Alex Gibson

• Alex Gibson 22 May 2026 23:50 UTC

  2 points

  0

  on: Which tech­ni­cal AI safety fields are go­ing to be au­to­mated first?

  My model of things is that there is a core set of generally applicable research skills, and then there is topic specific technical knowledge required to conduct research in that particular area.

  I don’t think models are bottlenecked by technical knowledge. I think they just don’t currently have the general capability required to do broad exploratory research, outside of narrowly specified verifiable problems.

  I would guess all these subfields will get automated at the same time, once said capability is developed.

  Different groups have specific agendas, and within said agendas you can try to automate the production of incremental papers (which are important!) But in the limit you’re going to have to develop concepts beyond the current frame if you don’t want to stagnate, which requires general exploratory research ability.

• Alex Gibson 21 May 2026 8:25 UTC

  21 points

  1

  in reply to: Julian Bradshaw’s comment on: anaguma’s Shortform

  To be fair I think the idea of using algebraic number theory to approach the problem had been tried before (Tsimerman mentions he tried a similar approach that the model ultimately succeeded with, but didn’t persist with it.) It’s quite a general trick to use algebraic number theory for constructions in the plane, as you have the lattice associated with the ring of integers of number fields.

  I personally am blown away by the proof but it would be far more impressive had it come up with a novel connection between fields, or indeed if it had turned out there wasn’t a counterexample and it proved a tight upper bound (See Gowers’ initial reaction.)

Neu­ral Net­works learn Bloom Filters

• Alex Gibson 25 Jan 2026 11:35 UTC

  1 point

  0

  in reply to: leogao’s comment on: leogao’s Shortform

  There are surely reasons to do ambitious interp that are not the stated goal of ambitious interp?

• Alex Gibson 5 Jan 2026 14:39 UTC

  2 points

  0

  in reply to: Fabien Roger’s comment on: Ger­ard Boxo’s Shortform

  Anthropic practically entrapped Claude to get that behavioural evidence.

• Alex Gibson 5 Jan 2026 1:51 UTC

  2 points

  0

  in reply to: TristanTrim’s comment on: Se­man­tic Topolog­i­cal Spaces

  Good luck with it. I do think the broad direction is pretty promising.

• Alex Gibson 4 Jan 2026 22:53 UTC

  2 points

  0

  in reply to: TristanTrim’s comment on: Se­man­tic Topolog­i­cal Spaces

  I think even formally defining what you want the underlying set of ideal space to be would be a good post.

• Alex Gibson 4 Jan 2026 19:43 UTC

  5 points

  0

  on: Se­man­tic Topolog­i­cal Spaces

  Do you have formal definitions of what exactly you mean by the input space, or what you mean by the output space? What are the underlying sets, and what topology are you equipping them with? Wouldn’t the output space just be the interval $[0,1]$, and the input space $[0,1{]}^N$?

• Alex Gibson 3 Jan 2026 17:44 UTC

  8 points

  0

  in reply to: Linda Linsefors’s comment on: Ro­ta­tions in Superposition

  Ok I have a neat construction for z=1, https://​​www.lesswrong.com/​​posts/​​g9uMJkcWj8jQDjybb/​​ping-pong-computation-in-superposition that works pretty well ($T=\frac{D^2}{d^2}$ with $D(1+\frac{2}{d})$ width and $L+3$ layers), and zero error. Note that $\frac{D^2}{d^2}$ is exact here, not asymptotic.

  I’m trying to find a similar construction that scales like $z$ in the number of parameters required, without just scaling the number of layers up. I’d also be curious if it’s possible to avoid scaling parameters linearly with $z$, but it seems quite difficult.

• Alex Gibson 2 Jan 2026 17:41 UTC

  1 point

  0

  on: De­bunk­ing claims about sub­quadratic attention

  Text diffusion LLMs can be more efficient than autoregressive models in practice because it is usually more efficient on GPUs to do one big operation than many small operations in sequence, even when both require the same number of FLOPs^[1].

  My mental model was that autoregressive models are slow during decoding because of the memory transfers required on each token. You need to swap the entire KV cache in and out of Global Memory on each token. I imagine this is what you mean here, just wanted to check this model is along the right lines?

  I feel like there must be a way to allow for more flexibility in memory usage. There are clearly scenarios where what you want is MCMC style, constant memory /​ markov search, i.e: recall. In cases like this, autoregressive transformers are just painful because they inherently tie up iterations with memory usage. But there are scenarios where constant memory loses as well, i.e: sparse recall tasks.

Ping pong com­pu­ta­tion in superposition

• Alex Gibson 26 Dec 2025 20:04 UTC

  1 point

  0

  in reply to: Linda Linsefors’s comment on: Ro­ta­tions in Superposition

  We could allocate more of the total storage to on-indicators information and less to the rotated vector. Such a shift may be more optimal.

  This is all I mean. Having the small circuits do error correction on on-indicator neurons is just a way of increasing that total percentage storage allocated to on-indicators in the larger network in an embedding agnostic manner. You can change your method for constructing the larger network later and this strategy would be orthogonal to such a change.

  I think allocating a higher percentage to on-indicators should still apply even when adding cross-circuit computation.

  Possibly there are some things you can eliminate right away? But I think often not. In the transformer architecture, at the start, the network just has the embedding vector for the first token and the positional embedding. After the first attention, the network has a bit more information, but not that much, the softmax will make sure the network just focus on a few previous words (right?). And every step of computation (including attention) will come with some noise, if superposition is involved.

  The assumption “softmax will make sure the network just focus on a few previous words (right?)” is true for many attention heads, but not all of them. Some attention heads attend broadly across the whole sequence, aggregating many different tokens together to get the ‘gist’ of a text.

  By the end of the first layer of GPT-2 Small, it has constructed a continuous linear summary of the previous $50$ tokens, and so has a Word2Vec style vector in its residual stream. So it knows that the text is about World War I, or about AI, that it is written in British English, that is is formal/​informal, etc, all by the end of the first attention layer (before the first MLP). This is lots of information to go on in terms of turning off circuits etcetera (think Mixture-Of-Experts).

  There is a regime where the (updated) framework works. See figure 8-11 for values T(d/​D)^2 < 0.004. However for sizes of networks I can run on my laptop, that does not leave room for very much superposition.

  Nice, ok. So asymptotically it works fine then? So the next step theory wise is having a framework that allows for cross-circuit computation, I guess.

  Do you want to have a call some time in January?
  There are probably lots of thing that isn’t explained as well as it could have been in the post

  I would be grateful if you get the time. I have recently had some more ideas that are more useful potentially about this stuff that it might be worth discussing.

• Alex Gibson 20 Dec 2025 14:08 UTC

  LW: 1 AF: 1

  0

  AF

  in reply to: Linda Linsefors’s comment on: Ro­ta­tions in Superposition

  To clarify where i’m coming from, I read the previous post as showing that assuming inactive circuits never activate due to superposition noise, we could get $T=O\left(\frac{D^2}{d^2}\right)$. This post shows that inactive circuits erroneously activate in practice, violating that assumption. I’m curious what asymptotics are possible if we remove this assumption and force ourselves to design the network to prevent such erroneous activations. I may be misinterpreting things, though.

  If I understand your correctly, this is already what we are doing. Each on-indicator is distributed over $S$ pairs of neurons in the Large Network, where we used $S=6$ for the results in this post.

  
  Agnostic of the method for embedding the small circuits in the larger network, currently only $1$ out of $d$ neurons in each small network is being allocated to storing whether the small network is on or off. I’m suggesting increasing it to $cd$ for some small fixed $c$, increasing the size of the small networks to $(1+c)d$ neurons. In the rotation example, $d$ is so small that it doesn’t really make sense. But i’m just thinking about asymptotically. This should generalise straightforwardly to the “cross-circuit” computation case as well.

  The idea is that while each of the $cd$ indicator neurons would be the same as each other in the smaller network, when embedded in the larger network, the noise each small network neuron (distributed across $S$ neurons in the large network) receives is hopefully independent.

  If we assume that which circuits are active never changes across layers (which is true for the example in this post) there is another thing we can do. We can encode, the on-indicators, at the start, in superposition, and then just copy this information from layer to layer. This prevents the parts of the network that is responsible for on indicators from seizing. The reasons we didn’t do this is we wanted to test a method that could be used more generally.

  This method also works under the assumptions specified in Section 5.2, right? Under Section 5.2 assumptions, it suffices to encode the circuits which are active on the first layer, of which there are at most $z$. Even if you erroneously believe one of the $z$ circuits is active on a later layer, when it has turned off, the gain comes from eliminating the other $T-z$ inactive circuits. If the on-indicators don’t seize, then you can stop any part of the circuit from seizing in the Section 5.2 scenario.

  I agree shared state/​cross-circuit computation is an important thing to model, though. I guess that’s what you mean by more generally? In which case I misunderstood the post completely. I thought it was saying that the construction of the previous post ran into problems in practice. But it seems like you’re just saying, if we want this to work more generally, there are issues?

  ---------------------------------------

  This series of posts is really useful, thank you! I have been thinking about it a lot for the past couple of days.

• Alex Gibson 18 Dec 2025 21:34 UTC

  LW: 3 AF: 2

  0

  AF

  on: Ro­ta­tions in Superposition

  If I understand correctly, inactive circuits mistakenly activating is the main failure mode—once this happens, things go downhill quickly. So the bottleneck is robustly knowing which circuits should be active.

  Could we use O(d) redundant On-indicators per small circuit, instead of just 1, and apply the 2-ReLU trick to their average to increase resistance to noise?

  In the Section 5 scenario, would it help to use $T$ additional neurons to encode the network’s best guess for the active circuits early on, before noise accumulates, and preserve this over layers? You could do something like track the circuits which have the most active neuron mass associated with them in the first layer of your constructed network (though this would need guarantees like circuits being relatively homogeneous in the $L^1$ norm of their activations).

  The reason I think this is a reasonable idea is that LLMs do seem to compute binary indicators of when to use circuits, separate from the circuits themselves. Ferrando et al. found models have features for whether they recognize an entity, which gates fact lookup. In GPT2-Small, the entity recognition circuit is just a single first-layer neuron, while the fact-lookup circuit it controls is presumably very complex (GDM couldn’t reverse-engineer it). This suggests networks naturally learn simple early gating for complex downstream computations.

• Alex Gibson 6 Sep 2025 0:43 UTC

  3 points

  −1

  on: In­ter­pretabil­ity is the best path to alignment

  Interesting post, thanks.

• Alex Gibson 11 Aug 2025 19:13 UTC

  1 point

  0

  in reply to: Zephaniah Roe’s comment on: Alter­na­tive Models of Superposition

  I guess I mean it purely as “I don’t think this applies to to the Toy Model setting”, as opposed to saying it’s not a potentially valuable loss to study.

• Alex Gibson 11 Aug 2025 18:44 UTC

  8 points

  1

  on: Alter­na­tive Models of Superposition

  The linear model claim is scoped to reconstruction loss, where you genuinely don’t see superposition as far as i’m aware. And in this case, the reconstruction loss would be poor, because the vectors are nested so close to each other that adjacent features false fire.

• Alex Gibson 23 Jul 2025 18:02 UTC

  9 points

  2

  in reply to: johnswentworth’s comment on: $500 Bounty Prob­lem: Are (Ap­prox­i­mately) Deter­minis­tic Nat­u­ral La­tents All You Need?

  I’m confused by this. The KL term we are looking at in the deterministic case is
  , right?

• Alex Gibson 6 Jul 2025 15:59 UTC

  2 points

  0

  on: Small foun­da­tional puz­zle for causal the­o­ries of mechanis­tic interpretability

  Am I right that the line of argument here is not about the generalization properties, but a claim about the quality of explanation, even on the restricted distribution? As in, we can use the fact that our explanation fails to generalize to the inputs (0,1) and (1,0) as a demonstration that the explanation is not mechanistically faithful, even on the restricted distribution?

  Sometimes models learn mechanisms that hold with high probability over the input distribution, but where we can easily construct adversarial examples. So I think we want to allow explanations that only hold on narrow distributions, to explain typical case behaviour. But I think these explanations should come equipped with conditions on the input distribution for the explanation to hold. Like here, your causal model $M^{\ast }$ should have the explicit condition “x_1=x_2”.

• Alex Gibson 30 Jun 2025 6:26 UTC

  1 point

  0

  in reply to: Lucius Bushnaq’s comment on: [Paper] Stochas­tic Pa­ram­e­ter Decomposition

  If there is some internal gradient descent reason for it being easier to learn to read off orthogonal vectors then I take it back. I feel like I am being too pedantic here, in any case.