In this draft, we study a novel problem, called lexical invariance, using the medium of multisets and graphs. Traditionally in the NLP domain, lexical invariance indicates that the semantic meaning of a sentence should remain unchanged regardless of the specific lexical or word-based representation of the input. For example, "The movie was extremely entertaining" would have the same meaning as "The film was very enjoyable". In this paper, we study a more challenging setting, where the output of a function is invariant to any injective transformation applied to the input lexical space. For example, multiset {1, 2, 3, 2} is equivalent to multiset {a, b, c, b} if we specify an injective transformation that maps 1 to a, 2 to b and 3 to c. We study the sufficient and necessary conditions for a most expressive lexical invariant (and permutation invariant) function on multisets and graphs, and proves that for multisets, the function must have a form that only takes the multiset of counts of the unique elements in the original multiset as input. For example, a most expressive lexical invariant function on {a, b, c, b} must have a form that only operates on {1, 1, 2} (meaning that there are 1, 1, 2 unique elements corresponding to a, c, b). For graphs, we prove that a most expressive lexical invariant and permutation invariant function must have a form that only takes the adjacency matrix and a difference matrix as input, where the (i, j)th element of the difference matrix is 1 if node i and node j have the same feature and 0 otherwise. We perform synthetic experiments on TU datasets to verify our theorems.

There have been several studies on automatically generating piano covers, and recent advancements in deep learning have enabled the creation of more sophisticated covers. However, existing automatic piano cover models still have room for improvement in terms of expressiveness and fidelity to the original. To address these issues, we propose a learning algorithm called AMT-APC, which leverages the capabilities of automatic music transcription models. By utilizing the strengths of well-established automatic music transcription models, we aim to improve the accuracy of piano cover generation. Our experiments demonstrate that the AMT-APC model reproduces original tracks more accurately than any existing models.

Fox News host Sean Hannity says the vice president has a'lot to answer for' ahead of the 2024 election on'Hannity.' HANNITY – Fox News host says the vice president has a'lot to answer for' ahead of the 2024 election. HUGH HEWITT – Why I am voting for Trump. HOMETOWN HAZARD – Kamala Harris failed Oakland and would do the same for America. GUTFELD – Despite Teamsters embracing Trump, they decided to endorse nobody.

Want to Get Into Founder Mode? Paul Graham's viral essay explains why Brian Chesky and Steve Jobs ruled and professional managers stink. But if a manager is smart and the founder is meh, who's better? Fledgling founders entering a three-month residency at Y Combinator often start their term with a bang: Brian Chesky, the cofounder and CEO of Airbnb, fires off an inspirational speech. His company, of course, started with three nobodies going through the program. This year, Chesky topped himself.

Things to Do in L.A. Tap to enable a layout that focuses on the article. UC chancellors get big raises, putting them between $785,000 and nearly $1.2 million The UC regents approved pay raises for seven chancellors at their September meeting. At UC Irvine, above, the chancellor will earn $895,000 a year, effective this month. University of California chancellors will get big salary boosts -- near or exceeding 30% in most cases -- as the Board of Regents agreed Thursday that higher pay was needed to bring leaders of the nation's top public university system closer to what their peers earn. The increases, which will be paid through private sources rather than tuition dollars or state funding, are effective this month and will vary by campus.

Gov. Gavin Newsom signed three bills to combat deepfake election content and remove deceptive material from social media, but two are facing court challenges.

Apple's iPhone 16 released in Japan A man holds a new iPhone 16 at an Apple store in Tokyo's Shibuya Ward on Friday. The new iPhone 16 smartphone series of U.S. technology giant Apple went on sale in Japan on Friday, with more than 10 enthusiasts lined up at an Apple store in Tokyo's Shibuya Ward in the morning to buy iPhone 16 handsets. The store moved its opening time earlier to 8 a.m., but shoppers started to stand in line before the opening. At the start of the line was an engineer in his 30s, who bought the top-of-the-line Pro Max model. I'll be happy if it learns about the ways I use it and makes it easier for me to operate it, he said. All models are equipped with the Apple Intelligence generative artificial intelligence system, designed to help users draft emails and create summaries of transcripts of phone calls.

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The suspect in Charlie Kirk's assassination has been captured, FBI director Kash Patel announced MSNBC sparks outrage for'disgusting' Charlie Kirk comments following Utah shooting Tragedy as Charlie Kirk's wife left behind with two young children after conservative activist is fatally shot A DEI mayor, an inconvenient crime and video they never wanted you to see: MAUREEN CALLAHAN knows why the Left has sympathy for that killer... but none for his victim Sweater weather starts here - the cozy, chic pieces from Soft Surroundings you'll actually wear all season We only had one symptom we dismissed... but then we were diagnosed with the rarest form of melanoma Soft-touch prosecutor let felon walk free... before crook'slit Auburn professor's throat in random attack' I tried the 30 cent'miracle chill pill' before a big event.. now I'm taking it for everything Donald Trump and House Republicans lead prayers for Charlie Kirk's family after conservative star is fatally shot Prince Harry says his father King Charles is'great' following their first meeting in 19 months... which was over a cup of tea and just 55 minutes long Liberal media defends thug who killed Ukrainian woman in cold blood: 'This man was hurting' Knifeman accused of stabbing Ukrainian refugee to death gives chilling reason for the attack... as he speaks for the first time from jail on the murder that shocked America Fox News reveals new lineup and elevates star White House reporter who's sparred with Trump Horrific new details of passenger injuries after they were'thrown' around Delta flight during'severe turbulence' Antarctica's'Doomsday Glacier' is on the verge of COLLAPSING: Huge ice sheet the size of Great Britain could cause global sea levels to rise by 2 FEET, study warns READ MORE: 'Doomsday Glacier' melting'much faster' than previously thought With the potential to cause sea levels across the planet to rise, it's no wonder the Thwaites Glacier has earned the nickname the'Doomsday Glacier.' Now, scientists have revealed concerning findings about how and when the glacier could collapse. Researchers from the British Antarctic Survey (BAS) used underwater robots to take new measurements of the glacier, which is the same size as Great Britain. The data indicates that the Thwaites Glacier and much of the West Antarctic Ice Sheet could be lost entirely by the 23rd century. Worryingly, if it collapses entirely, the experts say global sea levels would rise by two feet (65cm) - plunging huge areas underwater. With the potential to cause seas across the planet to rise, it's no wonder the Thwaites Glacier has earned the nickname the'Doomsday Glacier' The Thwaites Glacier is roughly 74.5 miles (120km) across - the same size as Great Britain or Florida - making it the widest glacier on the planet Ice shelf connected to Antarctic's doomsday glacier is CRACKING The Thwaites Glacier is roughly 74.5 miles (120km) across - the same size as Great Britain or Florida.

'Meeting a real-life cyborg was gobsmacking' For the past 20 years, self-declared cyborg artist Neil Harbisson has provoked debate with his eyeborg - a surgically attached antenna. Harbisson, who grew up in Barcelona, is colour blind, having been born with the rare condition achromatopsia, which affects one in 33,000 people. This means he sees in what he calls greyscale - only black, white and shades of grey. But he decided to have surgery in 2004 which changed his life - and his senses - attaching an antenna to the back of his head, which transforms light waves into sounds. When film director Carey Born came across Harbisson, classed by Guinness World Records as the first officially recognised'cyborg', she was gobsmacked and astonished.