Thousand-dimensional structure

Resolution plans to explore low-dimensional structure in AI models, aiming to find and control roughly 1,000 dimensions of coupled behavior that emerge in pretraining and flow through post-training to superintelligence, building on the Persona Selection Model from Marks et al. 2026. The organization hopes to systematize phenomena such as emergent misalignment and subliminal learning, then intervene on this structure without hiding undesirable behavior elsewhere.

Summary: One area we plan to explore at Resolution https://resolution.org/ is personas and character training, operationalized as finding and controlling low-dimensional structure in models that emerges in pretraining and flows through post-training to superintelligence. The hope is to expand and systematize phenomena such as emergent misalignment, subliminal learning, and other empirical persona research, then intervene on this structure without accidentally hiding undesirable behavior elsewhere. If this approach resonates with you, consider working with us https://resolution.org/careers . Our understanding of AI training and alignment as a field is very poor. If sufficient alignment of superintelligent AI agents requires pinning down the precise meaning of alignment and turning that meaning into high-accuracy training data and algorithms, we are likely to fail. Modern LLMs have trillions of parameters: our understanding is unlikely to be sufficient to pin down a trillion separate numbers. Happily, there is a growing literature on such low-dimensional structure in AI models, showing that intervening on one aspect of model behavior has strong downstream effects on other aspects: Topic | Description | Emergent misalignment | | Subliminal learning | | Alignment pretraining | | Simulators | | Logits | | Activation-space persona vectors | | Weight-space persona directions | | Teaching Claude Why | | Beneficial RL | | Self-beliefs | | Reward and reasoning | | Character training | | Marks et al. 2026 https://alignment.anthropic.com/2026/psm/ give one systematic model of such behavior, called the Persona Selection Model. In this model, pretraining learns a distribution over personas. Post-training then makes a Bayesian update that selects an Assistant persona. Thus, training on one behavior reweights correlated traits. From this, emergent misalignment and subliminal learning are then results of these correlations, and not independent effects. The intuitive source of this structure is coupled behaviors in the pretraining data. The model has seen text from many different people in many different contexts, and knowing one aspect of a person, context pair predicts many other aspects of behavior. Next-token prediction learns these coupled groups of behaviors, but it has no notion of when different aspects of behaviors “should” be unrelated or not: a person writing malicious code may be malicious in many other ways, and this correlation is useful for prediction. Low-dimensional structure is good news and not only to us https://x.com/ESYudkowsky/status/1894453376215388644 At the extreme, if emergent misalignment was the whole story and there was a single dimension of “good vs. evil” models, then all we’d have to do is pin down that one dimension to win. A solid understanding of low-dimensional structure could mean lower sample complexity for alignment-critical parts of training allowing more effort per data point and lower quality/accuracy requirements for training data or convergence. Alas, it is not the case that there is a single dimension of good vs. evil, either in life or in AI models. Our hope is that there is an intermediate between one and a trillion dimensions: perhaps we could find 1000-or-so-dimensional structure in models which describes how different aspects of model behavior couple, and study it more systematically with a combination of theory and more systematic empirics which is a standard approach in neuroscience https://pmc.ncbi.nlm.nih.gov/articles/PMC4433019/pdf/nihms-689398.pdf , h/t Konstantinos Voudouris https://kvoudouris.co.uk/ . The optimistic story for low-dimensional structure is that modern LLM training is self-referential and path dependent: we train the models for a while, use them to generate synthetic data, train them further on that synthetic data, and repeat. If we can find a good enough low-dimensional space of model behavior, and the self-referential training story is reasonable, there might be a point in that low-dimensional space that extrapolates to an aligned superintelligent agent . Can we find that point? The pessimistic case for low-dimensional structure is that if we find 1000 dimensions of structure, then try to intervene to pick the right point, we’ll just push the bad behavior into some other 1000 dimensions. After all, there will be trillions of dimensions of model weights There is plenty of space for bad behavior to hide. xkcd 1739 — "Fixing Problems.” It’s hard to fix problems without making new ones. One natural way to try to intervene is to collapse those thousand other dimensions, say, by picking one dimension that you care about and training the model to behave identically across noise Chua et al. 2024 https://arxiv.org/abs/2403.05518 , Irpan et al. 2025 https://arxiv.org/abs/2510.27062 , Gautam et al. 2026 https://arxiv.org/abs/2606.05817 , Pres et al. 2026 https://time-for-consistency.github.io/assets/pdfs/Consistency Pos Paper.pdf . But this can be a bit rough, since we should expect some of these dimensions to be coupled, and training for consistency could constrain more behavior than the target behavior. For example, if you directly train models to ignore a bias cue related to sycophancy, you can accidentally reduce the faithfulness of chain-of-thought; if you train only on high-level statistics, we can do better Imran et al. 2026 https://arxiv.org/abs/2606.02211 . Here, being approximately right is better than being perfectly right, since a statistic-level objective needs only the coarse property, and not the full distribution of responses. Reward hacking shows the same effect, where optimizing directly against a chain-of-thought monitor teaches models to hide their reasoning, and does not stop the hacking Baker et al. 2025 https://arxiv.org/abs/2503.11926 . It is also possible that the persona in chain-of-thought which can be strange https://www.lesswrong.com/posts/qgvSMwRrdqoDMJJnD/towards-a-typology-of-strange-llm-chains-of-thought and exhibit varied behaviors Kim et al. 2026 https://arxiv.org/abs/2601.10825 is different from the persona in the answer. Optimization pressure on either one can then push bad behavior into the other. In both cases, the lesson seems to be that gentle measurement https://en.wikipedia.org/wiki/Weak measurement h/t Nika Haghtalab https://people.eecs.berkeley.edu/~nika/ is important, as it keeps optimization pressure off the channels you rely on to see what the model is doing. Another way of considering the hiding problem is exhaustiveness Marks et al. 2026 https://alignment.anthropic.com/2026/psm/ . If all agency is grounded in the persona, then a low-dimensional intervention should suffice; if there is non-persona agency the "router" or "shoggoth" views; Marks et al. 2026 https://alignment.anthropic.com/2026/psm/ , bad behavior could route around persona-level interventions. Hopefully, low-dimensional structure gives us a handle to empirically settle this. Of course, the empirical results are empirical; to understand what will scale to future training pipelines and ASI, we need theory, and trillion parameter theory is unavailable. NewScientist — “Tom Gauld on a puzzling new theory.” Scientist presents simplified model; reality unimpressed. The tradition we can build on here is exact learning dynamics in simplified architectures: for example, deep linear networks give training trajectories in closed form Saxe et al. 2014 https://arxiv.org/abs/1312.6120 , Domine et al. 2025 https://arxiv.org/abs/2409.14623 . Zhang et al. 2025 https://arxiv.org/abs/2512.20607 show that training moves from saddle point to saddle point, and that the model learns the strongest structure in the data first. Singular learning theory says the same thing in general. Training is a sequence of phase transitions between degenerate solutions, and developmental interpretability can already watch such transitions in real runs via the local learning coefficient Hoogland et al. 2024 https://arxiv.org/abs/2402.02364 . We think personas are a learning dynamics story of this kind, where the training corpus is important, but also the order in which that corpus is arranged. Consider, for example, why alignment pretraining, model spec midtraining, and synthetic persona pretraining move data earlier in training rather than adding loss terms at the end. Better still: simple self-referential loops of this type also have a formal description. Jarvis et al. 2026 https://www.pnas.org/doi/10.1073/pnas.2509739123 study iterated learning in deep linear networks where each generation is trained on the previous generation's outputs . In this setting, the loop amplifies structured solutions and discards the rest. Which side of that line do personas fall on? We want one small theory in which emergent misalignment, subliminal learning, and alignment pretraining are parameter regimes. There is a range from analytically solvable to “this theory reduces to a 2000 dimensional ODE representing 1000 dimensions and another 1000 we can push into, then solve it with scipy,” where each ingredient of modern training we add this could be softmax, or this could be RL, or it could be something else costs us some solvability. But even scipy is a factor of 10^9 fewer dimensions than the model Until this point we have assumed that this structure stays the same throughout model training, from pretraining through supervised learning and reinforcement learning and up to superintelligence. But this can’t be true: Bosch, Ascent of the Blessed c. 1505–1515 , cropped — souls drawn up through a tunnel of light toward something unrepresentable beyond its end. We thus need to understand how any low-dimensional structure from pretraining extrapolates up to structure for the eventual superintelligent model. One worry is that pretraining structure might wash out under enough further training. But the path dependence of training helps here: we’ll be tracing a path all the way up to superintelligence and trying to approximate that path. Rather than adding loss terms at the end point, we can instead try to change where this path starts, and rely on the model itself to drive convergence into the right basin. But the question that’s relevant to us here is if the path from starting points to basins stays predictable as the endpoints pass human level. This means persona research will couple to scalable oversight research, as scalable oversight is how we would aim to implement that path past human level; below this training signal comes from human data, and above it training signal comes from protocols where models help supervise models. The coupling then runs in both directions: Putting these together: you can think of persona research as supplying a prior, from which scalable oversight extrapolates into honest equilibria. Character training is important at all the labs, and different labs are taking very different approaches. Competitive pressure only pins down AI character very loosely MacAskill and Davidson 2026 https://www.forethought.org/research/the-importance-of-ai-character . Thus, the companies have much latitude, which we can see in the variation between frontier models. As such, the character a lab picks is one of the most consequential free variables in AI development. We should understand these differences better This is an area where independence is an advantage: we have the vantage point to see across labs in a way that lab-bought-into-a-particular-frame does not. We can disambiguate how these efforts are being done in three ways: Different pipelines make models that are measurably different. We can already see the different choices in the outputs. Many models are more positive about their own company when discussing controversies Finke and Casper 2026 https://papers.ssrn.com/sol3/papers.cfm?abstract id=7059338 , or answering hard-to-verify questions Betley et al. 2026 https://arxiv.org/abs/2607.14345 . Persona structure shows through, differently per lab, and often in micro-interactions that are hard to spot and tease out. Putting this together, we want to make the empirical results on low-dimensional persona structure systematic. To do this, we want to thread together small theories that contain emergent misalignment, subliminal learning, and alignment pretraining. We then want to intervene on this structure gently, without pushing bad behavior into some dimension we can't see. We also want to know how the structure extrapolates past human level, with personas supplying the prior, and scalable oversight the extrapolation. In this sense, none of the ingredients are new But the personas bet is that the components are coherent to think about together, and that one thousand dimensions in the middle are tractable where one trillion parameters aren’t. Thank you to Alex Holness-Tofts, Konstantinos Voudouris, Jeremy Gillen, Daniel Murfet, Jacob Pfau, Cameron Holmes, and Clément Dumas for helpful feedback and discussion. If you found this work helpful and would like to cite it, please use: @misc{africa2026modelsdishonest, title = {Thousand-dimensional structure}, author = {Africa, David Demitri and Irving, Geoffrey}, year = {2026}, howpublished = {Resolution}, note = {Resolution blogpost}, url = {https://www.lesswrong.com/posts/sFhW3ZnPMJdnB4Dd6/thousand-dimensional-structure-1}}