ICML 2026 论文列表

International Conference on Machine Learning

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Self-Prophetic Decoding to Unlock Visual Search in LVLMs

Zhendong He, Qiyuan Dai, Guanbin Li, Liang Lin, Sibei Yang

展开摘要

Large Vision-Language Models (LVLMs) are rapidly evolving toward true multimodal reasoning, with visual search representing a concrete instantiation of the thinking-with-images paradigm. However, LVLM visual search faces two key challenges: incompatibility among intrinsic capabilities after post-training, and interference in long multi-step reasoning contexts. To address these, we identify two novel insights. First, self-regulation between pre- and post-training LVLMs leverages the intrinsic single-step capabilities of the pre-training model to mitigate capability deterioration and long-context interference. Second, probability-based prophetic sampling, replacing naive prompting, provides a probabilistic interface where the pre-training model acts as a prophet and the post-training model selectively accepts prophetic tokens under its output distribution, preserving coherent multi-step reasoning. Building on these insights, we introduce SeProD, a self-prophetic decoding framework that leverages intrinsic single-step capabilities to enable coherent multi-step reasoning in a training-free, plug-and-play manner. Experiments show that SeProD consistently improves multiple visual-search LVLMs across all 12 splits of 4 visual search benchmarks, as well as across general VQA benchmarks, without added computational overhead, thanks to its parallel prophetic acceptance mechanism.

Poster
The Heterogeneous Safety Impacts of Benign Multilingual Fine-Tuning

Will Hawkins, Kai Rawal, Jonathan Rystrøm, Stratis Tsirtsis, Zihao Fu, Greta Warren, Ryan Brown, Eoin D. Delaney, Sandra Wachter, Brent Mittelstadt, Chris Russell

展开摘要

Fine-tuning a large language model is a ubiquitous method for enhancing its capability on a specific downstream task. However, prior work has shown that this increase in capability comes with a cost: it can increase a model's tendency to respond to unsafe adversarial prompts, even when fine-tuning with non-adversarial data. We present the first comprehensive empirical study of this phenomenon in multilingual settings by fine-tuning Llama-3.2, Qwen3, and Gemma-3 models using benign data translated across nine languages. We find that safety outcomes are highly sensitive to both the choice of fine-tuning language and the evaluation language, with adversarial compliance rates increasing four-fold in some settings. Multilingual safety drift is decoupled from general capability metrics, and occurs heterogeneously across languages and models. Fine-tuning in non-English languages often induces smaller internal representational drifts than English, but these shifts lead models to default to either exaggerated compliance or refusal. As such, assessing fine-tuning impacts solely in English provides inadequate assurance for deployment. To facilitate further research into these cross-lingual safety blind spots, we release the Multilingual-Benign-Tune dataset and the SORRY-Bench-Multilingual evaluation suite.

Poster
Towards Diverse Scientific Hypothesis Search with Large Language Models

Haorui Wang, Parshin Shojaee, Kazem Meidani, Kunyang Sun, José Miguel Hernández-Lobato, Teresa Head-Gordon, Jiajun He, Chandan K. Reddy, Chao Zhang, Yuanqi Du

展开摘要

Large language models (LLMs) are on the rise for accelerating scientific discovery, most recently in advanced tasks such as generating valid scientific hypotheses. Yet in many discovery settings, the goal is not to identify a single best hypothesis since validation can be noisy and expensive, and scientists benefit from a set of high-quality alternative hypotheses that hedge against downstream uncertainty for the best solutions. Nevertheless, commonly used evolutionary search recipes tend to prioritize optimization over exploration in hypothesis generation, and the resulting selection pressure during the search process leads to diversity collapse. Motivated by these limitations, we formulate hypothesis search as a sampling problem, where the objective is to efficiently produce diverse, high-quality hypotheses under a fixed validation budget. Building on this perspective, we propose EvoDiverse, an evolutionary framework inspired by the classical parallel tempering algorithm that searches hypotheses at multiple temperature levels and enables principled information exchange across temperatures to improve exploration without disrupting convergence. Across domains including molecular discovery, equation discovery, and algorithm discovery, our approach consistently improves both hypothesis quality and diversity under the same validation budget, and produces candidates that remain robust under more expensive downstream computational validations.

Poster
MIMO-LP: A Multi-Input Multi-Output Framework for Subgraph-based Link Prediction

Yixin Song, Guangchi Liu, Xiangyu Xu, Shaofeng Li, Zhen Ling, Yiwei Wang, Yujun Cai

展开摘要

Link prediction (LP) is a fundamental problem in graph learning and can be broadly categorized into node-based and subgraph-based approaches. While subgraph-based LP methods often achieve superior predictive performance by exploiting localized structural information, they suffer from efficiency bottlenecks due to the high computational cost of per-query subgraph message-passing during both training and inference. To address this challenge, we propose MIMO-LP, a Multi-Input Multi-Output (MIMO) framework that accelerates subgraph-based LP. Given a batch of query node pairs and their corresponding subgraphs extracted from a shared full graph, MIMO-LP superposes their message-passing processes into a shared latent space while ensuring minimal interference among them. This design enables MIMO-LP to multiplex multiple queries within a single forward pass during both training and inference, substantially reducing redundant message-passing computations in overlapping subgraph regions. Extensive experiments demonstrate that MIMO-LP achieves a 14x-44x speedup over existing one-to-one subgraph-based methods, while maintaining comparable predictive performance.

Poster
Geodesic Calculus on Implicitly Defined Latent Manifolds

Florine Hartwig, Josua Sassen, Juliane Braunsmann, Martin Rumpf, Benedikt Wirth

展开摘要

Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based on this, we develop tools for a discrete Riemannian calculus approximating classical geometric operators. These tools are robust against inaccuracies of the implicit representation often occurring in practical examples. To obtain a suitable implicit representation, we propose to learn an approximate projection onto the latent manifold by minimizing a denoising objective. This approach is independent of the underlying autoencoder and supports the use of different Riemannian geometries on the latent manifolds. The framework in particular enables the computation of geodesic paths connecting given end points and shooting geodesics via the Riemannian exponential maps on latent manifolds. We evaluate our approach on various autoencoders trained on synthetic and real data.

Poster
UAV$^2$: A Unified and Adaptive Scheduling Framework for UAV Autopilot System with Reinforcement Learning

Zeying Li, Shuai Zhao, Chaowen Wu, Boyang Li, Kai Huang

展开摘要

Unmanned aerial vehicle (UAV) autopilot systems typically comprise navigation and flight-control modules, and their effective scheduling is critical to achieving high flight performance. However, most existing UAV platforms adopt a split architecture in which navigation and flight control are deployed on separate hardware devices. This separation restricts system-wide observability and prevents holistic scheduling and optimization across the entire autopilot pipeline. Moreover, autonomous flight performance emerges from implicit, cross-coupled, and accumulated interactions among multiple factors, rendering traditional model-based or heuristic scheduling approaches ineffective. To address these challenges, we propose UAV$^2$, a unified and adaptive scheduling framework for UAV autopilot systems with reinforcement learning, targeting flight performance optimization. UAV$^2$ integrates navigation and flight control onto a single onboard computing platform and operating system, formulates the scheduling problem as a partially observable Markov decision process, and learns scheduling policies from runtime execution feedback. The proposed approach is trained and evaluated in a hardware-in-the-loop simulation environment. Experimental results demonstrate that the learned scheduling policy consistently outperforms fixed-rate scheduling strategies in terms of flight robustness and tracking performance.

Poster
Deliberate Evolution: Agentic Reasoning for Sample-Efficient Symbolic Regression with LLMs

Xinyu Pang, Zhanke Zhou, Xuan Li, Fangrui Lv, Shanshan Wei, Sen Cui, Bo Han, Changshui Zhang

展开摘要

Symbolic regression (SR) discovers compact mathematical expressions from data, yet recent LLM-based evolutionary methods remain sample-inefficient because they rely mainly on scalar feedback such as MSE. We identify a core limitation: existing methods conflate candidate proposal with search guidance, requiring the LLM to infer how to evolve an expression, diagnose its errors, and reuse past experience from a single score. To address this, we propose Deliberate Evolution (DE), an agentic framework that decouples symbolic generation from search control. DE guides LLM proposals with adaptive operators for search direction, analytical tools for structural diagnosis, and reflective memory for trajectory-level experience. Experiments on LLM-SRBench show that DE consistently outperforms representative LLM-based SR baselines across diverse scientific domains while using only 40% of the standard sample budget. Code is available at https://github.com/Xinyu-Pang/Deliberate-Evolution.

Poster
Thinking in Latent Space: Progressive Multimodal Simplification for Visual Reasoning

Yuesen Tang, Yiming Yang, Tengfei Bao, Yu Tong

展开摘要

Recent Multimodal Large Language Models (MLLMs) have advanced cross-modal reasoning by extending Chain-of-Thought (CoT) prompting to visual tasks. However, existing methods still rely heavily on explicit textual reasoning steps, leading to information loss, unstable perception–reasoning interaction, and high computational cost. Inspired by human cognition, we argue that effective visual reasoning emerges from a dynamic interplay between perception and latent thought, rather than a purely linear verbalization process. Motivated by this insight, we propose Latent-Driven Progressive Visual Reasoning (LDPVR), a framework that formulates multimodal reasoning as a Markov Chain of Recursive State Simplification, where explicit textual states are progressively refined under the guidance of latent transitions. Central to LDPVR is Interleaved Latent Grounding, which leverages latent semantic intent to actively retrieve fine-grained visual evidence and drive robust state evolution, enabling the model to iteratively reduce uncertainty before committing to simplified textual states. To optimize this process, we introduce a three-stage curriculum combining supervised fine-tuning, latent-text distillation, and reinforcement learning via Group Relative Policy Optimization (GRPO). Experiments on six multimodal reasoning benchmarks demonstrate that LDPVR improves reasoning accuracy while maintaining low inference latency.

Poster
RAD: Retrieval High-quality Demonstrations to Enhance Decision-making

Lu Guo, Yixiang Shan, Zhengbang Zhu, Qifan Liang, Lichang Song, Ting Long, Weinan Zhang, Yi Chang

展开摘要

Offline reinforcement learning (RL) learns policies from fixed datasets, thereby avoiding costly or unsafe environment interactions. However, its reliance on finite static datasets inherently restricts the ability to generalize beyond the training distribution. Prior solutions based on synthetic data augmentation often fail to generalize to unseen scenarios in the (augmented) dataset. To address these challenges, we propose Retrieval High-quAlity Demonstrations (RAD) for decision-making, which innovatively introduces a retrieval mechanism into offline RL. Specifically, RAD retrieves high-return and reachable states from the offline dataset as target states, and leverages a generative model to generate sub-trajectories conditioned on these targets for planning. Since the targets are high-return states, once the agent reaches such a target, it can continue to obtain high returns by following the associated high-return actions, thereby improving policy generalization. Extensive experiments confirm that RAD achieves competitive or superior performance compared to baselines across diverse benchmarks, validating its effectiveness. Our code is available at https://github.com/LeahGL/RAD.

Poster
Learning Query-Aware Budget-Tier Routing for Runtime Agent Memory

Haozhen Zhang, Haodong Yue, Tao Feng, Quanyu Long, Jianzhu Bao, Bowen Jin, Weizhi Zhang, Xiao Li, Jiaxuan You, Chengwei Qin, Wenya Wang

展开摘要

Memory is increasingly central to Large Language Model (LLM) agents operating beyond a single context window, yet most existing systems rely on offline, query-agnostic memory construction that can be inefficient and may discard query-critical information. Although runtime memory utilization is a natural alternative, prior work often incurs substantial overhead and offers limited explicit control over the performance-cost trade-off. In this work, we present **BudgetMem**, a runtime agent memory framework for explicit, query-aware performance–cost control. BudgetMem structures memory processing as a set of memory modules, each offered in three budget tiers (i.e., Low/Mid/High). A lightweight router performs budget-tier routing across modules to balance task performance and memory construction cost, which is implemented as a compact neural policy trained with reinforcement learning. Using BudgetMem as a unified testbed, we study three complementary strategies for realizing budget tiers: implementation (method complexity), reasoning (inference behavior), and capacity (module model size). Across LoCoMo, LongMemEval, and HotpotQA, BudgetMem surpasses strong baselines when performance is prioritized (i.e., high-budget setting), and delivers better accuracy–cost frontiers under tighter budgets. Moreover, our analysis disentangles the strengths and weaknesses of different tiering strategies, clarifying when each axis delivers the most favorable trade-offs under varying budget regimes. Code is available at https://github.com/ViktorAxelsen/BudgetMem

Poster
Regret Minimization With a Crowd of Awakening Experts

Anna Lunghi, Gianmarco Genalti, Alberto Marchesi, Matteo Castiglioni

展开摘要

We study the Awakening Crowd of Experts (ACE) problem, an online learning problem where the set of experts available to the learner grows at each round. ACE is a special case of the well-known sleeping experts problem (Kleinberg et al., 2010), where the number of experts is huge $(K=T)$. Existing results on sleeping experts preclude any learner from achieving a sublinear regret when the number of available experts is linear in $T$. Inspired by real-world applications, such as Q\&A platforms and social proof marketing, we thus focus on the awakening version of the sleeping experts problem, where a new expert arrives at every round and never leaves. We show that in the stochastic version of ACE, it is possible to obtain regret $\tilde{\mathcal{O}}(T^{2/3})$ using an unusual pessimism in the face of the uncertainty principle. Moreover, we characterize the dependence of the regret on the stability of an optimal strategy. For both results, we present matching lower bounds. Surprisingly, the adversarial version of ACE is sensibly harder. In particular, we provide a lower bound precluding sublinear $\alpha$-regret when the competitive ratio is constant. We provide an algorithm to face this crucial trade-off between competitive ratio and regret, and bound its $\alpha$-regret, almost matching the aforementioned lower bound. As a corollary, we get a $\tilde{\mathcal{O}}(\log(\log(T))$ competitive ratio when an optimal strategy enjoys a reward linear in $T$.

Poster
Beyond Explicit Edges: Robust Reasoning over Noisy and Sparse Knowledge Graphs

Hang Gao, Dimitris N. Metaxas

展开摘要

GraphRAG is increasingly adopted for converting unstructured corpora into graph structures to enable multi-hop reasoning. However, standard graph algorithms rely heavily on static connectivity and explicit edges, often failing in real-world scenarios where Knowledge Graphs (KGs) are noisy, sparse, or incomplete. To address this limitation, we introduce INSES (Intelligent Navigation and Similarity Enhanced Search), a dynamic framework designed to reason beyond explicit edges. INSES couples LLM-guided navigation, which prunes noise and steers exploration, with embedding-based similarity expansion to recover hidden links and bridge semantic gaps. Recognizing the computational cost of graph reasoning, we complement INSES with a lightweight router that delegates simple queries to Naïve RAG and escalates complex cases to INSES, balancing efficiency with reasoning depth. Experimental results show that INSES performs favorably compared to established RAG and GraphRAG baselines on multiple benchmarks. In particular, on the MINE benchmark, it exhibits notable robustness and adaptability across KGs constructed by varying methods. Our code and data are publicly available at https://github.com/hanggao-gh/INSES.

Poster
Emergence of Biased Consensus in Multi-Agent LLM Debates

Maya Okawa

展开摘要

Multi-agent LLM debates achieve strong performance on decision-making tasks as well as problem-solving benchmarks, yet their safety and fairness risks remain poorly understood. Notably, interaction can amplify the biases of single LLMs, raising concerns for real-world deployment. We identify the emergence of collective (often biased) norms in multi-agent LLM debates and show that noise (e.g., LLM sampling temperature) is a key driver. To explain this, we propose an analytical framework drawing on physics-inspired theoretical models of social dynamics. We predict a phase transition to collective bias when conformity surpasses a critical threshold given the LLMs' initial bias and debate noise. We test the theoretical predictions through controlled experiments and observe a finite-size crossover consistent with an underlying phase transition. We further find that agent heterogeneity suppresses emergence by smoothing (rounding) this transition. Finally, we show that these insights generalize to realistic decision-making tasks, including investment decisions and LLM-as-a-judge evaluation.

Poster
ACON: Optimizing Context Compression for Long-horizon LLM Agents

Minki Kang, Wei-Ning Chen, Dongge Han, Huseyin A Inan, Lukas Wutschitz, Yanzhi Chen, Robert Sim, Saravan Rajmohan

展开摘要

Large language models (LLMs) are increasingly deployed as agents in dynamic real-world environments, where success depends on maintaining precise records of actions and observations. However, the resulting unbounded context growth in long-horizon agentic tasks makes two critical bottlenecks: prohibitive inference memory costs and reasoning degradation due to irrelevant information. Existing compression methods fail to fully address this, often relying on brittle heuristics or requiring parameter updates impractical for proprietary or large-scale LLMs. We introduce Agent Context Optimization (ACON), a unified framework that optimally compresses both observations and history into concise, informative representations. Distinct from prior works, ACON employs an optimization in natural language space: it iteratively refines compression guidelines based on failure analysis of the agent, ensuring critical state information is preserved without model fine-tuning. To further minimize computational overhead, we distill the optimized compressor into smaller models. Experiments on AppWorld, OfficeBench, and Multi-objective QA demonstrate that ACON reduces peak token usage by 26–54\% while improving task success over existing compression baselines. Notably, it enables smaller LMs to function effectively as long-horizon agents, achieving up to 46% performance improvement by mitigating context distraction. Our code is available at https://github.com/microsoft/acon.

Poster
Neural-Inspired Modeling of Auditory Selection and Compensation for Audio-Visual Speech Separation

Xinmeng Xu, Haoran Xie, Xiaohui Tao, Lin Li, S. Joe Qin

展开摘要

Current audio-visual speech separation (AVSS) models typically rely on implicit multimodal fusion, but the absence of explicit modality alignment and reliability modeling often causes semantic misalignment and contaminates speech representations. The brain addresses this with a hierarchy: top-down auditory selection uses visual priors to maintain target-consistent acoustics, while bottom-up cross-modal compensation integrates temporally aligned articulatory cues to reconstruct and stabilize speech. Guided by this principle, we present Neuro-SCNet, an AVSS architecture that makes selection and compensation explicit and reliability-aware. The Auditory Selection Mechanism applies top-down, visually guided gain along the audio pathway to isolate target time-frequency units and suppress distractors. The module preserves the auditory trace with an identity bypass and adds controlled visual refinements via a residual path. A synchrony-driven gate reduces the influence of low-confidence visual cues. Additionally, a lightweight pre-alignment for visual feature pre-processing estimates and corrects small temporal offsets, and a compact magnitude-phase encoder is used to preserve fine acoustic detail to stabilize reconstruction. Evaluations on LRS2, LRS3, and VoxCeleb2 show state-of-the-art separation with improved efficiency, supporting the value of explicit selection and reliability-aware compensation.

Poster
ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion

Yingda Fan, Dan Lu, Xiaowei Jia

展开摘要

Time series modeling increasingly demands high-quality supervision, yet target observations remain scarce—exogenous inputs are broadly available, but target measurements are often unavailable due to cost, infrastructure, or accessibility constraints. Can models trained on observed locations reconstruct target time series where measurements have never been collected? We term this zero-shot time series reconstruction. A naive approach—directly mapping exogenous inputs to targets—can yield predictions at unobserved locations, but without target signals, such models fail to capture the intrinsic dynamics of the target variable, producing overly smooth outputs that underestimate extremes. This reveals systematic errors that call for explicit modeling and calibration. We propose ZeroDiff, which constructs an informed prior from exogenous variables alone, then learns to calibrate reconstruction errors through diffusion—training on observed locations and generalizing to unobserved ones. Experiments across diverse real-world datasets demonstrate significant improvements over existing approaches. Our code is available at https://github.com/YingdaFan/ZeroDiff-ICML2026.

Poster
Pareto-Guided Optimal Transport for Multi-Reward Alignment

Ying Ba, Tianyu Zhang, Mohan Zhou, Yalong Bai, Wenyi Mo, Guiwei Zhang, Bing Su, Ji-Rong Wen, Ji-Rong Wen

展开摘要

Text-to-image generation models have achieved remarkable progress in preference optimization, yet achieving robust alignment across diverse reward models remains a significant challenge. Existing multi-reward fusion approaches rely on weighted summation, which is costly to tune and insufficient for balancing conflicting objectives. More critically, optimization with reward models is highly susceptible to reward hacking, where reward scores increase while the perceived quality of generated images deteriorates. We demonstrate that optimizing against a unified global target under heterogeneous reward upper bounds can induce reward hacking, a risk further exacerbated by the inherent instability of weak reward models. To mitigate this, we propose a Pareto Frontier-Guided Optimal Transport (PG-OT) framework. Our method constructs a prompt-specific Pareto frontier and maps dominated samples toward it via distribution-aware optimal transport. Furthermore, we develop both online and offline optimization strategies tailored to diverse reward signal characteristics. To provide a more rigorous assessment, we introduce the Joint Domination Rate (JDR) and Joint Collapse Rate (JCR) as principled metrics to quantify multi-reward synergy and reward hacking. Experimental results show that our approach outperforms strong baselines with an 11% gain in JDR and achieves a near 80% win rate in human evaluations.

Poster
FLIPS: Instance-Fingerprinting for LLMs via Pseudo-random Sequences

Richardeau Gurvan, Gohar Dashyan, Erwan Le Merrer, Gilles Tredan

展开摘要

Literature reveals that a Large Language Model's (LLM) behavior is not only conditioned by its original weights but also its instance-level parameters, such as instructional prompt, sampling configuration or quantization. A model that generates safe outputs under one configuration may produce toxic content under another. However, current LLM identification techniques (such as fingerprinting) focus on intellectual property protection, and their design favors robustness to changes in these instance-level parameters. This poses a critical challenge for AI regulation in which compliance assessments target actual deployed behaviors, not model provenance. In this paper, we introduce instance-level fingerprinting, a regulator-oriented paradigm that distinguishes configurations of the same LLM. Our method FLIPS, exploits biases in generated binary random sequences to reach 96% (closed-set) and 90% (open-set, where some targets are unknown) identification accuracy across 237 model instances, versus 35% for the adapted LLMmap baseline. This shows that instance-level fingerprinting is both necessary for regulation and practically feasible. Code available at https://github.com/GurvanR/FLIPS-LLM-Instance-Fingerprinting.

Poster
AdvEvo-MARL: Shaping Internalized Safety through Adversarial Co-Evolution in Multi-Agent Reinforcement Learning

Zhenyu Pan, Yiting Zhang, Zhuo Liu, Yolo Y. Tang, Zeliang Zhang, Haozheng Luo, Chenwei Xu, Yuwei Han, Jianshu Zhang, Dennis Wu, Hong-Yu Chen, Haoran Lu, Haoyang Fang, Manling Li, Chenliang Xu, Philip S. Yu, Han Liu

展开摘要

LLM-based multi-agent systems excel at planning, tool use, and role coordination, but their openness and interaction complexity also expose them to jailbreak and adversarial collaboration. Existing defenses fall into two lines: (i) self-verification that asks each agent to pre-filter unsafe instructions before execution, and (ii) external guard modules that police behaviors. The former often underperforms because a standalone agent lacks sufficient capacity to detect cross-agent unsafe chains and delegation-induced risks; the latter increases system overhead and creates a single-point-of-failure—once compromised, system-wide safety collapses, and adding more guards worsens cost and complexity. To solve these challenges, we propose AdvEvo-MARL, a co-evolutionary multi-agent reinforcement learning framework that internalizes safety into task agents. Rather than relying on external guards, AdvEvo-MARL jointly optimizes attackers (which synthesize evolving jailbreak prompts) and defenders (task agents trained to both accomplish their duties and resist attacks) in adversarial learning environments. To stabilize learning and foster cooperation, we introduce a public baseline for advantage estimation: agents within the same functional group share a group-level mean-return baseline, enabling lower-variance updates and stronger intra-group coordination. Across representative attack scenarios, AdvEvo-MARL consistently keeps attack-success rate (ASR) below 20\%, whereas baselines reach up to 38.33\%, while preserving or even improving task accuracy (up to +3.67\%). These results show that safety and utility can be jointly improved without relying on extra guard agents or added system overhead.

Poster
Grokking Finite-Dimensional Algebra

Pascal Junior Tikeng Notsawo, Guillaume Dumas, Guillaume Rabusseau

展开摘要

This paper investigates the grokking phenomenon, which refers to the sudden transition from a long memorization to generalization observed during neural networks training, in the context of learning multiplication in finite-dimensional algebras (FDA). While prior work on grokking has focused mainly on group operations, we extend the analysis to more general algebraic structures, including non-associative, non-commutative, and non-unital algebras. We show that learning group operations is a special case of learning FDA, and that learning multiplication in FDA amounts to learning a bilinear product specified by the algebra’s structure tensor. For algebras over the reals, we connect the learning problem to matrix factorization with an implicit low-rank bias, and for algebras over finite fields, we show that grokking emerges naturally as models must learn discrete representations of algebraic elements. This leads us to experimentally investigate the following core questions: (i) how do algebraic properties such as commutativity, associativity, and unitality influence both the emergence and timing of grokking, (ii) how structural properties of the structure tensor of the FDA, such as sparsity and rank, influence generalization, and (iii) to what extent generalization correlates with the model learning latent embeddings aligned with the algebra’s representation. Our work provides a unified framework for grokking across algebraic structures and new insights into how mathematical structure governs neural network generalization dynamics.

Poster