Inductive Bias
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20 papers in the last four weeks, up 186% on the four weeks before. 0.2% of all new papers.
Latest papers 158
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 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 species and tropical Grassmannian to show that tropical attention provides a natural geometric framework for phylogenetic inference. On empirical 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.
A Theory of Time-Sensitive Language Generation: Sparse Hallucination Beats Mode Collapse
We study language generation in the limit under a global preference ordering on strings, as introduced by Kleinberg and Wei. As is done in previous work, we aim for breadth, but impose an additional requirement of timeliness: higher-ranked strings should be generated earlier. A string is then only credited if it is generated before a deadline, where its deadline is defined by a function that maps a string's rank in the target language to the time by which it must be produced. This is in keeping with a central consideration in machine learning, where inductive bias favors
simpler'' or more plausible'' outputs, all else being equal. We show that timely generation is impossible in a strong sense for eventually consistent generators -- the protagonists of most prior related work. Under what is perhaps the mildest natural relaxation of consistency, a hallucination rate that vanishes over time, we show that we can circumvent our impossibility result. In particular, we can achieve optimal density with respect to any superlinear deadline function. We also show this is tight by ruling out timely generation with linear deadlines and vanishing hallucination rate.PhysEDA: Physics-Aware Learning Framework for Efficient EDA With Manhattan Distance Decay
Electronic design automation (EDA) addresses placement, routing, timing analysis, and power-integrity verification for integrated circuits. Learning methods -- attention (Transformer) and reinforcement learning (RL) -- have recently emerged on EDA tasks, yet face two common bottlenecks: vanilla attention's quadratic complexity limits scaling, and data-scarce models overfit statistical noise and amplify weak long-range correlations against the underlying physics. We observe that EDA tasks share a physical prior -- pairwise electrical and routing interactions decay exponentially along Manhattan distance -- and integrate it as a unified inductive bias into both architecture and training. We propose PhysEDA, comprising two components Physics-Structured Linear Attention (PSLA) folds the separable Manhattan decay into the linear-attention kernel as a multiplicative bias, reducing complexity from quadratic to linear; Potential-Based Reward Shaping (PBRS) constructs a physical potential from the same kernel, providing dense reward signal under sparse RL while preserving the optimal policy via the policy-invariance theorem. Across three EDA scenarios -- decoupling-capacitor placement, macro placement, and IR-drop prediction -- PhysEDA improves zero-shot cross-scale transfer by 56.8% and achieves 14x inference speedup with 98.5% memory savings on 100x100 grids; PBRS adds another 10.8% in sparse-reward DPP.
Learning Point Cloud Geometry as a Statistical Manifold: Theory and Practice
Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete observations of the underlying scene geometry. This makes reliable geometric reasoning challenging and degrades downstream perception performance. Existing approaches attempt to compensate for these limitations by estimating local geometry, but often rely on hand-crafted statistics or end-to-end supervised learning, which can suffer from limited scalability or require large amounts of accurately labeled data. To address these challenges, we explicitly model point cloud geometry under a principled mathematical formulation. We represent local geometry as a statistical manifold induced by a family of Gaussian distributions, where each point is associated with a Gaussian capturing its local geometric structure. Based on this formulation, we introduce Point-to-Ellipsoid (POLI), a deep neural estimator that predicts per-point Gaussian geometry. POLI learns a mapping from point cloud observations to their underlying geometry in a self-supervised manner, removing the need for labeled data while preserving strong geometric inductive biases. The resulting representation integrates seamlessly into existing robotic perception pipelines without architectural modifications. Extensive experiments show that POLI enables accurate and robust geometry estimation and consistently improves performance across diverse robotic perception tasks.
SSDA: Bridging Spectral and Structural Gaps via Dual Adaptation for Vision-Based Time Series Forecasting
Large vision models (LVMs) have recently proven to be surprisingly effective time series forecasters, simply by rendering temporal data as images. This success, how ever, rests on a largely unexamined premise: the rendered time series images are sufficiently close to natural images for knowledge in pre-trained models to transfer effectively. We argue that two gaps still remain, i.e., spectral and structural gaps, fundamentally limiting the potential of LVMs for time series forecasting. Spectrally, we systematically reveal that rendered time series images exhibit a markedly shallower power spectrum than the natural images LVMs are pre-trained to recognize. Structurally, reshaping 1D temporal sequences into 2D grids fabricates spurious spatial adjacencies while severing genuine temporal continuities, misleading the spatial inductive biases of pre-trained LVMs. To bridge these gaps, we propose SSDA, a dual-branch network that spectrally and structurally adapts to unlock the full potential of LVMs for time series forecasting. At the data level, a Spectral Magnitude Aligner (SMA) applies 2D FFT to selectively enhance the magnitude spectrum toward natural-image statistics while preserving phase. At the model level, a Structural-Guided Low-Rank Adaptation (SG-LoRA) injects position-aware temporal encodings into patch embeddings and adapts at tention via low-rank updates. The two branches are further adaptively fused to produce the final forecast. Extensive experiments on seven real-world benchmarks demonstrate that SSDA consistently outperforms strong LVM- and LLM-based baselines under both full-shot and few-shot settings. Code is publicly available at https://anonymous.4open.science/r/SSDA-8C5B.
Continuity Laws for Sequential Models
Inductive biases influence the behavior and performance of sequential models. In this work, we study an underexplored inductive bias in sequential modeling: continuity in time. We ask a simple question: do models motivated by continuous-time formulations, such as state-space models, actually behave continuously in time, and does this translate into better performance on tasks with continuous temporal structure? To answer this, we formalize model continuity as convergence under temporal refinement, where a model is continuous if its predictions approach an underlying continuous trajectory as the temporal discretization is refined. We show that S4 exhibits stable continuous behavior, whereas S6 (the core of Mamba) can be more sensitive to input amplitude and selective dynamics, despite being derived from a continuous dynamical system. To study whether this distinction matters for learning, we also need a corresponding notion of task continuity. We therefore introduce a metric to quantify the continuity of datasets directly from their temporal structure. Across benchmarks, we find a clear empirical alignment between task continuity, model continuity, and model performance. Beyond an inductive bias, continuity also has practical consequences: we show that it enables a simple temporal subsampling strategy that improves both efficiency and performance.
Have Graph -- Will Lift? The Case for Higher-Order Benchmarks
After a somewhat rocky start, geometry and topology have established a foothold in machine learning. Message passing, either on graphs or higher-order complexes, is one of the main drivers of geometric deep learning, and paradigms that were once considered to be firmly in the realm of the abstract-like sheaves-have been "tamed" to serve as novel inductive biases for model architectures in topological deep learning. The veritable diversity of models, however, is in stark contrast to the scarcity of suitable benchmark datasets. As a result, researchers often resort to lifting existing graph datasets to include higher-order information. In this opinion paper, I want to encourage the community to also source new datasets, which may be used to prop up the foundations of our research field.
No Triangulation Without Representation: Generalization in Topological Deep Learning
Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated by the fact that topological objects permit operations, such as structural refinements, that are not appropriate for graph data. In this work, we extend MANTRA, a benchmark dataset containing manifold triangulations, to a larger class of manifolds with more diverse homeomorphism types. We show that, unlike prior claims, both graph neural networks (GNNs) and higher-order message passing (HOMP) methods can saturate the benchmark. However, we find that this is contingent on the right representation and feature assignment, emphasizing their importance in baseline models. We thus provide a novel evaluation protocol based on representational diversity and triangulation refinement. Surprisingly, we find no indication that existing models are capable of generalizing beyond the combinatorial structure of the data. This points towards a research gap in developing models that understand topological structure independent of scale. Our work thus provides the necessary scaffolding to evaluate future models and enable the development of topology-aware inductive biases.
Geometric Kolmogorov--Arnold Network (GeoKAN)
We introduce Geometric Kolmogorov--Arnold Networks (GeoKANs), a family of geometry-aware KAN-type models in which approximation is carried out in learned, geometry-adapted coordinates rather than in fixed Euclidean input coordinates. GeoKAN achieves this by learning a diagonal Riemannian metric that warps the input before basis expansion and feature mixing. The learned metric provides a geometric inductive bias through local length scaling and volume distortion, and in physics-informed settings it also affects the differential structure seen by the model. Within this framework, we develop three main variants, namely GeoKAN-NNMetric, GeoKAN-, and LM-KAN. For LM-KAN, we further consider three basis-specific versions, LM-KAN-RBF, LM-KAN-Wav, and LM-KAN-Fourier. These variants allow us to study geometry-aware KAN models both as general function approximators and as surrogates in physics-informed learning. By stretching regions with rapid variation and compressing smoother regions, GeoKAN reallocates representational resolution in a task-dependent manner, allowing the model to place capacity where it is most needed. As a result, GeoKAN is well suited to sharp, stiff, localized, and strongly non-uniform regimes arising in scientific machine learning and differential-equation problems.
In-Context Black-Box Optimization with Unreliable Feedback
Black-box optimization in science and engineering often comes with side information: experts, simulators, pretrained predictors, or heuristics can suggest which candidates look promising. This information can accelerate search, but it can also be biased, input-dependent, or misleading. Feedback-aware BO methods typically handle one task at a time, limiting their ability to generalize over multiple sources of feedback. In-context optimizers address cross-task adaptation, but usually assume that optimization history is the only available signal at test time. We study feedback-informed in-context black-box optimization (FICBO), where a pretrained optimizer conditions on both the observed history and cheap auxiliary feedback for the current candidate set. We introduce a structured feedback prior that models how feedback sources vary in their access, relevance, and distortion relative to the true objective, and use it to pretrain a feedback-aware transformer. At test time, the model estimates source reliability in context by comparing observed objective values with auxiliary signals, improving query selection. On synthetic and real-world tasks, FICBO effectively exploits informative feedback while remaining robust to weak or misleading sources, improving over other baselines. Empirical investigations further illustrate how the model perceives test-time sources, offering insights into its interpretability and decision-making process.
BoostLLM: Boosting-inspired LLM Fine-tuning for Few-shot Tabular Classification
Large language models (LLMs) have recently been adapted to tabular prediction by serializing structured features into natural language, but their performance in low-data regimes remains limited compared to gradient-boosted decision trees (GBDTs). In this work, we revisit the boosting paradigm, traditionally associated with tree ensembles, and ask whether it can be applied as a general training principle for LLM fine-tuning. We propose BoostLLM, a framework that transforms parameter-efficient fine-tuning into a multi-round residual optimization process by training sequential PEFT adapters as weak learners. To incorporate tabular inductive bias, BoostLLM integrates decision-tree paths as a second input view alongside raw features; analysis reveals that the path view acts as a structured teacher in early training steps before the model shifts toward feature-driven representations. Empirically, BoostLLM achieves consistent improvements over standard fine-tuning across multiple LLM backbones and datasets, matching or surpassing XGBoost across a wide range of shot counts and outperforming GPT-4o-based methods with a 4B model. We further show that the framework scales: pairing with stronger tree models and extended boosting horizons yields additional gains under appropriate stabilization. These results suggest that boosting can serve as a general training principle for LLM fine-tuning, particularly in low-data regimes for structured data.
Understanding diffusion models requires rethinking (again) generalization
This position paper argues that understanding generalization in diffusion models requires fundamentally new theoretical frameworks that go beyond both classical statistical learning theory and the benign overfitting paradigm developed for supervised learning. In diffusion models, unlike in supervised learning, memorization of training data and generalization to novel samples are incompatible: a model that has fully memorized its training set generates copies rather than novel data. Several theoretical explanations for why practical diffusion models nevertheless generalize have been proposed, based on capacity limitations, implicit regularization from optimization, or architectural inductive biases, but their interactions remain unclear. We argue that the field should pivot from explaining why the diffusion models do not memorize to investigating what the model actually learns during pre-memorization phase. To highlight our stance, we conduct empirical study of diffusion models trained on CIFAR-10, and we distill the findings into concrete open questions that we believe are key to improve understanding of generalization in diffusion models.
Multi-Level Bidirectional Biomimetic Learning for EEG-Based Visual Decoding
EEG-based visual neural decoding aims to align neural responses with visual stimuli for tasks such as image retrieval. However, limited paired data and a fundamental mismatch between high-fidelity digital images and biological visual perception - distorted by retinotopic mapping and subject-specific neuroanatomy - severely impede cross-modal alignment. To address this, we propose MB2L, a Multi-Level Bidirectional Biomimetic Learning framework that incorporates structured physiological inductive biases into representation learning. Specifically, we propose Adaptive Blur with Visual Priors to mitigate perceptual-structural mismatch by reweighting visual inputs according to retinotopic priors. We further propose Biomimetic Visual Feature Extraction to learn multi-level visual representations consistent with hierarchical cortical processing, enhancing subject-invariant encoding. These modules are jointly optimized via Multi-level Bidirectional Contrastive Learning, which aligns EEG and visual features in a shared semantic space through bidirectional contrastive objectives. Experiments show MB2L achieves 80.5% Top-1 and 97.6% Top-5 accuracy on zero-shot EEG-to-image retrieval, significantly outperforming prior methods and demonstrating strong generalization across subjects and experimental settings.
Intervention Complexity as a Canonical Reward and a Measure of Intelligence
The Legg--Hutter universal intelligence measure provides a rigorous scalar assessment of general intelligence as expected reward across all computable environments, weighted by simplicity. However, the measure presupposes an externally specified reward function, raising the question of whether the reward primitive is inherently arbitrary or whether a canonical choice exists. We propose a new measure, called intervention complexity, that has five natural properties: environment-derivedness, universality, minimality, sensitivity, and achievement preference. Given a resource function rho encoding an inductive bias (such as program length, execution time, or energy), rho-intervention complexity is a universal reward. The result yields a family of canonical rewards indexed by resource bias, providing a principled completion of the Legg--Hutter framework that does not require external normative input. We further propose a two-dimensional characterisation of intelligence: agent competence (how well the agent performs relative to the oracle optimum) and learning efficiency (how quickly this competence improves with experience). A separation theorem establishes that the choice of resource bias determines the computability of the resulting measure: action-count IC is computable in polynomial time, while program-length IC without oracle access is uncomputable, with the gap between oracle and bare IC precisely quantifying the information-theoretic content of learning. We discuss implications for superintelligence and for pre-training universal agents.
Structured Diffusion Bridges: Inductive Bias for Denoising Diffusion Bridges
Modality translation is inherently under-constrained, as multiple cross-modal mappings may yield the same marginals. Recent work has shown that diffusion bridges are effective for this task. However, most existing approaches rely on fully paired datasets, thereby imposing a single data-driven constraint. We propose a diffusion-bridge framework that characterizes the space of admissible solutions and restricts it via alignment constraints, treating paired supervision as an optional heuristic rather than a prerequisite. We validate our method on synthetic and real modality translation benchmarks across unpaired, semi-paired, and paired regimes, showing consistent performance across supervision levels. Notably, \textbf{it achieves near fully-paired quality with a substantial relaxation in pairing requirements, and remaining applicable in the unpaired regime}. These results highlight diffusion bridges as a flexible foundation for modality translation beyond fully paired data.
Graph World Models: Concepts, Taxonomy, and Future Directions
As one of the mainstream models of artificial intelligence, world models allow agents to learn the representation of the environment for efficient prediction and planning. However, classical world models based on flat tensors face several key problems, including noise sensitivity, error accumulation and weak reasoning. To address these limitations, many recent studies use graph structure to decompose the environment into entity nodes and interactive edges, and model virtual environments in a structured space. This paper systematically formalizes and unifies these emerging graph-based works under the concept of graph world models (GWMs). To the best of our knowledge, GWMs have not yet been explicitly defined and surveyed as a unified research paradigm. Furthermore, we propose a taxonomy based on relational inductive biases (RIB), categorizing GWMs by the specific structural priors they inject: (1) spatial RIB for topological abstraction; (2) physical RIB for dynamic simulation; and (3) logical RIB for causal and semantic reasoning. For each model category, we outline the key design principles, summarize representative models, and conduct comparative analyses. We further discuss open challenges and future directions, including dynamic graph adaptation, probabilistic relational dynamics, multi-granularity inductive biases, and the need for dedicated benchmarks and evaluation metrics for GWMs.
Decoupling the Benefits of Subword Tokenization for Language Model Training via Byte-level Simulation
Subword tokenization is an essential part of modern large language models (LLMs), yet its specific contributions to training efficiency and model performance remain poorly understood. In this work, we decouple the effects of subword tokenization by isolating them within a controlled byte-level pretraining pipeline. We formulate and test hypotheses across various dimensions, including sample throughput, vocabulary scaling, and the linguistic prior of subword boundaries. By simulating these effects in a byte-level setting, we refine our understanding of why subword models outperform raw byte models and offer insights to improve the pretraining of future byte-level and subword models. Specifically, our experiments highlight the critical role of increased training throughput and the integration of subword boundaries as either explicit priors or inductive biases.
What Kind of Language is Easy to Language-Model Under Curriculum Learning?
Many of the thousands of attested languages share common configurations of features, creating a spectrum from typologically very rare (e.g., object-verb-subject word order) or impossible languages to very common combinations of features (e.g., subject-object-verb word order). One central question is under what conditions such typological tendencies can be predicted, and specifically whether the learning bias of language models (LMs) is sufficient to reproduce such patterns. In this study, we add one dimensionality to such analysis -- the learning scenario for LMs -- to explore its interaction with the inductive bias of LMs. Specifically, as a first study, we examine the effect of curriculum learning (CL), as a developmentally motivated learning scenario, i.e., starting with simpler sentences rather than randomly-ordered input. We expand existing LM-based exploration (El-Naggar et al., 2025a,b) with a simple CL variant and find that CL substantially impacts the apparent inductive bias of LMs.
Fine-tuning vs. In-context Learning in Large Language Models: A Formal Language Learning Perspective
Large language models (LLMs) operate in two fundamental learning modes - fine-tuning (FT) and in-context learning (ICL) - raising key questions about which mode yields greater language proficiency and whether they differ in their inductive biases. Prior studies comparing FT and ICL have yielded mixed and inconclusive results due to inconsistent experimental setups. To enable a rigorous comparison, we propose a formal language learning task - offering precise language boundaries, controlled string sampling, and no data contamination - and introduce a discriminative test for language proficiency, where an LLM succeeds if it assigns higher generation probability to in-language strings than to out-of-language strings. Empirically, we find that: (a) FT has greater language proficiency than ICL on in-distribution generalization, but both perform equally well on out-of-distribution generalization. (b) Their inductive biases, measured by the correlation in string generation probabilities, are similar when both modes partially learn the language but diverge at higher proficiency levels. (c) Unlike FT, ICL performance differs substantially across models of varying sizes and families and is sensitive to the token vocabulary of the language. Thus, our work demonstrates the promise of formal languages as a controlled testbed for evaluating LLMs, behaviors that are difficult to isolate in natural language datasets. Our source code is available at https://github.com/bishwamittra/formallm.
Insect-inspired modular architectures as inductive biases for reinforcement learning
Most reinforcement-learning (RL) controllers used in continuous control are architecturally centralized: observations are compressed into a single latent state from which both value estimates and actions are produced. Biological control systems are often organized differently. Insects, in particular, coordinate navigation, heading stabilization, memory, and context-dependent action selection through distributed circuits rather than a single monolithic controller. Motivated by this contrast, we study an RL policy architecture that decomposes control into interacting modules for sensory encoding, heading representation, sparse associative memory, recurrent command generation, and local motor control, with a learned arbitration mechanism that allocates motor authority across modules. The model is evaluated on a two-dimensional navigation task that require simultaneous food seeking, obstacle avoidance, and predator escape. In a six-seed predator-navigation experiment trained with Proximal Policy Optimization (PPO) for 75 updates, the modular policy achieves the strongest final mean performance among the tested controllers, with final episodic return versus for a centralized gated recurrent unit (GRU) and for a centralized multilayer perceptron (MLP). The modular policy also attains the lowest final value loss and stable PPO optimization statistics while driving module-assignment entropy to , indicating highly selective control allocation. These results suggest that distributed control can serve as a useful inductive bias for RL problems involving dynamically competing behavioral objectives.
Directional Confusions Reveal Divergent Inductive Biases Through Rate-Distortion Geometry in Human and Machine Vision
To humans, a robin seems more like a bird than a bird seems like a robin, but does this asymmetry also hold for machine vision? Humans and modern vision models can match each other in accuracy while making systematically different kinds of errors, differing not in how often they fail, but in who gets mistaken for whom. We show these directional confusions reveal distinct inductive biases invisible to accuracy alone. Using matched human and deep neural network responses on a natural-image categorization task under 12 perturbation types, we quantify asymmetry in confusion matrices and link its organization to the geometry of the information--error trade-off - how efficiently, and how gracefully, a system generalizes under distortion. We find that humans exhibit broad but weak asymmetries across many class pairs, whereas deep vision models show sparser, stronger directional collapses into a few dominant categories. Robustness training reduces overall asymmetry magnitude but fails to recover this human-like distributed structure. Generative simulations further show that these two asymmetry organizations shift the trade-off geometry in opposite directions even at matched accuracy, explaining why the same scalar asymmetry score can reflect fundamentally different generalization strategies. Together, these results establish directional confusion structure as a sensitive, interpretable signature of inductive bias that accuracy-based evaluation cannot recover.
Locating acts of mechanistic reasoning in student team conversations with mechanistic machine learning
STEM education researchers are often interested in identifying moments of students' mechanistic reasoning for deeper analysis, but have limited capacity to search through many team conversation transcripts to find segments with a high concentration of such reasoning. We offer a solution in the form of an interpretable machine learning model that outputs time-varying probabilities that individual students are engaging in acts of mechanistic reasoning, leveraging evidence from their own utterances as well as contributions from the rest of the group. Using the toolkit of intentionally-designed probabilistic models, we introduce a specific inductive bias that steers the probabilistic dynamics toward desired, domain-aligned behavior. Experiments compare trained models with and without the inductive bias components, investigating whether their presence improves the desired model behavior on transcripts involving never-before-seen students and a novel discussion context. Our results show that the inductive bias improves generalization -- supporting the claim that interpretability is built into the model for this task rather than imposed post hoc. We conclude with practical recommendations for STEM education researchers seeking to adopt the tool and for ML researchers aiming to extend the model's design. Overall, we hope this work encourages the development of mechanistically interpretable models that are understandable and controllable for both end users and model designers in STEM education research.
SpatiO: Adaptive Test-Time Orchestration of Vision-Language Agents for Spatial Reasoning
Understanding visual scenes requires not only recognizing objects but also reasoning about their spatial relationships. Unlike general vision-language tasks, spatial reasoning requires integrating multiple inductive biases, such as 2D appearance cues, depth signals, and geometric constraints, whose reliability varies across contexts. This suggests that effective spatial reasoning requires spatial adaptability: the ability to flexibly coordinate different reasoning strategies depending on the input. However, most existing approaches rely on a single reasoning pipeline that implicitly learns a fixed spatial prior, limiting their ability to adapt under distribution changes. Multi-agent systems offer a promising alternative by aggregating diverse reasoning trajectories, but prior attempts in spatial reasoning primarily employ homogeneous agents, restricting the diversity of inductive biases they can leverage. In this work, we introduce SpatiO, a heterogeneous multi-agent framework for spatial reasoning that coordinates multiple vision-language specialists with complementary inductive biases. To enable effective collaboration, we propose Test-Time Orchestration (TTO), an calibration mechanism that dynamically evaluates and reweights agents based on their observed reliability during inference, without modifying model parameters. Extensive experiments on diverse spatial reasoning benchmarks, including 3DSRBench, STVQA-7k, CV-Bench, and Omni3D-Bench, demonstrate that SpatiO consistently improves spatial reasoning performance over both closed-source and open-source baselines. The project page is available at https://cy-h1329.github.io/spatio/.
Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms
In this paper, it is shown, for the first time, that centralized performance is achievable in decentralized learning without sharing the local datasets. Specifically, when clients adopt an empirical risk minimization with relative-entropy regularization (ERM-RER) learning framework and a forward-backward communication between clients is established, it suffices to share the locally obtained Gibbs measures to achieve the same performance as that of a centralized ERM-RER with access to all the datasets. The core idea is that the Gibbs measure produced by client~ is used, as reference measure, by client~. This effectively establishes a principled way to encode prior information through a reference measure. In particular, achieving centralized performance in the decentralized setting requires a specific scaling of the regularization factors with the local sample sizes. Overall, this result opens the door to novel decentralized learning paradigms that shift the collaboration strategy from sharing data to sharing the local inductive bias via the reference measures over the set of models.
LKV: End-to-End Learning of Head-wise Budgets and Token Selection for LLM KV Cache Eviction
Long-context inference in Large Language Models (LLMs) is bottlenecked by the linear growth of Key-Value (KV) cache memory. Existing KV cache compression paradigms are fundamentally limited by heuristics: heuristic budgeting relies on statistical priors rather than task objectives, causing resource misallocation, while heuristic selection relies on coupled query-key interactions or static inductive biases (e.g., attention sinks). To address this limitation, we introduce LKV (Learned KV Eviction), which formulates KV compression as an end-to-end differentiable optimization problem. LKV integrates LKV-H to learn task-optimized global budgets, and LKV-T to derive intrinsic KV importance without materializing attention matrices. This design bypasses heuristic proxies, strictly aligning compression with task objectives. Extensive evaluations demonstrate that LKV achieves state-of-the-art performance on both LongBench and RULER benchmarks at high compression rates. In particular, on LongBench, LKV achieves near-lossless performance with only 15% KV cache retention. Crucially, our analysis identifies learned budgeting as the dominant driver of fidelity, demonstrating that data-driven allocation is essential to overcome the limitations of hand-crafted heuristics.
DSAINet: An Efficient Dual-Scale Attentive Interaction Network for General EEG Decoding
In real-world applications of noninvasive electroencephalography (EEG), specialized decoders often show limited generalizability across diverse tasks under subject-independent settings. One central challenge is that task-relevant EEG signals often follow different temporal organization patterns across tasks, while many existing methods rely on task-tailored architectural designs that introduce task-specific temporal inductive biases. This mismatch makes it difficult to adapt temporal modeling across tasks without changing the model configuration. To address these challenges, we propose DSAINet, an efficient dual-scale attentive interaction network for general EEG decoding. Specifically, DSAINet constructs shared spatiotemporal token representations from raw EEG signals and models diverse temporal dynamics through parallel convolutional branches at fine and coarse scales. The resulting representations are then adaptively refined by intra-branch attention to emphasize salient scale-specific patterns and by inter-branch attention to integrate task-relevant features across scales, followed by adaptive token aggregation to yield a compact representation for prediction. Extensive experiments on five downstream EEG decoding tasks across ten public datasets show that DSAINet consistently outperforms 13 representative baselines under strict subject-independent evaluation. Notably, this performance is achieved using the same architecture hyperparameters across datasets. Moreover, DSAINet achieves a favorable accuracy-efficiency trade-off with only about 77K trainable parameters and provides interpretable neurophysiological insights. The code is publicly available at https://github.com/zy0929/DSAINet.
Diverse Dictionary Learning
Given only observational data , where both the latent variables and the generating process are unknown, recovering is ill-posed without additional assumptions. Existing methods often assume linearity or rely on auxiliary supervision and functional constraints. However, such assumptions are rarely verifiable in practice, and most theoretical guarantees break down under even mild violations, leaving uncertainty about how to reliably understand the hidden world. To make identifiability actionable in the real-world scenarios, we take a complementary view: in the general settings where full identifiability is unattainable, what can still be recovered with guarantees, and what biases could be universally adopted? We introduce the problem of diverse dictionary learning to formalize this view. Specifically, we show that intersections, complements, and symmetric differences of latent variables linked to arbitrary observations, along with the latent-to-observed dependency structure, are still identifiable up to appropriate indeterminacies even without strong assumptions. These set-theoretic results can be composed using set algebra to construct structured and essential views of the hidden world, such as genus-differentia definitions. When sufficient structural diversity is present, they further imply full identifiability of all latent variables. Notably, all identifiability benefits follow from a simple inductive bias during estimation that can be readily integrated into most models. We validate the theory and demonstrate the benefits of the bias on both synthetic and real-world data.
Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows
Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal dynamics, and therefore can assign high probability to anomalous or out-of-distribution samples. We address this structural limitation by relocating the notion of anomaly to a prescribed latent space. We introduce explicit inductive biases in conditional normalizing flows, modeling time-series observations within a discrete-time state-space framework that constrains latent representations to evolve according to prescribed temporal dynamics. Under this formulation, expected behavior corresponds to compliance with a specified distribution over latent trajectories, while anomalies are defined as violations of these dynamics. Anomaly detection is consequently reformulated as a statistically grounded compliance test, such that observations are mapped to latent space and evaluated via goodness-of-fit tests against the prescribed latent evolution. This yields a principled decision rule that remains effective even in regions of high observation likelihood. Experiments on synthetic and real-world time-series demonstrate reliable detection of anomalies in frequency, amplitude, and observation noise, while providing interpretable diagnostics of model compliance.
Distributional Regression with Tabular Foundation Models: Evaluating Probabilistic Predictions via Proper Scoring Rules
Modern tabular foundation models such as TabPFN and TabICL naturally produce full predictive distributions, while the benchmarks used to evaluate them (TabArena, TALENT, and others) still rely almost exclusively on point-estimate metrics (RMSE, ). This mismatch implicitly rewards machine learning models or pipelines that elicit a good conditional mean while ignoring the quality of the predictive distribution. We make the case for using proper scoring rules for training, fine-tuning, and benchmarking (ranking) of tabular foundation models. Although all strictly proper scoring rules are theoretically equivalent at the population level, they may differ on finite data: We demonstrate analytically and empirically that different scoring rules can induce different inductive biases during finite-sample optimization, leading to different model performance. We validate this finding by running fine-tuning experiments with TabPFN and TabICL using different scoring rules for various data sets, revealing non-trivial interactions between training objectives and evaluation metrics. Our results show that practitioners can adapt tabular foundation models to task-specific scoring objectives, and that the choice of scoring rule can influence model behavior in practice.
A Theory of How Pretraining Shapes Inductive Bias in Fine-Tuning
Pretraining and fine-tuning are central stages in modern machine learning systems. In practice, feature learning plays an important role across both stages: deep neural networks learn a broad range of useful features during pretraining and further refine those features during fine-tuning. However, an end-to-end theoretical understanding of how choices of initialization impact the ability to reuse and refine features during fine-tuning has remained elusive. Here we develop an analytical theory of the pretraining fine-tuning pipeline in diagonal linear networks, deriving exact expressions for the generalization error as a function of initialization parameters and task statistics. We find that different initialization choices place the network into four distinct fine-tuning regimes that are distinguished by their ability to support feature learning and reuse and therefore by the task statistics for which they are beneficial. In particular, a smaller initialization scale in earlier layers enables the network to both reuse and refine its features, leading to superior generalization on fine-tuning tasks that rely on a subset of pretraining features. We demonstrate empirically that the same initialization parameters impact generalization in ResNets trained on CIFAR-100 and SVHN as well as Transformers trained on modular arithmetic tasks. Overall, our results demonstrate an alytically how data and network initialization interact to shape fine-tuning generalization, highlighting an important role for the relative scale of initialization across different layers in enabling continued feature learning during fine-tuning.
MedFeat: Model-Aware and Explainability-Driven Feature Engineering with LLMs for Tabular Prediction
In clinical tabular prediction, classical machine learning models with feature engineering often outperform neural methods. LLMs are increasingly used to automate this process, acting as domain experts that propose diverse feature transformations to boost downstream performance. However, the feature generation process of existing LLM-based methods is agnostic to the downstream learner: the LLM receives no signal about which features currently drive predictions or where the model's representational capacity falls short, so proposals are neither targeted to promising regions of the feature space nor tailored to the learner's inductive bias. This shortcoming is amplified in healthcare data, which simultaneously exhibits class imbalance, heterogeneous feature spaces, and strict interpretability requirements. In this paper, we propose MedFeat, the first feature engineering framework inspired by the workflow of machine learning practitioners, leveraging model-awareness and feature importance signals to iteratively guide feature discovery for clinical tabular learning. We evaluate MedFeat on a broad range of challenging real-world clinical tasks and show that it statistically significantly outperforms state-of-the-art baselines, with an average F1 improvement of more than 10% over the baseline across models with distinct inductive biases.
Categorize Early, Integrate Late: Divergent Processing Strategies in Automatic Speech Recognition
In speech language modeling, two architectures dominate the frontier: the Transformer and the Conformer. However, it remains unknown whether their comparable performance stems from convergent processing strategies or distinct architectural inductive biases. We introduce Architectural Fingerprinting, a probing framework that isolates the effect of architecture on representation, and apply it to a controlled suite of 24 pre-trained encoders (39M-3.3B parameters). Our analysis reveals divergent hierarchies: Conformers implement a "Categorize Early" strategy, resolving phoneme categories 29% earlier in depth and speaker gender by 16% depth. In contrast, Transformers "Integrate Late," deferring phoneme, accent, and duration encoding to deep layers (49-57%). These fingerprints suggest design heuristics: Conformers' front-loaded categorization may benefit low-latency streaming, while Transformers' deep integration may favor tasks requiring rich context and cross-utterance normalization.
MauBERT: Universal Phonetic Inductive Biases for Few-Shot Acoustic Units Discovery
This paper introduces MauBERT, a multilingual extension of HuBERT that leverages articulatory features for robust cross-lingual phonetic representation learning. We continue HuBERT pre-training with supervision based on a phonetic-to-articulatory feature mapping in 55 languages. Our models learn from multilingual data to predict articulatory features or phones, resulting in language-independent representations that capture multilingual phonetic properties. Through comprehensive ABX discriminability testing, we show MauBERT models produce more context-invariant representations than state-of-the-art multilingual self-supervised learning models. Additionally, the models effectively adapt to unseen languages and casual speech with minimal self-supervised fine-tuning (10 hours of speech). This establishes an effective approach for instilling linguistic inductive biases in self-supervised speech models.
Soft Geometric Inductive Bias for Object Centric Dynamics
Physical systems are naturally parameterized in terms of geometric entities and their transformations. While exact equivariance can be a powerful inductive bias, real-world applications frequently exhibit approximate or broken symmetries in practice. We introduce object-centric world models that provide a soft geometric inductive bias without enforcing exact symmetries. By embedding object states as Clifford multivectors, our models encourage physically meaningful transformations while retaining the expressivity needed to handle asymmetric dynamics. We evaluate our approach on 2D rigid-body dynamics, 3D charged-particle systems, and real-world driving trajectories. Compared to both unstructured baselines and strictly equivariant models, our soft Clifford transformer achieves better long-horizon fidelity, particularly in regimes with broken symmetries. These results suggest that geometric algebra offers an effective middle ground, delivering sample-efficient dynamics without the inflexibility of hard mathematical constraints.
Aligning Inductive Bias for Data-Efficient Generalization in State Space Models
The remarkable success of modern AI has been closely tied to scaling laws, yet the finite supply of high-quality data makes data efficiency--learning more from less--an increasingly important frontier. A model's inductive bias is a critical lever for data efficiency, but foundational sequence models such as State Space Models (SSMs) often rely on fixed, task-agnostic biases. When this fixed prior is misaligned with the underlying structure of a task, the model may require additional samples to overcome its own bias before learning the relevant signal. In this work, we introduce a principled framework for understanding and aligning the inductive bias of linear time-invariant SSMs. We first formalize this bias through an SSM-induced kernel and show theoretically and empirically that its spectrum is governed by the model's frequency response. This characterization motivates Task-Dependent Initialization (TDI), a fast power-spectrum matching method that aligns the initial SSM bias with the task's spectral characteristics before downstream training. Across controlled synthetic experiments, trainable one-layer SSMs, and deep SSMs on diverse real-world benchmarks, TDI can improve data-efficient generalization primarily when task-relevant spectral structure is present and the default SSM bias is spectrally mismatched. Our results provide both a theoretical lens and a practical tool for task-adaptive inductive bias, suggesting a path toward more data-efficient sequence modeling.
A Theoretical Analysis of Provable Compositional Generalization in Neural Networks: A Necessary and Sufficient Condition
Compositional generalizationthe ability to systematically process novel combinations of known componentsis a hallmark of human intelligence; however, its theoretical foundation in neural networks is not yet well understood. This paper establishes a necessary and sufficient condition for provable compositional generalization, precisely characterizing its boundary. Conceptually, the condition consists of two principles: (i) structural alignment, where a model's computational graph aligns with a task's true compositional hierarchy, and (ii) unambiguous minimized representations, where each component encodes adequate but not redundant information on the training data. The result is fully proved and machine-verified in Lean 4 and holds even in few-shot and one-shot regimes. The necessity direction establishes that provable compositional generalization cannot circumvent these requirements, while the sufficiency direction yields a unified inductive bias that jointly governs architectural design, training data properties, and regularization strategies. Building on this condition, we develop an example algorithmic approach, illustrate it through a controlled minimal example, and further demonstrate the condition on the SCAN jump task. All conclusions are derived mathematically without reliance on empirical validation. Our work provides a theoretical characterization of provable compositional generalization.
KTO: Model Alignment as Prospect Theoretic Optimization
Kahneman & Tversky's tells us that humans perceive random variables in a biased but well-defined manner (1992); for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases -- the success of these objectives (e.g., DPO) over cross-entropy minimization can partly be ascribed to them belonging to a family of loss functions that we call (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect theory literature. Using a Kahneman-Tversky model of human utility, we propose a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, as current methods do. We call this approach KTO, and it matches or exceeds the performance of preference-based methods at scales from 1B to 30B, despite only learning from a binary signal of whether an output is desirable. More broadly, our work suggests that there is no one HALO that is universally superior; the best loss depends on the inductive biases most appropriate for a given setting, an oft-overlooked consideration.
Self-Supervised Cardiac Phase Detection via Single-Parameter Latent Orbits
Accurate identification of end-diastole (ED) and end-systole (ES) in echocardiography underpins the quantification of ventricular function, yet manual selection of these key frames is subjective and introduces clinically significant inter-operator variability. Recent self-supervised methods either prescribe strict periodic trajectories or learn an unconstrained low-dimensional motion subspace from reconstruction or registration objectives. The former offers interpretability but imposes restrictive assumptions on temporal progression, whereas the latter leaves cardiac phase implicit and ED/ES must be recovered through post-hoc geometric processing of the learned trajectory. We translate the physiological observation that cardiac phase is a one-dimensional signal into a prior by constraining the latent motion component to a single-parameter latent orbit, i.e., a global linear trajectory in latent space indexed by a bounded scalar phase variable. Mapping this variable through a sinusoidal nonlinearity yields an oscillatory motion signal with consistent temporal ordering, enabling direct identification of ED and ES from the learned phase signal. This inductive bias allows the model to capture an interpretable representation of the cardiac cycle, while maintaining flexibility to capture irregular heartbeats. Trained on EchoNet-Dynamic without annotations, our minimal single-parameter cardiac phase model learns an effective latent orbit, significantly improves upon the previous state of the art in ED localisation and matches it in ES localisation while using a more constrained representation and fewer training epochs. This demonstrates that a principled physiological inductive bias can match or exceed the performance of more complex representations. Code is available at: https://github.com/BonniciJ/OrbitalEcho/