Frontier labs are actively using the Jacobian Lens (J-lens) to illustrate and evaluate opaque recurrence (also known as recurrent depth or looped transformers). Opaque recurrence—the architecture famously integrated into OpenAI's GPT-6 Astra where a model cycles through hidden computational loops rather than outputting legible text tokens—has traditionally been a black box for alignment monitoring. However, the Jacobian Lens provides a mathematical framework to peer inside these internal loops.
How the Jacobian Illustrates Opaque Recurrence is as follows:
1.Linearizing Virtual Depth -
In a standard transformer, information moves linearly through a fixed stack of separate layers. Under opaque recurrence, the model dynamically reuses the same physical weights across sequential iterations. The Jacobian Lens acts as a translation dictionary between the intermediate hidden states (of these loops and the final vocabulary prediction. By taking the partial derivatives of the output function with respect to the loop state, it creates a local linear approximation. Because models utilizing recurrent depth execute reasoning steps in a compressed, non-verbal internal format, traditional text-based "Chain of Thought" (CoT) tracking breaks down. The Jacobian allows researchers to project these abstract, looped representations straight into a probability distribution over the model's vocabulary (a process known as the READ operation). This maps out exactly how a piece of information shifts and matures with each loop iteration, translating hidden computational cycles into a readable cognitive trajectory.
2.Analyzing Workspace Survival across Loops -
A primary application of this technique is mapping whether these loops sustain a functional "Global Workspace"—a central, privileged subcomponent of representational space where the model aggregates its most causally potent concepts. State-of-the-art research has specifically scaled the Jacobian Lens to recurrent structures to determine how "hidden thinking" handles feedback. For example, the paper Looped Transformers under the Jacobian Lens explicitly “extends the Jacobian lens to weight-tied virtual depth and compares workspace dynamics... finding that recurrence preserves a causal workspace while reshaping how information and interventions propagate across layers and iterations.”
Here is my short talk from the Models of Consciousness 6 conference of the Association for Mathematical Consciousness Science. I think the microtubule-centered quantum consciousness (MCQC) discourse has often blurred the line between science and mysticism and has made it harder for life sciences professionals to give serious consideration to quantum effects in biological systems. Some leading proponents of MCQC were reportedly invited to the conference but did not attend; I would have welcomed a direct scientific exchange. https://t.co/dcY7GGWTcX
World’s highest IQ record holder just dropped a bombshell on X.
Dr. YoungHoon Kim (IQ 276 — officially recognized by Guinness World Records and Giga Society) declared:
“As the world’s highest IQ record holder, I believe that Jesus Christ is God, the way and the truth and the life.”
When skeptics pushed back, the 36-year-old South Korean neuroscientist replied with powerful simplicity: “Amen. Christ is my logic.”
He went further: “The Bible doesn’t need to be updated. The world needs to catch up.”
Now with over 14 million views, Dr. Kim is using his platform to lead souls to God — proving that true intelligence doesn’t run from the Cross.
It kneels before it.
Details in comments 👇
#JesusIsLord #FaithAndReason #HighestIQ #BibleTruth #ChristIsKing
Musician Kid Rock is drawing attention after speaking openly about his belief in Jesus Christ. Emphasizing forgiveness and a personal relationship with Christ, he shared that Jesus is real, is the Son of God, and can be known personally. His remarks have sparked conversations across social media, with many believers celebrating the message and the power of God’s grace to transform lives.
#Jesus #ChristianNews #Faith #KidRock #JesusSaves #Forgiveness #Christianity #GodIsGood #Hope #FaithJourney
🚨 ANTHROPIC JUST PUBLISHED A 36-PAGE SECURITY GUIDE THAT BASICALLY TELLS YOU TO STOP TRUSTING YOUR OWN AI AGENTS.
If you run agents on Claude Code, MCP servers, or automation tools, pay attention.
The attack timeline has collapsed.
AI models compress the gap between a vulnerability and a working exploit from months to hours, for mere dollars.
Agents introduce new autonomous risks, from tool poisoning to context memory manipulation.
The most useful idea in the guide is Anthropic's new security test:
Does a control make an attack impossible, or just tedious?
Automated attackers have unlimited patience. They will grind straight through friction like rate limits and 2FA. To defend at the speed of AI, you need hard barriers and automated defensive operations.
Here is how Anthropic says you should lock down agents:
→ Treat static API keys as compromised. Use short-lived tokens that expire in minutes.
→ Apply "Least Agency": explicitly limit what each tool can DO.
→ Sandbox agents that process untrusted inputs like emails and web pages.
→ Scope permissions dynamically per task, not permanently.
I've added the link to the guide in the 🧵↓
The more you watch Elon Musk, the more obvious it becomes that this was never just about money. He could have walked away years ago and lived in total comfort for the rest of his life. Instead, he chose constant pressure, sleepless nights, and one impossible mission after another. He does it because he genuinely believes humanity can achieve so much more if we push ourselves harder.
He is 54 years old and still working with the intensity of someone half his age. Grinding until 3am at the office, working every waking hour seven days a week. People keep betting against him, and he keeps winning. You can disagree with him on things, but you cannot deny the level of dedication, sacrifice, and belief he has put into pushing humanity forward.
History is repeating itself once again.
Godspeed, SpaceXAI.
Dear Lord Jesus, please bless Pam Bondi and heal her - Ms. Bondi has accomplished much to restore true democracy and the rule of law in our fair country!! ✝️🇺🇸💯
The Bible:
· 0 errors
· 66 books
· 40+ authors
· 0 contradictions
· 3 different languages
· 3 different continents
· 63K+ cross-references
· written over 1500 years
· all telling the same story
This is how we know it’s God-inspired and not man-made.
Do you know what happened in the last 24 hours?
1. Late on Thursday night @FBI agents landed at New York Stewart International Airport with Mohammad al Saadi in handcuffs. Al Saadi, the leader of an Iran-backed Iraqi terror group is allegedly responsible for more than 20 attacks across Europe and Canada and for planning attacks in the U.S..
2. Jose Enrique Martinez Flores, who goes by “Chuqui," the highest ranking Tren de Aragua leader to be extradited to the U.S., also just landed in the U.S. in shackles. Flores allegedly oversaw TdA’s drug trafficking, extortion rackets, prostitution rings and murder operations.
Then, last night, in an operation that makes any fictional representation look amateurish, American operators, working with local Nigerian forces, killed Abu-Bilal-al-Minuki, the second in command for ISIS global operations, a man with the blood of countless innocents on his hands, including many Christians.
This is just one day in the Counterterrorism operations of President @realDonaldTrump.
We salute the intelligence professionals, Law Enforcement Officers, Diplomats, Military operators and support personnel who make these operations possible 24/7.
@WhiteHouse@DeptofWar@TheJusticeDept@StateDept