LessWrong 2.0 Reader

Btw, I think my explanation of why to not have objects for events was not very good. I think I can explain it a bit better now. If you think that would be useful to you, lmk.

In an ideal world, global enforcement of AI regulation might make sense. However, in reality, I see little value in EU-specific regulations like these. They are unlikely to impact frontier AI companies such as OpenAI, Anthropic, Google DeepMind, xAI, and DeepSeek, all of which are based outside the EU. These firms might accept the cost of exiting the EU market if regulations become too burdensome.

While the EU market is significant, in a fast-takeoff, winner-takes-all AI race (as outlined in the AI-2027 forecast), market access alone may not sway these companies’ safety policies. Worse, such regulations could backfire, locking the EU out of advanced AI models and crippling its competitiveness. This could deter other nations from adopting similar rules, further isolating the EU.

As an EU citizen, I view the game theory in an "AGI-soon" world as follows:

Alignment Hard
EU imposes strict AI regulations → Frontier companies exit the EU or withhold their latest models, continuing the AI race → Unaligned AI emerges, potentially catastrophic for all, including Europeans. Regulations prove futile.

Alignment Easy
EU imposes strict AI regulations → Frontier companies exit the EU, continuing the AI race → Aligned AI creates a utopia elsewhere (e.g., the US), while the EU lags, stuck in a technological "stone age."

Both scenarios are grim for Europe.

I could be mistaken, but the current US administration and leaders of top AI labs seem fully committed to a cutthroat AGI race, as articulated in situational awareness narratives. They appear prepared to go to extraordinary lengths to maintain supremacy, undeterred by EU demands. Their primary constraints are compute and, soon, energy - not money! If AI becomes a national security priority, access to near-infinite resources could render EU market losses a minor inconvenience. Notably, the comprehensive AI-2027 forecast barely mentions Europe, underscoring its diminishing relevance.

For the EU to remain significant, I see two viable strategies:

1. Full integration with US AI efforts, securing a guarantee of equal benefits from aligned superintelligence. This could also give EU AI safety labs a seat at the table for alignment discussions.
2. Develop an autonomous EU AI leader, excelling in capabilities and alignment research to negotiate with the US and China as an equal. This would demand a drastic policy shift, massive investment in data centers and nuclear power, and deregulation, likely unrealistic in the short term.

I fixed this at some point in the meantime, thanks for flagging!

Yeah I think that’d be reasonable too. You could talk about these clusters at many different levels of granularity, and there are tons I haven’t named. 

You're correct that this is what happens at one of the abstraction layers. But the choice of that layer is pretty arbitrary. By abstraction layers:

L1: hypervisor interface: uncountably many VMs

L2: hypervisor implementation: countably many VMs

L3: semiconductors: no VMs, only high and low signals

L4: electrons: no high and low signals, only electromagnetic fields

So yes, on L2 the number of VMs is finite. But why morality should count what happens on L2 and not on L1 or L3, L4? This is too arbitrary.

I agree with your broader point, but it's actually more than 10,000 people per year. 

It will probably be lengthy but thank you very much for contributing! DM me if you come across any "legal" question about the AI Act :). 

It is time for us to interpret some linear machine learning models. These models are linear, but I can generalize these algorithms to produce multilinear models which have stronger capabilities while still behaving mathematically. Since one can stack the layers to make non-linear models, these types of machine learning algorithms seem to have enough performance to be more relevant for AI safety.

Our goal is to transform a list of $n\times n$-matrices $(A_1,...,A_r)$ into a new and simplified list of $d\times d$-matrices $(X_1,\dots ,X_r)$. There are several ways in which we would like to simplify the matrices. For example, we would sometimes simply like for $d<n$, but in other cases, we would like the matrices $X_j$ to all be real symmetric, complex symmetric, real Hermitian, complex Hermitian, complex anti-symmetric, etc. 

We measure similarity between tuples of matrices using spectral radii. Suppose that $(A_1,\dots ,A_r)$ are $n\times n$-matrices and $(X_1,\dots ,X_r)$ are $d\times d$-matrices. Then define an operator $\Gamma (A_1,\dots ,A_r:X_1,\dots ,X_r)$ mapping $n\times d$ matrices to $n\times d$

-matrices by setting $\Gamma (A_1,\dots ,A_r:X_1,\dots ,X_r)\left(X\right)=A_{1}X{X}_1^{\ast }+\dots A_{r}X{X}_r^{\ast }$. Then define $\Phi (X_1,\dots ,X_r)=\Gamma (X_1,\dots ,X_r;X_1,\dots ,X_r)$. Define the similarity between $(A_1,\dots ,A_r)$ and $(X_1,\dots ,X_r)$ by setting

$\parallel (A_1,\dots ,A_r)\simeq (X_1,\dots ,X_r){\parallel }_2$

$=\frac{\rho \left(\Gamma \right(A_1,\dots ,A_r;X_1,\dots ,X_r\left)\right)}{\rho \left(\Phi \right(A_1,\dots ,A_r\left){)}^{1/2}\rho \right(\Phi (X_1,\dots ,X_r){)}^{1/2}}$

where $\rho$ denotes the spectral radius. Here, $\parallel (A_1,\dots ,A_r)\simeq (X_1,\dots ,X_r){\parallel }_2$ should be thought of as a generalization of the cosine similarity to tuples of matrices.

Suppose that $K$ is either the field of real or complex numbers. Let $M_n\left(K\right)$ denote the set of $n$ by $n$ matrices over $K$. 

Let $n,d$ be positive integers. Let $T:M_d\left(K\right)\to M_d\left(K\right)$ denote a projection operator. Here, $T$ is a real-linear operator, but if $K$ is not complex, then $T$ is not necessarily complex linear. Here are a few examples of such linear operators $T$ that work:

 $K=C:T_1\left(X\right)=(X+X^T)/2$ (Complex symmetric)

$K=C:T_2\left(X\right)=(X-X^T)/2$ (Complex anti-symmetric)

$K=C:T_3\left(X\right)=(X+X^{\ast })/2$ (Complex Hermitian)

$K=C:T_4\left(X\right)=\text{Re}\left(X\right)$ (real, the real part taken elementwise).

$K=R:T_5\left(X\right)=(X+X^T)/2$ (Real symmetric)

$K=R:T_6\left(X\right)=(X-X^T)/2$ (Real anti-symmetric)

$K=C:T_7\left(X\right)=\text{Re}\left(X\right)+\text{Re}(X{)}^T$ (real symmetric)

$K=C:T_8\left(X\right)=\text{Re}\left(X\right)-\text{Re}(X{)}^T$ (real anti-symmetric)

Caution: These are special projection operators on spaces of matrices. The following algorithms do not behave well for general projection operators; they mainly behave well for $T_1,\dots ,T_8$ along with operators that I have forgotten about.

We are now ready to describe our machine learning algorithm's input and objective.

Input: $r$-matrices $A_1,\dots ,A_r\in M_n\left(K\right)$

Objective: Our goal is to obtain matrices $(X_1,\dots ,X_r)\in M_d\left(K\right)$  where $T\left(X_j\right)=X_j$ for all $j$ but which locally maximizes the similarity$\parallel (A_1,\dots ,A_r)\simeq (X_1,\dots ,X_r){\parallel }_2$.

In this case, we shall call $(X_1,\dots ,X_r)$ an $L_{2,d}$-spectral radius dimensionality reduction (LSRDR) along the subspace $\text{im}\left(T\right).$

LSRDRs along subspaces often perform tricks and are very well-behaved.

If $(X_1,\dots ,X_r),(Y_1,\dots ,Y_r)$ are LSRDRs along subspaces, then there are typically some $\lambda ,C$ where $Y_j=\lambda C{X}_j{C}^{-1}$ for all $j$. Furthermore, if $(X_1,\dots ,X_r)$ is an LSRDR along a subspace, then we can typically find some matrices $R,S$ where$X_j=T\left(R{A}_{j}S\right)$ for all $j$. 

The model $(X_1,\dots ,X_r)$ simplifies since it is encoded into the matrices $R,S$, but this also means that the model $(X_1,\dots ,X_r)$ is a linear model. I have just made these observations about the LSRDRs along subspaces, but they seem to behave mathematically enough for me especially since the matrices $R,S$ tend to have mathematical properties that I can't explain and am still exploring.

Thanks Ryan! I will look into suggested courses.