Baran Hashemi

Baran Hashemi, Nikolai Hartmann, Sahand Sharifzadeh et al. · deepmind

Simulating high-resolution detector responses is a computationally intensive process that has long been challenging in Particle Physics. Despite the ability of generative models to streamline it, full ultra-high-granularity detector simulation still proves to be difficult as it contains correlated and fine-grained information. To overcome these limitations, we propose Intra-Event Aware Generative Adversarial Network (IEA-GAN). IEA-GAN presents a Relational Reasoning Module that approximates an event in detector simulation, generating contextualized high-resolution full detector responses with a proper relational inductive bias. IEA-GAN also introduces a Self-Supervised intra-event aware loss and Uniformity loss, significantly enhancing sample fidelity and diversity. We demonstrate IEA-GAN's application in generating sensor-dependent images for the ultra-high-granularity Pixel Vertex Detector (PXD), with more than 7.5 M information channels at the Belle II Experiment. Applications of this work span from Foundation Models for high-granularity detector simulation, such as at the HL-LHC (High Luminosity LHC), to simulation-based inference and fine-grained density estimation. To our knowledge, IEA-GAN is the first algorithm for faithful ultra-high-granularity full detector simulation with event-based reasoning.

Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg et al.

Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the 3-day workshop *Benchmarks in Leipzig* with 35 participants at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. We present the resulting collection of 100 questions. We evaluated these questions in three stages: a single attempt by five state-of-the-art LLMs, followed by a 20-runs-per-model evaluation with three of these models, and finally a 3-run attempt with two heavy-thinking models. After Stage 1, 41 questions remained completely unsolved; after Stage 2, this count dropped to 16; and we concluded Stage 3 with only 2 unsolved questions. This demonstrates that the mathematical reasoning capabilities of LLMs are becoming impressive.

Baran Hashemi, Nikolai Hartmann, Thomas Kuhr et al.

The pixel vertex detector (PXD) is an essential part of the Belle II detector recording particle positions. Data from the PXD and other sensors allow us to reconstruct particle tracks and decay vertices. The effect of background hits on track reconstruction is simulated by adding measured or simulated background hit patterns to the hits produced by simulated signal particles. This model requires a large set of statistically independent PXD background noise samples to avoid a systematic bias of reconstructed tracks. However, data from the fine-grained PXD requires a substantial amount of storage. As an efficient way of producing background noise, we explore the idea of an on-demand PXD background generator using conditional Generative Adversarial Networks (GANs) with contrastive learning, adapted by the number of PXD sensors in order to both increase the image fidelity and produce sensor-dependent PXD hitmaps.

Baran Hashemi, Roderic G. Corominas, Alessandro Giacchetto

How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based approach to computational enumerative geometry, specifically targeting the computation of $ψ$-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task, we compute intersection numbers across a wide value range from $10^{-45}$ to $10^{45}$. To capture the recursive nature inherent in these intersection numbers, we propose the Dynamic Range Activator (DRA), a new activation function that enhances the Transformer's ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. To the best of our knowledge, there has been no prior work on modeling recursive functions with such a high-variance and factorial growth. Beyond simply computing intersection numbers, we explore the enumerative "world-model" of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover, through abductive hypothesis testing, probing, and causal inference, we uncover evidence of an emergent internal representation of the the large-genus asymptotic of $ψ$-class intersection numbers. These findings suggest that the network internalizes the parameters of the asymptotic closed-form and the polynomiality phenomenon of intersection numbers in a non-linear manner. This opens up new possibilities in inferring asymptotic closed-form expressions directly from limited amount of data.

Baran Hashemi

Using FlowBoost, a closed-loop deep generative optimization framework for extremal structure discovery, we investigate $\ell^p$-generalizations of the finite free Stam inequality for real-rooted polynomials under finite free additive convolution $\boxplus_n$. At $p=2$, FlowBoost finds the Hermite pair as the unique equality case and reveals the spectral structure of the linearized convolution map at this extremal point. As a result, we conjecture that the singular values of the doubly stochastic coupling matrix $E_n$ on the mean-zero subspace are ${2^{-k/2}:k=1,\ldots,n-1}$, independent of $n$. Conditional on this conjecture, we obtain a sharp local stability constant and the finite free CLT convergence rate, both uniform in $n$. We introduce a one-parameter family of $p$-Stam inequalities using $\ell^p$-Fisher information and prove that the Hermite pair itself violates the inequality for every $p>2$, with the sign of the deficit governed by the $\ell^p$-contraction ratio of $E_n$. Systematic computation via FlowBoost supports the conjecture that $p^*\!=2$ is the sharp critical exponent. For $p<2$, the extremal configurations undergo a bifurcation, meaning that they become non-matching pairs with bimodal root structure, converging back to the Hermite diagonal only as $p\to 2^-$. Our findings demonstrate that FlowBoost, can be an effective tool of mathematical discovery in infinite-dimensional extremal problems.

Chris Teska, Kurt Pasque, Ruriko Yoshida et al.

In this work, we introduce a Tropical Axial Attention neural reasoning architecture that replaces vanilla softmax dot-product attention with max-plus operators, inducing a piecewise-linear structure aligned with dynamic programming formulations. From multi-species sequence alignments, our model learns all possible pairwise distances and is trained using a combination of $\ell_1$ and tropical symmetric distance metric losses with an ultrametric violation penalty. We leverage the well known isomorphic relationship between the space of all phylogenetic trees with $n$ species and tropical Grassmannian to show that tropical attention provides a natural geometric framework for phylogenetic inference. On empirical $DS1-DS11$ alignments, where true trees are unknown, the tropical model produces distance matrices that are substantially closer to their BME-induced tree metrics than the baseline models. These results suggest that tropical attention is a useful geometric inductive bias for neural phylogenetic inference, especially under distribution shift and when tree-metric consistency is important.

Richard Hildebrandt, Evangelos Kourlitis, Baran Hashemi et al.

We introduce a new strategy for compositional neural surrogates for radiation-matter interactions, a key task spanning domains from particle physics through nuclear and space engineering to medical physics. Exploiting the locality and the Markov nature of particle interactions, we create a \emph{next-particle prediction} kernel using hybrid discrete-continuous transformer models based on Riemannian Flow Matching on product manifolds. The model generates variable-sized typed sets of particles and radiation side effects that are the result of the interaction of an incident particle with a material volume. The resulting kernel can be composed to simulate unseen large-scale material distributions in a zero-shot manner. Unlike mechanistic simulators, our model is designed to be differentiable, provides tractable likelihoods for future downstream applications. A significant computational speed-up on GPU compared to CPU-bound mechanistic simulation is observed for single-kernel execution. We evaluate the model at the kernel level and demonstrate predictive stability over multi-round autoregressive rollouts. We additionally release a novel 20M-event radiation-matter interaction dataset for further research.

Baran Hashemi, Claudius Krause

In modern collider experiments, the quest to explore fundamental interactions between elementary particles has reached unparalleled levels of precision. Signatures from particle physics detectors are low-level objects (such as energy depositions or tracks) encoding the physics of collisions (the final state particles of hard scattering interactions). The complete simulation of them in a detector is a computational and storage-intensive task. To address this computational bottleneck in particle physics, alternative approaches have been developed, introducing additional assumptions and trade off accuracy for speed.The field has seen a surge in interest in surrogate modeling the detector simulation, fueled by the advancements in deep generative models. These models aim to generate responses that are statistically identical to the observed data. In this paper, we conduct a comprehensive and exhaustive taxonomic review of the existing literature on the simulation of detector signatures from both methodological and application-wise perspectives. Initially, we formulate the problem of detector signature simulation and discuss its different variations that can be unified. Next, we classify the state-of-the-art methods into five distinct categories based on their underlying model architectures, summarizing their respective generation strategies. Finally, we shed light on the challenges and opportunities that lie ahead in detector signature simulation, setting the stage for future research and development.

Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck et al.

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 39 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation of mathematical reasoning capabilities by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can succeed at the more accessible research-level questions, but still encounter significant difficulties on more challenging problems. Quantitatively, Grok-4 achieves the highest accuracy of 52% on final-answer subproblems, while GPT-5 obtains the best performance for proof generation, achieving a fully correct solution for 22% of problems. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

Baran Hashemi, Kurt Pasque, Chris Teska et al.

Can algebraic geometry enhance the sharpness, robustness, and interpretability of modern neural reasoning models by equipping them with a mathematically grounded inductive bias? To answer this, we introduce Tropical Attention, an attention mechanism grounded in tropical geometry that lifts the attention kernel into tropical projective space, where reasoning is piecewise-linear and 1-Lipschitz, thus preserving the polyhedral decision structure inherent to combinatorial reasoning. We prove that Multi-Head Tropical Attention (MHTA) stacks universally approximate tropical circuits and realize tropical transitive closure through composition, achieving polynomial resource bounds without invoking recurrent mechanisms. These guarantees explain why the induced polyhedral decision boundaries remain sharp and scale-invariant, rather than smoothed by Softmax. Empirically, we show that Tropical Attention delivers stronger out-of-distribution generalization in both length and value, with high robustness against perturbative noise, and substantially faster inference with fewer parameters compared to Softmax-based and recurrent attention baselines. For the first time, we extend neural algorithmic reasoning beyond PTIME problems to NP-hard and NP-complete problems, paving the way toward sharper and more expressive Large Reasoning Models (LRMs) capable of tackling complex combinatorial challenges in phylogenetics, cryptography, particle physics, and mathematical discovery.

Baran Hashemi

Simulating ultra-high-granularity detector responses in Particle Physics represents a critical yet computationally demanding task. This thesis aims to overcome this challenge for the Pixel Vertex Detector (PXD) at the Belle II experiment, which features over 7.5M pixel channels-the highest spatial resolution detector simulation dataset ever analysed with generative models. This thesis starts off by a comprehensive and taxonomic review on generative models for simulating detector signatures. Then, it presents the Intra-Event Aware Generative Adversarial Network (IEA-GAN), a new geometry-aware generative model that introduces a relational attentive reasoning and Self-Supervised Learning to approximate an "event" in the detector. This study underscores the importance of intra-event correlation for downstream physics analyses. Building upon this, the work drifts towards a more generic approach and presents YonedaVAE, a Category Theory-inspired generative model that tackles the open problem of Out-of-Distribution (OOD) simulation. YonedaVAE introduces a learnable Yoneda embedding to capture the entirety of an event based on its sensor relationships, formulating a Category theoretical language for intra-event relational reasoning. This is complemented by introducing a Self-Supervised learnable prior for VAEs and an Adaptive Top-q sampling mechanism, enabling the model to sample point clouds with variable intra-category cardinality in a zero-shot manner. Variable Intra-event cardinality has not been approached before and is vital for simulating irregular detector geometries. Trained on an early experiment data, YonedaVAE can reach a reasonable OOD simulation precision of a later experiment with almost double luminosity. This study introduces, for the first time, the results of using deep generative models for ultra-high granularity detector simulation in Particle Physics.

Gergely Bérczi, Baran Hashemi, Jonas Klüver

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes intractable. We introduce FlowBoost, a closed-loop generative framework that learns to discover rare and extremal geometric structures by combining three components: (i) a geometry-aware conditional flow-matching model that learns to sample high-quality configurations, (ii) reward-guided policy optimization with action exploration that directly optimizes the generation process toward the objective while maintaining diversity, and (iii) stochastic local search for both training-data generation and final refinement. Unlike prior open-loop approaches, such as PatternBoost that retrains on filtered discrete samples, or AlphaEvolve which relies on frozen Large Language Models (LLMs) as evolutionary mutation operators, FlowBoost enforces geometric feasibility during sampling, and propagates reward signal directly into the generative model, closing the optimization loop and requiring much smaller training sets and shorter training times, and reducing the required outer-loop iterations by orders of magnitude, while eliminating dependence on LLMs. We demonstrate the framework on four geometric optimization problems: sphere packing in hypercubes, circle packing maximizing sum of radii, the Heilbronn triangle problem, and star discrepancy minimization. In several cases, FlowBoost discovers configurations that match or exceed the best known results. For circle packings, we improve the best known lower bounds, surpassing the LLM-based system AlphaEvolve while using substantially fewer computational resources.