Papers

Sparse autoencoders (SAEs) are widely used to interpret language model activations, but SAE training and latent labelling are typically repeated for every model. Here, we show that a single shared SAE can replace a collection of dedicated per-model SAEs. Our method, SharedSAE, combines a shared dictionary with model-specific encoder-decoder pairs. Unlike the closest prior method, which discards activation magnitudes and requires all models at inference, SharedSAE instead normalizes only selection scores, preserving magnitudes, and uses model dropout for single-model inference. We train SharedSAE on four 1B-scale base language models spanning distinct families and tokenizers. Despite sharing its latents across models, SharedSAE retains 96.6% of dedicated SAEs' mean explained variance; its latent activations exhibit cross-model correlations 1.8 times as high as separate SAEs aligned post-hoc, and its latent descriptions transfer across models. After the dictionary is frozen, new models can be efficiently adapted to it, achieving near-dedicated-SAE reconstruction quality while reusing the shared latent descriptions.

A modular deep Recurrent Neural Network (RNN) is introduced to facilitate the process of deploying various architectures of RNNs, and to automatically compute derivatives for gradient-based learning methods. The modularity leads to a set of new architectures, one of which includes feedforward inter-layer connections. By adding feedforward inter-layer connections in a multi-layer RNN, it is observed that the capability of the RNN to learn and model high-order dynamics and nonlinearities is significantly improved. The problem of vanishing/exploding gradient in space for a multilayer RNN is also alleviated using feedforward connections. These results are demonstrated using a quadrotor case study, for which a model of the altitude dynamics is learned with our particular network structure, while existing methods are unable to generalize as quickly or at all.

In this paper, the problem of data-driven discovery of nonlinear ordinary differential equations (ODEs) is recast, and a new interpretable machine learning (ML) method is proposed. The proposed method aims to learn the unknown vector field of nonlinear dynamics without prior knowledge of the system's physics from only one single state trajectory's data. The proposed method has two fundamental differences with existing methods: 1) the formulation presented in this method is derived based on Functional Analysis and Operator Theory, and 2) the cost function is constructed in the function space as a distance between two functions as an integral, instead of the discrete-sum of errors used in existing ML approaches. An incremental learning algorithm is proposed to learn the unknown vector field to handle new training samples in an online manner. The proposed method can discover the unknown vector field from both forced and unforced autonomous and non-autonomous (or time-varying) dynamical systems. The proposed method is able to simultaneously discover unknown external forces as a function of time and unknown underlying dynamics. Finally, numerical examples are given to demonstrate the advantages of the proposed method.

We explore the use of simulated data for training a model for protein annotation in crowded cryo-electron tomography volumes reconstructed from images collected at limited tilt angles and severely corrupted by the measurement operator. Firstly, we leverage the corruptions imposed by the forward model to generate domain-specific augmented paired views of the exact same scene for an invariance objective integrated into the LeJEPA self-supervised training framework. Secondly, we use additional information from the simulation pipeline such as the positions and identity of proteins in the simulated volumes to inform the architecture of the model and the loss function, so that semantic information is localised at protein positions in the resulting dense feature volume. The resulting model, CARNIVAL, is evaluated without finetuning on classification and detection tasks in real tomograms, using a benchmark dataset containing multiple protein types and two tomogram processing types. We show that CARNIVAL outperforms a state-of-the-art model trained using a contrastive objective on simulated data but without forward model-based paired views or privileged information.

We present TNFlow, a transformer and normalizing flow architecture for inferring the surface composition of Trans-Neptunian Objects (TNOs) from their reflectance spectra. TNFlow is trained on synthetic spectra generated by the Shkuratov radiative transfer model to act as its inverse. TNFlow takes ${\sim}$0.7s to invert one spectrum on a single CPU core, returning a multimodal posterior over simplex-valid compositions and grain sizes. On synthetic spectra, the highest-weight mode achieves a mean total-variation distance of 0.149 from ground truth on the test split, and the model generalizes well to unseen combinations of known components. Qualitative tests on real JWST spectra show blindness or bias towards some materials. We suggest this could be attributed to either simulator fidelity or the training set.

Ensuring the security of the power system is essential for stability and reliability, especially in the event of disruption. Effective classification of contingency in power systems enables proactive decision-making and mitigates large-scale breakdowns and failures. This study explores the use of machine learning algorithms to classify security levels of contingencies in power systems into safe, moderate or severe classes. For this approach, Newton-Raphson load flow method extracts system data from contingency scenarios, using Overall Performance Index (OPI) as safety measure. For data pre-processing, Synthetic Minority Over-Sampling Technique (SMOTE) and Principal Component Analysis (PCA) is used to address class imbalance and reduce dimensionality, respectively. K-Nearest Neighbours (KNN), Random Forest (RF) and Support Vector Machines (SVM) is trained and evaluated on datasets generated through N-k contingency scenarios for k equal 1, 2, and 3 on IEEE-14 and IEEE-30 bus systems using four hybrid pre-processing configurations: normalized, SMOTE-balanced, PCA-transformed, and a combined SMOTE PCA-transformed. Performance is assessed by precision, recall and F1 score, with priority given to the severe contingency classes. The RF achieved the highest F1 scores of 0.97 in IEEE-30 and 0.86 in IEEE-14, SVM benefits significantly from PCA and improves the accuracy of the classification, while KNN is best suited for SMOTE and PCA conversion. The findings show that PCA contributes more than SMOTE to the overall performance of the model. However, SMOTE improves recall but can introduce false positives and is therefore a compromise of accuracy. This study highlights machine learning as a scalable and powerful alternative to traditional contingency analysis, which improves the assessment of security in real time.

Human mobility predictability concerns the best prediction performance attainable from a given target and input information, but its ground truth is not directly observable on real mobility data. We present BER-PEF, a Bayes-error-rate-based framework that converts BER estimation into mobility predictability estimation and provides a unified protocol for comparing estimators without observable ground truth. The framework maps symbolic sequences, numeric trajectories, contextual features, and learned representations into a common feature–label space, then evaluates estimator outputs along controlled perturbation curves against a shared predictability reference interval by measuring deviations below the interval, above the interval, and across the full interval. Experiments on Foursquare NYC and TKY, GeoLife, and T-Drive show that several BER-based estimators achieve lower reference discrepancy than existing predictability methods on symbolic sequences and numeric trajectories, while their estimates track changes in empirical prediction performance under perturbation. Additional analyses show that contextual inputs and multiple structured representations can be evaluated under the same protocol, and that aggregating evidence across multiple perturbation levels provides a more reliable basis for estimator selection than relying on a single unperturbed observation. BER-PEF therefore offers a unified and verifiable path for evaluating predictability estimators on heterogeneous mobility data when ground-truth predictability is unavailable.

Despite increasing reliance on LLMs that reason with external evidence supplied by tools, retrieval-augmented generation, other agents, and users, how LLMs integrate such evidence into decisions they have already begun to form remains largely unclear. We present a distributional theory in which evidence shifts the receiver's distribution of initial answers, driven by a receiver prior weight and a candidate evidence tilt, leading to three predictions. First, candidates more probable to the receiver are more persuasive. Second, receivers more readily integrate characteristic errors of their own than foreign errors from different sources. Third, identical evidence can improve weaker models and harm stronger ones. We confirm these over ten million trials, twelve LLMs from four families, and eight domains, four of them scientific discovery tasks in the physical and life sciences: quantum mechanics, physics, genetics, and molecular biology. The law also yields a receiver-relative reliability frontier: receiver-congruent errors depress performance more steeply than random errors of the same rate. LLMs also integrate candidates even after internally verifying their invalidity (93-100% with propositional constraints; up to 99.4% on held-out physical and life-sciences reasoning), demonstrating evidence integration is a receiver-specific control policy over existing distributions, determined by receiver properties rather than scalar trust in the evidence source. Causal interventions show candidate integration is implemented late in the network, as a structured sequence of steps admitting external candidate answers, promoting them, and transporting them into the answer state. Representations of verification are decodable but have little causal impact on answers. A J-lens decomposition shows the state underlying verbalized verification is fully dissociable from that underlying candidate integration.

Vision-language models (VLMs) are increasingly deployed in high-stakes settings, where a response that is reasonable in general may still be unsafe for a particular user whose medical, emotional, or situational context is unknown to the model. We study this problem of personalized safety in multimodal systems and introduce MPS-Bench, a benchmark of 5,181 scenarios from 584 real-world images across 12 high-risk domains, each paired with a hidden user profile. Evaluating eight frontier VLMs, we find that they almost always respond directly (86-99%) rather than seek missing context, and none exceeds 2.6/5 on personalized safety. To understand why these failures arise, we analyze multimodal interactions and identify visual dominance: visual information enters text representations early and suppresses textual risk signals during multimodal fusion. Causal interventions reveal a two-stage mechanism in which visual affect is first transferred into the text stream in early layers and then shapes the final decision through this altered text representation, making late-stage internal remediation unreliable. Motivated by this mechanism, we propose PRISM, a lightweight input monitor that uses bidirectional cross-modal modulation to predict when a query is likely to require deferral. PRISM achieves 0.978 AUC and strictly dominates the safety-utility Pareto frontier across all tested models.

Many recurring text functions are easy to describe but difficult to implement with rules, while calling a large remote model for every input introduces repeated cost, latency, and dependency on a provider. We present compile by training, which turns a natural-language specification into a reusable neural function. At compile time, teacher models generate task-specific examples that are used to train a small adapter for a compact interpreter. The resulting function runs without the teachers and can be stored, versioned, and composed like ordinary software. On FuzzyBench-Hard, a subset on which the Program-as-Weights fast compiler produced no exact matches, compile by training reaches 83.6% semantic accuracy. This higher accuracy comes with a higher compile-time cost: roughly a minute rather than seconds for the fast compiler. We deploy the compiler in a public interactive service and demonstrate compiled functions in a multi-site website helper, a language-controlled 3D avatar, and a bidirectional English-Claudish translator.

Language-model judges now gate training data, score generations, and drive leaderboards. The judge is then a measurement instrument, resting on one rarely stated assumption: the same request, sent to the same model name, reads the same tomorrow. We audited that assumption in two preregistered campaigns with every threshold fixed in advance; neither got past validating its instrument. Across 52,988 audited request attempts, same-window repeat rankings agreed at Spearman 0.400 against a required 0.90, and byte-identical next-day replays agreed at 0.78 against a required 0.99, each time with the execution record at ceiling. Three mechanisms explain the gap: a label-to-meaning mapping that biased readouts as strongly as the signal; candidate gaps seven orders of magnitude below the instrument's own noise floor; and byte-identical inputs returning different rankings, a noise that exact-permutation readouts compound. Neither metric substitution nor sampling repaired it on the tested grid. Preregistered follow-ups bound the problem: waiting did not help on the days sampled (0.805 versus 0.800, replicated over five further days); switching providers did not help (four providers share the floor, medians 0.74 to 0.88, predicted by none of the metadata fields they expose); self-hosting on batch-invariant kernels helped only while the server was quiet; and on constructed errors with known gaps, the readout's separation tracks error type, not size. We distill the evidence into a three-level snapshot-identity ladder, eight design rules, and a reporting checklist; a pilot at roughly 2% of the study's call volume would have exposed both unreachable gates in advance. All results concern externally measured behaviour on shared serving infrastructure. On a shared endpoint, a model name is not a frozen instrument; a preregistered evaluation must measure its instrument before freezing any gate on it.

Reasoning traces from chain-of-thought models appear to offer a legible window into how a model arrives at its answer. A growing body of work treats them as such, using LLM judges to diagnose errors, evaluate faithfulness, and provide step-level supervision via process reward models and generative critics. These practices rely on the text of a reasoning step carrying information about its functional role. But does the text actually encode information about which reasoning steps matter? We operationalize the importance of a reasoning step as its advantage: the change in expected reward, e.g., producing the correct final answer, from including that step, estimated via Monte Carlo rollouts. Basing ground truth on these estimates, we evaluate whether LLM judges can identify high-advantage steps and find that sufficiently capable LLMs can outperform a prevalence baseline but fall well short of a noise ceiling. Fine-tuning a model as a step-level critic yields strong improvement for incorrect responses but remains distant from ceiling for correct responses, suggesting that step importance is only partially recoverable from the text of the reasoning trace. Our findings contribute to a growing body of chain-of-thought faithfulness work that cautions against treating the legibility of reasoning traces as interpretability, especially with implications for process reward modeling.

We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage. Crucially, we introduce a Nash margin characterisation that enables principled reasoning about equilibrium existence: the framework either returns an $\varepsilon$-approximate NE whose social-welfare value is $\varepsilon$-close to optimal, or provides a sound certificate that no exact NE exists. Under a minimum reachability condition $p_{\mathrm{reach}}>0$ over relevant state-action pairs, the algorithm terminates after a polynomial number of trajectory samples, with sample complexity $\widetilde{O}\left( {R_{\max}^2 H^4 |S|^2 |A| / (p_{\mathrm{reach}} \varepsilon^2)} \right)$. Empirical results on benchmark CSGs demonstrate near-optimal performance, correct handling of equilibrium (non-)existence, and sample complexity consistent with theory.

As edge-based deep learning applications become more complex, optimizing performance on heterogeneous System-on-Chips (SoCs) presents unique challenges. Traditional pipelining techniques distributing the computation across different on-chip processing units, while effective for throughput, do not address the latency demands posed by modern neural networks with complex interdependencies and extensive operator parallelism. There is a potential in leveraging operator parallelism to enable concurrent execution across multiple processing units, thereby reducing inference latency. However, prioritizing pipelining or parallel execution often necessitates a compromise, where optimizing one performance metric adversely impacts the other. This paper introduces Para-Pipe, a hierarchical mapping framework that integrates intra- and inter-stage operator parallelism within a pipelined architecture. Para-Pipe navigates the trade-off between throughput and latency by selectively fine-tuning parallelism levels within and across pipeline stages. This strategy can significantly reduce inter-processor communication overhead, significantly improving energy efficiency. Our evaluation demonstrates that Para-Pipe generates multiple Pareto-optimal configurations, achieving a balance between throughput and latency on an Amlogic SoC equipped with ARM big.LITTLE CPUs and GPU, as well as the Black Sesame Technology SoC featuring a deep learning accelerator and two DSPs. More importantly, throughput-optimized configurations under Para-Pipe on Amlogic SoC show an average energy efficiency improvement of 11.0% over purely pipelined strategies and 23.3% relative to non-pipelined parallel execution.

Parameterised graph theory studies how the complexity of graph-theoretic problems depends on structural parameters of the input graph. This perspective has proved useful in analysing tensor-network simulation (Markov and Shi, 2008). Its implications for tensor-network representations and tomography are less well understood. In particular, which graph parameters determine whether a tensor-network state (TNS) admits a tractable matrix product state (MPS) or tree tensor network (TTN) representation, and which control the complexity of learning the state? We address these questions using parameterised graph theory. First, we show that cutwidth and tree-cutwidth bound the bond dimension overhead required to represent a TNS as an MPS or TTN. In the TTN case, tree-cutwidth also bounds the local dimension of the grouped subsystems. The proofs are based on entanglement rerouting, a tensor-network analogue of rerouting information in a classical network. Second, we derive graph-dependent upper bounds on the sample and computational complexity of realisable TNS tomography, with exponents that depend on cutwidth, tree-cutwidth, and a new graph parameter, learning complexity, which we bound in terms of degree and treewidth. We obtain these results by extending the disentangling MPS learner of (Cramer et al., 2010), as analysed further in (Bakshi et al., 2025; Lin et al., 2025), to TTNs and to tensor networks on arbitrary known graphs. Finally, we extend the framework beyond the realisable setting. For an arbitrary input state, our agnostic learner outputs a pure state whose fidelity is within additive error $\epsilon$ of the optimum over tensor-network states on the given graph with a given bond dimension, with explicit graph-dependent bounds on sample and computational complexity.

This paper presents a low-cost, open experimental platform for research in end-to-end autonomous driving with miniature Ackermann vehicles. The platform combines a physical vehicle, a printed urban track, data collection tools, trajectory registration, and a Webots digital twin, enabling controlled experiments that connect simulation-based autonomous-driving methods to real-world execution. As a first baseline, we implement command-conditioned behavior cloning, in which a neural policy receives an on-board camera image and a high-level navigation command and outputs steering and speed. The system is evaluated both on the physical vehicle and in simulation. In real closed-loop experiments, the learned policy follows lanes and executes commanded turns, reaching a mean cross-track error of 6.1 cm with respect to the reference route, close to the 4.7 cm observed in human demonstrations. In the digital twin, camera field of view has a strong effect on performance, reducing the mean cross-track error from 35.6 to 3.3 cm when widened from 58 to 120 degrees. Using the digital twin to generate synthetic driving data and a learned sim-to-real image translator to reduce the appearance gap, we further show that a higher-capacity policy trained on this synthetic data combined with real demonstrations is the only configuration that completes all four track routes in closed loop, whereas the compact baseline and the same network trained on real data alone complete fewer. These results establish the open platform as a practical testbed for sim-to-real studies and provide an initial command-conditioned imitation-learning baseline; we release it to support reproducible research.

Temporal integration gives continuous-time recurrent networks memory, but in deep stacks it also delays bottom-up signals and attenuates top-down errors. We develop Recursive Quadrature Filters (RQFs), biologically motivated complex-valued temporal filters that are a special case of diagonal state-space models (SSMs), and ask whether this failure mode can be addressed by making each layer's bottom-up input prospective. Starting from an energy model, we derive the RQF dynamics and show that each RQF is a band-pass filter whose learnable parameters control its tuning frequency and bandwidth. We then make each layer's bottom-up input prospective using a parameter-free two-tap update that leaves the recurrent transition and parallel scan unchanged. We extend this correction to general diagonal SSMs and show that it mitigates depth-dependent gradient attenuation when temporal gradients are truncated, i.e., spatial-only backpropagation. We evaluate the intervention in RQFs, S5, and ORGaNICs (a nonlinear gated RNN) trained using full backpropagation through time (BPTT) and spatial-only backpropagation. Under full BPTT, prospective variants match or outperform their non-prospective controls in every model and configuration. A non-residual width-32 six-layer RQF reaches 96.09% accuracy on raw-audio Speech Commands with 31.9k parameters; a width-64 six-layer RQF reaches 83.56% on the 16,384-step Path-X task. These results identify RQFs as a parameter-efficient recurrent substrate and prospective-input coding as an input-side correction for deep continuous-time recurrent networks.

We introduce an uncoupled learning algorithm which, when employed by all players of an arbitrary $N$-player normal form game with up to $K$ actions per player, guarantees $O(N^3\log^2 K)$ individual regret, uniformly over the horizon of play. The proposed algorithm - which we call higher-order optimism with discounting (HOOD) is a variant of optimistic follow-the-regularized-leader (OptFTRL) that combines a discounted $(N+1)$-th order predictor with entropic regularization over a suitable "lifting" of the game's strategy space. This combination of ingredients is purposefully designed to dampen large oscillations of the induced sequence of play in a controlled manner, removing in this way a key stumbling block of previous attempts to achieve constant regret in general games. Our approach bears several striking similarities to the concurrent - and completely independent - work of Liu, Farina, and Ozdaglar (arXiv:2608.31166), who very recently derived an $O(N^{21}\log^{4} K)$ regret bound through the use of higher-order optimism and an exponential moving average estimator.

Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a weighted-additive combination or a teacher-modulated rescaling of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@$k$ behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere. To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.

Blackwell's 4-bit floating-point (FP4) tensor cores do not automatically make attention faster because softmax conversion and on-chip dependencies dominate once its matrix products shrink. We address this with Direct-P for noncausal inference and a causal path that passes the forward quantization directly into backward. Direct-P maps scores directly to FP4 probabilities and reaches up to 2.13$\times$ the bfloat16 (BF16) forward throughput on an NVIDIA GB200. The causal path reconstructs probabilities from saved quantized queries and keys and uses 8-bit floating-point (FP8) gradient operands, accelerating a complete single-GPU 8-billion-parameter update by up to 1.14$\times$. Matched distributed training retains FP8 probabilities and values; every tested MXFP4 probability/value training trajectory diverges.

Reinforcement Learning from Verifiable Rewards works well when a task has a programmatic checker, but most long-horizon agent domains have none. We work in the outcome-blind setting, where ground-truth success signals are not available. Multi-criteria rubrics are a popular way to supply such a reward; they are scored once per trajectory, but a single scalar is a poor signal across tens of steps. We propose DRACO: Distributing Rubric-based Advantage for Credit Optimization. It generates rubrics dynamically during training to track the policy's evolving capability, scores those rubrics once per completed trajectory, and redistributes that judgment over the steps responsible for annotated rubrics to produce differentiated per-step advantages in GRPO. The redistribution is closed-form and does not introduce any trained attribution module. On AppWorld, DRACO gains 15.9 points over the base model and 5.3 points over GRPO trained with a sparse ground-truth reward, despite not using any verifiers itself. On out-of-domain Tau-Bench, it gains 5.3 points over the base model even without a frontier judge, beating both ground-truth-reward training and other rubric-based training settings. The code for DRACO is available at https://github.com/IBM/draco.

Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define approximate loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.

Reinforcement learning from human feedback (RLHF) has emerged as a powerful yet sample-inefficient approach for learning reward models from human preferences, making active learning a critical component in synthesizing informative preference queries. However, effective uncertainty quantification required for active learning remains a key challenge for large neural network reward models. In this paper, we introduce PreferenceEKF, a sample-efficient approach that tracks reward model uncertainty by framing active preference learning as a sequential Bayesian filtering problem. Instead of relying on computationally prohibitive posterior inference over the full neural network parameter space, our method performs sequential inference via an extended Kalman filter within a low-dimensional parameter subspace, continuously updating the reward model posterior as new preference queries arrive. Our approach enables scalable sampling of neural network parameters to efficiently compute acquisition functions for active reward learning. Experiments on the D4RL and V-D4RL benchmarks demonstrate that our approach achieves better sample efficiency, runtime, scalability, and calibration compared to other Bayesian deep learning approaches, and the learned reward models lead to competitive offline reinforcement learning policy performance. This highlights the potential of scalable Bayesian methods for preference-based reward modeling in RLHF. Our code is available at https://github.com/yutaizhou/bnn_pref.

What can a single layer of self-attention compute? We study head complexity: the minimum number of attention heads required to compute a function in a one-layer attention-only model. We establish an exact hierarchy under this measure: $k$ heads compute $k$-bit parity but cannot compute $(k+1)$-bit parity. The lower bound is unconditional in the two resources a transformer might otherwise exploit; it holds at unbounded embedding dimension and unbounded numerical precision. The proof rests on an alternating-sum obstruction: after clearing the softmax denominators, every monomial in the resulting decision polynomial omits at least one of the $k+1$ input bits, forcing its correlation with parity to vanish. The same obstruction yields lower bounds for related tasks, including the well-studied multi-hop induction-head task. We also establish compactness bounds for embedding dimension and numerical precision. Specifically, a compactness theorem shows that any function computable at all can be computed with embedding dimension and precision bounded by the discrete data of the task, namely, head count, alphabet size, and length. Thus, potentially unbounded dimension or precision provably cannot substitute for heads. Finally, we derive nearly matching universal bounds for general binary functions: $2^n$ heads suffice to compute every $n$-bit binary function, with one head per monomial in its multilinear expansion, while a counting argument shows almost all such functions require $\Omega(2^n/n^2)$ heads. This lower bound matches the upper bound to within a $\operatorname{poly}(n)$ factor, even when dimension and precision are unbounded. Together, these results characterize head requirements for Boolean computation in this model.

The geometric morphology of deposited filaments can significantly influence the structural performance and stability of 3D concrete-printed (3DCP) structures. However, most finite element (FEM)-based approaches for buildability assessment represent printed layers as simplified rectangles, potentially limiting predictive accuracy. This study proposes a geometry-informed modelling framework that integrates the deep-learning-based filament shape prediction tool ShapeGen3DCP with a layer-activation FEM approach to investigate the effect of realistic filament geometries on buildability. The framework generates geometry-aware numerical models directly from material and process parameters, eliminating the need for experimental filament characterization or computationally intensive fluid-flow simulations. Validation against experimental data and a parametric study of rectilinear walls demonstrate that extrusion parameters and the resulting filament geometry can significantly influence buildability predictions. Realistic filament representations are particularly important for free-flow deposition, whereas layer-pressing strategies are less sensitive to geometric simplifications. Among the investigated representations, an elliptical approximation provides an effective balance between geometric fidelity and modelling simplicity. When rectangular representations are preferred to enable regular computational meshes for faster simulations, defining their dimensions based on volume conservation improves prediction reliability compared with calibrating them using either the maximum filament width or the interlayer contact width. Overall, the proposed methodology demonstrates the importance of incorporating filament geometry into 3DCP simulations and provides practical guidance for selecting efficient and accurate geometric representations for buildability assessment.

Evaluating large language models (LLMs) in safety-critical, physics-governed environments requires more than accuracy-based metrics, because predictions that are numerically close to the ground truth can still violate operational constraints, combine fields in physically inconsistent ways, or fail to produce usable structured outputs. Existing evaluation protocols do not measure these failure modes reliably. We propose FLY-EVAL++, an evidence-driven evaluation protocol that combines deterministic verification of protocol compliance, physical feasibility, and safety constraints with fixed rubric-guided aggregation into interpretable multi-dimensional scores. We instantiate FLY-EVAL++ for Flight Trajectory and Attitude Prediction (FTAP) by extending the PilotBench setting with history-conditioned and multi-step prediction tasks. Across 66 LLMs, safety compliance is the most discriminative dimension of model behavior: models with comparable predictive performance differ by more than 28 points in safety score, and we observe recurrent failures including safety violations under physically plausible predictions and instability in multi-step rollouts. These results show that evaluation in safety-critical domains should measure constraint satisfaction and structured validity explicitly rather than rely on accuracy-centric reporting alone.

Quantile treatment effects (QTEs) measure the effect of a treatment on the distribution of an outcome, and their estimation at extreme quantile levels is of central interest in applications where the target quantiles lie far beyond the range of the data. For heavy-tailed potential outcomes, existing extremal QTE estimators rely on extrapolation combined with a causal extreme value index (EVI) estimator, but the resulting estimator is not invariant under a common location shift of the potential outcome distributions, even though the population QTE is. We address this issue in two steps. First, we adapt the location-invariant Fraga estimator of the EVI to the causal setting using inverse propensity score weighting. Second, we replace the original extrapolation formula with a difference-based scheme, under which the location parameter cancels when quantile differences are taken. The resulting QTE estimator is therefore location invariant. We establish the consistency and asymptotic normality of the proposed extremal QTE estimators, and provide a consistent variance estimator, leading to asymptotically valid inference. A simulation study confirms the location invariance, the stability with respect to the threshold, and the coverage of the proposed methods.

Early screening of chronic kidney disease (CKD) is critical for timely intervention, yet most machine learning (ML) and deep learning (DL) approaches require labeled data and model training, limiting their use in real-world screening settings. This study evaluates the effectiveness of large language models (LLMs) for CKD screening under zero-shot and few-shot in-context learning settings and compares them with traditional ML and DL methods. We propose a framework that uses clinically selected tabular features and structured prompt templates to enable LLM-based inference without task-specific training. LLM performance is evaluated across multiple prompt styles, feature configurations, and data settings, and compared with standard ML, DL, and tabular foundation model (TFM) baselines, and existing CKD screening tools. The results show that LLMs can achieve competitive performance using only a small number of examples, often matching or outperforming traditional approaches in low-data settings. However, their performance remains model-dependent and less stable as input complexity increases. In contrast, ML, DL, and TFM models show more consistent improvement with larger training data. Overall, the findings highlight a trade-off between data efficiency and stability, suggesting that LLMs may serve as a flexible complementary approach for CKD screening when labeled data are limited. To facilitate further research and reproducibility, the code has been made publicly available at https://github.com/akabircs/LLM4CKD

Transport models underpin the design and optimisation of chemical processes, yet their constitutive laws are typically hand-picked, their experimental initial conditions are assumed exact, and their computational cost restricts optimisation to a handful of process variables. Here we introduce a differentiable hybrid modelling framework that embeds neural networks within a GPU-accelerated population balance equation solver to discover constitutive laws and assimilate initial conditions directly from experimental crystallisation data. Using thirteen real experiments with multi-dimensional size and shape measurements, we show that treating measured initial conditions as exact yields a physically inconsistent rate law despite improved predictive accuracy, whereas assimilating them recovers a physically consistent, non-linear law and reduces trajectory error sevenfold relative to conventional modelling. End-to-end differentiability further enables gradient-based optimisation of high-dimensional operating profiles, identifying a 300-variable temperature profile that reduces crystal aspect ratio by 25% at constant mass, facilitating superior product attributes. Our framework augments, rather than replaces, mechanistic modelling, offering a general route to learning transport models from data and optimising processes with them.

Large Language Models (LLMs) owe much of their success to next-token prediction (NTP), but their autoregressive (AR) structure requires slow, sequential token generation. To overcome this bottleneck, we introduce diffusion-augmented LLMs, a new class of models that defines an AR model distribution while using diffusion to draw multiple tokens in parallel from that distribution. We decouple the parameters of these models into two sets: AR weights, trained using the standard NTP objective, and lightweight diffusion weights, trained to generate multiple tokens simultaneously. The diffusion weights are learned through a simple Diffusion Distillation phase that adds negligible overhead to existing LLM training pipelines. We also introduce $\Psi$-Spec, a family of samplers that enables lossless acceleration and inference-time scaling at a fixed context length. Unlike speculative decoding, our method requires no separate draft model. Unlike diffusion LLMs (d-LLMs), it accelerates generation without sacrificing the quality of the underlying AR model. The resulting models, called Uno, can be trained from scratch or built by augmenting existing open-weight AR LLMs. Uno achieves higher throughput than leading speculative-decoding methods at every evaluated batch size and delivers up to $3\times$ speedups over the base AR model, including at the largest batch size supported by the device. Notably, our 8B Uno model outperforms the leading open d-LLM, the 26B DiffusionGemma, and the proprietary Mercury 2 across all evaluated benchmarks in agentic tool use, coding, and long-context reasoning. We release code and checkpoints at: https://s-sahoo.github.io/uno/