Understanding the structure of the homology embedding can thus disclose geometric or topological information from the data.

One key failure case was answers in the form of "the answer must be something that is ." Q: What might someone get from learning about science? Answer Choices: (a) headache (b) see things differently (c) increased knowledge (d) accidents (e) appreciation of nature A: The answer must be something that someone would get from learning about science. Learning about science would increase knowledge. Therefore, the answer is increased knowledge (c). These rationales, while perhaps useful to the model, read to us as opaque and unexplanatory. Sometimes the model will imply the answer that it has chosen in its question. Q: The christian rock band was on a large stage, the singer's foot got caught on a wire and he had a small what? Answer Choices: (a) commit sin (b) fail (c) disobey (d) stumble (e) boo boo A: The answer must be something that would cause the singer to stumble. The singer's foot got caught on a wire, so he would stumble.

Transformers have shown great power in time series forecasting due to their global-range modeling ability.

On a sunny day in San Francisco, along the city's waterfront, families dived into the wacky world of artificial intelligence inside the Exploratorium museum. Visitors made shadow puppets for AI to identify, used AI to generate songs, asked chatbots questions and faced off with AI in a game in which players tried to draw images that only humans would recognize. A giant robot hand moved around and people peered into a video game chip. They jotted down their hopes and worries about AI on cards displayed in the museum. Hope: AI will cure cancer.

Tesla shareholders sued Elon Musk and the electric vehicle maker for allegedly concealing the significant risk posed by company's self-driving vehicles. The proposed class-action suit, which accuses Musk and Tesla of securities fraud, was filed on Monday night. Tesla conducted its first public test of its self-driving taxis in late June near the company's headquarters in Austin, Texas. That test showed the vehicles speeding, braking suddenly, driving over a curb, entering the wrong lane and dropping off passengers in the middle of multilane roads. The National Highway Transit Safety Administration (NHTSA), the main transportation regulator in the US, is investigating the Robotaxi's pilot test.

The sea floor is home to all sorts of weird and wonderful creatures. But one in particular has become an online sensation, thanks to its impressive'buttocks'. A big–bottomed sea star has been spotted more than 1,000 metres (3,280ft) below the waves. And it appears to have a backside that will make even the most avid gymgoer jealous. This has led many baffled viewers to compare the creature to Patrick from the animated series Spongebob Squarepants.

We present MOSS, a multi-objective optimization framework for constructing stable sets of decision rules. MOSS incorporates three important criteria for interpretability: sparsity, accuracy, and stability, into a single multi-objective optimization framework. Importantly, MOSS allows a practitioner to rapidly evaluate the trade-off between accuracy and stability in sparse rule sets in order to select an appropriate model. We develop a specialized cutting plane algorithm in our framework to rapidly compute the Pareto frontier between these two objectives, and our algorithm scales to problem instances beyond the capabilities of commercial optimization solvers. Our experiments show that MOSS outperforms state-of-the-art rule ensembles in terms of both predictive performance and stability.

Local projections (LPs) are widely used in empirical macroeconomics to estimate impulse responses to policy interventions. Yet, in many ways, they are black boxes. It is often unclear what mechanism or historical episodes drive a particular estimate. We introduce a new decomposition of LP estimates into the sum of contributions of historical events, which is the product, for each time stamp, of a weight and the realization of the response variable. In the least squares case, we show that these weights admit two interpretations. First, they represent purified and standardized shocks. Second, they serve as proximity scores between the projected policy intervention and past interventions in the sample. Notably, this second interpretation extends naturally to machine learning methods, many of which yield impulse responses that, while nonlinear in predictors, still aggregate past outcomes linearly via proximity-based weights. Applying this framework to shocks in monetary and fiscal policy, global temperature, and the excess bond premium, we find that easily identifiable events-such as Nixon's interference with the Fed, stagflation, World War II, and the Mount Agung volcanic eruption-emerge as dominant drivers of often heavily concentrated impulse response estimates.

Tesla has publicly staked its future on its robotaxis. Now the company is planning to launch a public car service in the San Francisco Bay Area. Tesla is calling it a "robotaxi" service, but legally, this one will have to use cars with human drivers. The plan appears to put the electric carmaker in murky legal waters in a US state with the country's most tightly regulated autonomous vehicle industry--and where Tesla is already being sued for misleading language around its driver assistance tech. On Friday, a spokesperson for the California Public Utilities Commission, which regulates ride-hailing and taxi services in the state, said that Tesla informed the agency Thursday that it planned to expand an employee-only taxi service to friends and family of employees and "select" members of the public.

The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency components can be regarded as the coefficients of cosine and sine basis functions at tiered frequency levels, respectively. We find that existing Fourier-based methods face inconsistent starting cycles and inconsistent series length issues. They fail to interpret frequency components precisely and overlook temporal information. Accordingly, the novel Fourier Basis Mapping (FBM) method addresses these issues by integrating time-frequency features through Fourier basis expansion and mapping in the time-frequency space. Our approach extracts explicit frequency features while preserving temporal characteristics. FBM supports plug-and-play integration with various types of neural networks by only adjusting the first initial projection layer for better performance. First, we propose FBM-L, FBM-NL, and FBM-NP to enhance linear, MLP-based, and Transformer-based models, respectively, demonstrating the effectiveness of time-frequency features. Next, we propose a synergetic model architecture, termed FBM-S, which decomposes the seasonal, trend, and interaction effects into three separate blocks, each designed to model time-frequency features in a specialized manner. Finally, we introduce several techniques tailored for time-frequency features, including interaction masking, centralization, patching, rolling window projection, and multi-scale down-sampling. The results are validated on diverse real-world datasets for both long-term and short-term forecasting tasks with SOTA performance.