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Stephanie Chan

Publications and source records attributed to Stephanie Chan.

At least 19 recordsLinked to original sources
arXiv2026

From AGI to ASI

Over the last decade, building human-level artificial general intelligence has moved from far-fetched speculation to being a concrete next-decade target for many of the largest AI organisations. Achieving this goal would have profound and far-reaching impacts on human society, which raises many complex questions for the decade ahead. This report investigates how AI itself might continue to develop in a post-AGI world along the continuum of machine intelligence. The endpoint of this continuum, Universal AI, is theoretically well understood, which provides some formal grounding for the main focus of this report: the transition from human-level AGI to artificial general superintelligence, which can intuitively be understood as a system that is more intelligent and cognitively capable than large organisations of humans. After characterizing ASI, the report discusses four potential pathways from AGI to ASI: scaling AGI, AI paradigm shifts, recursive improvement, and ASI emerging from large-scale multi-agent collectives. The report then discusses possible frictions and bottlenecks along these pathways. Determining whether the impact of these frictions will be negligible or substantial raises a number of concrete open research questions. Due to large uncertainties for predicting ASI progress, it cannot be ruled out that AI progress might continue to accelerate over the next years. This could imply that the image of a single transformative step change, caused by the introduction of human-level AGI into our society, could be inaccurate. More apt might be the prospect of a series of transformative societal changes caused by AI-enabled progress and breakthroughs across many areas of science and technology. Preparing for this prospect requires a massively interdisciplinary endeavour of global scope and interest.

cs.AI↗
arXiv2026

Positive Alignment: Artificial Intelligence for Human Flourishing

Existing alignment research is dominated by concerns about safety and preventing harm: safeguards, controllability, and compliance. This paradigm of alignment parallels early psychology's focus on mental illness: necessary but incomplete. What we call Positive Alignment is the development of AI systems that (i) actively support human and ecological flourishing in a pluralistic, polycentric, context-sensitive, and user-authored way while (ii) remaining safe and cooperative. It is a distinct and necessary agenda within AI alignment research. We argue that several existing failures of alignment (e.g., engagement hacking, loss of human autonomy, failures in truth-seeking, low epistemic humility, error correction, lack of diverse viewpoints, and being primarily reactive rather than proactive) may be better addressed through positive alignment, including cultivating virtues and maximizing human flourishing. We highlight a range of challenges, open questions, and technical directions (e.g., data filtering and upsampling, pre- and post-training, evaluations, collaborative value collection) for different phases of the LLM and agents lifecycle. We end with design principles for promoting disagreement and decentralization through contextual grounding, community customization, continual adaptation, and polycentric governance; that is, many legitimate centers of oversight rather than one institutional or moral chokepoint.

cs.AI↗
arXiv2026

Architecting Trust in Artificial Epistemic Agents

Large language models increasingly function as epistemic agents -- entities that can 1) autonomously pursue epistemic goals and 2) actively shape our shared knowledge environment. They curate the information we receive, often supplanting traditional search-based methods, and are frequently used to generate both personal and deeply specialized advice. How they perform these functions, including whether they are reliable and properly calibrated to both individual and collective epistemic norms, is therefore highly consequential for the choices we make. We argue that the potential impact of epistemic AI agents on practices of knowledge creation, curation and synthesis, particularly in the context of complex multi-agent interactions, creates new informational interdependencies that necessitate a fundamental shift in evaluation and governance of AI. While a well-calibrated ecosystem could augment human judgment and collective decision-making, poorly aligned agents risk causing cognitive deskilling and epistemic drift, making the calibration of these models to human norms a high-stakes necessity. To ensure a beneficial human-AI knowledge ecosystem, we propose a framework centered on building and cultivating the trustworthiness of epistemic AI agents; aligning AI these agents with human epistemic goals; and reinforcing the surrounding socio-epistemic infrastructure. In this context, trustworthy AI agents must demonstrate epistemic competence, robust falsifiability, and epistemically virtuous behaviors, supported by technical provenance systems and "knowledge sanctuaries" designed to protect human resilience. This normative roadmap provides a path toward ensuring that future AI systems act as reliable partners in a robust and inclusive knowledge ecosystem.

cs.AI↗
arXiv2026

Thin sets in weighted projective stacks

We prove an upper bound for the number of rational points of bounded height in a weighted projective stack which lie in a given thin subset. As a consequence, we show that $100\%$ of hyperelliptic curves do not admit a prescribed on-trivial level structure.

math.NT↗
arXiv2025

Selmer groups of families of elliptic curves with an $\ell$-isogeny

For certain families of elliptic curves admitting a rational isogeny of prime degree $\ell$, we establish a central limit theorem for the Tamagawa ratio and derive bounds on its average value. By using the Tamagawa ratio to bound the size of the $\ell$-isogeny Selmer group from below, we show that for $\ell \in\{ 2, 3, 5, 7, 13\}$, there exist elliptic curves with arbitrarily large $\ell$-Selmer groups.

math.NT↗
arXiv2025

Relational reasoning and inductive bias in transformers and large language models

Transformer-based models have demonstrated remarkable reasoning abilities, but the mechanisms underlying relational reasoning remain poorly understood. We investigate how transformers perform \textit{transitive inference}, a classic relational reasoning behavior from psychology which elicits inference about indirectly related items (e.g., if $A > B$ and $B > C$, then $A > C$). We compare in-weights learning (IWL) and in-context learning (ICL) behaviors and mechanisms on these tasks, and fine profoundly different patterns of generalization. IWL models learn a linear embedding, which leads to transitive inference as well as other behavioral effects present in humans and animals. ICL models, in contrast, are capable of learning to generalize transitively, but only do so when it is necessitated by the training data, otherwise learning a match-and-copy strategy. Interestingly, pre-training ICL models on in-context linear regression tasks that provide them with a latent linear representation is sufficient to make the ICL behaviors and internal representations qualitatively and quantitatively more like IWL. In order to test whether the same inference patterns are present across in large language models, we leverage a congruency paradigm which allows us to differentially probe IWL and ICL generalization patterns without access to their training data. We indeed see IWL reasoning leads to more transitive generalization than ICL. Moreover, we find that prompting the ICL models to use a linear mental map led to increased transitive inference over different geometric prompts. Together, these results reveal that both the training regime and the geometric structure of induced representations critically determine transformers capacity for transitive inference.

cs.LG↗
arXiv2025

A new pointwise bound for $3$-torsion of class groups

Ellenberg--Venkatesh proved in 2007 that $h_3(d) \ll_\epsilon |d|^{1/3 + \epsilon}$, where $h_3(d)$ denotes the size of the $3$-torsion of the class group of $\mathbb{Q}(\sqrt{d})$. We improve this bound to $h_3(d) \ll_\epsilon |d|^{\kappa + \epsilon}$ with $\kappa \approx 0.3193 \cdots$. We also combine our methods with work of Heath-Brown--Pierce to give new bounds for average $\ell$-torsion of real quadratic fields.

math.NT↗
arXiv2025

Serre's problem for multiple conics

We prove the refined Loughran--Smeets conjecture of Loughran--Rome--Sofos for a wide class of varieties arising as products of conic bundles. One interesting feature of our varieties is that the subordinate Brauer group may be arbitrarily large. As an application of our methods, we answer a question of Lenstra by giving an asymptotic for the triples of integers $(a, b, c)$ for which the R\'edei symbol $[a, b, c]$ takes a given value. We also make significant progress on a question of Serre on the zero loci of systems of quaternion algebras defined over $\mathbb{Q}(t_1, \dots, t_n)$.

math.NT↗
arXiv2025

How do language models learn facts? Dynamics, curricula and hallucinations

Large language models accumulate vast knowledge during pre-training, yet the dynamics governing this acquisition remain poorly understood. This work investigates the learning dynamics of language models on a synthetic factual recall task, uncovering three key findings: First, language models learn in three phases, exhibiting a performance plateau before acquiring precise factual knowledge. Mechanistically, this plateau coincides with the formation of attention-based circuits that support recall. Second, the training data distribution significantly impacts learning dynamics, as imbalanced distributions lead to shorter plateaus. Finally, hallucinations emerge simultaneously with knowledge, and integrating new knowledge into the model through fine-tuning is challenging, as it quickly corrupts its existing parametric memories. Our results emphasize the importance of data distribution in knowledge acquisition and suggest novel data scheduling strategies to accelerate neural network training.

cs.CL↗
arXiv2025

Number fields generated by points in linear systems on curves

We develop techniques for determining the fibers of a morphism of curves $\phi: C \to D$ over a nonarchimedean local field $K$. These results have applications to studying closed point on curves over global fields since closed points on $C$ of large degree or of very small degree are known to all arise as fibers of morphisms.

math.NT↗
arXiv2024

LearnLM: Improving Gemini for Learning

Today's generative AI systems are tuned to present information by default, rather than engage users in service of learning as a human tutor would. To address the wide range of potential education use cases for these systems, we reframe the challenge of injecting pedagogical behavior as one of \textit{pedagogical instruction following}, where training and evaluation examples include system-level instructions describing the specific pedagogy attributes present or desired in subsequent model turns. This framing avoids committing our models to any particular definition of pedagogy, and instead allows teachers or developers to specify desired model behavior. It also clears a path to improving Gemini models for learning -- by enabling the addition of our pedagogical data to post-training mixtures -- alongside their rapidly expanding set of capabilities. Both represent important changes from our initial tech report. We show how training with pedagogical instruction following produces a LearnLM model (available on Google AI Studio) that experts substantially prefer across a diverse set of learning scenarios, with average preference strengths of +31\% over GPT-4o, +11\% over Claude 3.5 Sonnet, and +13\% over the Gemini 1.5 Pro model on which LearnLM was based.

cs.CY↗
arXiv2024

Solubility of a resultant equation and applications

The large sieve is used to estimate the density of integral quadratic polynomials $Q$, such that there exists an odd degree integral polynomial which has resultant $\pm 1$ with $Q$. Given a monic integral polynomial $R$ of odd degree, this is used to show that for almost all integral quadratic polynomials $Q$, there exists a prime $p$ such that $Q$ and $R$ share a common root in the algebraic closure of the finite field with $p$ elements. Using recent work of Landesman, an application to the average size of the odd part of the class group of quadratic number fields is also given.

math.NT↗
arXiv2024

Almost all elliptic curves with prescribed torsion have Szpiro ratio close to the expected value

We demonstrate that almost all elliptic curves over $\mathbb{Q}$ with prescribed torsion subgroup, when ordered by naive height, have Szpiro ratio arbitrarily close to the expected value. We also provide upper and lower bounds for the Szpiro ratio that hold for almost all elliptic curves in certain one-parameter families. The results are achieved by proving that, given any multivariate polynomial within a general class, the absolute value of the polynomial over an expanding box is typically bounded by a fixed power of its radical. The proof adapts work of Fouvry--Nair--Tenenbaum, which shows that almost all elliptic curves have Szpiro ratio close to $1$.

math.NT↗
arXiv2024

Towards Responsible Development of Generative AI for Education: An Evaluation-Driven Approach

A major challenge facing the world is the provision of equitable and universal access to quality education. Recent advances in generative AI (gen AI) have created excitement about the potential of new technologies to offer a personal tutor for every learner and a teaching assistant for every teacher. The full extent of this dream, however, has not yet materialised. We argue that this is primarily due to the difficulties with verbalising pedagogical intuitions into gen AI prompts and the lack of good evaluation practices, reinforced by the challenges in defining excellent pedagogy. Here we present our work collaborating with learners and educators to translate high level principles from learning science into a pragmatic set of seven diverse educational benchmarks, spanning quantitative, qualitative, automatic and human evaluations; and to develop a new set of fine-tuning datasets to improve the pedagogical capabilities of Gemini, introducing LearnLM-Tutor. Our evaluations show that LearnLM-Tutor is consistently preferred over a prompt tuned Gemini by educators and learners on a number of pedagogical dimensions. We hope that this work can serve as a first step towards developing a comprehensive educational evaluation framework, and that this can enable rapid progress within the AI and EdTech communities towards maximising the positive impact of gen AI in education.

cs.CY↗
arXiv2024

Many-Shot In-Context Learning

Large language models (LLMs) excel at few-shot in-context learning (ICL) -- learning from a few examples provided in context at inference, without any weight updates. Newly expanded context windows allow us to investigate ICL with hundreds or thousands of examples -- the many-shot regime. Going from few-shot to many-shot, we observe significant performance gains across a wide variety of generative and discriminative tasks. While promising, many-shot ICL can be bottlenecked by the available amount of human-generated examples. To mitigate this limitation, we explore two new settings: Reinforced and Unsupervised ICL. Reinforced ICL uses model-generated chain-of-thought rationales in place of human examples. Unsupervised ICL removes rationales from the prompt altogether, and prompts the model only with domain-specific questions. We find that both Reinforced and Unsupervised ICL can be quite effective in the many-shot regime, particularly on complex reasoning tasks. Finally, we demonstrate that, unlike few-shot learning, many-shot learning is effective at overriding pretraining biases, can learn high-dimensional functions with numerical inputs, and performs comparably to fine-tuning. We also find that inference cost increases linearly in the many-shot regime, and frontier LLMs benefit from many-shot ICL to varying degrees. Our analysis also reveals the limitations of next-token prediction loss as an indicator of downstream ICL performance.

cs.LG↗
arXiv2024

Genie: Generative Interactive Environments

We introduce Genie, the first generative interactive environment trained in an unsupervised manner from unlabelled Internet videos. The model can be prompted to generate an endless variety of action-controllable virtual worlds described through text, synthetic images, photographs, and even sketches. At 11B parameters, Genie can be considered a foundation world model. It is comprised of a spatiotemporal video tokenizer, an autoregressive dynamics model, and a simple and scalable latent action model. Genie enables users to act in the generated environments on a frame-by-frame basis despite training without any ground-truth action labels or other domain-specific requirements typically found in the world model literature. Further the resulting learned latent action space facilitates training agents to imitate behaviors from unseen videos, opening the path for training generalist agents of the future.

cs.LG↗