunami hitting the labour market", with young people worst affected, the head of the International Monetary Fund warned the World Economic Forum on Friday. Kristalina Georgieva told delegates in Davos that the IMF's own research suggested there would be a big transformation of demand for skills, as the technology becomes increasingly widespread. "We expect over the next years, in advanced economies, 60% of jobs to be affected by AI, either enhanced or eliminated or transformed - 40% globally," she said.

President Trump's favourite word is tariffs. He reminded the world of that in his pre-Christmas address to the nation. With the world still unwrapping the tariffs gift from the first year of his second term in office, he said they were bringing jobs, higher wages and economic growth to the US. What is less debatable is that they've refashioned the global economy, and will continue to do so into 2026. The International Monetary Fund (IMF) says that although the tariff shock is smaller than originally announced, it is a key reason why it now expects the rate of global economic growth to slow to 3.1% in 2026.

This study proposes a hybrid deep learning model for forecasting the price of Bitcoin, as the digital currency is known to exhibit frequent fluctuations. The models used are the Variational Mode Decomposition (VMD) and the Long Short-Term Memory (LSTM) network. First, VMD is used to decompose the original Bitcoin price series into Intrinsic Mode Functions (IMFs). Each IMF is then modeled using an LSTM network to capture temporal patterns more effectively. The individual forecasts from the IMFs are aggregated to produce the final prediction of the original Bitcoin Price Series. To determine the prediction power of the proposed hybrid model, a comparative analysis was conducted against the standard LSTM. The results confirmed that the hybrid VMD+LSTM model outperforms the standard LSTM across all the evaluation metrics, including RMSE, MAE and R2 and also provides a reliable 30-day forecast.

What is the Insurrection Act? Is Trump trying to dial back tensions with Brazil? Why was Letitia James indicted? Will a government shutdown hurt the economy? The United States's artificial intelligence (AI) investment boom might be an economic bubble that could burst, comparable to the dot-com bust in the early 2000s, according to the International Monetary Fund.

The UK is forecast to be the second-fastest growing of the world's most advanced economies this year and next, according to new projections from the International Monetary Fund (IMF). The rates of growth remain modest at 1.3% for both years, but that outperforms the other G7 economies apart from the US, in a torrid year of trade and geopolitical tensions. However, UK inflation is set to rise to the highest in the G7 in 2025 and 2026, the IMF predicts, driven by larger energy and utility bills. UK inflation is forecast to average 3.4% this year and 2.5% in 2026 but the IMF says this will be temporary, and fall to 2% by the end of next year. The G7 are seven advanced economies - the US, UK, France, Germany, Italy, Canada and Japan - but the group doesn't include fast-growing economies such as China and India.

Animals achieve energy-efficient locomotion by their implicit passive dynamics, a marvel that has captivated roboticists for decades.Recently, methods incorporated Adversarial Motion Prior (AMP) and Reinforcement learning (RL) shows promising progress to replicate Animals' naturalistic motion. However, such imitation learning approaches predominantly capture explicit kinematic patterns, so-called gaits, while overlooking the implicit passive dynamics. This work bridges this gap by incorporating a reward term guided by Impact Mitigation Factor (IMF), a physics-informed metric that quantifies a robot's ability to passively mitigate impacts. By integrating IMF with AMP, our approach enables RL policies to learn both explicit motion trajectories from animal reference motion and the implicit passive dynamic. We demonstrate energy efficiency improvements of up to 32%, as measured by the Cost of Transport (CoT), across both AMP and handcrafted reward structure.

The integration of solar power has been increasing as the green energy transition rolls out. The penetration of solar power challenges the grid stability and energy scheduling, due to its intermittent energy generation. Accurate and near real-time solar power prediction is of critical importance to tolerant and support the permeation of distributed and volatile solar power production in the energy system. In this paper, we propose a deep-learning based ultra-short-term solar power prediction with data reconstruction. We decompose the data for the prediction to facilitate extensive exploration of the spatial and temporal dependencies within the data. Particularly, we reconstruct the data into low- and high-frequency components, using ensemble empirical model decomposition with adaptive noise (CEEMDAN). We integrate meteorological data with those two components, and employ deep-learning models to capture long- and short-term dependencies towards the target prediction period. In this way, we excessively exploit the features in historical data in predicting a ultra-short-term solar power production. Furthermore, as ultra-short-term prediction is vulnerable to local optima, we modify the optimization in our deep-learning training by penalizing long prediction intervals. Numerical experiments with diverse settings demonstrate that, compared to baseline models, the proposed method achieves improved generalization in data reconstruction and higher prediction accuracy for ultra-short-term solar power production.

The Schrödinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique.