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How do LLMs do CoT reasoning internally?
In our new #ACL2026 paper, we show that reasoning unfolds as a structured trajectory in representation space. Correct and incorrect paths diverge, and we use this to predict correctness before the answer and correct errors mid-flight.
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In our new #ACL2026 paper, we show that reasoning unfolds as a structured trajectory in representation space. Correct and incorrect paths diverge, and we use this to predict correctness before the answer and correct errors mid-flight.
1/
Each reasoning step occupies a distinct region in representation space, and these regions become increasingly linearly separable with layer depth. This structure generalizes across tasks and answer formats.
2/
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Trajectories for correct and incorrect reasoning start out nearly identical but diverge systematically at late steps. Late-step trajectory features predict final-answer correctness with AUC 0.87 - before the answer is generated.
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"The pursuit of this improper investigation is a clear abuse of discretion." Judge Boasberg just got slapped down...again.
The walls are closing in on his crusade to jail Trump officials for DEPORTING Venezualan terrorists.
It's clear: time to impeach Rogue Judge Boasberg. 🧵
The walls are closing in on his crusade to jail Trump officials for DEPORTING Venezualan terrorists.
It's clear: time to impeach Rogue Judge Boasberg. 🧵
To review: last March, Judge Boasberg forced himself onto the "turn the planes around" case—just a few days after trying to foment a constitutional crisis at a Judicial Conference meeting.
He has spent the past year trying to jail prosecutors and cabinet Secretaries.
He has spent the past year trying to jail prosecutors and cabinet Secretaries.
Today, the D.C. Circuit issued an opinion, once again, in the appeal on Boasberg's attempt (extrajurisdictionally) to hold officials in contempt.
The Court found Boasberg's "inquest" was both wrong on the law and a violation of our Separation of Powers.
Let's break it down.
The Court found Boasberg's "inquest" was both wrong on the law and a violation of our Separation of Powers.
Let's break it down.
Rahul took a ₹60,00,000 home loan in 2020 for 20 years at 9% interest.
He paid it off in just 11 years and saved ₹30,60,475 in interest.
That’s 44% less interest. Same loan. Same bank.
Here are the 2 hacks he used 🧵👇
He paid it off in just 11 years and saved ₹30,60,475 in interest.
That’s 44% less interest. Same loan. Same bank.
Here are the 2 hacks he used 🧵👇
[1] First, the truth about home loans.
After paying EMIs for 10 full years, Rahul still owed ₹42.6L to the bank.
Only ₹17.4L of the actual loan was cleared.
After paying EMIs for 10 full years, Rahul still owed ₹42.6L to the bank.
Only ₹17.4L of the actual loan was cleared.
[2] Hack 1: Pay one extra EMI every year.
Rahul's EMI was ₹53,984.
Every bonus month, he paid one extra. That's it.
Just this one habit: ↳ Loan closed 44 months early ↳ Saved ₹14.85L in interest
One extra payment a year. Nothing more.
Rahul's EMI was ₹53,984.
Every bonus month, he paid one extra. That's it.
Just this one habit: ↳ Loan closed 44 months early ↳ Saved ₹14.85L in interest
One extra payment a year. Nothing more.
Why does the western “left” not get this they linked the Black struggle of the 60’s to LGBT liberation. In order to make an individuals identity the focus of politics and erase concrete material gains for the working class! All that was gained was gay marriage. What is next?
What’s next is more turning inward to identity ex. trans 🏳️⚧️ and fat people and furries and any kind of alternative way people choose to identify. When this is the parameters to wage revolutionary political struggle then this is what you get.
If you do not make it a collective struggle with material demands and a mass line. It is just vague phrases like liberation and freedom with virtue signaling symbols 🏳️⚧️ that all placate individuals whims and fancies!
I've lived in Switzerland. I've incorporated there. I've walked the lakeside in Zug at 8pm wondering where everyone went.
250 millionaires a month are moving to Switzerland. Most end up in Zurich or Geneva.
For many it works. But not for all.
I asked friends living there, compared it with the data and assembled this guide. I came to the conclusion there are two approaches to Switzerland for most of us.
A practical and unfiltered Swissmaxing thread 🇨🇭
🧵
250 millionaires a month are moving to Switzerland. Most end up in Zurich or Geneva.
For many it works. But not for all.
I asked friends living there, compared it with the data and assembled this guide. I came to the conclusion there are two approaches to Switzerland for most of us.
A practical and unfiltered Swissmaxing thread 🇨🇭
🧵
Many love the stability, the family life, the capacity of working remotely while immersed in nature.
In the end we all want two things: low taxes and a place where your daughter can walk at night safely.
The baseline: Switzerland has 0% capital gains tax on private investments. Federal level. Every canton.
Everything below is about optimizing on top of that.
Then there's the lump-sum tax, which can also change the math if you're a HNWI. More on that later.
Let's dive into it:
In the end we all want two things: low taxes and a place where your daughter can walk at night safely.
The baseline: Switzerland has 0% capital gains tax on private investments. Federal level. Every canton.
Everything below is about optimizing on top of that.
Then there's the lump-sum tax, which can also change the math if you're a HNWI. More on that later.
Let's dive into it:
1/ Zug 🇨🇭
"All roads lead to Zug." Zug is a beautiful lake town at the foot of the Alps. Clean air, crystal water, mountains in every direction. The old town is charming. Lakeside restaurants where you sit and watch the sunset over the Rigi.
The train station is so clean you could eat off the floor. Everything works. Everything is safe. Kids walk to school alone.
Zug has the lowest corporate tax in Switzerland (11.85%). The administration works for you. Setting up a company, dealing with authorities, the system serves you. One of the few places on earth where that's true.
That's the beauty of canton-competition in Switzerland: cantons market themselves to attract you. It makes the whole system work.
"All roads lead to Zug." Zug is a beautiful lake town at the foot of the Alps. Clean air, crystal water, mountains in every direction. The old town is charming. Lakeside restaurants where you sit and watch the sunset over the Rigi.
The train station is so clean you could eat off the floor. Everything works. Everything is safe. Kids walk to school alone.
Zug has the lowest corporate tax in Switzerland (11.85%). The administration works for you. Setting up a company, dealing with authorities, the system serves you. One of the few places on earth where that's true.
That's the beauty of canton-competition in Switzerland: cantons market themselves to attract you. It makes the whole system work.
Did you know?
the souls in Barzakh remember their loved ones and sometimes, when you miss them, they might be missing you too?
the souls in Barzakh remember their loved ones and sometimes, when you miss them, they might be missing you too?
Sometimes, when your heart aches for someone who’s gone…
It’s not just you missing them.
It might be their soul in Barzakh remembering you.
“And behind them is a barrier (Barzakh) until the Day they are resurrected.”
— Qur’an, 23:100
It’s not just you missing them.
It might be their soul in Barzakh remembering you.
“And behind them is a barrier (Barzakh) until the Day they are resurrected.”
— Qur’an, 23:100
Barzakh isn’t emptiness, it’s the unseen realm between this life and the next.
A world of rest, remembrance, and divine peace. Souls there are conscious, aware, and capable of love.
Because love doesn’t die, it simply changes world
A world of rest, remembrance, and divine peace. Souls there are conscious, aware, and capable of love.
Because love doesn’t die, it simply changes world
Good morning Arkansas! We're posted up in Joint Budget Committee today, where Co-chair Sen. Dismang is moving briskly through various House and Senate bills. Most of these are uncontroversial, but we'll see if anyone pipes up.
Notably, SB41 - appropriation for U of A Fayetteville - has been deferred by Sen Sullivan + Reps. McKenzie and Duke. U of A has come under quite a bit of fire this year; the cancelling of Emily Suski's contract as law school dean, debate over increase in student prices...
and the firing of a professor who spoke out against Israel's actions in Gaza have put the school under a microscope. Not sure about McKenzie and Duke, but Sullivan filed an amendment stripping funding to the King Fahd Center for Middle East Studies. So that's fun!
Today, we released PEFT v0.19.0 and it's a big one. Not only did we add 9 new PEFT methods, the release also contains a bunch of improvements to make PEFT more useful. Check the thread for details:
The release contains new functions to convert non-LoRA weights into LoRA weights. This allows them to be used in packages like Diffusers and vLLM that only support LoRA. Find more details here: huggingface.co/docs/peft/main…
LoRA fine-tuning can introduce so called "intruder dimensions" which contribute to forgetting (). We now have a utility function to remove intruder dimension, `reduce_intruder_dimension`. Call this on a fine-tuned LoRA model to reduce forgetting.huggingface.co/papers/2410.21…
Most people don't realize the "healthy" foods they eat every day actually build plaque inside their arteries.
Here are 10 foods to reverse the damage and protect your heart (backed by science): 🧵
1. Beets
Here are 10 foods to reverse the damage and protect your heart (backed by science): 🧵
1. Beets
Beets are loaded with nitrates that your body converts into nitric oxide.
Nitric oxide relaxes and widens your blood vessels, lowering blood pressure and improving circulation.
Drink raw beet juice or roast them to protect your arteries.
Nitric oxide relaxes and widens your blood vessels, lowering blood pressure and improving circulation.
Drink raw beet juice or roast them to protect your arteries.
2. Dark chocolate (85%+ cacao)
The flavanols in dark chocolate boost nitric oxide production and improve blood vessel flexibility.
Just 1-2 squares a day can lower blood pressure and reduce arterial stiffness.
Stick to 85% cacao or higher for real benefits.
The flavanols in dark chocolate boost nitric oxide production and improve blood vessel flexibility.
Just 1-2 squares a day can lower blood pressure and reduce arterial stiffness.
Stick to 85% cacao or higher for real benefits.
Some interesting names and organizations popping up in the DOJ's sprawling report documenting how the Biden DOJ weaponized the FACE Act to target pro-life Americans and throw them in jail.
Looky here--it's Matthew Colangelo, who a few months later left DOJ to help Alvin Bragg prosecute the president. Also Sparkle Sooknanan, now a DC district court judge attempting to block Trump's policies including deportation of illegals:
Looky here--it's Matthew Colangelo, who a few months later left DOJ to help Alvin Bragg prosecute the president. Also Sparkle Sooknanan, now a DC district court judge attempting to block Trump's policies including deportation of illegals:
And of course no anti-Trump, anti-conservative operation is complete without the key involvement of Lisa Monaco. She also was heavily involved in the criminal investigations against President Trump, particularly the documents case, and the J6 prosecutions.
After SCOTUS announced the Dobbs decision, Biden's DOJ convened a conference on reproductive rights.
One of the participants was the National Women's Law Center--run by Fatima Goss Graves, the wife of Matthew Graves, who as DC US Attorney at the time was busy criminally charging at least one J6er a day.
As I reported a few years ago, Goss Graves visited the Biden White House nearly 40 times while her husband was destroying the lives of Trump supporters who participated in the events of Jan. 6:
One of the participants was the National Women's Law Center--run by Fatima Goss Graves, the wife of Matthew Graves, who as DC US Attorney at the time was busy criminally charging at least one J6er a day.
As I reported a few years ago, Goss Graves visited the Biden White House nearly 40 times while her husband was destroying the lives of Trump supporters who participated in the events of Jan. 6:
The biggest difference between rich and poor countries is the degree of cooperation between strangers.
High-trust, trustworthy people create positive-sum cooperation and first-world conditions.
Low-trust, untrustworthy people create zero-sum competition and third-world conditions.
With low-trust immigrants, White liberals think they’re playing a positive-sum game, but they’re actually playing a negative-sum game, with a zero-sum future
High-trust, trustworthy people create positive-sum cooperation and first-world conditions.
Low-trust, untrustworthy people create zero-sum competition and third-world conditions.
With low-trust immigrants, White liberals think they’re playing a positive-sum game, but they’re actually playing a negative-sum game, with a zero-sum future
That's the charitable version. Truer among naive voters.
The uncharitable version? Race communism. I give you status, and you give me power. Truer among scheming leftists.
I guess you can't blame leftist elites for playing the game of democracy well.
Once the blank slate lie is baked into the fabric of liberal democracy, mass low-trust immigration becomes a long-term winning strategy
The uncharitable version? Race communism. I give you status, and you give me power. Truer among scheming leftists.
I guess you can't blame leftist elites for playing the game of democracy well.
Once the blank slate lie is baked into the fabric of liberal democracy, mass low-trust immigration becomes a long-term winning strategy
Obviously, many immigrants are high-trust(worthiness) and otherwise awesome
