Theoretical Foundations

Multimodal large language models (MLLMs) frequently suffer from object hallucinations, yet the visual perceptual mechanism underlying this failure remains poorly understood. In this work, we reveal that hallucinations are strongly associated with a human-like attention distraction phenomenon, where humans under divided focus experience degraded visual clarity and produce inaccurate descriptions, while in models the same mechanism manifests as spatial inconsistency in multi-head attention and temporal fading of attention to image tokens during decoding. We further provide theoretical insights that attention dispersion increases model complexity and degrades classification generalization. Motivated by these findings, we propose an Attention-Focused Approach for Improved Image Perception (AFIP), which corrects attention distraction via cross-head attention enrichment and reinforces visual grounding through dynamic historical attention enhancement. Extensive experiments on multiple benchmarks and models validate the effectiveness of AFIP without additional training. Code is available at: https://github.com/MIKUZ12/AFIP.

Multicalibration extends classical calibration by requiring predictions to be unbiased over a rich collection of functions, encompassing both prediction slices and subpopulations. It has emerged as a powerful framework for fairness, robustness, and reliable prediction, yet the theoretical understanding of multicalibration boosting (MCBoost) remains fragmented and often relies on restrictive assumptions. In this work, we develop a unified and refined perspective on MCBoost that subsumes existing variants, including multiaccuracy, BatchGCP, and BatchMVP. We uncover several phenomena that provide new insights into its practical behavior: even highly accurate and flexible predictors can remain substantially miscalibrated; enforcing multicalibration introduces a calibration-risk trade-off; and early stopping plays a central role in controlling this trade-off. On the theoretical side, we establish a general framework for MCBoost under weaker and more realistic conditions. We show that the boosting iterates converge to a Bregman projection of the population-optimal predictor onto the cumulative span generated by the audit class, thereby explicitly characterizing the function space on which multicalibration is achieved. We further derive convergence rates under different smoothness assumptions, finite-sample guarantees, and principled stopping rules that ensure multicalibration at termination. Finally, we extend the theory of universal adaptability under covariate shift, providing more general transfer guarantees and clarifying when multicalibrated predictors generalize across domains. These results provide a more complete theoretical foundation and practical guidance for multicalibration boosting, positioning it as both a unifying framework and a reliable post-processing approach for modern predictive models.

Machine-generated texts (MGTs) produced by large language models (LLMs) are increasingly prevalent across various applications, while their potential misuse in fake news propagation and phishing has raised serious concerns, highlighting the need for MGT detection. Existing paragraph-level detection methods commonly treat MGTs as entirely machine-like, overlooking the hidden human-like nature of machine-generated texts: even fully machine-generated texts may contain spans that are highly consistent with human writing. To this end, we first reveal the existence of such hidden human-like spans, and then theoretically analyze their impact on detection. Our analysis shows that these spans increase the sentence complexity for detection, thereby making MGT detection intrinsically harder. Based on this finding, we propose a model-agnostic stacked enhancement framework that improves existing detectors by reducing the influence of hidden human-like spans. Specifically, we model span-level retention decisions as a latent-variable problem and instantiate the optimization with a hard-EM-inspired procedure, where the detector iteratively filters confidently human-like subsequences and refines itself on the remaining text. Extensive experiments across various LLMs and practical scenarios demonstrate that the proposed framework consistently enhances existing detectors. Notably, the framework can also work in a training-free manner, offering flexibility and scalability for practical deployment.

Agentic AI orchestrators reduce the interface and assembly costs of composing information systems capabilities across organizational boundaries, seemingly accelerating modularization and organizational disaggregation. Yet AI-enabled capabilities whose outputs require evidence, review, signoff, or assignable responsibility may retain integrated accountability boundaries even when their technical interfaces become modular. We develop a capability-level theory of accountability-boundary placement in agentic ecosystems. We introduce accountability assets: complementary assets that make AI-supported outputs legitimate, auditable, reviewable, and assignable to a responsible party. We argue that verification cost and responsibility transferability determine whether the execution and accountability boundaries can move together. The theory identifies three boundary strategies: component, integrated, and dual-track. It also introduces rule debt, the governance burden that accrues when organizational decision rules migrate from formal information systems into ungoverned agentic execution environments. Integrating digital innovation, transaction cost, complementary-assets, digital platform governance, and IS control perspectives, we develop seven propositions linking agentic assembly-cost reductions, accountability assets, appropriability, orchestrator intent capture, and boundary misconfiguration to boundary strategy, value appropriation, and rule debt. The theory explains when digital modularization extends to organizational disaggregation and when accountability keeps capabilities integrated. Structured illustrations across document processing, legal services, audit, clinical decision support, and procurement discipline the boundary logic.

Neural networks acquire structured representations at specific moments during training, yet identifying these transitions typically relies on retrospective, label-dependent metrics. We introduce a bifurcation theory of representation dynamics to detect these moments in real time. Analyzing a passive GMM probe attached to the evolving encoder, we show the onset of structure corresponds to a supercritical pitchfork bifurcation driven by the loss Hessian. The system exhibits a theoretically predictable zero-crossing ($β_c$) that, compared to the network's current state ($β$), yields a dynamic ratio $β(t)/β_c(t)$: a universal, label-free phase coordinate for representation dynamics, computable entirely from hidden states. We empirically validate four distinct transition regimes predicted by this coordinate across diverse settings: SAEs on language models (Pythia), SSL (CIFAR), and grokking (modular arithmetic). Crucially, under finite dissipation, macroscopic symmetry-breaking can lag the initial zero-crossing by orders of magnitude, which providing a rigorous dynamical account of the delayed escape observed in grokking. Microscopically, the bifurcation creates a shared unstable subspace, forcing collective symmetry breaking. We term this the "feature lottery" in SAE training: a feature's terminal interpretability becomes predictable remarkably early. By only 5% of training, early atom purity robustly predicts final convergence purity, with top-decile early atoms achieving over 12x the baseline purity at convergence. Beyond explaining concept emergence, $β/β_c$ provides a practical early-warning indicator for training health, detecting the onset of usable structure, the crystallization of feature identity, and representational collapse epochs before downstream metrics react.

Humans, animals, and modern machine learning models exhibit impressive abilities to learn complex behaviors and generalize these behaviors to unseen situations. This ability requires us to learn rules and regularities that allow for such generalizations. At the same time, in most complex environments, any rule will have its exceptions. How do learning systems balance between learning general regularities and memorizing exceptions? We argue that a lack of task paradigms has hindered the study of this essential ability. To address this gap, we introduce a novel task, transitive inference with exceptions, that tests for relational generalization and memorization of an exception to the relational rule. We then analytically characterize the behavior of a simple, theoretically tractable model of neural network learning (kernel ridge regression) across a broad family of representations and task parameters. We find that these models can balance between relational generalization and memorization, but unlike for transitive inference without an exception, successful generalization is sensitive to the specific representational geometry. We explain why this task is more challenging mechanistically by drawing on our analytical theory. Finally, we validate our theoretical insights in pretrained language models that are finetuned on ordered relations, finding that these models successfully generalize according to the transitive rule, but also make the kinds of systematic mistakes predicted by our theory. Overall, our theory shows how learning systems can balance between relational generalization and memorization, explains how this can go wrong, and emphasizes the need for new task paradigms designed to probe this ability.

Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likelihood estimation for multimodal distributions with well-separated modes, which are commonly encountered in practical applications. We compare a novel diffusion-based denoising score matching estimator (DDSME) to the vanilla score matching estimator (SME) in this scenario. In particular, we prove statistical guarantees for both estimators, showing that the error bound for the vanilla SME worsens when the separation between the modes increases, which can be avoided in case of the DDSME with suitable hyperparameter tuning. This provides a novel theoretical explanation for the superior behavior of diffusion-based score matching over the vanilla version.

Backdoor poisoning attacks behave counter-intuitively in high dimensions: stronger training triggers can help the defender. We study regularised generalised linear models on Gaussian-mixture data in the proportional regime ($p/n \to κ$), varying the training trigger strength $α$ against a fixed test trigger. Three phenomena emerge: (i) clean test accuracy increases with $α$; (ii) attack success peaks at a finite $α$ and then declines; and (iii) the most damaging trigger direction is the minimum eigenvector of the data covariance. We prove all three results in closed form for the squared loss, and extend (i) and (ii) to general convex GLM losses via a Gaussian-proxy fixed-point system. We identify a finite-sample noise floor proportional to $κ$ as the mechanism behind (i), invisible to classical $n \gg p$ analysis. Experiments on CIFAR-10 and Gaussian surrogates match the theory closely; ResNet-18 experiments show the same phenomena beyond the convex setting.

We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on the length of the prompt, which we show empirically to be tight up to a factor less than 10, across architectures and model sizes. Our analysis also provides a theoretical explanation for previously observed empirical failures of transformers on simple sequence tasks, such as copying and cramming. Formally, we prove that (i) the maximal length of accessible sequences (those that the transformer can output for some prompt) grows linearly with the prompt length, (ii) beyond a critical threshold, the proportion of accessible sequences decays exponentially with sequence length, and (iii) the linear coefficient relating prompt length to accessible sequence length admits a theoretical upper bound. Notably, these results hold even with unbounded context and computation time.

Compositional score-based approaches to simulation-based inference (SBI) approximate the posterior over a shared parameter given $n$ independent observations by aggregating individually learned posterior scores: currently, there are two main propositions of such methods (Geffner et al. (2023), Linhart et al. (2026)). As the resulting composite score does not correspond to the score of any distribution along the forward diffusion path of the true multi-observation posterior, sampling from it via a reverse SDE leads to an irreducible bias. Annealed Langevin dynamics provides a principled alternative: it treats the composite score as the genuine score of a sequence of tractable bridging densities and samples from them in succession. When properly tuned, it could lead to a controllable bias. However, its hyperparameters, namely step sizes, the number of steps per level, and the number of annealing levels, have so far been chosen empirically. We derive Wasserstein bounds for annealed Langevin with approximate scores and translate them into explicit decision rules for these hyperparameters that guarantee a prescribed sampling accuracy, while highlighting different theoretical aspects of each composite score formulation. In the Gaussian setting, we obtain closed-form expressions for all relevant quantities and prove that the bridging densities of Linhart et al. (2026) consistently admit larger step sizes and require fewer total Langevin steps than those of Geffner et al. (2023). Furthermore, we show empirically that the tuning obtained in the Gaussian setting generalizes to more complex problems, thus providing a well-understood and theoretically grounded starting point for practitioners using compositional score-based approaches.

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a Dual-Channel Tensor Neural Network (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a structure-aware conformal ROC procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a conformal structure selector that, to our knowledge, is the first distribution-free procedure for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.

Presupposition projection in conditionals is central to theories of meaning and pragmatics, yet it remains largely unevaluated in large language models. We address this gap through a parallel behavioral study comparing human judgments and LLM predictions on a normed dataset of conditional sentences that controls the relation between the antecedent and the projected presupposition. We collect likelihood ratings from 120 participants and four LLMs under matched contextual conditions. Results show that humans integrate probabilistic and pragmatic cues in their judgment, whereas LLMs show variable alignment with human patterns. Using a linguistically motivated checklist within an LLM-as-a-Judge framework, we further evaluate model reasoning. We observe models that best match human ratings often lack coherent pragmatic reasoning, while models with stronger reasoning produce less human-like judgments. These findings suggest that LLMs' performance on such tasks may result from surface pattern matching rather than pragmatic competence. Our findings highlight the importance of benchmarks grounded in linguistic theory for comparing humans and models.

This paper provides an algebraic exposition of the theory of dyadic morality (TDM), a psychological model of moral judgment grounded in a simple two-node template: an intentional agent causing harm to a vulnerable patient. We formalize TDM using structural causal modeling (SCM) notation and identify three psychological operators (typecasting operator, completion operator, and valence-dependent inference mechanism) that extend standard SCM to capture how people compute moral judgments under constraints. We address scalability challenges arising from TDM's dyadic limitation, showing how moral cognition compresses multi-node scenarios through node collapse and sequential processing. Drawing on this algebraic framework, we demonstrate concrete applications to AI policy design: detecting conflicting obligations, structuring helpfulness policies to preserve user agency, and designing post-failure communication as causal interventions. Finally, we recommend scoped, contextual measurement of mind perception over universal averaging to operationalize the theory empirically. This algebraic formalization enables neurosymbolic AI systems to compute morality in a way that is both mathematically rigorous and faithful to human moral cognition.

Scaling LLMs requires tremendous computational resources, and recent advances in AI have gone hand in hand with massive amounts of capital expenditure. While it is established that scaling up LLMs reliably increases model quality (quantified in terms of loss or downstream evaluations), it is unclear how these quality improvements translate to potential revenue, and whether revenue increases would offset costs of larger-scale training and inference. In this work, we develop an economic model for characterizing the rational behavior of an LLM training firm by combining scaling laws with microeconomic theory. Under our model of firm behavior, LLM quality can be increased with more parameters and training tokens, leading to more potential adoption by consumers, who each have a quality threshold for using the LLM. On the other hand, additional parameters and training tokens both incur additional costs. We analyze the profit maximization problem for this model under compute-bound and data-bound regimes. In the compute-bound regime, optimal model size and token budget track hardware efficiency $E$ (FLOPs/$) at a near-linear rate; total training cost then scales sub-quadratically in $E$. Data efficiency improvements incentivize larger models and training expenditure. When we are limited to $D$ data, profit-optimal training expenditure scales as $D^2/E$, i.e, increase with data and decreases with hardware efficiency (as well as data efficiency). Finally, we analyze practical trends in training expenditure: current trends are consistent with our most permissive model variants in the compute-bound regime, but are not profit-optimal in the data-bound regime or assuming hardware advances will stall. Overall, our results provide a theory of profit-optimal LLM training, providing a foundation for engaging critically with industry statements and supporting long-term economic decision making.

We put forth a critical theoretical framework for analyzing generative models both descriptively and normatively. Our thesis is that generative models automate the production not only of intellectual labor or intelligence, but of a broader set of human social capacities we name "social doing." We do this by historicizing the commodification of sociality in the digital economy, leading to the availability of social data as the precondition for generative models. We elaborate our definition of "social doing" by drawing a distinction between "use" and "exchange" sociality and further differentiate between the ways that generative models either substitute for or mediate existing social relations and processes. We then turn to existing empirical research on how people use generative model-based products and the effects that their use has upon them. In this, we introduce the concept of Synthetic Sociality, a social reality in part fabricated by Silicon Valley's privately owned and undemocratically governed generative models. Lastly, we offer a normative analysis based on our findings and framework, and discuss future design opportunities.

Valiant's 1984 paper is widely credited with introducing the PAC learning model, but it, in fact, introduced a different model: unlike PAC learning, the learner receives only positives, may issue membership queries, and must output a hypothesis with no false positives. Prior work characterized variants, including the case without queries. We revisit Valiant's original model and ask: Which classes are learnable in it? For every finite domain, including Valiant's Boolean-hypercube setting, we show that a class is learnable if and only if every realizable positive sample can be certified by a poly-size adaptive query-compression scheme. This is a new variant of sample compression where the learner certifies samples via a short interaction with the membership oracle. Our characterization shows that learnability in Valiant's model is strictly sandwiched between learnability in the PAC model and the variant of Valiant's model without membership queries. This is one of the rare cases where introducing membership queries changes the set of learnable classes, and not just the sample or computational complexity. Next, we study the natural extension of the model to arbitrary domains. While we do not obtain an exact characterization, our techniques readily generalize and show that the same strict sandwiching persists. Finally, we show that $d$-dimensional halfspaces, which are not learnable without queries, are learnable with queries: we give a $\mathrm{poly}(d) \tilde{O}(1/ε)$ sample and $\mathrm{poly}(d) \mathrm{polylog}(1/ε)$ query algorithm, and prove that at least $Ω(d)$ samples or queries are necessary. To our knowledge, this is the first algorithm for halfspaces in Valiant's model. Together, these results uncover a surprisingly rich theory behind Valiant's original notion of learnability and introduce ideas that may be of independent interest in learning theory.

Discrepancies between an agent's actual knowledge and what a person thinks the agent knows can hinder interactions. If an agent could detect such discrepancies, it could provide feedback to account for them and improve current and future interactions. Using the I-POMDP as a framework for a second-order Theory of Mind (ToM-2), this work endows an agent with the ability to model the evolution of a person's erroneous beliefs about an agent and the cognitive biases and heuristics (CBH) from which they arise. In doing so, the agent can detect when CBH might be at play during an interaction and adaptively generate feedback that accounts for them. An in-person user study shows how a ToM-2 learner can account for the effects of a teacher's CBH to significantly improve the informativeness of teacher actions, and subjective results suggest people find the ToM-2 learner's feedback more useful.

We introduce missingness-MDPs (miss-MDPs), a novel subclass of partially observable Markov decision processes (POMDPs) that incorporates the theory of missing data. A miss-MDP is a POMDP whose observation function is a missingness function, specifying the probability that individual state features are missing (i.e., unobserved) at a time step. The literature distinguishes three canonical missingness types: missing (1) completely at random (MCAR), (2) at random (MAR), and (3) not at random (MNAR). Our planning problem is to compute near-optimal policies for a miss-MDP with an unknown missingness function, given a dataset of action-observation trajectories. Achieving such optimality guarantees for policies requires learning the missingness function from data, which is infeasible for general POMDPs. To overcome this challenge, we exploit the structural properties of different missingness types to derive probably approximately correct (PAC) algorithms for learning the missingness function. These algorithms yield an approximate but fully specified miss-MDP that we solve using off-the-shelf planning methods. We prove that, with high probability, the resulting policies are epsilon-optimal in the true miss-MDP. Empirical results confirm the theory and demonstrate superior performance of our approach over two model-free POMDP methods.

Self-supervised learning (SSL) is recognized as an essential tool for building foundation models for Artificial Intelligence applications. The advances in SSL have been made thanks to vigorous arguments about the principles of SSL and through extensive empirical research. The aim of this paper is to contribute to the development of the underpinning theory of SSL, focusing on the deep clustering approach. By analogy to supervised learning, we formulate SSL as K-L divergence optimization. The mode collapse is prevented by imposing an optimisation constraint on the teacher distribution. This leads to normalization using inverse cluster priors. We show that using Jensen inequality this normalization simplifies to the popular batch centering procedure. Distillation and centering are common {heuristics-based} practices in SSL, {but our work underpins them theoretically.} The theoretical model developed not only supports specific existing successful SSL methods, but also suggests directions for future investigations.

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.

Continual learning requires new-task adaptation without damaging previously acquired capabilities. Recent forward-pass and zeroth-order (ZO) results show that low-query adaptation may retain better than first-order (FO) descent, but the usual view of ZO as noisy FO estimation does not explain why. We give a local randomized gradient-shaping analysis: finite differences expose a raw shape that is mean-aligned with FO, while the norm-matched comparator fixes the expected squared adaptation norm. Under this controlled comparison, forgetting depends on how the adaptation shape exposes retention curvature. For norm-matched ZO, the expected shaped retention curvature obeys an exact identity that preserves the isotropic retention floor while contracting only the anisotropic component. Projecting this identity onto the incoming gradient yields the observable FO--ZO quadratic forgetting gap: ZO improves mean forgetting precisely when the FO direction has above-average retention curvature, by a query-dependent fraction of that curvature excess. A practical finite-query accounting separates the mean mechanism from one-batch sampling and smoothing perturbations. As an algorithmic transfer, RISE applies the calibrated ZO shape to exact FO gradients inside parameter blocks. Its target is a stability--plasticity tradeoff: randomized shaping may reduce the retention exposure paid by FO, exact gradients remove finite-smoothing bias from finite-difference ZO, and blockwise sampling supplies many local shaping directions after one gradient computation. The blockwise analysis separates mean-step damage from centered random exposure, showing how block-diagonal curvature, cross-block coupling, and local shaping diagnostics specify where this exact-gradient transfer is most likely to be visible.

Continual Pre-Training (CPT) is essential for enabling Language Models (LMs) to integrate new knowledge without erasing old. While classical CPT techniques like data replay have become the standard paradigm, the mechanisms underlying how LMs acquire and retain facts over time, termed as continual Factual Knowledge Acquisition (cFKA), remain unclear. In this work, we present a theoretical framework that characterizes the training dynamics of cFKA using a single-layer Transformer, offering a unified explanation for the behavior of representative CPT methods. Our analysis reveals that regularization-based methods merely adjust the convergence rate of parameters without altering the inherent forgetting tendency, whereas data replay methods succeed in shifting convergence dynamics and stabilizing pretrained knowledge. Building on these insights, we propose a novel generative data replay approach, called \textbf{S}electing \textbf{T}okens via attenti\textbf{O}n \textbf{C}ontribution~(STOC), which identifies influential factual snippets to guide replay data generation. Extensive experiments on both synthetic and real-world datasets validate our findings and demonstrate that STOC effectively enhances cFKA by mitigating catastrophic forgetting.

We propose a game-theoretic framework for adaptive multi-agent intelligent systems. Unlike classical game theory, which often treats strategies as primitive objects chosen by perfectly rational agents, the proposed framework provides a mathematical foundation for studying equilibrium in NeuroAI and can be viewed as an extension of game theory under relaxed assumptions, including partial observability, bounded computation, and uncertainty. At its core, Multilevel Interactive Equilibrium (MIE) generalizes the classical Nash equilibrium to intelligent systems with internal computation. Rather than being defined solely at the level of observable behavior, equilibrium emerges when neural learning dynamics, cognitive representations, and behavioral strategies mutually stabilize between interacting agents. This framework applies uniformly to interactions between two biological brains, two artificial agents, or hybrid human-AI systems. We discuss applications of multilevel game theory to human-autonomous vehicle driving, human-machine interaction, human-large language model (LLM) interaction, and computational psychiatry. We also outline experimental strategies and computational methods for estimating MIE and discuss challenges and prospects for future research.

Accurate and effective discrete image tokenization is crucial for long image sequence processing. However, current methods rigidly compress all content at a fixed rate, ignoring the variable information density of images and leading to either redundancy or information loss. Inspired by information entropy, we propose TaTok, a Theoretically grounded adaptive image Tokenization framework. We rigorously identify two key drawbacks in existing methods: information insufficiency when reconstructing images with patch tokens alone, and information redundancy among patch tokens. To address these, we introduce global tokens that model mutual information across patch tokens, and a Dynamic Token Filtering (DTF) algorithm based on cumulative conditional entropy to eliminate redundancy. Experiments confirm TaTok's state-of-the-art performance, delivering a 1.3x gFID improvement and 8.7x inference speedup. By allocating tokens according to information richness, TaTok enables more compressed yet accurate image tokenization, offering valuable insights for future research.

Futrell and Mahowald (2025) frame the success of neural language models (LMs) as supporting gradient, usage-based linguistic theories. I argue that LMs can also instantiate theories based on formal structures - the types of theories seen in the generative tradition. This argument expands the space of theories that can be tested with LMs, potentially enabling reconciliations between usage-based and generative accounts.

We study multi-robot persistent monitoring on weighted graphs, where node weights encode monitoring priorities and edge weights encode travel distances. The goal is to design joint robot trajectories that minimize the worst-case weighted latency across all nodes over an infinite time horizon. The widely adopted worst-case latency objective evaluates team performance over the entire time horizon and therefore may fail to distinguish strategies with poor transient behavior but strong asymptotic performance. To address this limitation, we propose a family of tail-performance objectives that generalize the standard objective and study the resulting functional optimization problems. We establish several key theoretical properties, including the existence of optimal strategies, relationships among the proposed objectives and their corresponding optimization problems, approximation by periodic solutions to arbitrary accuracy, and reductions to event-driven decision models with discretized waiting times. Building on these results, we construct an equivalent event-driven Markov decision process (MDP), called the Tail Worst-case Latency-Optimizing Markov Decision Process (TWLO-MDP), which reformulates the tail-performance objective as a standard average-reward criterion. We then develop reinforcement-learning-based solution methods for the TWLO-MDP and introduce the multi-robot monitoring benchmark (M2Bench), a unified platform that supports the evaluation and comparison of heuristic and learning-based monitoring algorithms. Experiments on synthetic and realistic monitoring scenarios show that our methods effectively reduce the worst-case weighted latency and outperform representative baselines.

We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the model, and appealing to non-hierarchical methods to estimate correlations using Glauber calculus, we prove a quantitative mean-field limit result and a next-order characterization of correlations. For iid uniformly distributed tokens, the limiting correlation equation can be solved in closed form and we obtain a rigorous explanation of the empirically observed \emph{lost-in-the-middle} phenomenon: the token retrieval profile, as a function of the source position in the prompt, is $\mathsf{U}$-shaped, with primacy, recency, and a unique interior minimum under an explicit smallness condition.

Deep continual learning requires models to adapt to new tasks without retraining from scratch. However, neural networks can lose their ability to adapt to new tasks after training on previous ones, a phenomenon known as loss of plasticity. There have been several explanations and diagnostics proposed for plasticity loss. Motivated by the philosophy that "all models are wrong, but some are useful", we ask: can existing diagnostics predict a neural network's plasticity? In this work, we take a practical view to interpret plasticity as trainability, i.e., a neural network's future optimization gain on a target task. We first take a theoretical approach, showing, by constructing a few counterexamples, that some widely adopted diagnostics of plasticity, including representation rank and neural tangent kernel rank, can fail to predict the loss of trainability in both regression and classification settings. We instead propose a novel metric, called optimization readiness, which combines gradient strength and gradient reliability. We prove that optimization readiness lower bounds one-step optimization gain under standard smoothness assumptions, providing a theoretical guarantee for its predictive power. Empirically, we show that across commonly used deep continual learning settings, such as Slowly-Changing Regression and Permuted MNIST, optimization readiness more reliably ranks checkpoints by trainability than prior diagnostics, even with substantially fewer samples.

Modern deep learning treats neural networks primarily as endpoint functions from inputs to outputs. Inspired by the shift from force to geometry in physics, we ask whether a network should instead be understood through the geometry of its internal propagation. We define a neural propagation field as the collection of hidden-state trajectories and local Jacobian operators across depth. Endpoint losses constrain only the boundary behavior of this field, leaving its interior geometry underdetermined. We show that endpoint-equivalent models can differ by orders of magnitude in trajectory and Jacobian structure, and introduce observable field metrics such as path sensitivity, solver consistency, and trajectory/Jacobian retention. In controlled teacher-flow and PDE systems, endpoint fitting fails to recover the underlying propagation law. In real multi-path tasks, field-aware objectives improve unseen-path generalization, OOD robustness, and calibration when aligned with the observation structure, but can collapse when over-constrained. In continual learning, field-preservation regularization complements replay and distillation: on Split CIFAR-100, DER++ with field preservation improves average accuracy, backward transfer, and field-retention metrics. These results identify propagation-field quality as a measurable and trainable property of neural networks beyond endpoint performance.

Hopfield networks and their generalizations have established deep connections among biological associative memories, statistical physics, and transformers. Yet most models treat retrieval as a fixed query-to-memory mapping, ignoring the role of external context in recall. In this work, we propose a two-stage associative memory architecture, wherein a context-gate subcircuit reshapes the retrieval energy landscape before and during recall. We show theoretically that context gating increases inter-memory separation while inducing sparsity, translating into exponential improvements in retrieval. Crucially, we prove that the system admits a unique self-consistent fixed point, revealing that the resulting retrieval state is driven by both a direct contextual bias and a second-order retrieval-gate feedback loop. We then bridge this theory to transformers; specifically, we evaluate a first-order approximation on Llama-3, confirming that in-context learning acts as context-gated retrieval. Native dynamics mirror our theory: context localizes a memory subspace, enabling the zero-shot query to cleanly discriminate. Ultimately, this framework provides a mechanistic link between associative memory theory and LLM phenomenology.

Diffusion models perform remarkably well on high-dimensional data such as images, often using only a modest number of reverse-time steps. Despite this practical success, existing convergence theory does not fully explain why such samplers remain efficient in high dimensions. Many prior KL guarantees bound the discretization error in terms of the ambient dimension, while other improved results replace this dependence using intrinsic-dimensional or geometric structure assumptions. In this work, we develop an alternative information-theoretic perspective on diffusion sampler convergence. We prove that, for Gaussian mixture targets, the discretization error is controlled by the Shannon entropy of the latent mixture component rather than by the ambient dimension. Consequently, the leading step complexity scales linearly with latent entropy and depends only logarithmically on the second moment of the data. Our analysis also extends to discrete target distributions, where the relevant complexity is the entropy of the target rather than the dimension of the embedding space. These results suggest that diffusion sampling can remain efficient in high-dimensional spaces when the data distribution admits a compact latent representation, as is widely believed to be the case for natural images.

We study Slowly Annealed Langevin Dynamics (SALD), a sampler for tracking a path of moving target distributions and approximating the terminal target through time slowdown. We establish non-asymptotic convergence guarantees via a KL differential inequality, showing that slowdown improves tracking through contraction of intermediate targets and the complexity of the path. Motivated by training-free guided generation with pretrained score-based generative models, we further introduce Velocity-Aware SALD (VA-SALD), which explicitly incorporates the underlying marginal distributions of the pretrained model and uses slowdown to correct the additional deviation induced by guidance. This yields a principled framework for training-free guided generation for diffusion-based and related generative model families, together with convergence guarantees that clarify the roles of intermediate functional inequalities and guidance bias. Code is available at https://github.com/anitan0925/sald.

Recursive retraining of generative models poses a critical representation challenge: when synthetic outputs are curated based on a fixed reward signal, the model tends to collapse onto a narrow set of outputs that over-optimize that objective. Prior work suggests that such collapse is unavoidable without adding real data into the mix. We revisit this conclusion from an alignment perspective and show that collapse can be mitigated through curation based on multiple reward functions. We formalize the dynamics of recursive training under heterogeneous preferences and prove that, under certain conditions, the model converges to a stable distribution that allocates probability mass across competing high-reward regions. The limiting distribution preserves diversity and provably satisfies a weighted Nash bargaining solution, offering a formal interpretation of value aggregation in synthetic retraining loops.

Building on the abstract Generalized Singular Value Decomposition (GSVD) theory of Brown et al. [2025], we prove that most modern neural architectures admit a generalized SVD representation in which they are left-invertible before a final linear layer, with no change in input-output behavior. Furthermore, the left-invertible nonlinear portion of the input-output behavior can be made to be \emph{norm preserving}, meaning that perturbations in the left-invertible ``embedding'' (the activations prior to the final linear layer in this representation) correspond proportionally to changes in the input, i.e., distance in feature space can be calibrated directly to distance in input space. We provide a data-driven algorithm for estimating this representation from trained models and propose a model architecture that naturally facilitates the decomposition. We then provide a proof-of-concept that the learned representation can be used to identify adversarial perturbations to model inputs, and develop the theory necessary for future applications to areas such as model bias and invertibility.

Recent non-asymptotic analyses have substantially advanced the theory of distributional policy evaluation, but they largely concern synchronous full-state updates under a generative model, model-based estimators, accelerated variants, or different approximation architectures. Standard categorical temporal-difference learning is typically used in a different regime. It asynchronously performs a single-state update at each iteration and, in online settings, is driven by a Markovian trajectory. This leaves an important gap between existing finite-iteration theory and the categorical recursions most closely aligned with practical distributional temporal-difference implementations. We bridge this gap for two categorical policy-evaluation methods: scalar categorical temporal-difference learning in the Cramér geometry and multivariate signed-categorical temporal-difference learning in the maximum mean discrepancy geometry. After suitable isometric embeddings, both algorithms take the form of asynchronous single-state stochastic-approximation recursions that contract in a statewise supremum norm. This permits finite-iteration guarantees in discounted problems under both i.i.d. and Markovian state sampling, and in undiscounted fixed-horizon problems under i.i.d. episodic sampling.

We theoretically study the hallucination phenomena in two canonical diffusion samplers: the stochastic Denoising Diffusion Probabilistic Model (DDPM) and the deterministic Denoising Diffusion Implicit Model (DDIM). We analyze the reverse ODE (DDIM) and SDE (DDPM) for a Gaussian mixture target, proving that after a critical time $τ$, (a) DDIM can become stuck on the segment connecting the two nearest modes and (b) DDPM stochasticity helps it become unstuck from this region, thus avoiding hallucination. Our empirical validation verifies that DDPM has a significantly lower hallucination rate than DDIM when this region is entered. Building on our observations, we exhibit how using additional stochastic steps can help DDIM avoid hallucinations and offer new insights on how to design improved samplers.

Sign-based optimization algorithms, such as SignSGD and Muon, have garnered significant attention for their remarkable performance in training large foundation models. Despite this empirical success, we still lack a theoretical understanding of when and why these sign-based methods outperform vanilla SGD. The core obstacle is that under standard smoothness and finite variance conditions, SGD is known to be minimax optimal for finding stationary points measured by $\ell_2$-norms, thereby fundamentally precluding any complexity gains for sign-based methods in standard settings. To overcome this barrier, we analyze sign-based optimizers leveraging $\ell_1$-norm stationarity, $\ell_\infty$-smoothness, and a separable noise model, which can better capture the coordinate-wise nature of signed updates. Under this distinct problem geometry, we derive matched upper and lower bounds for SignSGD and explicitly characterize the problem class in which SignSGD provably dominates SGD. Specifically, we compare the \emph{upper bound of SignSGD} with the \emph{lower bound of SGD}, illustrating that SignSGD effectively reduces the complexity by a factor of $d$ under \emph{sparse noise}, where $d$ is the problem dimension. Furthermore, we elevate this framework to the matrix domain, providing an equivalent optimal lower bound for the Muon optimizer, proving that extending the sign operator to matrices preserves this optimal scaling with dimensionality. Finally, we bridge our theoretical bounds to practice, demonstrating that the theoretical superiority of SignSGD accurately predicts its faster convergence during the pretraining of a 124M parameter GPT-2 model.

We study agency under partial observability in deterministic physical or simulated worlds, where apparent randomness arises from uncertainty over initial conditions, fixed law bits, and unrolled exogenous noise. We model sensing and actuation as bridge interfaces split between agent-controlled parameters and environment-controlled channel state, inducing a deterministic POMDP through a prior over latent microstates and many-to-one observation coarsening. Within this framework, we prove a separation between prediction, compression, and empowerment. Perfect prediction can be achieved either by identifying the hidden quotient relevant to the target family or by overwrite control that makes the future target action-determined; high empowerment alone is insufficient. Under refinable interfaces and sufficient memory, action-conditioned observation-compression progress reduces posterior uncertainty about the latent quotient, and when refinement requires steering world-side channel conditions, this creates target-conditioned interface empowerment. A bit-string specialization with a conserved information budget makes the resulting tradeoff explicit: prediction by identification requires internal capacity at least the relevant latent entropy, whereas overwrite control requires terminal action capacity over the controlled quotient. For modern AI agents, the results suggest a design principle rather than a theorem of inevitability: objectives should distinguish hidden-state identification, interface refinement, task-relevant controllability, and mere overwrite or distractor control. Human--AI alignment is partly an interface-design problem, where the relevant bridge is between human intent, agent internal state, external tools, and world-side channel conditions. This is a working draft: feedback and criticism is most welcome.

While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains largely confined to tabular or linearizable settings. We identify the cause of this gap as an emergent isolation of three traditions: (i) measure-theoretic MDP foundations on general spaces limit their analysis to exact dynamic programming and ignore all error sources of a learning process; (ii) deterministic error propagation analysis addresses the approximation error via concentrability coefficients without a finite-sample analysis of the estimation error; and (iii) PAC generalization bounds characterize the estimation errors of simplified topologies. We bridge these traditions with a unified theoretical framework for fitted Q-iteration (FQI) on general measurable Borel spaces. Our main result provides a finite-sample, adaptive-data performance bound by chaining measure-theoretic probability with Bellman-operator contraction in Banach spaces. We prove that sequential Rademacher complexity controls Bellman-regression generalization under policy-dependent data collection. We further extend this analysis to provide the first cumulative, pathwise online regret guarantee for FQI in continuous spaces. These results lay the necessary foundations for the formal analysis of many modern deep RL algorithms.

Information is one of the most widely-discussed concepts of the current era. However, a great deal of insightful work notwithstanding, it is yet to be given wholly convincing logical or mathematical foundations. Without them, we lack adequate reasoning tools for understanding the complex ecosystems of systems upon which the society depends. We seek to rectify this by taking a first step towards developing an inferentialist semantic theory of information. There are three key interacting components. First, conceptual analysis: the metaphysics of information. Dretske expressed the key concepts of information in terms of intentionality, truth, and transmissibility. We replace truth with inferability, and trace the consequences of this replacement. Second, logic: proof-theoretic semantics (P-tS) provides a mathematical-logical realization of inferentialist reasoning. Using P-tS, we develop the first steps towards a mathematical-logical theory of an inferentialist primitive unit of information, the 'inferon'. This proof-theoretic approach counterpoints the model-theoretic view of information articulated in situation theory. Furthermore, we argue that it facilitates addressing all three components of van Benthem and Martinez's categorization of the understandings of information, as range, as correlation, and as code. Our focus is on information-as-correlation. Third, systems: the P-tS tools we develop provide the basis for a mathematical account of distributed systems modelling -- a key tool from informatics for understanding the organization of information processing systems. This yields a reasoning-based theory of information flow in models of distributed systems. Overall, we seek to give a conceptually rigorous mathematical-logical account of information and its role within informatics, grounded in inference and reasoning.

There is an increasing number of algorithmic computations in theoretical physics. These, while conceptually simple, can nevertheless be time-consuming and contain subtleties that should not be overlooked. Given the recent improvement of Large Language Models (LLM), it is natural to investigate whether LLMs equipped with a computer algebra system (CAS) runtime and sufficiently informative context can reliably carry out these algorithmic tasks. In this work, we interface Claude with Maple, and apply this framework to cosmological perturbations in modified theories of gravity. We demonstrate the current capabilities of this approach, the typical failures, and how the same can be improved. We find that a frontier LLM supplied with worked examples is able to solve most test problems.

Biological neural systems achieve remarkable robustness and adaptability in uncertain environments through sparse, event-driven spike-based information processing and adaptive regulation. Inspired by this paradigm, this paper develops a neuromorhpic disturbance observer (NDO) and control framework that replaces conventional continuous-time signal representations with spike-timing encoding. Both disturbance estimates and control inputs are constructed via integrate-and-fire (IF) neuron dynamics from discrete spike events, yielding intrinsically event-driven updates. An adaptive-threshold triggering mechanism is inspired by spike-frequency adaptation (SFA), enabling history-dependent regulation of spike generation. Simulation results demonstrate that the proposed framework achieves neurally inspired robustness and adaptability, while the adaptive-threshold spiking scheme reduces spike events to 42.6% of the fixed-threshold case under noisy conditions.

What does it mean to understand the world? Contemporary world models often operationalize understanding as accurate future prediction in latent or observation space. Developmental cognitive science, however, suggests a different view: human understanding emerges through the construction of internal theories of how the world works, even before mature language is acquired. Inspired by this theory-building view of cognition, we introduce Learning-to-Theorize, a learning paradigm for inferring explicit explanatory theories of the world from raw, non-textual observations. We instantiate this paradigm with the Neural Theorizer (NEO), a World Theory Model, that induces latent programs as a learned Language of Thought and executes them through a shared transition model. In NEO, a theory is represented as an executable, compositional program whose learned primitives can be systematically recombined to explain novel phenomena. Experiments show that this formulation enables explanation-driven generalization, allowing observations to be understood in terms of the programs that generate them.

As LLM-based agents are increasingly interacting in multi-party settings, they need to properly handle information asymmetry, i.e., knowing when and to whom to disclose information is appropriate. Yet, existing benchmarks fail to measure this ability in realistic multi-party settings. Thus, we introduce SOTOPIA-TOM, a multi-dimensional benchmarking framework to evaluate LLM agents' ability to successfully navigate information asymmetric and privacy sensitive multi-party interactions. We create an interaction environment which enables both public (broadcast) and private (direct message) communication, and craft 160 human-reviewed scenarios across eight industry sectors, each involving 3 to 5 agents with partitioned private knowledge and channel-dependent sharing policies. To measure interaction abilities, we create a multi-dimensional evaluation framework to assess how well agents share useful information, seek missing details, coordinate efficiently, and protect privacy, which we also combine into a composite INFOMGMT metric. Results show that, across 6 LLM backbones and prompting strategies (vanilla, CoT-privacy, and ToM-based interventions), even the largest high-reasoning model (GPT-5) reaches only a 62% INFOMGMT score, which indicates persistent deficiencies in information seeking and privacy-aware decision-making. Additionally, ToM-based interventions more consistently improve the overall coordination-privacy balance (for example, relative to the vanilla baseline, ToM-Coach reduces critical privacy violations on GPT-4o from 9.9% to 2.2% while increasing the composite InfoMgmt score more than 2.5x from 15% to 40%). Overall, SOTOPIA-TOM exposes persistent limitations of current LLM agents in complex, information-asymmetric coordination and provides an extensible testbed for developing more privacy-aware, theory-of-mind capable multi-agent systems.

The Free Energy Principle (FEP) is a leading framework for mathematically modeling self-organization and learning, while Integrated Information Theory (IIT) is a computational ontology of consciousness oriented around irreducible cause and effect. While conceptual unifications have been proposed and appear to be supported by empirical findings, the absence of a rigorous mathematical mapping places upper bounds on their precision and testability. This work proposes that information can be defined as the deviation $ψ$ of realized dynamics from a constrained maximum-caliber (MaxCal) path ensemble over a finite time horizon. Under this definition, each of the cause/effect repertoires central to IIT 3.0 emerge directly from MaxCal variational principles, allowing IIT's phenomenological calculus to be re-derived from constrained entropy-maximization (CMEP). This framework supplies a theoretical bridge to active inference, which is mathematically dual to CMEP under Langevin dynamics, and offers a principled route for extending IIT to new dynamical regimes. When the approach is applied under the Central Limit Theorem (CLT) for Markov chains and via large deviations theory (LDT) to Ising models, information $ψ$ is shown to be equivalent to prediction error under accompanying predictive coding models. This may hold relevance to the ``hill-shaped trajectory'' of $Φ$ observed in neuronal cultures adapting to sensory inputs. Together, these results provide a physically and mathematically grounded rationale for studying the convergence of FEP, IIT, and thermodynamic frameworks of cognition such as recent work grounding consciousness in violations of the Fluctuation-Dissipation Theorem (FDT).

We introduce the Banach-Butterfly Invariant (BBT), an influence-adaptive Banach geometry on the Walsh-Hadamard butterfly factorization. For a Boolean function $f:\{-1,+1\}^n\to\{-1,+1\}$ with coordinate influences $\mathrm{Inf}_\ell(f)$, BBT assigns exponent $p_\ell = 1+\mathrm{Inf}_\ell(f)$ to butterfly layer $\ell$, yielding the contraction invariant $μ(f)=\prod_\ell 2^{-\mathrm{Inf}_\ell/(1+\mathrm{Inf}_\ell)}$. We prove a Jensen lower bound $\log_2μ(f) \ge -I(f)/(1+I(f)/n)$ and that $μ$ is strictly Schur-convex in the influence vector (modulo permutation), giving scaling classes $μ\sim 2^{-n/2}$ (parity), $2^{-Θ(\sqrt{n})}$ (majority), $2^{-1/2}$ (dictators). $\log_2μ$ is rational but not polynomial in the Fourier coefficients while $μ$ is algebraic, and $μ$ separates functions with identical total influence (122 pairs at $n=3$). Using the certified $n \le 4$ ternary Walsh-threshold universe from a companion synthesis manuscript as a finite testbed, we compute exact MILP minimum-support certificates for all 65,536 Boolean functions at $n=4$ (mean 6.42, max 9, all-odd by a parity argument) and on 10,000 of the 616,126 NPN-canonical representatives we enumerate at $n=5$ (matching OEIS A000370). Conditional Spearman $ρ(μ,|\mathrm{supp}|)$ at fixed total influence is $+0.571$ in the largest stratum at $n=4$ but reverses to $-0.38$ at $n=5$ under both function-uniform and NPN-canonical sampling: $μ$ is a valid Schur-convex concentration invariant, not a universal monotone predictor of minimum support across $n$. A companion application paper validates a real-valued WHT activation-energy proxy inspired by this theory on five pretrained LLMs at W2A16, cutting wikitext-2 perplexity by 15-58% versus vanilla auto-round; the transfer from Boolean theory to the real-valued proxy is qualitative, not formal.

In deep networks with small initialization, training exhibits long plateaus separated by sharp feature-acquisition transitions. Whereas shallow nonlinear networks and deep linear networks are well studied, extending these analyses to deep nonlinear networks remains challenging. We derive an exact identity for the imbalance of Frobenius norms of layer weight matrices that holds for any smooth activation and any differentiable loss and use this to classify activation functions into four universality classes. On the permutation-symmetric submanifold, the identity combines with an approximate balance law to reduce the full matrix flow to a scalar ODE, giving a critical-depth escape time law $τ_\star = Θ(\varepsilon^{-(r-2)})$ governed by the number $r$ of layers at the bottleneck scale rather than the total depth $L$. We find that this same $r-2$ exponent is recovered under He-normal initialization with $r$ bottleneck layers rescaled by $\varepsilon$, where the symmetry manifold is preserved by the flow but not attracting. We find close agreement between our theory and numerical simulations.

Training large language models (LLMs) is highly memory-intensive, as training must store not only weights and optimizer states but also intermediate activations for backpropagation. While existing memory-efficient methods largely focus on gradients and optimizer states, activation compression is less well established due to the lack of LLM-tailored theory and guarantees. In this work, we develop a theoretical framework showing that activation compression is safe for linear operators when activation compression is unbiased, but problematic for nonlinear ones. We further derive gradient variance bound and establish convergence guarantees for applying activation compression to all linear operators under the standard $L$-smoothness assumption, showing that it does not change the convergence rate. Guided by the theory, we propose an activation-gradient co-compression method that reuses low-rank activation factors to compress linear-layer gradients without extra computation or additional gradient error. We conduct extensive experiments on Qwen and LLaMA models using a pretraining benchmark and multiple fine-tuning benchmarks to validate our theory and demonstrate competitive performance of our method in both accuracy and compression efficiency. We provide our code in the supplementary material for reproducibility.

We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions corresponding to noise, the kernel's near-zero eigenvalues trap residual error in a test-invisible reservoir. Within the signal channel, minibatch SGD ensures that coherent population signal accumulates via fast linear drift, while idiosyncratic memorization is suppressed into a slow, diffusive random walk. We prove generalization survives even when the kernel evolves $\mathcal{O}(1)$ in operator norm, the full feature-learning regime. This theory naturally explains disparate phenomena in deep learning theory, such as benign overfitting, double descent, implicit bias, and grokking. Lastly, we derive an exact population-risk objective from a single training run with no validation data, for any architecture, loss, or optimizer, and prove that it measures precisely the noise in the signal channel. This objective reduces in practice to an SNR preconditioner on top of Adam, adding one state vector at no extra cost; it accelerates grokking by $5 \times$, suppresses memorization in PINNs and implicit neural representations, and improves DPO fine-tuning under noisy preferences while staying $3 \times$ closer to the reference policy.

Surprisal theory links human processing effort to the predictability of an upcoming linguistic unit, but empirical work often leaves the notion of a unit underspecified. In practice, experimental stimuli are segmented into linguistically motivated units (e.g., words), while pretrained language models assign probability mass to a fixed token alphabet that typically does not align with those units. As a result, surprisal-based predictors depend implicitly on ad hoc procedures that conflate two distinct modeling choices: the definition of the unit of analysis and the choice of regions of interest over which predictions are evaluated. In this paper, we disentangle these choices and give a unified framework for reasoning about surprisal over arbitrary unit inventories. We argue that surprisal-based analyses should make these choices explicit and treat tokenization as an implementation detail rather than a scientific primitive.

This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in the single agent's model. We first show that, under discretely sampled actions, the value function in the exploratory formulation converges to the one in the relaxed control formulation as the time grid refines. Leveraging the relaxed control formulation, we derive the exploratory Hamilton-Jacobi-Bellman (HJB) equation, in which the controlled common noise gives rise to an additional nonlinear functional of policy, rendering the policy iteration intricate. Under certain concavity condition, we establish the existence and uniqueness of the optimal one-step policy iteration via a first-order condition using the partial linear functional derivative with respect to policy. The policy improvement at each iteration is verified by relating to an entropy-regularized optimization problem over the space of policies. In the mean-field setting, we introduce the integrated q-function (Iq-function) defined on the state distribution and the policy, and it is shown that an optimal policy is identified as a two-layer fixed point to the argmax operator of the Iq-function. Finally, we provide the explicit characterization of an optimal policy as a Gaussian distribution in the general linear-quadratic (LQ) setting.

Large language models can now generate substantial code and draft research text, but research-software projects require more than either artifact alone. The mathematical thesis, executable system, benchmark surface, and public claims must mature together, yet often drift apart. We identify two LM-specific failure modes: hallucination accumulation, in which claims exceed what code or theory supports and unsupported assertions propagate across sessions; and desynchronization, in which code, theory, or the model's own world model fall out of alignment. We propose Comet-H, an iterative prompt automaton that orchestrates ideation, implementation, evaluation, grounding, and paper-writing as coupled coordinates of a single workspace state. At each step, a controller selects the next prompt by scoring it against what the workspace currently lacks, carries unfinished follow-up work forward with a half-life, and re-checks the paper and README against the code and benchmarks whenever documentation changes. We frame prompt selection as a small contextual bandit problem over prompt families, with prompts as arms, workspace deficits as context, and a hand-weighted linear score. This transparent scorer, paired with a fading record of unfinished work, bounds long-horizon follow-ups, requires no learned policy, and makes each prompt choice legible from the workspace. We created a portfolio of 46 research-software repositories across two dozen domains. We study A3 in depth, a Python static-analysis tool built entirely within the loop, which reaches (F1 = 0.768) on a 90-case benchmark, compared with a next-best baseline of 0.364. Across approximately 400 commits, we find that audit-and-contraction passes dominate the later phases of every successful trajectory.

Deep learning models are used in critical applications, in which mistakes can have serious consequences. Therefore, it is crucial to understand how and why models generate predictions. This understanding provides useful information to check whether the model is learning the right patterns, detect biases in the data, improve model design, and build systems that can be trusted. This work proposes a new method for interpreting Convolutional Neural Networks in image classification tasks. The approach works by selecting the most representative feature maps that contribute to each prediction. To solve this combinatorial problem, we encode it into a quantum constrained optimization problem and propose to solve it using quantum annealing. We evaluate our method against the state-of-the-art explainable AI techniques, specifically GradCAM and GradCAM++, and observe an improved class disentanglement, i.e. the model's decision boundaries become more distinct and its reasoning more transparent. This demonstrates that our approach enhances the quality of explanations, making it easier to understand which features the model relies on for specific predictions. In addition, we study the computational behavior of the quantum annealing algorithm. Specifically, we analyze the minimum energy gap of the system during computation and the probability that the algorithm finds the correct solution. These analyses provide theoretical insight into why the method works effectively in practice.

Cognitive science often evaluates theories through narrow paradigms and local model comparisons, limiting the integration of evidence across tasks and realizations. We introduce an automated adversarial collaboration framework for adjudicating among competing theories even when the candidate models and experiments must be discovered during the adjudication process. The system combines LLM-based theory agents, program synthesis, and information-theoretic experimental design in a closed loop. In a simulation study spanning three classic categorization theories, the framework recovered the ground-truth theory across noise settings with weaker reliability in the hardest settings. Together, the framework and findings provide a concrete proof of concept for closed-loop, in-silico theory adjudication in cognitive science.

Current LLM agents operate under an implicit but universal assumption: execution is a transaction -- the user submits a request, the agent works in isolation, and only upon completion does the dialogue resume. This forces users into a binary choice: wait for a potentially incorrect output, or interrupt and lose all progress. We reject this assumption and propose the stream paradigm, in which agent execution and user intervention are concurrent, interleaved processes sharing a bidirectional channel. We formalize this paradigm through a reversibility taxonomy that classifies every agent action as Idempotent, Reversible, Compensable, or Irreversible, and arrive at a core conclusion: an agent's flexibility is bounded by its reversibility. We prove that conflicting compensable actions impose unavoidable adaptation costs and that conflicting irreversible actions make full specification satisfaction impossible -- these costs are properties of the action space, not of the algorithm. Guided by this insight, we present the Revision Absorber, a reactive algorithm based on the Earliest-Conflict Rollback rule that is structurally optimal under mild assumptions. Experiments on StreamBench with real LLM agents validate all predictions: the Absorber matches the quality of a brute-force full-restart baseline while wasting an order of magnitude fewer steps of already-completed work, turning mid-execution revisions from a dead-end into a first-class interaction.

Current video moment retrieval excels at action-centric tasks but struggles with narrative content. Models can see \textit{what is happening} but fail to reason \textit{why it matters}. This semantic gap stems from the lack of \textbf{Theory of Mind (ToM)}: the cognitive ability to infer implicit intentions, mental states, and narrative causality from surface-level observations. We introduce \textbf{StoryTR}, the first video moment retrieval benchmark requiring ToM reasoning, comprising 8.1k samples from narrative short-form videos (shorts/reels). These videos present an ideal testbed. Their high information density encodes meaning through subtle multimodal cues. For instance, a glance paired with a sigh carries entirely different semantics than the glance alone. Yet multimodal perception alone is insufficient; ToM is required to decode that a character smiling'' may actually be concealing hostility.'' To teach models this reasoning capability, we propose an \textbf{Agentic Data Pipeline} that generates training data with explicit three-tier ToM chains (intent decoding, narrative reasoning, boundary localization). Experiments reveal the severity of the reasoning gap: Gemini-3.0-Pro achieves only 0.53 Avg IoU on StoryTR. However, our 7B \textbf{Shorts-Moment} model, trained on ToM-guided data, improves +15.1% relative IoU over baselines, demonstrating that \textit{narrative reasoning capability matters more than parameter scale}.

A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements provided by users and should incorporate the relative salience of particular topics. We address this issue by modelling consensus as an interval in a one-dimensional opinion space derived from potentially high-dimensional data via embedding and dimensionality reduction. We define an objective that maximizes expected agreement within a hypothesis interval where the expectation is over an underlying distribution of issues, implicitly taking into account their salience. We propose an efficient Empirical Risk Minimization (ERM) algorithm and establish PAC-learning guarantees. Our initial experiments demonstrate the performance of our algorithm and examine more efficient approaches to identifying optimal consensus regions. We find that through selectively querying users on an existing sample of statements, we can reduce the number of queries needed to a practical number.

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and performance of neural networks. We pull together major strands of ongoing research in deep learning theory and identify five growing bodies of work that point toward such a theory: (a) solvable idealized settings that provide intuition for learning dynamics in realistic systems; (b) tractable limits that reveal insights into fundamental learning phenomena; (c) simple mathematical laws that capture important macroscopic observables; (d) theories of hyperparameters that disentangle them from the rest of the training process, leaving simpler systems behind; and (e) universal behaviors shared across systems and settings which clarify which phenomena call for explanation. Taken together, these bodies of work share certain broad traits: they are concerned with the dynamics of the training process; they primarily seek to describe coarse aggregate statistics; and they emphasize falsifiable quantitative predictions. We argue that the emerging theory is best thought of as a mechanics of the learning process, and suggest the name learning mechanics. We discuss the relationship between this mechanics perspective and other approaches for building a theory of deep learning, including the statistical and information-theoretic perspectives. In particular, we anticipate a symbiotic relationship between learning mechanics and mechanistic interpretability. We also review and address common arguments that fundamental theory will not be possible or is not important. We conclude with a portrait of important open directions in learning mechanics and advice for beginners. We host further introductory materials, perspectives, and open questions at learningmechanics.pub.

How might implicit aesthetic perspectives shape what Information Systems (IS) scholarship recognises as worthy of study (or not)? In this hermeneutic literature analysis, we surface foundational aesthetic assumptions underpinning IS research. We identify four perspectives (aesthetics as imitation, sensory experience, world-making, and political doing) that guide how IS scholars perceive and appreciate sociotechnical phenomena. These perspectives influence what becomes recognisable as legitimate research and what remains unseen. By making aesthetic assumptions explicit, we show how they form epistemic infrastructure that conditions horizons of inquiry. We apply this framework to algorithmic management and digitally mediated intimacy, revealing how alternative perspectives open new research questions whilst exposing dimensions that dominant framings overlook. This analysis foregrounds the importance of aesthetic philosophy to IS literature, offering a vocabulary for articulating how aesthetic perspectives shape theorising, method, and contribution.

Graph Neural Networks (GNNs) excel on relational data, but standard benchmarks unrealistically assume the graph is centrally available. In practice, settings such as Federated Graph Learning, distributed systems, and privacy-sensitive applications involve graph data that are localized, fragmented, noisy, and privacy-leaking. We present a unified framework for this setting. We introduce LoGraB (Local Graph Benchmark), which decomposes standard datasets into fragmented benchmarks using three strategies and four controls: neighborhood radius $d$, spectral quality $k$, noise level $σ$, and coverage ratio $p$. LoGraB supports graph reconstruction, localized node classification, and inter-fragment link prediction, with Island Cohesion. We propose AFR (Adaptive Fidelity-driven Reconstruction), a method for noisy spectral fragments. AFR scores patch quality via a fidelity measure combining a gap-to-truncation stability ratio and structural entropy, then assembles fragments using RANSAC-Procrustes alignment, adaptive stitching, and Bundle Adjustment. Rather than forcing a single global graph, AFR recovers large faithful islands. We prove heat-kernel edge recovery under a separation condition, Davis--Kahan perturbation stability, and bounded alignment error. We establish a Spectral Leakage Proposition: under a spectral-gap assumption, polynomial-time Bayesian recovery is feasible once enough eigenvectors are shared, complementing AFR's deterministic guarantees. Experiments on nine benchmarks show that LoGraB reveals model strengths and weaknesses under fragmentation, AFR achieves the best F1 on 7/9 datasets, and under per-embedding $(ε,δ)$-Gaussian differential privacy, AFR retains 75% of its undefended F1 at $ε=2$. Our anonymous code is available at https://anonymous.4open.science/r/JMLR_submission