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arXiv

MGMCL: Multi-Granularity Manifold Contrastive Learning With Neural ODEs for Cross-Subject EEG Emotion Recognition

Xiang Xie

Cross-subject electroencephalogram (EEG)-based emotion recognition remains challenging due to substantial inter-individual variability and discrete formulation that overlooks affective continuity. Existing methods operate in Euclidean space and focus on marginal distribution alignment, failing to preserve the semantic structure of emotions across subjects. This article proposes MGMCL, reconceptualizing emotion recognition as learning continuous representations on symmetric positive definite (SPD) Riemannian manifolds. The frame?work introduces multi-granularity manifold contrastive learning at instance, emotion, and trajectory levels while preserving semantic ordering. Neural ordinary differential equations on manifolds model continuous emotion dynamics. Cross-subject generalization employs Gromov-Wasserstein manifold alignment. Weakly-supervised learning enables continuous valence-arousal-dominance prediction from discrete labels. Extensive experiments on three public datasets demonstrate state-of-the-art performance: 91.23% accuracy on SEED, 73.82% on SEED-IV, and 76.38% on DEAP, achieving consistent improvements of 1.89%, 1.66%, and 1.28% over previous best methods, respectively.

arXiv

FSTC-Encoder: Feature--Spatial--Temporal Correlation Learning for Generalizable RF Sensing

Jing Wang, Zhu Wang, Changlong Cheng, Yifan guo, Yin Zhang

Heterogeneous RF sensing differs substantially in feature structure, spatial layout, and temporal scale, making existing models difficult to reuse across devices, environments, and RF modalities. We propose FSTC-Encoder, which unifies heterogeneous RF representation learning through feature, spatial, and temporal correlation modeling. Structure-aware feature encoding accommodates different signal structures, set-based spatial encoding aggregates variable observations, and hierarchical temporal encoding jointly captures local variations and long-range dependencies. Across sensing tasks and modalities, FSTC-Encoder retains the same spatial--temporal backbone architecture while varying only the feature configuration and task head. Across Widar3.0, CSI-Bench, and XRF55, FSTC-Encoder achieves 92.15% mean Accuracy under multi-factor cross-domain protocols, ranks first on three of four additional sensing tasks, remains consistently strong across WiFi, millimeter-wave radar, and RFID, and reduces the cross-modality performance gap from 18.85% to 12.93% through cross-RF learning. These results demonstrate that FSTC-Encoder achieves high domain robustness, task generality, and modality extensibility.

arXiv

Optimal Learning Under Tsybakov Noise

Steve Hanneke, Hongao Wang, Mingyue Xu

Probably Approximately Correct (PAC) learning [Val84] is a fundamental learning model that has been extensively investigated. In this model, $\mathcal{H} \subseteq \{0,1\}^{\mathcal{X}}$ is a concept class, and $h^*\in\mathcal{H}$ is the target concept to be learned. Having access to i.i.d. labeled examples from a distribution $\mathcal{D}$ over $\mathcal{X}\times\{0,1\}$, which admits $h^*$ as the best concept in $\mathcal{H}$, the goal is to design a learning algorithm that outputs a hypothesis having low error competitive to $h^{*}$ with high probability. This model was initially studied under the realizable setting, which assumes that $h^*$ has no error. A natural relaxation is to allow label noise, that is, the true label can be flipped with probability $η\in(0,1/2)$. In reality, certain labels might be extremely noisy, especially for those points near the decision boundary. Hence, it is natural to allow very noisy points, though only rarely. This is quantified by a noise model introduced by [MT99] and [Tsy04], now known as Tsybakov noise. For learning general concept classes, [MN06] gave the general upper and lower bounds for error guarantees under Tsybakov noise. However, their upper and lower bounds differ by a logarithmic factor. Resolving this gap has remained a well-known open question for the past twenty years. In this work, we resolve this open question by improving the upper bound to match the best known lower bound, thus establishing the optimal error guarantee for learning under Tsybakov noise. Our learning algorithm operates by adaptively partitioning the instance space into regions, roughly corresponding to different noise levels, and returning a hypothesis in the concept class satisfying a specific error constraint for each region. Our technique shares a conceptual foundation with several recent advances in non-realizable learning, such as [HLZ24] and [Han25].

arXiv

Model Predictive Control of Hybrid Dynamical Systems

Ricardo G. Sanfelice, Berk Altin

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.

arXiv

Constrained Learning with Universally Learnable Concept Classes

Herlock SeyedAbolfazl Rahimi, Spyridon Pougkakiotis, Dionysis Kalogerias

We study constrained statistical learning over infinite-dimensional hypothesis classes in the fully nonconvex setting, and establish universal PACC learnability of the solutions of dual algorithms: Probably Approximately Correct on Constraints, guaranteeing optimality and constraint satisfaction at once. This strengthens near-PACC results, whose feasibility residual no amount of data can remove. Optimality is caught between generalization, governed by Rademacher complexity and favoring small classes, and strong Lagrangian duality, which rests on Lyapunov convexity for vector measures and needs decomposability, a demand pulling the other way. We reconcile the two by posing the population problem over a universal RKHS $\mathcal{H}_K$, dense in a decomposable envelope, and learning over norm balls of growing radius. This yields the Tikhonov complexity $\mathfrak{T}^{\varepsilon}_{n}$, the least RKHS norm reaching an $\varepsilon$-optimal Lagrangian level set; we prove it finite, obtain exact learnability of the optimal value, and make the sample threshold explicit and polynomial in $1/\varepsilon$ under a source condition. Feasibility is harder: absent convexity the Lagrangian may not attain its infimum, and dual information pins down only an averaged constraint-risk vector, not the risks of any returned predictor. We introduce the closure-realization gap $\varepsilon^\star_\infty$, an index of how well $\mathcal{H}_K$ retrieves feasible solutions from dualization; it is a property of the problem, not of a modeling choice. Learnability is exact when $\varepsilon^\star_\infty=0$, in particular under dual differentiability, and near-PACC with residual exactly $\varepsilon^\star_\infty$ otherwise. Finally, no distribution-free threshold exists already in the unconstrained specialization, so universality is the canonical frame for dual algorithms over large hypothesis classes.

arXiv

Does a Toehold Make a Bidder Bolder? Preemption and Multiplicity in Multi-Round Takeover Auctions

Zain Naboulsi

A bidder can quietly buy a stake in a company before making an offer for it. That stake, a toehold, is supposed to pay for itself twice: it makes the bidder willing to bid harder, and it frightens rivals into staying out of the fight. The first effect is arithmetic. The second is what would justify the cost and exposure of taking one at all. Yet toeholds are rare in practice, a standing puzzle. We ask whether that second effect is there once the contest is modelled as several rounds of escalating offers rather than the single exchange classical models assume. We turn it into a game a computer can solve, and certify the answers to an accuracy a referee can check. Three findings. The auction fixes what the toehold-holder earns but not how it bids: the same contest supports a bidder who opens aggressively against a rival who folds, and one who opens cheaply against a rival who does not, with the same profit either way. Aggressive preemptive bidding still appears when the toehold is removed entirely, so it comes from bidding in public and in turns, not from owning the stake. And the tidy "bigger toehold, more deterrence" relationship holds only in a contest cut short after one round; give it a real second round and it stops responding. So the two reasons to buy a toehold do not fare alike. The profit reason holds up; the deterrence reason does not, which suggests why toeholds may be rarer than theory predicts, alongside the procedural costs of disclosure and price impact that this model omits. A warning follows for anyone computing economics from a game solver: solve this auction once and it returns a confident figure for what a preemptive bid is worth; solve it again from a different start and it returns a different one, equally converged. We also report which solvers cope with contests of this shape, including versions too large to enumerate. Code is released.

arXiv

Rethinking Learning-Based Influence Maximization: Simple Neural Surrogates and Native Discrete Search

Yiqiao Liao, Parinaz Naghizadeh

Existing learning-based influence maximization frameworks rely heavily on complex neural architectures and continuous optimization over seed representations. We challenge this paradigm with SIMBA, a diffusion-model-agnostic framework pairing a lightweight neural surrogate with direct discrete search. SIMBA introduces three key components: 1) uniformly anchored node embeddings that eliminate initialization noise and encourage learning driven by graph topology and diffusion pattern, 2) a shallow two-layer graph neural network surrogate predicting final infection states, and 3) batched multi-swap simulated annealing that explores combinatorial seed space without gradients or continuous relaxation. By shifting compute from complex representation learning to effective discrete search, SIMBA drastically cuts time-to-solution while achieving superior influence spread and data efficiency. Our code is available at https://github.com/yl489/rethink-IM.

arXiv

Exact Rank and Convex Calibration Dimension Lower Bounds for the Multi-Label F1 Loss

Mingyuan Zhang

The instance-wise $F_1$ measure is a central performance measure for multi-label classification. For a problem with $s$ labels, it defines a $2^s\times 2^s$ loss matrix. Previous work exhibited $s^2+1$-coordinate affine and shifted low-rank representations and used them to construct quadratic-dimensional convex calibrated surrogates. We determine the exact rank. Under the convention $F_1(\varnothing,\varnothing)=1$, the $F_1$ score matrix, the shifted loss matrix, and the unshifted loss matrix all have rank $s^2-s+2$, while the column-affine dimension of the loss is $s^2-s+1$. The proof factors the nonempty score matrix through subset-incidence matrices and a positive-definite Cauchy matrix. Exact rank does not, by itself, lower-bound the dimension of an arbitrary convex calibrated surrogate. We therefore analyze the Bayes geometry of $F_1$ directly. We construct a distribution for which precisely all supersets of a fixed core label set are Bayes optimal, and show that the corresponding active loss columns, restricted to the witness support, have affine dimension $hn$, where $n=s-\lfloor s/3\rfloor$ and $h=\lceil(s\lfloor s/3\rfloor)^{1/2}\rceil-1$. Applying the feasible-subspace lower bound for convex calibration dimension gives \[ \operatorname{CCdim}(L^{F_1}) \ge \left(\frac{2}{3\sqrt{3}}-o(1)\right)s^2. \] Together with the quadratic upper bound, this establishes $\operatorname{CCdim}(L^{F_1})=Θ(s^2)$.

arXiv

DRBENCHER: Can Your Agent Identify the Entity, Retrieve Its Properties and Do the Math?

Young-Suk Lee, Ramon Fernandez Astudillo, Radu Florian

Deep research agents increasingly interleave web browsing with multi-step computation, yet existing benchmarks evaluate these capabilities in isolation, creating a blind spot in assessing real-world performance. We introduce DRBENCHER, a synthetic benchmark generator for questions that require both browsing and computation, synthesized answer-first from knowledge-graph chains with no seed passages or provenance text. It enforces four criteria: verifiability (gold answers are computed by executing parameterized code over knowledge-graph values), complexity (multi-hop entity identification, property retrieval, and domain-specific computation), difficulty (a two-stage verification cascade filters out questions solvable by the generating model), and diversity (a greedy max-min embedding filter maximizes coverage). These criteria are realized via a unified answer-first pipeline spanning five domains: biochemistry, financial, geophysical, security, and history. Human evaluation shows 76% validity, with 35% of errors due to outdated knowledge-graph entries, highlighting an inherent limitation of systems that reason over evolving data. Automatic evaluation shows that the strongest frontier model achieves only 20% answer accuracy. Compared to manually constructed benchmarks (BrowseComp+, MATH-500, GPQA), DRBENCHER achieves the highest semantic diversity. We release DrBencher pipeline and the human-verified benchmark data at https://github.com/IBM/DrBencher.

arXiv

SciVisAgentBench: A Benchmark for Evaluating Scientific Data Analysis and Visualization Agents

Kuangshi Ai, Haichao Miao, Kaiyuan Tang, Nathaniel Gorski, Jianxin Sun, Guoxi Liu, Helgi I. Ingolfsson, David Lenz, Hanqi Guo, Hongfeng Yu, Teja Leburu, Michael Molash, Bei Wang, Tom Peterka, Chaoli Wang, Shusen Liu

Recent advances in large language models (LLMs) have enabled agentic systems to translate natural-language intent into executable scientific visualization (SciVis) tasks. Despite rapid progress, the community lacks a principled and reproducible benchmark for evaluating these emerging SciVis agents in realistic, multi-step analysis settings. We present SciVisAgentBench, a comprehensive and extensible benchmark for evaluating scientific data analysis and visualization agents. Our benchmark is grounded in a structured taxonomy spanning four dimensions: application domain, data type, complexity level, and visualization operation. It currently comprises 108 expert-crafted cases covering diverse SciVis scenarios. To enable reliable assessment, we introduce a multimodal outcome-centric evaluation pipeline that combines LLM-based judging with deterministic evaluators, including image-based metrics, code checkers, rule-based verifiers, and case-specific evaluators. We also conduct a validity study with 12 SciVis experts to examine the agreement between human and LLM judges. Using this framework, we evaluate representative SciVis agents and general-purpose coding agents to establish initial baselines and reveal capability gaps. SciVisAgentBench is designed as a living benchmark to support systematic comparison, diagnose failure modes, and drive progress in agentic SciVis. The benchmark is available at https://scivisagentbench.github.io/.

arXiv

MonitorBench: A Comprehensive Benchmark for Chain-of-Thought Monitorability in Large Language Models

Han Wang, Yifan Sun, Brian Ko, Mann Talati, Jiawen Gong, Zimeng Li, Naicheng Yu, Xucheng Yu, Wei Shen, Vedant Jolly, Huan Zhang

Large language models (LLMs) can generate chains of thought (CoTs) that are not always causally responsible for their final outputs. When such a mismatch occurs, the CoT no longer faithfully reflects the actual reasons (i.e., decision-critical factors) driving the model's behavior, leading to the reduced CoT monitorability problem. This limits the use of CoTs for reliable oversight. However, a comprehensive and fully open-source benchmark for thoroughly evaluating CoT monitorability remains lacking. To address this gap, we propose MonitorBench, a systematic benchmark for evaluating CoT monitorability in LLMs. MonitorBench provides: (1) a diverse set of 1,514 test instances with carefully designed decision-critical factors across 19 tasks spanning 7 categories to characterize when CoTs can be used to monitor the factors driving LLM behavior; and (2) two prompting stress-test settings to quantify the extent to which CoT monitorability can be degraded. Extensive experiments show that CoT monitorability is a conditional property affected by the evaluated LLM, monitor LLM, and task characteristics. Across these factors, monitorability is higher when decision-critical factors shape the intermediate reasoning process, rather than merely influencing the final answer. Under stress-test prompting, most evaluated LLMs can intentionally reduce monitorability, mainly on tasks where decision-critical factors are not structurally required by the reasoning process. Overall, MonitorBench provides a basis for further research on AI control, reasoning faithfulness, stress-test monitorability, and monitoring scaffords. The code is available at https://github.com/ASTRAL-Group/MonitorBench.

arXiv

Bridging the Evaluation Gap: Standardized Benchmarks for Multi-Objective Search

Hadar Peer, Carlos Hernandez, Sven Koenig, Ariel Felner, Oren Salzman

Empirical evaluation in multi-objective search (MOS) has historically suffered from fragmentation, relying on heterogeneous problem instances with incompatible objective definitions that make cross-study comparisons difficult. This standardization gap is further exacerbated by the realization that DIMACS road networks, a historical default benchmark for the field, exhibit highly correlated objectives that fail to capture diverse Pareto-front structures. To address this, we introduce the first comprehensive, standardized benchmark suite for exact and approximate MOS. Our suite spans four structurally diverse domains: real-world road networks, structured synthetic graphs, game-based grid environments, and high-dimensional robotic motion-planning roadmaps. By providing fixed graph instances, standardized start-goal queries, reference exact Pareto-optimal solution sets, and a standardized approximate ($\varepsilon$-dominance) evaluation protocol, this suite captures a full spectrum of objective interactions: from strongly correlated to strictly independent. Ultimately, this benchmark provides a common foundation to ensure future MOS evaluations are robust, reproducible, and structurally comprehensive.

arXiv

LAUDE: LLM-Assisted Unit Test Generation and Debugging of Hardware DEsigns

Deeksha Nandal, Riccardo Revalor, Soham Dan, Debjit Pal

Unit tests are critical in the hardware design lifecycle to ensure that component design modules are functionally correct and conform to the specification before they are integrated at the system level. Thus developing unit tests targeting various design features requires deep understanding of the design functionality and creativity. When one or more unit tests expose a design failure, the debugging engineer needs to diagnose, localize, and debug the failure to ensure design correctness, which is often a painstaking and intense process. In this work, we introduce LAUDE, a unified unit-test generation and debugging framework for hardware designs that cross-pollinates the semantic understanding of the design source code with the Chain-of-Thought (CoT) reasoning capabilities of foundational Large-Language Models (LLMs). LAUDE integrates prompt engineering and design execution information to enhance its unit test generation accuracy and code debuggability. We apply LAUDE with closed- and open-source LLMs to a large corpus of buggy hardware design codes derived from the VerilogEval dataset, where generated unit tests detected bugs in up to 100% and 93% of combinational and sequential designs and debugged up to 93% and 84% of combinational and sequential designs, respectively.

arXiv

Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective

Michael Hintermüller, Michael Hinze, Denis Korolev

In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique for the optimal control of neural differential equations. This leads to an ordinary differential equation constrained optimization problem with controls acting as coefficients and a specific loss function. We implement our approach on the basis of a DG(0) Galerkin discretization of the neural ODE, leading to an explicit Euler time marching scheme. The resulting optimization problem is solved using the Adam algorithm and a BFGS method adapted to the $H^1$ topology induced by the regularization term. Finally, we apply our method to the construction of neural networks for the classification of data sets, where we present results for a selection of well known examples from the literature.

arXiv

Mesh-Attention: A New Communication-Efficient Distributed Attention with Improved Data Locality

Sirui Chen, Jingji Chen, Siqi Zhu, Ziheng Jiang, Yanghua Peng, Xuehai Qian

Distributed attention is essential for scaling large language models (LLMs) to long contexts, yet existing methods either have limited parallelism or incur high communication costs. Ulysses uses efficient all-to-all communication but cannot scale beyond the number of attention heads, whereas Ring-Attention removes this limit at the cost of high per-GPU communication. In our analytical Q-KV interaction matrix model, Ring-Attention assigns each GPU an entire row, preserving Q locality while sacrificing KV locality. Each GPU therefore receives nearly all KV partitions, and its communication grows linearly with sequence length. We present Mesh-Attention, which instead assigns each GPU a 2D tile to balance Q and KV locality, so that it collects only subsets of Q and KV partitions. This gives Mesh-Attention asymptotically lower communication complexity than Ring-Attention without limiting parallelism. Mesh-Attention further uses KV Partition Rotation (KVR), greedy scheduling, and topology-aware GPU mapping to balance traffic, overlap communication with computation, and reduce traffic over low-bandwidth links. Across experiments on up to 256 GPUs and 1M-token sequences, Mesh-Attention achieves average speedups of 17.00x, 2.62x and 2.94x (up to 32.27x, 4.36x and 4.59x) over Ring-Attention, USP (Ulysses degree 8) and StarTrail, respectively. It maintains this performance advantage as GPU count and sequence length increase while substantially reducing communication overhead at scale.

arXiv

Multi-Granular Node Pruning for Causal Circuit Discovery

Muhammad Umair Haider, Hammad Rizwan, Hassan Sajjad, A. B. Siddique

Circuit discovery aims to identify minimal subnetworks that are responsible for specific behaviors in large language models (LLMs). Existing approaches primarily rely on iterative edge pruning, which is computationally expensive and limited to coarse-grained units such as attention heads or MLP blocks, overlooking finer structures like individual neurons. We propose a node-level pruning framework for circuit discovery that addresses both scalability and granularity limitations. Our method introduces learnable masks across multiple levels of granularity, from entire blocks to individual neurons, within a unified optimization objective. Granularity-specific sparsity penalties guide the pruning process, allowing a comprehensive compression in a single fine-tuning run. Empirically, our approach identifies circuits that are smaller in nodes than those discovered by prior methods; moreover, we demonstrate that many neurons deemed important by coarse methods are actually irrelevant, while still maintaining task performance. Furthermore, our method has a significantly lower memory footprint, 5-10x, as it does not require keeping intermediate activations in the memory to work.

arXiv

Med-CRAFT: An Information System for Explainable and Configurable Construction of Multimodal Medical QA Datasets

Shenxi Liu, Kan Li, Mingyang Zhao, Yuhang Tian, Bin Li

Data-intensive artificial intelligence applications increasingly rely on large-scale, high-quality, explainable, and reproducible datasets, yet the construction of such datasets often remains labor-intensive, weakly traceable, and difficult to configure. This problem is particularly critical in multimodal medical scenarios, where each question-answer sample should be semantically consistent, grounded in visual and temporal evidence, and controllable in terms of reasoning complexity. To address these challenges, we propose Med-CRAFT, an information system for explainable and configurable construction of multimodal medical question answering datasets from instructional videos. Med-CRAFT organizes dataset construction as a provenance-aware pipeline that transforms raw medical instructional videos into structured operation knowledge graphs, evidence-grounded reasoning paths, and natural-language question-answer pairs.

arXiv

The Belief-Desire-Intention Ontology for modelling mental reality and agency

Sara Zuppiroli, Carmelo Fabio Longo, Anna Sofia Lippolis, Rocco Paolillo, Lorenzo Giammei, Miguel Ceriani, Francesco Poggi, Antonio Zinilli, Andrea Giovanni Nuzzolese

The Belief-Desire-Intention (BDI) model is a cornerstone for representing rational agency in artificial intelligence and cognitive sciences. Yet, its integration into structured, semantically interoperable knowledge representations remains limited. This paper presents a formal BDI Ontology, conceived as a modular Ontology Design Pattern (ODP) that captures the cognitive architecture of agents through beliefs, desires, intentions, and their dynamic interrelations. The ontology ensures semantic precision and reusability by aligning with foundational ontologies and best practices in modular design. Two complementary lines of experimentation demonstrate its applicability: (i) coupling the ontology with Large Language Models (LLMs) via Logic Augmented Generation (LAG) to assess the contribution of ontological grounding to inferential coherence and consistency; and (ii) integrating the ontology within the Semas reasoning platform, which implements the Triples-to-Beliefs-to-Triples (T2B2T) paradigm, enabling a bidirectional flow between RDF triples and agent mental states. Together, these experiments illustrate how the BDI Ontology acts as both a conceptual and operational bridge between declarative and procedural intelligence, paving the way for cognitively grounded, explainable, and semantically interoperable multi-agent and neuro-symbolic systems operating within the Web of Data.

arXiv

Intelligence Foundation Model: A New Perspective to Approach Artificial General Intelligence

Borui Cai, Yao Zhao

We propose a new perspective for approaching artificial general intelligence (AGI) through an intelligence foundation model (IFM). Unlike existing foundation models (FMs), which specialize in pattern learning within specific domains such as language, vision, or time series, IFM aims to acquire the underlying mechanisms of intelligence by learning directly from diverse intelligent behaviors. Vision, language, and other cognitive abilities are manifestations of intelligent behavior; learning from this broad range of behaviors enables the system to internalize the general principles of intelligence. Based on the fact that intelligent behaviors emerge from the collective dynamics of biological neural systems, IFM consists of two core components: a novel network architecture, termed the state neural network, which captures neuron-like dynamic processes, and a new learning objective, neuron output prediction, which trains the system to predict neuronal outputs from collective dynamics. The state neural network emulates the temporal dynamics of biological neurons, allowing the system to store, integrate, and process information over time, while the neuron output prediction objective provides a unified computational principle for learning these structural dynamics from intelligent behaviors. Together, these innovations establish a biologically grounded and computationally scalable foundation for building systems capable of generalization, reasoning, and adaptive learning across domains, representing a step toward truly AGI.

arXiv

TempoBench: Reasoning Execution Without Causal Attribution Is Just Simulation

Nikolaus Holzer, William Fishell, Baishakhi Ray, Mark Santolucito

Current training paradigms, optimized for long-horizon reasoning trace execution, have made Large Language Models (LLMs) excel at pattern matching and forward simulation of reasoning, but underperform at counterfactual causal understanding and reasoning. We introduce TempoBench, the first formally verifiable temporal benchmark that isolates counterfactual causal attribution over execution trajectories, and we show that LLMs categorically fall back to brute-force simulation-based reasoning to solve causal reasoning problems. Built from synthesized deterministic Mealy machines, TempoBench provides an infinitely scalable corpus of trajectory-based causal reasoning problems with controllable complexity and provably correct causal labels. Frontier models reach 96% step accuracy simulating a system forward, and fall to 32% when asked which inputs were necessary for an observed output, displaying what we call the SIM/MIN gap. Our findings show that LLMs cannot reliably identify minimal necessary causes, often confusing ``possible inputs'' with ``necessary causes,'' demonstrating an inability to understand which inputs were not needed. This failure is critical for deployment in causal inference tasks such as debugging, root cause analysis, and task planning where agents must use counterfactual reasoning to plan for specific desired outcomes. We show that training on TempoBench yields a targeted gain on causal benchmarks in open-source models while matching general-purpose, math, and code reasoning datasets on standard benchmarks. This indicates counterfactual causal reasoning is a learnable, architecturally distinct capability that sits on top of existing reasoning competencies.

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