Paper Deep Dive — Large Discovery Models: giving an LLM a value signal for what to try next

An LLM can propose candidates but cannot reliably grade its own proposals. Large Discovery Models tilts the LLM's proposal distribution by an acquisition value drawn from a Gaussian process surrogate, so search keeps working when every evaluation is expensive. From the equations to the reported numbers.

Large Discovery Models: Empirically-grounded Model-Based Open-Ended Search

Cheap grading versus expensive grading

When an LLM does maths or code, grading is cheap. Proofs go to a checker, programs go to unit tests. The paper calls this the regime where a cheap, repeatable verifier exists (§1) — which is exactly why "generate a lot, let the verifier pick" works so well as inference-time scaling.

Scientific discovery breaks that. The candidate space is vast, structured, and cannot be written out in advance. Evaluation depends on simulation, accelerator experiments, or physical assays; each one is expensive, cannot be repeated freely, and comes back late or noisy (§1). So a discovery system has to decide not only which candidates to evaluate but which hypotheses get to enter the search at all. The Large Discovery Model (LDM) splits those two jobs between two components: the LLM proposes, and a separate statistical model prices what it proposes.

An analogy: bringing an appraiser to a flea market

You (the LLM) have a good eye. Having read a great deal, you never reach for a shape that could not possibly be genuine. But you cannot tell what is real. So you bring an appraiser (the surrogate). The appraiser only has data from pieces it has actually appraised, and it answers with both an estimate and its own uncertainty — "I'd say 80, but I'm not confident."

What decides which piece goes for a full appraisal is not the score itself but what one unit of budget buys you there. A piece everyone agrees is an 85 may be worth less of your attention than one estimated at 70 with a wide margin for error. The number that captures this decision value is the acquisition function, and it is the centre of the paper (§3).

Defining discovery, and four kinds of "unknown"

The paper starts with an operational definition (Definition 1): a sequential process in which an agent generates hypotheses or designs, submits a limited number to an external evaluator, and uses the returned observations to update its beliefs and steer the next round. A discovery occurs when that process identifies a previously unknown, non-trivial relationship, mechanism, or design supported by empirical evidence. The authors add the caveat themselves — this covers only the class of science that can be posed as search.

Design space is then partitioned into four epistemic regimes (§2). Known knowns are evaluated designs the surrogate predicts with low uncertainty $\sigma_t(x)$. Known unknowns are designs the search can formulate and the surrogate can model, but whose rewards remain unresolved — high $\sigma_t(x)$. Unknown knowns live in an external database or a parallel search, real but absent from the current context. Unknown unknowns are beyond the procedure's reach, or outside the surrogate's modelling support so that a prediction there means nothing.

Three operations follow. Exploitation picks high-mean designs among known knowns. Exploration evaluates reachable but uncertain ones to collapse $\sigma_t$. Discovery moves the search frontier itself — the boundary of what the current procedure can formulate, reach, and meaningfully model. The paper's distinction is sharp: evaluating an untested design is not discovery. An untested design inside the surrogate's support is a known unknown, and resolving it is exploration.

Three components and one equation

LDM has three parts (§3). The generative foundation model $p_{\theta,\alpha}(x\mid\mathcal{C}_t)$ is the proposal distribution conditioned on the search context, where $\theta$ is the weights and $\alpha$ is the inference configuration (prompting strategy, temperature, compute budget). The probabilistic surrogate is a posterior conditioned on evaluated data $\mathcal{D}_t$, returning predictive mean $\mu_t(x)$ and uncertainty $\sigma_t(x)$. The acquisition function $a_t(x)$ turns those two into a scalar: the value of spending computation or an experiment on this candidate. The search policy $\pi_t$ is defined as the solution to a variational problem (Eq. 2).

Written out in words, the rule is: look across every way $q$ of spreading probability over candidates and keep the one that maximises average acquisition value minus a fine for straying. $\mathbb{E}_{x\sim q}[a_t(x)]$ is the score you would average by drawing from $q$, the KL term is how far $q$ has wandered from what the LLM would have said, and $1/\eta$ is the price charged per unit of wandering.

In plain terms: "favour candidates with high acquisition value, but do not drift too far from what the LLM would have proposed." The first term pulls probability mass toward valuable candidates, the second penalises departing from the prior, and $\eta$ sets how hard the first term pulls. The solution is closed-form (Proposition 1, Eq. 3).

So the optimal search distribution is just the LLM's proposal distribution multiplied by $\exp\{\eta\,a_t(x)\}$ and renormalised ($Z_t$ is the division that makes it sum to one), which says that each extra point of acquisition value makes a candidate $e^{\eta}$ times likelier to be drawn. Nothing new is built to search with; an existing source of proposals is simply re-weighted. The paper reads this through infinite-armed bandits: since designs cannot be listed in advance, they surface from a reservoir. The LLM is that reservoir, and the acquisition value tilts where it flows (§3.1).

Both endpoints are spelled out. As $\eta\to0$ the tilt vanishes and search becomes pure LLM generation with no data feedback. As $\alpha\to0$ the reservoir spreads toward a uniform measure and, with $\eta$ large, you recover classical Bayesian optimisation. LDM is the regime between those two limits. If the Bayesian machinery is unfamiliar, Bayesian Thinking from Scratch is the easier entry point.