Publications – Max Zimmer

A mathematician using AI tools must decide which systems to use, how to combine them, and how to verify their results. Published benchmarks offer limited guidance for an open research problem, while testing every alternative is often far too expensive. We call the problem of finding and adapting a suitable resource configuration the capability estimation problem (CEP). We introduce Zero, a meta-agent that uses published research and evidence from its own attempts to select resources. Zero constructs workflows for agents and tools and revises them during execution, allowing researchers to inspect and interactively steer the work. Using Zero, we resolve open questions on Lagrangian relaxation through counterexample construction and Lean formalization, adapt prover choices during a formalization campaign, and extend a machine-learning theory harness with formal verification.
Offline compaction of the key–value cache (KV-cache) reduces the cost of repeatedly querying a fixed context by constructing a smaller cache once and reusing it subsequently. The central challenge of compaction is deciding which cache entries to delete and which to retain. Existing methods score each candidate for deletion on its own, with the rest of the cache being held fixed. However, softmax renormalization of the attention operation couples these decisions in a nonlinear manner: removing one entry changes the attention weights of every remaining one. In this work, we introduce KV-Surgeon, which uses calibration data to take interactions into account in a tractable way. We derive a quadratic surrogate that admits closed-form expressions for jointly making the optimal greedy removal decision as well as compensation within the remaining entries. On QuALITY, LongHealth, and Long Code Arena, and at every evaluated compaction ratio, KV-Surgeon substantially advances the cost–accuracy Pareto frontier of dense and mixture-of-experts models from 4B to 30B parameters. At 50\times compaction, KV-Surgeon improves question-answering accuracy by up to four points over attention matching (Zweiger et al., 2026), the state of the art, at comparable cost. Lastly, we introduce an even faster variant, which also exceeds the state of the art while requiring only two fifths of its cost.
We study the numerical approximation of Schrödinger Bridges in the setting where samples from the target distribution are unavailable and only an unnormalized target density is given. In this regime, the widely used iterative proportional fitting (IPF) procedure (and its variants) often exhibits severe numerical instabilities, stemming from ill-conditioned underlying control problems and from the fact that the optimal solution may lie far from the initialization. To address these issues, we propose a trust region variant of IPF that constrains successive updates to remain at a fixed Kullback-Leibler divergence from the current iterate. This restriction significantly improves numerical stability. Moreover, we show that the resulting method admits an interpretation as a mirror descent scheme with an adaptively chosen step size. We demonstrate the effectiveness of our approach on several challenging sampling tasks.
Agents pair reasoning models with harnesses that organize model calls, execute tools, load skill instructions, and retain history in memory. Understanding agent performance requires linking execution conditions to outcomes, behavior, and resource use. We introduce AlphaDiana, a measurement system with modular interfaces for datasets, agents, environments, and scorers. It preserves harness-native control loops while controlling file reuse and memory retention separately. AlphaDiana supports macro analyses of complete agents and micro interventions on agent components such as tools, skills, and memory under matched conditions. We study three open-source models and three open-source harnesses on five answer-based benchmarks, with two models also tested on two interactive benchmarks. We find that harnesses do not consistently improve the accuracy of reasoning: gains on questions unsolved by the model alone can be outweighed by losses on questions it answers correctly without tools. This inconsistency extends to component interventions: neither skill guidance nor retained history reliably improves accuracy. Behavior and output-token use must be assessed with correctness: low token entropy can accompany wrong answers, and less output per execution can mean more output tokens per correct answer when accuracy falls. AlphaDiana links answer correctness and execution status to traces and resource records for comparing agents and diagnosing failures under shared task and resource policies.
Spike-and-slab regression is a standard Bayesian formulation of variable selection: it returns a posterior distribution over which candidate effects are active rather than a single selected subset, so that every candidate effect carries an inclusion probability. Its cost grows exponentially with the number of candidate effects, so the posterior can be enumerated exactly only when the number of predictors is small. Beyond that reach, the posterior has to be approximated, typically by Markov chain Monte Carlo over the model space, which requires a fresh run for every dataset and, within a fixed budget of steps, may fail to converge. We present LinearPFN, a prior-data fitted transformer network that amortizes spike-and-slab inference for linear models with main effects and pairwise interactions. The network is pretrained once on synthetic datasets, drawn from an explicitly specified prior, and a single forward pass over a new dataset returns posterior inclusion probabilities, posterior-mean coefficients and posterior predictive distributions with no per-dataset fitting. The prior is conjugate by design, so that the posterior for each fixed set of active effects has a closed form, and wherever the exact posterior is still computable by enumeration we verify the network’s outp