Orioles pitcher Shane Baz drilled with 105.1 mph line drive in scary scene NFL's battle with drinking and driving continues as Keenan Allen formally charged in Indianapolis Anthony Molina and Matthew Liberatore's struggles make over 8 runs the play for Giants-Cardinals Shota Imanaga's home run struggles and Wrigley wind make over 7.5 the play for Braves-Cubs Jaxson Dart's girlfriend Marissa Ayers shines in Week 1 win, a Giants-Cowboys fan fight & Ole Miss tension MLB's most electric slugger just had one of the slowest, most disrespectful walk-off home runs of all time James Franklin makes Virginia Tech press conference extremely awkward with bizarre'Hey Michael' moment Texans' Azeez Al-Shaair to be fined once again by NFL for wearing Pro-Palestinian personal message on eyeblack Stephen A. Smith calls out NBA star Kawhi Leonard for letting Clippers take the fall for salary cap scandal Sophie Cunningham says she's talked with NBA Commissioner Adam Silver amid search for WNBA's next commissioner Ryan Day hints at day of reckoning, vows to make'hard decisions' after Ohio State's late-game Texas breakdown Elon Musk proposes AI competitors'grade' each other's safety models Trump shooter Thomas Crooks' FBI files reveal bizarre details Charlie Kirk's family files claim against Utah Valley University over security failures OutKick Sports Mets are'trash' because they're not listening to former NJ Gov Chris Christie, Stephen A Smith says Former major league pitcher Collin Balester discusses his take on Mets pitcher Jefry Yan's wild strikeout celebration that has been raising eyebrows around baseball. Stephen A. Smith has figured out the crux of the New York Mets' issues. The Mets are batting .238 A fan holds up a sign during the 11th inning of a baseball game between the New York Mets and the Baltimore Orioles on Tuesday, Sept. 15, 2026, in New York. Where the problem lies is anyone's guess.

Florida State fans pining for Jimbo Fisher's return are living in the past, not in reality Roman Reigns survives Penta's World Heavyweight Championship challenge, LA Knight makes a statement of his own Introducing OutKick's first original animated series, 'Sports Talk with Cal McCallister' WWE star Roxanne Perez reminds fans to respect wrestlers' boundaries while on the road: 'We are just humans' Ryan Serhant predicts the next US real estate EPICENTER is'dead center' in America #shorts Democrats believe they can use AI dispute for'more political power,' expert says AG Todd Blanche defends Trump's criticism of Supreme Court mail ballot ruling AG Todd Blanche defends Trump's criticism of Supreme Court mail ballot ruling Sen Rand Paul accuses Dems of bribing voters, calls out'terrible' welfare system There's a lot of good in the Protect College Sports Act, says Baseball Hall of Famer AI companies have been saying this'very consistently,' Axios co-founder GOP lawmaker slams Dems' push to rein in Trump on Iran: 'Political stage' OutKick CC Sabathia says Yankees could do a better job helping young players handle the pinstripes: 'Different beast' The Hall of Famer pointed to Anthony Volpe, Gary Sanchez and more who got'labels' right away from the fan base Are the Yankees under the most pressure to win a World Series? Opening Day is tonight, with the New York Yankees facing off with the San Francisco Giants. Colin Cowherd asks if the Yankees are under the most pressure entering this season to win a World Series. It's been said many times over a century: earning your pinstripes with the New York Yankees is one of the hardest things to do in baseball. Just take Anthony Volpe's rollercoaster career with the ballclub, which has once again become a storyline as they head toward the postseason.

Florida State fans pining for Jimbo Fisher's return are living in the past, not in reality Roman Reigns survives Penta's World Heavyweight Championship challenge, LA Knight makes a statement of his own Introducing OutKick's first original animated series, 'Sports Talk with Cal McCallister' WWE star Roxanne Perez reminds fans to respect wrestlers' boundaries while on the road: 'We are just humans' Chiefs' new stud Kenneth Walker runs wild, Bo Nix melts down as Kansas City obliterates Broncos in MNF blowout NFL legend Drew Brees reportedly almost pulled off a shocking comeback for Broncos' AFC title game'WHY THE HELL ARE WE HELPING THEM': Trump unloads on NATO'SHE HAS DONE NOTHING': AOC hit with BRUTAL 2028 assessment Lindsay Clancy holdout juror's brother reveals details behind guilty choice Lake Bachar's 2.02 home ERA and Jacob Misiorowski's struggles against Pittsburgh make this the value play I always have a lot of ideas on how to make sports better. I've always said that sports betting is a great way to make games more interesting, and it should be legal everywhere. Clearly, people seem to share that view, since it's become more accessible across America. One other thing I think baseball should do is eliminate the division system. I've also said that if you have a losing team for 10+ years, you should be forced to sell it.

AEW and Ring of Honor star Lee Moriarty welcomes Katsuyori Shibata's challenge for Pure Championship NCAA wins Tenth Circuit'stay', but faces more eligibility lawsuits from 2022 class athletes in chaotic time Jacob Misiorowski's MLB-leading ERA and WHIP make Milwaukee Brewers the pick against Atlanta Braves Texas AG Ken Paxton sends message to WNBA amid'concerns' over treatment of Sophie Cunningham supporters NFL to NCAA? Courtroom chaos Is giving pro athletes a bizarre path back to college, and it's only just begun Another sex toy was thrown during a WNBA game, and Dream's Angel Reese absolutely lost it AEW star Willow Nightingale shares how she's able to keep her joyful personality going Peyton Manning's freshman son makes his debut, but freak running back steals the show How Kirk Cousins and Fernando Mendoza are building'great' relationship through Raiders work, faith and more IndyCar star Alex Palou reflects on White House, Oval Office visit with Trump: 'incredible experience' I was a sports columnist at the Seattle Times for 11 years. BREAKING: Iran's president calls for END of war Sophie Cunningham calls for'bold' commissioner amid women's sports debate Are American workers really using AI? Gen. Jack Keane details US military strategy as Trump warns of Iran's nuclear threat ISIS indoctrinating Americans with'ease,' ex-NYPD detective warns OutKick Sports Giants vs. Red Sox betting preview: Logan Webb and Sonny Gray both locked in for under play A new survey sheds light on how much fans talk about their teams, and which fans do the most talking. It was not an overly impressive preseason betting day from me, but it was still profitable. I took the 1st quarter to be tied in the Chargers and 49ers game. I wasn't watching as it happened, and I checked the score in the second quarter, seeing it was 17-3.

Chain-of-thought (CoT) reasoning is critical for improving the interpretability and reliability of Large Vision-Language Models (LVLMs). However, existing training algorithms such as SFT, PPO, and GRPO may not generalize well across unseen reasoning tasks and heavily rely on a biased reward model. To address this challenge, we reformulate reasoning in LVLMs as posterior inference and propose a scalable training algorithm based on amortized variational inference. By leveraging diversity-seeking reinforcement learning algorithms, we introduce a novel sparse reward function for token-level learning signals that encourage diverse, high-likelihood latent CoT, overcoming deterministic sampling limitations and avoiding reward hacking. Additionally, we implement a Bayesian inference-scaling strategy that replaces costly Best-of-N and Beam Search with a marginal likelihood to efficiently rank optimal rationales and answers. We empirically demonstrate that the proposed method enhances the state-of-the-art LVLMs on seven reasoning benchmarks, in terms of effectiveness, generalization, and interpretability.

We begin by characterizing the space of elements that test an agent's ability to optimally allocate1031 their limited resources to goods and services they desire. In economics and decision theory, the1032 most primitive approach to describing the preferences of decision-makers is to use a function that1033 maps a set of possible choices to the agent's optimal choice within that set. Under a set of intuitive1034 assumptions, such as transitivity (i.e., if bundle X is preferred to bundle Y, and Y is preferred to1035 bundle Z, then X must be preferred to Z), it becomes possible to "rationalize" preferences by instead1036 describing a utility function. This function assigns a real number to each bundle, and the agent selects1037 the bundle with the highest utility.1038 In this paper, we focus on these "rationalizable" preferences, where agent choice can be implemented1039 as utility maximization constrained by prices and income. The solution to these consumer choice1040 problems provides ...

Large language models (LLMs) are increasingly being asked to make economically rational decisions and indeed are already being applied to economic tasks like stock picking and financial analysis. Existing LLM benchmarks tend to focus on specific applications, making them insufficient for characterizing economic reasoning more broadly. In previous work, we offered a blueprint for comprehensively benchmarking strategic decision-making Raman et al. [2024]. However, this work did not engage with the even larger microeconomic literature on non-strategic settings. We address this gap here, taxonomizing microeconomic reasoning into 58distinct elements, each grounded in up to 10distinct domains, 5perspectives, and 3types. The generation of benchmark data across this combinatorial space is powered by a novel LLM-assisted data generation protocol that we dub auto-STEER, which generates a set of questions by adapting handwritten templates to target new domains and perspectives. By generating fresh questions for each element, auto-STEER induces diversity which could help to reduce the risk of data contamination. We use this benchmark to evaluate 27LLMs spanning a range of scales and adaptation strategies, comparing performance across multiple formats--multiple-choice and free-text question answering--and scoring schemes. Our results surface systematic limitations in current LLMs' ability to generalize economic reasoning across types, formats, and textual perturbations, and establish a foundation for evaluating and improving economic competence in foundation models.

In Major League Baseball, strategy and planning are major factors in determining the outcome of a game. Previous studies have aided this by building machine learning models for predicting the winning team of any given game. We extend this work by training a comprehensive set of machine learning models using a common dataset. In addition, we relate the win probabilities produced by these models to win strength as measured by score differential. In doing so we show that the most common machine learning models do indeed demonstrate a relationship between predicted win probability and the strength of the win. Finally, we analyze the results of using predicted win probabilities as a decision making mechanism on run-line betting. We demonstrate positive returns when utilizing appropriate betting strategies, and show that naive use of machine learning models for betting lead to significant loses.

The star pitcher has been studying aerospace engineering at MIT. Now his pitches will take flight in professional baseball. Like almost any MIT student, Mason Estrada wants to take what he learned on campus and apply it to the working world. Unlike any other current MIT student, Estrada's primary workplace is a pitcher's mound. Estrada, the star pitcher for MIT's baseball team, has signed a contract with the Los Angeles Dodgers, who selected him in the seventh round of the Major League Baseball draft on July 14. The right-hander, whose fastball has reached 96 miles per hour, is taking a leave of absence from the Institute and reported to the Dodgers' instructional camp in Arizona.

Statistical topic modeling is widely used in political science to study text. Researchers examine documents of varying lengths, from tweets to speeches. There is ongoing debate on how document length affects the interpretability of topic models. We investigate the effects of aggregating short documents into larger ones based on natural units that partition the corpus. In our study, we analyze one million tweets by U.S. state legislators from April 2016 to September 2020. We find that for documents aggregated at the account level, topics are more associated with individual states than when using individual tweets. This finding is replicated with Wikipedia pages aggregated by birth cities, showing how document definitions can impact topic modeling results.