Papers

While recent studies have explored human behavior and preference simulation using large language models (LLMs), it remains unclear how well LLMs can simulate subjective evaluations from real learners in educational settings. We investigate this question using real learner evaluation data on feedback for high-school biology questions at both the group and individual levels. We compare performance with and without learner-specific information, such as personality traits and evaluation examples, across six models. Our results show that LLMs still have a limited ability to simulate learner evaluations. Providing learner profiles and examples improves score calibration and individual-level simulation, but more often fails to improve group-level consistency. These findings highlight the need to investigate which learner information and adaptation strategies are effective for learner preference simulation.

Scaling up robotic manipulation is primarily bottlenecked by the scarcity of real-world robot data. While recent approaches leverage human video demonstrations to mitigate this shortage, they remain computationally expensive and still rely on paired human-robot data for domain alignment. Although current state-of-the-arts excel at long-horizon tasks, they struggle with the delicate and precise control required for complex tool manipulation. To overcome these limitations, we introduce P2P-T, from Pixel to Poses for Tool Manipulation, a data-efficient, object-centric framework that learns tool use directly from human demonstrations. P2P-T bridges the cognitive and physical execution gap through a two-stage approach. First, pretraining an object-centric world model to extract stable pose priors; second, integrating these priors into an efficient, pose-aware low-level policy. By utilizing a robust automated data processing pipeline powered by modern foundation models, P2P-T completely bypasses the need for human-robot aligned data. This reduces overall training overhead drastically. With minimal per-task fine-tuning, our framework achieves a 73% improvement over the previous state of the art in execution performance on complex, real-world tool manipulation tasks that currently remain out of reach for standard large-scale pretrained models.

We study the supervised classification problem for interacting particle systems (IPS) from trajectory observations. The IPS belongs to one of K classes, each characterized by a distinct interaction drift. Given a learning dataset, the goal is then to predict the class label of a newly observed system based on the trajectory of a single particle. This setting raises several statistical challenges. First, the particles within each system interact and are therefore dependent. Second, although the full particle system is Markovian, the trajectory of a single particle is not. To address these difficulties, we exploit the McKean-Vlasov limit of the IPS, which describes the dynamics of a typical particle as the number of particles tends to infinity. We propose a plug-in classification procedure based on estimating the interaction drift associated with each class from discretely observed trajectory data. Hence, for each class, we provide a new nonparametric estimator of the drifts by minimizing a ridge-regularized least-squares contrast over a B-spline basis. In particular, our theoretical findings reveal that the convergence rate of the resulting classifier is of order N -1/6+$\epsilon$ for any $\epsilon$ > 0, where N denotes the number of particles in each system. Numerical experiments illustrate the performance of the proposed method and show that it outperforms an end-to-end neural network baseline that does not exploit the underlying particle-system structure.

We study collective charge excitations in three-dimensional $\mathcal{PT}$-symmetric nodal-ring semimetals (PTNRs) and their gapped counterparts (GNRs) in the presence of band tilt, together with Weyl semimetals (WSMs). Within a low-energy two-band description, we consider untilted systems as well as in-plane and axial tilts. Using the random-phase approximation, we obtain the density of states, Drude weights, dielectric functions, and plasmon dispersions at low doping and in the intrinsic limit. The mass gap and the two inequivalent tilt directions generate distinct Fermi-surface topologies and thereby control the formation and damping of plasmons. By comparing the collective modes with the particle-hole continuum, we identify the regimes in which plasmons remain well defined. We also calculate the response of untilted and tilted WSMs and contrast it with that of PTNRs and GNRs. The two classes of semimetals differ in the carrier-density dependence and isotropy of the plasmon frequency as well as in interband screening and their response to tilt. These differences reflect their distinct Fermi-surface geometries and interband structures. Our results establish how mass and tilt govern collective charge dynamics through their interplay with intraband spectral weight and interband particle-hole excitations.

A critical analysis of contemporary approaches to the study of conscious states. The review focuses on methods of classification, clustering, modeling of brain states under anesthesia and identification of measurable neurobiological characteristics of brain function. A comparative analysis was conducted in the following three major areas: automatic detection of states of consciousness using neural networks based on EEG and fMRI data; modeling of the structural-functional dynamics of the brain under the effects of anesthetics; and detection of neurophysiological indicators which correlate with the level of consciousness. The obtained conclusions demonstrate the growing effectiveness of deep neural models in the classification and prediction of brain states and the analysis of dynamic structural-functional connectivity. Nonetheless, significant limitations were also identified, including the limited interpretability of the models, the lack of standardized metrics, and the problem of the specificity of consciousness markers. Our findings support the need for developing hybrid, generalizible, physiologically grounded architectures. Furthermore, such approaches may improve the translational potential of computational models in clinical neuroscience. Diverse methods of machine and computational modeling have demonstrated their effectiveness in tasks of automatic clustering and classification of brain states, the development of multilevel models and the identification of connectivity patterns correlated with levels of consciousness. A larger-scale analysis and a larger dataset, as well as the implementation of model interpretability approaches are required for the practical application of the analyzed models. The models based on EEG and LFP are the most promising for clinical application due to their availability and the possibility of real-time monitoring.

We use lattice gauge theory to investigate the Peskin-Takeuchi S parameter in SU(3) gauge theory with eight light fundamental fermions (eight-flavor QCD), a candidate for walking technicolor. We develop a new approach to computing S using the first time moment of current correlators, in addition to the conventional vacuum-polarization method, and obtain consistent results. Finite-volume (FV) corrections are estimated using data at multiple lattice volumes and a formula motivated by chiral perturbation theory. At the smallest fermion mass, the one-doublet contribution is S = 0.281(5)(17), smaller than the value $\sim 0.35$ in scaled-up 2+1-flavor QCD (without subtracting the SM contribution). However, contrary to naive expectations, S toward smaller fermion masses is not necessarily suppressed once FV corrections are included. The resulting Gasser-Leutwyler parameter $L_{10}^r(M_\rho)$ is similar to that in real-world QCD. We also determine the vector and axial-vector meson decay constants, $F_\rho$ and $F_{a_1}$. The ratio $F_\rho/F_\pi$ is stable against the fermion mass and consistent with the KSRF estimate, implying a $\rho\pi\pi$ coupling similar to that in real-world QCD. We predict the techni-rho decay width into weak bosons to be $\Gamma_\rho/M_\rho \lesssim 0.24/N$, where N is the number of weak doublets. We further find that the rho- and $a_1$-dominated Weinberg spectral-function and Das-Mathur-Okubo sum rules are satisfied, yielding S and $L_{10}^r(M_\rho)$ consistent with our main results. We discuss implications for BSM model building.

The emergence of the digital transition brought an increasing need to control the processing of digital information, including in Law Enforcement Agencies (LEAs). At the EU level, in recent years, many regulations have emerged to control data processing and exchange. Texts other than the GDPR, such as the ”Law Enforcement Directive (LED)”, appeared to regulate specifically how Law Enforcement Agencies (LEAs) could process data. A formal representation of these regulations can be part of decision systems that support LEAs in processing data in compliance with the regulations. Although many new formalisms have emerged to represent legal norms and rules, few are provided with a reasoning mechanism. Furthermore, systems used in decision-making processes in critical contexts such as medical diagnoses or legal decisions cannot be fully automated, and the explainability of their results is essential to ensure user confidence in decisions. This explainability aspect, while crucial, is lacking in most modern approaches that rely on machine learning. This paper describes a framework to operate formal rules from regulations, by focusing on explainability of the decision. After describing the general architecture of the proposed decision support framework, the paper showcases how symbolic AI and the SPARQL query language can support legal reasoning. It then describes an algorithm to generate a justification for the reasoning results, and outlines the procedure to be followed when the reasoning does not lead to a satisfactory conclusion. We notably focus on a method based on decision trees to determine what additional information to request from the user.

Let $\lambda_k(G)$ be the $k$th eigenvalue of the normalized Laplacian of a finite undirected weighted graph $G$ with positive degrees, where $k$ is an integer satisfying $1\le k\le |V(G)|$. Let $\varphi_k(G)$ be the minimum possible maximum conductance of $k$ disjoint nonempty vertex sets. We prove $\varphi_k(G)\le C\sqrt{\lambda_k(G)\log(k+1)}$ for an absolute constant $C$. The number of sets and the spectral index are both $k$, and conductance is measured in the original graph. The logarithmic dependence is optimal up to an absolute constant. The proof combines geometric partitioning of the spectral embedding with minimum-cut improvement and adaptive projections in coefficient space. A single conductance threshold is used throughout the construction. The resulting maps have disjoint supports, and the sum of their Gram matrices is bounded below by an absolute positive multiple of the identity. A dyadic maximal estimate bounds the sum of their internal energies uniformly over unit coefficient vectors. A dimension argument using local eigenvalues then yields exactly $k$ disjoint sparse cuts.

Exo-to-egocentric video generation aims to synthesize what a person sees from their own viewpoint given third-person footage and a target head trajectory. The task requires transferring appearance and semantics across large viewpoint changes while hallucinating content never observed by the exocentric camera. Existing approaches either impose additional input requirements, such as a ground-truth initial egocentric frame or multiple synchronized exocentric views, or remain limited to category-specific settings. EgoX is the first to address cross-activity and in-the-wild generalization, but requires a human-provided caption of the non-existent egocentric view at inference and introduces a computationally expensive geometry-guided attention bias that can propagate reconstruction errors and suppress textual and visual context. We therefore propose Ego-Forge, a caption-free and bias-free framework for exo-to-egocentric generation. It introduces Dynamic Captioning, which derives conditioning tokens directly from the model's hidden states and adapts them to the diffusion timestep and network depth, replacing external text conditioning. By scaling training by an order of magnitude and using all available exocentric viewpoints, Ego-Forge learns cross-view correspondence implicitly and eliminates the need for geometry-guided attention, requiring only a lightweight depth prior. Ego-Forge achieves state-of-the-art performance on Ego-Exo4D, runs faster end-to-end, requires no external annotation at inference, and generalizes to in-the-wild scenes, including cases where over-reliance on geometry blocks appearance inference. Our model and source code will be made publicly available.

Sparse autoencoders (SAEs) are an important tool for mechanistic interpretability, but interpreting their many features remains challenging. Existing methods characterize input-side activation patterns and output-side intervention effects, yet often leave their functional connection implicit, while input-side evidence collection typically relies on costly large-corpus scans. We introduce functional interpretation, which characterizes an SAE feature as a mapping from its activating input semantics to its output effects under intervention, and present Dual-End Agentic Feature Interpretation (DAFI), an agent that actively gathers evidence and refines input-side, output-side, and functional interpretations through component-specific feedback. Its short-context token probing enables on-demand activation evidence collection without a full corpus scan. On GemmaScope, DAFI improves Input score by 13.1 percentage points over SAGE and Output score by 38.9 points over Token Change, while being substantially more token-efficient than a general-purpose coding agent. Skills distilled from successful refinements raise the held-out joint pass rate from 58.0% to 92.0% and improve both interpretation quality and efficiency when transferred to a new model-SAE setting. Across features with reliable endpoint interpretations, 70.7% exhibit non-equivalent input and output semantics. On AxBench, DAFI also improves steering-feature selection over output-score filtering. Code is available at https://github.com/THUAIS-Lab/DAFI.

LLM agents solve complex tasks by iteratively changing files, invoking local tools, and interacting with remote services, which modifies state across their local environment and remote services. Today, agents and users must manage these changes explicitly, whether reverting exploratory actions or recovering from erroneous ones. Doing so safely requires coordinated actions, yet current agent harnesses lack unified abstractions and mechanisms for managing local and remote state consistently and efficiently. We describe Planarian, an agent runtime with state management that enables agents and users to recover from erroneous actions and explore alternative executions over consistent local and remote environment state. Planarian introduces the abstraction of agent statepoints, which are consistent, restorable point-in-time versions of the environment state. Planarian exposes three state-management primitives to agents and users: (i) snapshot creates a new statepoint spanning local and remote state without requiring external services to support checkpoints: it relies on efficient incremental process and file system snapshotting to capture local sandboxed state, and transparently records compensating actions to undo remote state changes; (ii) rollback restores the environment to a previous statepoint by reverting to a prior local checkpoint and replaying compensating actions for remote state changes; and (iii) fork creates multiple isolated branches from a statepoint, enabling the agent to explore alternatives in parallel. We show that Planarian enables agents to undo mistakes and explore alternatives in parallel, improving task quality by up to 15x, and allows users to recover from erroneous actions with only 3% overhead.

We investigate the local stability of direct Mach configurations for the two-dimensional steady compressible Euler equations. Given a piecewise constant direct Mach configuration with subsonic flow behind both the reflected shock and the Mach stem, we prove that under a transversality condition on the shock polar loops and a suitable condition on the truncation segment, every sufficiently small perturbation of the incoming flow gives rise to a Mach configuration that is a small perturbation of the background one, in the sense that the reflected shock, the Mach stem and the slip line, together with the downstream subsonic flow, stay close to their background counterparts. The triple point is fixed at the origin, and the domain is truncated at a finite distance. Euler–Lagrange coordinates are employed to transform the unknown contact discontinuity curve (slip line) into a fixed boundary and to write the full Euler system as a first-order elliptic system for the flow direction and pressure coupled to transport equations for the Bernoulli and entropy quantities. The key idea in dealing with the contact discontinuity is to solve a mixed boundary value problem, in divergence form with discontinuous coefficients, for a single elliptic equation, so that continuity of the scalar unknown and its conormal flux allows reconstruction of the flow direction and pressure with the required contact discontinuity conditions.

Many temporal link predictors summarize past interactions through learned node representations. We examine whether simple counts of recurring interaction patterns can provide competitive predictions without learning these representations. We propose a temporal link predictor based on statistical language modelling. It pools transition and co-occurrence counts across sources to predict links that a source has never formed. We smooth sparse estimates using destination frequencies or Kneser-Ney continuation counts. A shared log-linear rule combines these estimates with popularity, source history, and recency, without node embeddings. In our main evaluation, the model achieves the highest MRR among the compared methods on 7 out of 16 datasets from TGB and TGB-Seq. It also outperforms EdgeBank and Base3 on all 16 datasets and the heuristic family on 14. These gains extend to datasets designed to limit repeated edges. With only 9–13 learned parameters, our model provides a simple and competitive baseline for evaluating future neural temporal link predictors.

We prove Keller's conjecture for every split finite-dimensional algebra over an arbitrary field.

Large language models (LLMs) typically generate text autoregressively (AR), predicting one token at a time. Block diffusion language models (dLLMs) instead generate blocks sequentially while denoising multiple tokens in parallel within each block, offering a promising way to accelerate generation. Rather than training such models from scratch, recent work adapts strong pretrained AR models into block dLLMs through distillation. On-policy distillation (OPD) has been widely used for LLM training because it supervises the student on states generated by its current policy, rather than only on fixed offline trajectories. By training on the states the student actually visits, it reduces the mismatch between training and generation and can provide more relevant supervision as the student evolves. Recent work has extended this idea to AR-to-block-diffusion conversion. However, this setting introduces a fundamental mismatch in supervision: the block-diffusion student and the causal AR teacher condition on different information at the same training state. The student predicts from the entire partially denoised block, including visible future context, whereas the standard AR teacher target is defined only from the causal prefix. As a result, the teacher distribution used for distillation is not fully aligned with the information available to the student. We therefore introduce d-OPD, a future-aware on-policy distillation method that corrects the AR teacher distribution to better align with the student-visible state by incorporating visible future information within each block, providing supervision that better matches the information used by the student. Across Qwen3 models from 0.6B to 8B, d-OPD improves the six-benchmark average by up to $4.0$ points over OPDLM and reduces training time by $1.35$-$1.58\times$. The code is available at https://github.com/mit-han-lab/d-OPD.

Hadwiger's conjecture (1943) states that every graph $G$ with chromatic number at least $t$ contains a $K_t$-model: a collection of $t$ vertex-disjoint connected subgraphs $T_1,\dots,T_t$ such that for all $1\le i<j\le t$ some vertex in $T_j$ has a neighbour in $T_i$. Replacing "some" in this definition by "every" gives rise to the significantly stronger notion of a dominating $K_t$-model introduced by Illingworth and Wood (2024). They raised the question whether every graph of chromatic number at least $t$ contains a dominating $K_t$-model. This statement is a significant strengthening of Hadwiger's conjecture and has come to be known as the dominating Hadwiger conjecture. We provide our own exposition of a disproof of this conjecture found by ChatGPT 6 Astra Ultra. The construction is the complement of a pseudorandom triangle-free graph that is obtained by randomly subsampling a block geometric graph based on the Suzuki-Tits ovoid.

Let $\Omega\subset\mathbb C$ be a bounded simply connected Lipschitz domain with conformal metric $g=\omega|dz|^2$, where $\omega\in C^2(\Omega)\cap L^\infty(\Omega)$ is positive in the interior and may tend to zero at the boundary. If the Gaussian curvature satisfies $K_g\leq K$, $K>0$, and $KM<4\pi$, where $M=\int_\Omega\omega\,dA$, then the Neumann eigenvalues, numbered by $0=\mu_1(\Omega;\omega)<\mu_2(\Omega;\omega)\leq\mu_3(\Omega;\omega)\leq\cdots$, satisfy $\frac{1}{\mu_2(\Omega;\omega)}+\frac{1}{\mu_3(\Omega;\omega)}\geq\frac{2}{\mu_2(D_K(M))}$. Here $D_K(M)$ is the geodesic disk of area $M$ in the surface of constant curvature $K$. We prove that equality holds exactly when the interiors are isometric. This completes Conjecture 1.2 of Langford–Laugesen; in particular, the model disk maximizes the first positive Neumann eigenvalue in this class.

This paper examines whether a cointegration-based pairs trading strategy between PepsiCo and The Coca-Cola Company is statistically robust and economically exploitable. We first test for cointegration and estimate the spread's mean-reversion dynamics over 2013-2018, then hold these statistical parameters fixed and optimise a threshold-based trading strategy in-sample over 2018-2023. Robustness is assessed through transaction-cost and parameter sensitivity tests, walk-forward validation, and Adjusted and Deflated Sharpe Ratios. The strategy is then evaluated out-of-sample from 2023 to the present, including an analysis of time-varying hedge ratios using rolling OLS and a Kalman filter. The results show that weakening mean-reversion dynamics in the spread undermine the effectiveness of the strategy out-of-sample.

The ongoing transition toward quantum-safe networking has motivated the development of hybrid network architectures integrating Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC). However, the experimental evaluation of hybrid QKD-PQC network architectures remains constrained by the high cost and limited accessibility of quantum hardware, as well as by the limited support for hybrid QKD-PQC networks in existing emulation platforms. Quditto is an open-source emulation platform originally designed for QKD networks that enables cost-effective and reproducible experimentation without requiring dedicated physical quantum infrastructure. Building on this foundation, this work presents Quditto as a hybrid QKD-PQC network emulation platform featuring automated and scalable cloud-native orchestration. The proposed platform introduces four principal contributions: a cloud-native orchestrator enabling fully automated infrastructure deployment across cloud and multi-cluster environments; an optimized provisioning workflow enabling large-scale quantum-safe network emulation; native integration of post-quantum nodes enabling unified emulation of hybrid QKD-PQC networks; and a secure key management module providing persistent and access-controlled storage of cryptographic material. Experimental validation demonstrates sublinear orchestration-time scaling with network size and successful end-to-end hybrid QKD-PQC key establishment on a representative spine-leaf deployment, thereby enabling the systematic evaluation of quantum-safe networking mechanisms in large-scale heterogeneous network environments.

Coding agents are increasingly deployed for iterative development on real repositories, yet existing evaluation barely answers a basic question: do coding agents reuse existing code or reinvent the wheel? The question matters: every duplicated implementation is a fix applied twice and agents produce code far faster than humans can audit, so redundancy accumulates unsupervised. Thus, we present RepoReuse, a multi-turn benchmark for auditing code reuse in real repositories, where requirements are revealed turn by turn and the workspace accumulates across turns. It is built by a fully automated pipeline combining AST-based dependency graphs, guided evidence collection, and execution-verified task synthesis, and scales readily to new repositories. Beyond pass rates, we measure the reuse rate together with recall and cross-turn structural redundancy. An audit over 3{,}000 turns shows that agents progressively stop exploring relevant repository code, reuse their own history less even when it is fully in the workspace, and leave duplicated logic in 50.8% of task chains by turn~5—all while pass rates barely move. Such deficiencies are invisible to pass rates, underscoring the need to evaluate code generation beyond functional correctness.

Supervised fine-tuning can teach language models undesired behaviours alongside desired ones. Inoculation prompting (IP) aims to limit unwanted generalisation by requesting the undesired behaviour during training and removing the request at inference. However, undesired behaviour can still appear under unrelated prompts. IP can also hinder learning of the desired behaviour. We address these limitations in settings where both behaviours co-occur in most training examples, so filtering out examples with undesired behaviour leaves only a small clean subset. We introduce stratified inoculation prompting (SIP). SIP leverages a small clean subset to demonstrate that desired behaviour should persist without the undesired one across different contexts. SIP oversamples these clean examples under diverse non-eliciting prompts while inoculating the rest. SIP substantially reduces expression of undesired behaviour while preserving more of the desired behaviour than IP. These gains persist even when we extend IP to oversample the same clean subset at the same rate as SIP. Moreover, SIP yields lower emergent misalignment rates in all harmful-advice setups we tested. SIP can be further extended to limit the undesired behaviour even under prompts that explicitly request it. We introduce backdoor dilution, which weakens expression under the inoculation prompt, and password-locked inoculation, which concentrates elicitation on a designated password. Taken together, our findings show that changing the training contexts for a small clean subset can significantly improve selective generalisation.

We study the uniform null-controllability, in the vanishing viscosity limit, of the transport–diffusion equation $u_t + M u_x = \varepsilon u_{xx}$ on $[0,L]$ with a Dirichlet boundary control at $x=0$. Our results concern the uniform null-controllability time $T_{\mathrm{unif}}$, defined as the infimum of the times for which the null-controllability cost remains bounded as $\varepsilon \to 0$. We determine this time exactly for both signs of the transport velocity: $T_{\mathrm{unif}} = 2 L / M$ in the positive-speed case $M>0$, and $T_{\mathrm{unif}} = (2 + 2 \sqrt{2}) L / |M|$ in the negative-speed case $M<0$. The positive-speed result disproves the conjecture $T_{\mathrm{unif}}=L/M$ suggested by Coron and Guerrero. For negative speed, the conjectured threshold had already been disproved by Lissy. Our result determines the exact threshold. We establish the lower bounds by constructing adjoint solutions that violate uniform observability below the respective thresholds. In the positive-speed case, the construction exploits the asymptotic structure of the Blaschke products and model spaces associated with the exponential family generated by the adjoint spectrum. The same model-space structure is used to reduce the upper-bound problems for both signs of $M$ to infinite-time observability inequalities, which are proved through a representation of the boundary-to-interior map and estimates of its Hilbert–Schmidt norm.

Virtual simulators are widely used for studying complex physical phenomena, from particle collisions to rocket propulsion. Such "computer experiments" can be highly time-intensive, and a Bayesian surrogate model can be used for efficient emulation with reliable uncertainty quantification. To train accurate surrogates with a limited sample size $n$, recent work has explored the incorporation of monotonicity (or isotonicity) information, which can often be elicited from physical systems. In practical applications with many input variables, however, existing Bayesian isotonic models can face statistical and computational limitations, which may result in worse performance compared to models that do not incorporate isotonicity. We propose a new transformed additive isotonic model (TAIM), which aims to tame this "curse-of-dimensionality". TAIM makes use of a flexible transformed additive isotonic modeling framework, which leverages a data-estimated link transformation and a monotone basis model with spike-and-slab priors on basis weights. Prediction-wise, TAIM achieves (up to log factors) a posterior contraction rate of $O(n^{-1/3})$ when the true black-box function is in a transformed additive isotonic form with mild smoothness conditions. Such a rate does not depend on the input dimension $d$ for terms involving $n$, which softens the effect of dimensionality on posterior predictions. Computation-wise, TAIM allows for efficient posterior inference via a carefully designed Gibbs sampler, where each sampling iteration requires only linear work in $d$. We further present an extension of TAIM that can model potential deviations from transformed additivity. Numerical experiments and two applications show the effectiveness of TAIM for isotonic surrogate modeling with many input variables.

We construct a Hausdorff saturated directed space whose directed path space between two distinct points has nontrivial fundamental group although the corresponding trace space is a square. A clock is a directed space with submetrizable underlying space; a timed space is a saturated directed space equipped with a regular directed map to a clock. Over every fixed clock, timed spaces form a locally presentable category, and their quotients from paths to traces are trivial Hurewicz fibrations with continuous sections. For Hausdorff saturated directed spaces whose compact subspaces are metrizable, these quotients are trivial q-fibrations. We construct a globular clock containing the directed circle and admitting regular maps from all q-cofibrant globular realizations, whereas a finite cellular example admits no regular map to the circle. Normalization also gives a proof of the quotient theorem for execution paths and establishes the homotopy lifting property for nondecreasing reparametrizations.

Fully homomorphic encryption (FHE) enables neural network inference directly on encrypted inputs, but it remains orders of magnitude slower than plaintext in- ference. Applying the server's plaintext weights to encrypted activations involves plaintext-ciphertext multiplications (PMult) and accounts for more than half of inference time in recent systems. Ternary quantization can replace these multipli- cations with additions and subtractions, but the savings rarely materialize under packed execution. A single PMult applies a weight group fixed by the packing layout and can be avoided only when all its weights share the same ternary value. Ternarizing all groups, however, largely degrades accuracy. We present FIONA, an offline optimizer that selectively ternarizes weights within a given packing layout based on the estimated effect of ternary conversion on the model's performance. FIONA encourages a shared ternary value within each weight group and retains full-precision weights for sensitive groups, so ternar- ized and full-precision paths coexist within a layer. It then compiles these hybrid operators exactly, applying common scaling factors once to accumulated inputs and reusing sums across outputs. Weight ternarization can also narrow the input ranges of downstream polynomials. FIONA fits lower-degree replacements under a cumulative accuracy budget, reducing multiplicative depth and bootstrapping. On VGG11, ViT, and BERT, FIONA reduces PMult operations by 53.4-79.5% and accelerates end-to-end encrypted inference by 2.38x, 1.68x, and 1.84x, re- spectively, with less than 1% accuracy loss across all three models.

Interference is commonly treated as geometric overlap between learned features. We introduce effective interference, which combines feature geometry and code statistics to capture realized interactions, distinguishing constructive from destructive interference and frequent weak interactions from rare strong ones. Under local fixed-support assumptions, we characterize how architectural constraints shape interference through four mechanisms: feature orthogonalization, bias compensation, gain adaptation, and encoder-decoder separation. Experiments with sparse autoencoders show that constrained architectures selectively reduce overlap among co-active features, while bias, gain, and encoder freedom allow constructive cross-contributions to remain. Together, these results show that interference in learned representations depends not only on feature geometry, but also on how features are used and on the architecture that produces their codes.

While Large Reasoning Models (LRMs) excel at complex reasoning, alignment through reinforcement learning often induces systemic overconfidence. In production environments, where logits may be unavailable, robust black-box uncertainty quantification (UQ) is essential for trustworthiness and safety. Focusing on question-answering for LRMs, we show that existing black-box methods, such as paraphrase-based self-consistency and confidence verbalization, offer little to no improvement over simple repeated sampling, suggesting that alignment suppresses useful output variability. We introduce prompt-level relaxation operators that broaden the model's effective output distribution by approximating the effect of an optimal policy obtained with a stronger KL-regularization parameter, hence closer to the reference model. Theoretically, we demonstrate that relaxation improves calibration. We propose Jailbreak for Uncertainty (J4U), a jailbreak-derived technique for UQ that empirically reproduces the behavioral signatures predicted by our relaxation theory. Across 3 datasets and 4 LRMs, including a closed-source production model, J4U's improvement over repeated sampling achieves statistical significance in up to 6 times more LRM-dataset-metric settings than the strongest black-box UQ state-of-the-art baseline we evaluate, with average ECE reductions up to 5 times larger. These results provide a practical tool for UQ in black-box LRM deployment.

The evaluation cost of transformers with softmax attention scales quadratically with sequence length. Kernel attention addresses this by replacing softmax with a more general kernel function. In this paper, we aim to identify kernels that retain the expressivity of attention while enabling quasi linear computation. To quantify expressivity, we introduce a capacity for each kernel, measuring the maximum sequence length for which the attention matrix can approximate the identity. A higher capacity thus indicates greater expressivity. We show that expressive kernels like softmax, Gauss, and Laplace have infinite capacity. In contrast, common quasi linear kernels, such as those derived from finite dimensional feature maps, exhibit finite capacity. As a solution, we propose additive kernels constructed from univariate spline and polynomial exponential kernels. We prove that these maintain infinite capacity while allowing quasi linear computation via sorting. Finally, we implement additive sorting kernels efficiently and benchmark them against modern softmax backends, demonstrating advantages for long sequences.

Estimating probability densities from a finite set of samples typically requires dataset-specific model fitting. We introduce PRODiGI, a pretrained data-to-program model that infers an explicit, executable generative program in a single forward pass. Pretrained on synthetic datasets paired with their ground-truth programs, PRODiGI accommodates diverse generative families and data dimensionalities through template prediction and non-autoregressive program parameter decoding. Its inferred programs support direct sampling, density and score evaluation, and inspection independently of the pretrained model. We further introduce program-space fine-tuning, which refines differentiable program parameters by matching generated and empirical samples while keeping model parameters intact. Experiments show that PRODiGI achieves lower average density and score MAE than existing pretrained models, while offering multi-fold speedups over its closest competitors. Program-space fine-tuning further reduces generation MMD by 84%. By turning empirical data into explicit, reusable programs, PRODiGI introduces a new direction for fast, interpretable tabular generative modeling.

Reinforcement learning can turn one language model into several specialists, each excellent at a single skill such as mathematics, coding or following instructions, but users need one model with all of these skills. Multi-teacher on-policy distillation (MOPD) merges them by letting the specialists teach one student: the student answers each prompt, and the specialist for that prompt's domain gives feedback on every token. This routing decides which specialist teaches, but not how strongly its feedback moves the shared student. In Qwen3.5 models at three sizes, we find that MOPD's student does not beat one taught by the best single specialist and gains little of the mathematics specialist's advantage. The feedback is unbalanced: instruction-following feedback is several times more spread out than mathematics feedback and dominates the student's updates. We propose Domain-Normalized MOPD (DN-MOPD), which keeps the routing and rescales each domain's feedback by its measured spread. On six public benchmarks, DN-MOPD improves the average score over MOPD at every size, across three random seeds and under two answer-length limits, and recovers most of the lost mathematics gain. Controls with fixed domain weights show that the gain comes mainly from turning down instruction-following feedback rather than turning up mathematics alone, and that fixed weights close to those DN-MOPD measures perform comparably. Combining specialists therefore requires deciding not only which one teaches, but also how strongly its feedback counts.