Symbolic regression discovers interpretable mathematical expressions from data and is central to scientific modeling. Recent neural approaches typically linearize expression trees into token sequences for sequential generation, but this representation weakens access to the underlying hierarchy and makes it difficult to enforce structure-dependent constraints. Hybrid neural--evolutionary frameworks further combine neural generators with genetic programming (GP), yet training can be unstable due to distribution mismatch between neural samples and GP-refined elites. We propose \textbf{GCN-SR}, a graph-based symbolic regression framework that generates expressions directly in an explicit tree form. GCN-SR introduces \textbf{Symbolic Perfect Binary Trees (SPBTs)}, a fixed-topology scaffold that enables batched tree generation and supports an autoregressive generator based on a Graph Convolutional Network (GCN) while preserving hierarchical structure. To leverage GP refinement without unstable target matching, we further introduce \textbf{Similarity-Weighted Policy Gradient (SWPG)}, which uses GP only to construct similarity-weighted reward signals. Experiments on standard symbolic regression benchmarks, together with extensive ablations, show that GCN-SR consistently outperforms strong neural and hybrid baselines.
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Theory · Learning Theory
Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems algorithm by Kerenidis and Prakash. These algorithms were initially believed to be strong candidates for exponential speedups, but a lower bound ruling out similar classical improvements remained absent. In breakthrough work by Tang, it was demonstrated that this lack of progress in classical lower bounds was for good reasons. Concretely, she gave a classical counterpart of the quantum recommender systems algorithm, reducing the quantum advantage to a mere polynomial. Her approach is quite general and was named \emph{quantum-inspired classical} algorithms. Since then, almost all the initially exponential quantum machine learning speedups have been reduced to polynomial via new quantum-inspired classical algorithms. From the current state-of-affairs, it is unclear whether we can hope for exponential quantum speedups for any natural machine learning task. In this work, we present the first such provable exponential separation between quantum and quantum-inspired classical algorithms for the basic problem of solving a linear system when the input matrix is well-conditioned and has sparse rows and columns.
Deep Learning · Graph Neural Networks
Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions. In this work, we propose a unified framework that explicitly models graph data as a mixture of probabilistic graph generative models represented by graphons. To characterize and estimate these graphons, we leverage graph moments (motif densities) to cluster graphs generated from the same underlying model. We establish a novel theoretical guarantee, deriving a tighter bound showing that graphs sampled from structurally similar graphons exhibit similar motif densities with high probability. This result enables principled estimation of graphon mixture components. We show how incorporating estimated graphon mixture components enhances two widely used downstream paradigms: graph data augmentation via mixup and graph contrastive learning. By conditioning these methods on the underlying generative models, we develop graphon-mixture-aware mixup (GMAM) and model-aware graph contrastive learning (MGCL). Extensive experiments on both simulated and real-world datasets demonstrate strong empirical performance. In supervised learning, GMAM outperforms existing augmentation strategies, achieving new state-of-the-art accuracy on 6 out of 7 datasets. In unsupervised learning, MGCL performs competitively across seven benchmark datasets and achieves the lowest average rank overall.
Applications · Computer Vision
Diffusion-based camouflaged object detection (COD) has recently shown great potential. In contrast to existing approaches that rely on multiple sample steps to refine the predicted masks, we propose CODiff, which reformulates the diffusion process to enable one-step mask prediction while maintaining competitive accuracy. Specifically, we first establish the theoretical feasibility of one-step sampling for COD. Based on this, we design a dedicated network for one-step inference with a global semantic guidance mechanism to guide the denoising process globally and hierarchical condition integration blocks to provide fine-grained structural semantics. In addition, we design a straight-forward regularization to learn better intermediate features by bridging the representation gap between the condition backbone and the diffusion model. Extensive experiments demonstrate that CODiff achieves state-of-the-art performance across multiple benchmarks, improving MAE by over 22\% on the challenging COD10K dataset. The code will be released upon publication.
Applications · Time Series
Modern deep learning for asset allocation typically separates forecasting from optimization. We argue this creates a fundamental mismatch where minimizing prediction errors fails to yield robust portfolios. We propose the Signature Informed Transformer to address this by unifying feature extraction and decision making into a single policy. Our model employs path signatures to encode complex path dependencies and introduces a specialized attention mechanism that targets geometric asset relationships. By directly minimizing the Conditional Value at Risk we ensure the training objective aligns with financial goals. We prove that our attention module rigorously amplifies signature derived signals. Experiments across diverse equity universes show our approach significantly outperforms both traditional strategies and advanced forecasting baselines. The code is available at: https://anonymous.4open.science/r/Signature-Informed-Transformer-For-Asset-Allocation-DB88
Deep Learning · Large Language Models
Despite the growing reasoning capabilities of recent large language models (LLMs), their internal mechanisms during the reasoning process remain underexplored. Prior approaches often rely on human-defined concepts (e.g., overthinking, reflection) at the word level to analyze reasoning in a supervised manner. However, such methods are limited, as it is infeasible to capture the full spectrum of potential reasoning behaviors, many of which are difficult to define in token space. In this work, we propose an unsupervised framework (namely, RISE: Reasoning behavior Interpretability via Sparse auto-Encoder) for discovering reasoning vectors, which we define as directions in the activation space that encode distinct reasoning behaviors. By segmenting chain-of-thought traces into sentence-level 'steps' and training sparse auto-encoders (SAEs) on step-level activations, we uncover disentangled features corresponding to interpretable behaviors such as reflection and backtracking. Visualization and clustering analyses show that these behaviors occupy separable regions in the decoder column space. Moreover, targeted interventions on SAE-derived vectors can controllably amplify or suppress specific reasoning behaviors, altering inference trajectories without retraining. Beyond behavior-specific disentanglement, SAEs capture structural properties such as response length, revealing clusters of long versus short reasoning traces. More interestingly, SAEs enable the discovery of novel behaviors beyond human supervision. We demonstrate the ability to control response confidence by identifying confidence-related vectors in the SAE decoder space. These findings underscore the potential of unsupervised latent discovery for both interpreting and controllably steering reasoning in LLMs.
Applications · Computer Vision
Infrared and visible image fusion aims to integrate complementary information from both modalities. However, most existing methods rely on Euclidean representations, which inherently impose geometric constraints that hinder effective semantic modelling. Specifically, Euclidean geometry imposes rigid distance metrics that distort multi-modal feature interactions, particularly in preserving parent-to-child semantic hierarchies. To overcome this, we introduce a text-driven fusion framework empowered by hyperbolic manifold learning. In particular, our approach models text-attribute correlation during training by leveraging BLIP-extracted prompts to align with vision-attribute, thereby enabling the formation of adaptive enhancement strategies semantically. Within the hyperbolic space, the text prompts act as topological anchors, guiding vision-attribute alignment through hyperbolic embeddings that naturally expand with semantic granularity. Using the Poincaré ball's negative curvature, we encode coarse-to-fine semantics without Euclidean distance saturation, while its exponentially growing periphery prevents texture distortion during cross-modal fusion. During inference, the fusion process autonomously adapts to the input content using learned text-attribute priors, eliminating any dependence on textual input. The experimental results show that the proposed method outperforms existing state-of-the-art methods on existing publicly available benchmark datasets.
Reinforcement Learning · Everything Else
Many real-world tasks are non-verifiable—there is no objective ground truth, and quality must be judged subjectively—making reward design for RL difficult. Existing approaches based on scalar rubric scores or single comparisons are often noisy, poorly calibrated, or provide sparse learning signals. We introduce Tournament Style RL (TSRL), which constructs rewards from rubric-guided pairwise judgments against a fixed set of anchor responses, using win-rate as the reward for policy optimization. This aggregation of comparisons against anchor responses yields a signal that is more robust to the judge noise by stabilizing the reference frame, reducing the variance in reward. We test across four non-verifiable tasks and two backbone LLMs, and find that TSRL improves average win-rate by $+43.8$ points over the base model and $+22.8$ points over the strongest baseline. TSRL scales with the number of anchors, remains robust under weak or partially corrupted judges, the results are supported by blinded human preference studies.
Applications · Social Sciences
We present the first large-scale empirical analysis of disempowerment patterns in real-world AI assistant interactions, analyzing 1.5 million consumer Claude.ai conversations using a privacy-preserving approach. We focus on situational dis-empowerment potential, which occurs when AI assistant interactions risk leading users to form distorted perceptions of reality, make inauthentic value judgments, or act in ways misaligned with their values. Quantitatively, we find that severe forms of disempowerment potential occur in fewer than one in a thousand conversations, though rates are substantially higher in personal domains like relationships and lifestyle. Qualitatively, we uncover several concerning patterns, such as validation of persecution narratives and grandiose identities with emphatic sycophantic language, definitive moral judgments about third parties, and complete scripting of value-laden personal communications that users appear to implement verbatim. Analysis of historical trends reveals an increase in the prevalence of disempowerment potential over time. We also find that interactions with greater disempowerment potential receive higher user approval ratings, possibly suggesting a tension between short-term user preferences and long-term human empowerment.
Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call **weak verification**. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call **strong verification**. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. We formalize this tension through **weak-strong verification policies**, which decide when to accept or reject based on weak verification and when to defer to strong verification. We introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, we show that optimal policies admit a two-threshold structure and that **calibration** and **sharpness** govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors without assumptions on the query stream, the language model, or the weak verifier. Experiments on mathematical reasoning and sequential decision-making demonstrate that our algorithm achieves reliability comparable to exhaustive strong verification while significantly reducing verification cost.
Theory · Game Theory
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a lottery over options that clears all stakeholders' acceptability bars? We study a query model where the algorithm proposes lotteries and receives only binary accept/reject feedback. We give deterministic and randomized algorithms that either find a unanimously acceptable lottery or certify infeasibility; adaptivity can avoid eliciting many stakeholders' constraints, and randomization further reduces the expected elicitation cost relative to full elicitation. We complement these upper bounds with worst-case lower bounds (in particular, linear dependence on the number of stakeholders and logarithmic dependence on precision are unavoidable). Finally, we develop learning-augmented algorithms that exploit natural forms of advice (e.g., likely binding stakeholders or a promising lottery), improving query complexity when predictions are accurate while preserving worst-case guarantees.
Probabilistic Methods · Variational Inference
Generative Flow Networks (GFlowNets) are a flexible family of amortized samplers trained to generate discrete and compositional objects with probability proportional to a reward function. To this end, they learn a policy function over an intractably large state graph by minimizing a stochastic objective over sampled trajectories. However, learning efficiency is constrained by the model’s ability to rapidly explore diverse high-probability regions during training. To mitigate this issue, recent works have focused on incentivizing the exploration of unvisited and valuable states via curiosity-driven search and self-supervised random network distillation, which tend to waste samples on already well-approximated regions of the state space. In this context, we propose *Adaptive Complementary Exploration* (ACE), a principled algorithm for the effective exploration of novel and high-probability regions when learning GFlowNets. To achieve this, ACE introduces an *exploration* GFlowNet explicitly trained to search for high-reward states in regions underexplored by the *canonical* GFlowNet, which learns to sample from the target distribution. Through extensive experiments, we show that ACE consistently and significantly improves upon prior work in terms of approximation accuracy to the target distribution and discovery rate of diverse high-reward states.
High-performance GPU kernels are critical for efficient LLM serving, yet their optimization remains a bottleneck requiring deep system expertise. While code LLMs show promise in generating functionally correct code, kernel optimization is intrinsically a search problem over a vast optimization space. The fundamental mismatch prevents existing LLM agents from efficiently exploring the optimization space for diverse hardware and compute patterns. To bridge the gap, we present KernelBand, a framework that formulates kernel optimization as a Multi-Armed Bandit (MAB) problem, explicitly balancing exploration and exploitation to unlock the potential of code LLMs. To navigate the infinite arm space of optimization strategies applied to candidate kernels, we design two key mechanisms: a hardware-aware pruning strategy via profiling bounds and a trace-driven clustering algorithm that leverages Lipschitz continuity. Theoretically, we prove that KernelBand reduces the regret bound to depend on the compact covering number of runtime clusters, ensuring sample-efficient discovery of high-performance kernels. Extensive experiments on TritonBench-G with three GPU architectures and four code LLMs show that KernelBand consistently and substantially outperforms state-of-the-art methods with over 33% average improvement.
Deep Learning · Large Language Models
LLMs cannot reliably recognize their parametric knowledge boundaries and often hallucinate answers to outside-of-boundary questions. In this paper, we introduce MASH (Modeling Abstention via Selective Help-seeking), a training framework that readily extracts abstentions from LLMs. Our key idea is that any external help-seeking by an LLM, i.e. search tool use, can serve as a proxy for abstention if the external help (search) is appropriately penalized while also rewarding answer accuracy. MASH operationalizes this idea using reinforcement learning with a pay-per-search reward. We run experiments on three knowledge-intensive QA datasets. Our results show that MASH substantially improves upon the selective help-seeking performance of prior efficient search approaches; on multi-hop datasets, it improves answer accuracy by 7.6%. Furthermore, MASH demonstrates strong off-the-shelf abstention performance, showcasing behavior competitive with prior abstention methods that additionally require predetermining model knowledge boundaries to construct training data. Overall, we show that MASH training effectively aligns search tool use with parametric knowledge, which can be successfully leveraged for making abstention decisions and efficient search tool use.
Reinforcement Learning · Planning
The ability to plan with temporal abstractions is central to intelligent decision-making. Rather than reasoning over primitive actions, we study agents that compose pre-trained policies as temporally extended actions, enabling solutions to complex tasks that no constituent alone could solve. Such compositional planning remains elusive as compounding errors in long-horizon predictions make it challenging to estimate the visitation distribution induced by sequencing policies. Motivated by the *geometric policy composition* framework introduced in Thakoor et al. (2022), we address these challenges by learning predictive models of multi-step dynamics, so-called *jumpy world models*, that capture state occupancies induced by pre-trained policies across multiple timescales in an off-policy manner. Building on Temporal Difference Flows (Farebrother et al., 2025), we enhance these models with a novel consistency objective that aligns predictions across timescales, improving long-horizon predictive accuracy. We further demonstrate how to combine these generative predictions to estimate the value of executing arbitrary sequences of policies over varying timescales. Empirically, we find that compositional planning with jumpy world models significantly improves zero-shot performance across a wide range of base policies on challenging manipulation and navigation tasks, yielding an average 200% relative improvement over planning with primitive actions on long-horizon tasks.
Theory · Deep Learning
Many geometric-statistics and manifold-learning pipelines produce bundle-valued observations (for example, tangent vectors) that lie in different fibers. Forming empirical averages, therefore, requires transporting data to a common reference fiber, which can introduce curvature- and holonomy-driven effects. We study transported empirical means for a measurable section s: M → E of a rank-k vector bundle (E, π, M) equipped with a bundle metric and a compatible metric connection, and we derive finite-sample, dimension-free concentration bounds in the reference fiber E_{x₀}. Using sharp Hilbert-space inequalities due to Pinelis, we obtain Hoeffding- and Bernstein-type tail bounds controlled by a uniform per-sample bound B and a variance proxy σ². When minimizing geodesics are not unique, we isolate a deterministic holonomy ambiguity term Δ_{hol} and bound it in terms of bundle curvature and loop geometry; for the specific case E = T S²_{r} we give sharp area-based formulas. The resulting bias–variance decomposition provides practical uncertainty quantification for bundle-valued averaging and clarifies when curvature-driven transport ambiguity is negligible relative to sampling error.
Applications · Neuroscience, Cognitive Science
Clinical brain-to-text interfaces are designed for paralysed patients who cannot provide extensive training recordings. Pre-training improves data-efficient generalisation by learning statistical priors across subjects, but these priors critically depend on context. While natural speech might unfold gradually over minutes, most methods pre-train with only a few seconds of context. Thus, we propose *MEG-XL*, a model pre-trained with 2.5 minutes of MEG context per sample, 5-300× longer than prior work, and equivalent to 191k tokens, capturing extended neural context. Fine-tuning on the task of word decoding from brain data, MEG-XL matches supervised performance with a fraction of the data (e.g. 1hr vs 50hrs) and outperforms brain foundation models. We find that models pre-trained with longer contexts learn representations that transfer better to word decoding. Our results indicate that long-context pre-training helps exploit extended neural context that other methods unnecessarily discard.
Deep Learning · Theory
Modern foundation models are evaluated through broad capabilities such as arithmetic, reasoning, safety, and robustness, yet it remains unclear in a principled sense when *finite tests* can meaningfully certify such claims. We develop a rigorous theory of capability evaluation by formalizing evaluation as inference over a task family and asking when guarantees over the full family can be inferred from a strict subset of tests. We analyze two canonical regimes. In stochastic multi-environment evaluation, we characterize when uniform certification is possible across multiple environments and show that the sample complexity is governed by a $\chi^2$-radius of the environment family, yielding near-optimal evaluation protocols with matching lower bounds under a natural overlap condition. In contrast, for worst-case, rule-like capabilities, we establish fundamental impossibility results. Even for structured model classes such as Boolean circuits of bounded size, black-box evaluation cannot, in general, certify global properties. Together, these results provide a principled framework for understanding when finite evaluation can and cannot certify capabilities.
Social Aspects · Robustness
Split Federated Learning (SFL) enables privacy-preserving collaborative training by partitioning models between clients and a server. However, under non-IID data distributions, SFL often suffers from biased optimization and unstable convergence, while existing solutions largely adapt techniques from conventional federated learning. In this work, we observe that the split architecture of SFL inherently alters how client information is represented and coordinated, opening opportunities for bias compensation beyond parameter-level aggregation. Based on this insight, we propose BESplit, an architecture-aware framework that exploits the intrinsic structure of SFL to mitigate non-IID effects. First, to prevent biased local data from dominating global updates, we introduce Evidential Aggregation (EA) to perform fine-grained reweighting of client contributions based on evidential uncertainty. Second, to further reduce distributional skew, we develop Bias-Compensated Collaboration (BCC) to align split-layer representations by pairing complementary clients. Finally, Dual-Teacher Distillation (DTD) is incorporated to synchronize knowledge between decoupled client and server models, enabling independent local inference. Extensive experiments on five benchmark datasets demonstrate that BESplit consistently outperforms state-of-the-art methods in accuracy, convergence stability, and computational efficiency under diverse non-IID settings.
Optimization · Discrete and Combinatorial Optimization
Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches. At the same time, these problems are often accompanied by rich domain knowledge derived from physical laws, operational requirements, and expert heuristics. Such knowledge is frequently expressed as rules involving logical propositions and linear inequalities. Existing neuro-symbolic methods typically enforce these rules approximately through soft penalties, assume input-independent rules when designing specialized architectures, or rely on non-differentiable post-processing at inference time to achieve hard constraint satisfaction. While recent advances in differentiable optimization layers enable end-to-end feasibility enforcement within neural networks, extending these approaches to logical or mixed-integer rules remains challenging due to inherent nonconvexity. In this work, we propose a unified end-to-end framework for enforcing hard, input-dependent mixed integer linear constraints within neural networks. Our approach represents rules as disjunctive constraints and applies hierarchical convex relaxations to obtain convex hull formulations. These relaxations yield tractable linear constraints that can be embedded as differentiable optimization layers while enabling exact rule satisfaction. We demonstrate the effectiveness of the proposed framework on real-world datasets, achieving perfect rule satisfaction and strong predictive performance.