Papers

We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tensor networks (FCTNs) with nuclear-norm-regularized bond corrections. Each bond matrix is parameterized as a baseline all-ones matrix plus a low-rank correction $C_{ij} = U_{ij}V_{ij}^\top$, and the nuclear norm of the correction implemented via the variational Frobenius norm penalty on the factors drives unnecessary bonds to zero. We prove that under faithfulness, positivity, and a no-implicit-rerouting assumption on the local tensor architecture, every optimal FCTN with zero reconstruction error $\varepsilon = 0$ has effective graph exactly equal to the moral graph. For the approximate regime ($\varepsilon > 0$), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter $\beta$. The effective graph is read directly from the optimized bond matrices.

Sensor-based AI systems are rarely operated under the conditions under which they were trained: devices, personnel and recording epochs change, and each change degrades performance in ways a random train-test split cannot reveal. We propose a staged, accountable evaluation protocol that treats the evaluation of a deployed model as a measurement with declared reference levels and a quantified uncertainty. Four cumulative generalisation stages hold out devices, subjects and time. Each stage is judged on quantiles of repeated trainings against chance references with the correct class count, an out-of-present-scope rate exposes silent misdirection towards classes that are no longer present in deployment relative to training, and an explicit decision rule ties roll-out decisions not to means but to 5% quantiles. We demonstrate the protocol on infrastructure-free geomagnetic localisation with smartphone-based recurrent classifiers in two real underground mines, including a replication of the scheme's training stages at the second site. Unchanged models are re-evaluated on data recorded 34 months after the training campaign, on a device generation unknown at training time and with a held-out surveyor. The 5% quantile of their present-conditioned precision there is 0.39 over 299 repeated trainings, 16.5 times the chance level; across the composition of the 42 reachable location classes the figure varies by +/-0.08, several times the spread between repeated runs. Repeated trainings of a single configuration show why means mislead: a bimodal configuration passes a mean-based test decisively while its 5% quantile lies more than an order of magnitude below chance.

Graph-data workloads such as diffusion estimation, ranking, semi-supervised learning, and network optimization often solve many Laplacian or symmetric diagonally dominant M-matrix (SDDM) systems with the same coefficient matrix. Approximate Cholesky preconditioners eliminate vertices one at a time and store the resulting sparse approximate factorization, the factor, whose construction cost is amortized across these solves. But eliminating a vertex, the pivot, creates a dense Schur-complement clique among its $d$ active neighbors. We introduce CAST (Canonical Approximate Schur Tree), which replaces this clique with a weighted random spanning tree sampled directly from it. Every realization is connected and contains exactly d-1 edges, while reweighting each selected edge by the reciprocal of its tree-inclusion probability makes the update unbiased. The distribution is independent of the ordering of the pivot neighbors, and we prove that its leverage-score marginals minimize the largest normalized reweighted-edge contribution among unbiased inverse-marginal one-tree estimators. We also introduce CAST-$\rho$, which replaces each pivot neighbor with $\rho$ copies, each carrying a $1/\rho$ share of that neighbor's incident weight, samples a weighted random spanning tree on the expanded clique, and contracts the copies back to the original neighborhood. The resulting update remains unbiased and connected, can be sampled exactly in $O(\rho d)$ time, and satisfies a $1/\rho$ bound on the second moment of the normalized local Schur error. Increasing $\rho$ therefore reduces certified local sampling variability, but may increase construction cost and downstream fill. Empirically, we observe that CAST-1 is the faster default, whereas CAST-2 is preferable when its additional edge contributions remain inexpensive.

Field-programmable gate arrays (FPGAs) enable efficient neural-network inference, but most deployment flows either accelerate multiply-accumulate operations or convert pretrained quantized models into lookup tables (LUTs). We present DiffLUT-Net, an FPGA-native network connected by six-input LUTs that are trained from scratch. We jointly learn the 64 truth-table entries of a LUT and the source to each of its six input ports using a differentiable LUT function relaxation and hardware source selection. After training, the truth tables and connections are discretized, unused logic can be pruned, and the network is exported directly as synthesizable Verilog. Across five benchmarks, DiffLUT-Net achieves favorable accuracy-resource trade-offs. These results demonstrate the effectiveness of jointly learning LUT functions and sparse connectivity for compact FPGA-native inference. The code is available at https://github.com/TUDa-HWAI/DiffLUT-Network.

A verifier for robot policies reads a candidate behavior and returns a score for how well it did, used both to evaluate vision-language-action policies and to train them. Verifiers range from success detectors and reward models to runtime monitors, safety filters, and temporal-logic specifications. We survey roughly 150 verifiers and compare them along two properties. Availability is how much a verdict costs, how early in a rollout the verdict arrives, and how often a verdict can be asked for. Availability rises as verdicts get cheaper, earlier, and denser. Credibility is how much a high score tells us about the task. Credibility falls as the judgment becomes gameable and self-serving. We group the verifiers by who supplies the judgment: human verifiers, rule-based and formal verifiers, learned and pretrained verifiers, and model-intrinsic verifiers. Across the four families, we find that credibility falls as availability rises. Regardless of who supplies the judgment, there is no free checker. We then examine what validates a verifier itself, and how much a high score tells us. Three measures appear in the literature: agreement with human labels, the performance of the policy it trains, and behavior under reward hacking. We close with nine metrics that make a verifier claim checkable, and coordinates for the verifiers still to be built.

Local heatwave hazard depends on fine-scale air temperature, but ground stations are sparse and reanalysis products such as ERA5 cannot resolve the terrain and land-surface contrasts that shape real heat exposure. We present a conditional diffusion emulator for high-resolution 2-m temperature downscaling, conditioned on static geography, a training climatology, exact-time ERA5 temperature, and solar and temporal features, guided at inference by score-based data assimilation (SDA): a differentiable Gaussian observation likelihood steers the diffusion score toward sparse revealed temperature observations without any retraining. On a controlled 32-case synthetic-grid protocol over AORC, guidance improves hidden-cell reconstruction over both ERA5 and a strong observation-proximal nearest-neighbor baseline once observation density reaches 1% (RMSE 0.318 vs.\ 0.431~K, winning all 32 cases), while sparser regimes still favor direct interpolation. We further map the full guidance-strength landscape across three observation densities, showing that the optimal strength shifts systematically with density and that over-guiding causes sharp, predictable degradation – giving a concrete operating recipe rather than a single untuned setting. The resulting fields are intended as a temperature layer for downstream heatwave-hazard products such as threshold exceedance and cumulative heat-burden. The present evidence is a controlled synthetic-grid validation; station-network and held-out-year evaluations are the next steps toward deployment.

Exploration drill targeting in structurally complex terranes is hindered by sparse sampling, heterogeneous datasets, and the ambiguity of geophysical inversions. Here, we present an uncertainty-aware 3D workflow for the acceleration of time-to-discovery in brownfield explorations and apply it to the Kogodai prospect in the Rudny Altai metallogenic province. We jointly analyse existing drilling and geophysical data in a comprehensive approach, revealing hidden patterns in already available data. Drillholes and trenches were desurveyed to a common 3D reference frame, and assays were composited to a consistent spatial support to facilitate joint modelling with geophysical inputs. We develop Bayesian deep-learning models to predict 3D fields of Cu grade together with chargeability and apparent resistivity while quantifying epistemic uncertainty via Monte Carlo sampling. The original contribution of this work is to treat the problem not as pointwise regression between co-located observations, but as joint learning of spatially continuous 3D fields from sparse, heterogeneous exploration evidence. The resulting 3D predictions delineate a principal mineralized trend and several localized candidate zones that coincide with elevated induced polarization (IP) responses, while uncertainty mapping highlights where predictions are robust versus where additional drilling would be most informative. The continuous Cu-grade field can also be thresholded to produce binary prospectivity maps, allowing the sensitivity of target delineation to the chosen cutoff to be evaluated. The outputs are intended for qualitative interpretation and risk-aware drill targeting rather than resource estimation, and we discuss key limitations arising from incomplete provenance metadata for geophysical products and heterogeneity of historical sampling.

Repeated-sampling evaluations increasingly extrapolate pass@k far beyond the number n of samples collected per problem. We show that, in the pooled/random-task conditional-Binomial model, fixed-n success counts identify only the n free moments of the latent per-task success distribution. Consequently, direct pass@k is identified for k <= n, but generic extrapolated pass@k, tail exponents, and tail constants are not identified for k > n, even with arbitrarily many exchangeable tasks at the same rollout budget. This is stronger than the observation that the usual estimator is undefined beyond n: it characterizes the information missing from the fixed-depth count-law experiment. We give exact count-law-preserving constructions with incompatible extrapolations, state the exceptional unique-extension case, and compute sharp population identified intervals through Hausdorff principal representations. On the public 10,000-rollout-per-problem release of Brown et al., counterfactual n = 16 evaluations leave failure at k = 1000 ambiguous by factors from 1.5 to over 2,600 across four MATH/GSM8K/CodeContests configurations. The calibration shows that intermediate-scale failure share alone does not determine width. Our result does not reject parametric inference-time scaling laws; it supplies the nonparametric baseline against which their assumptions can be evaluated. We give an exact, conservative one-coordinate finite-task confidence certificate and a reporting standard separating direct estimates, identified sets, and model-conditioned forecasts.

The edge-of-chaos condition preserves first-order input perturbations in wide randomly initialized networks, but physics-informed losses, score matching and derivative regularization depend on higher input derivatives. For smooth scalar-input fully connected networks, using a joint Gaussianity of the finite derivative jet that holds in the infinite-width limit at each fixed depth, we derive mean-field recursions through third order that are exact at the variance fixed point, with finite-depth corrections that decay geometrically. At criticality, the first-derivative variance is depth-invariant, whereas the second-derivative variance grows linearly whenever the activation has nonzero curvature. The resulting third-order system closes on mean-field susceptibilities. For residual networks with branch scale L^{-1/2}, we prove that every fixed finite derivative order has uniformly bounded variance under explicit regularity assumptions. Simulations verify the critical growth laws, the residual bound, and the closed recursion. The results concern initialization, not trained-network performance.

Retrieval-augmented generation (RAG) grounds a language model in retrieved documents, which reduces hallucination but creates a new attack surface: if retrieved text is tampered with, the model may repeat the falsehood. We study how much a small quantized model, Llama 3.1 8B, degrades when a fraction of its retrieved context is poisoned. Three corruption strategies are tested, entity swap, number swap, and negation, each applied to zero, one, two, or three of the three retrieved passages, over a factorial sweep of 588 runs on a fact-checking task built from FEVER. Accuracy falls from 77.9% on clean context to 43.5% when all three passages are corrupted. Entity swap flips the largest share of answers that were correct on clean context. Number-based corruption stays flat while poisoned passages are a minority and jumps once they form a majority, a pattern we re-check with query-level bootstrap intervals. The model rarely invents new falsehoods; its dominant reaction is to abstain, and a lexical overlap proxy of unsupported generation falls under attack rather than rising. The study is a small-scale measurement with coarse automated labels; we treat the strategy contrasts as suggestive until decoding is controlled and stronger adjudication is in place.

Large Language Models (LLMs) often generate natural-language comments while writing code, and these comments become part of the context used to generate the code that follows. However, it remains unclear which properties of comments affect code-generation performance. We study this question through observational analyses and controlled interventions. On LiveCodeBench, neither comment frequency nor broad comment intent reliably predicts pass@1. We then prefill weaker recipient models with comment blocks written by stronger source models, allowing us to separate comment surface form from the solution content they convey. Comments from source solutions that pass the tests raise recipient pass@1 by 17.2% on average. In contrast, comments describing failed solutions provide no reliable gain, while comments written for a different problem reduce pass@1 by 20.8%. Finally, across a wide range of models and prompt variants, most recipient models show no significant recovery of the external-comment gain, and the best case recovers only 24%. These results show that comments help code generation not merely because they are comments, but because they can provide correct solution content that prompting cannot reliably elicit.

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling model capacity while preserving efficient inference in large foundation models. However, most MoE models use a fixed top-$k$ expert selection policy, assigning the same expert budget to every token even when fewer experts may be sufficient. Inference-time dynamic top-$k$ routing can reduce computation without retraining, but existing methods often overlook the distributional shift caused by deviating from the training-time routing configuration. We show that reducing the number of activated experts consistently increases the RMS scale and variance of SMoE outputs, inducing a representation mismatch that contributes to downstream performance degradation in addition to the loss of expert capacity. To address this correctable component, we propose Layer-wise Distribution Alignment (LDA), a lightweight inference-time correction that uses layer-wise calibration statistics to align reduced-routing representations with the default configuration. Across multiple SMoE LLMs, benchmarks, and routing strategies, LDA recovers much of the performance lost induced by the distributional shift under reduced routing while preserving sparse-inference efficiency with negligible overhead.

Ultra-low-bit language models promise reductions in storage and memory traffic, but a nominal "1.58-bit" label does not specify the deployed representation or its execution cost. We study a scale-up of an aggressive post-training conversion pipeline from Qwen3-4B to Qwen3-8B. The conversion uses KOTMS rotation, E2M-ATQ adaptive ternarisation, and GPTQ-style error compensation in a weight-only A16 configuration. We do not claim these algorithms as new. Our contribution is the end-to-end scale-up characterisation: an external reproduction gate, matched 4B/8B capability analysis, cross-corpus perplexity, effective-bit accounting, lossless lattice-aware packing, and direct packed execution. The 8B model reaches a three-corpus perplexity ratio of 1.361x, with WikiText-2, C4, and PTB ratios of 1.318x, 1.393x, and 1.371x. On eight zero-shot tasks at n = 500, mean accuracy is 64.6% versus 72.4% for FP16, corresponding to 78.5% chance-corrected retention and a 7.8-point absolute cost. The matched 4B run retains 69.6%, yielding an 8.9-point 8B advantage. The packed checkpoint is 8.24 GiB and preserves the recorded perplexity to measurement precision. Direct packed execution reaches 15.52 tokens/s in 7.35 GiB, while a preliminary packed GEMV remains slower than FP16 cuBLAS. The result is a validated scale-up baseline: model size improves robustness to aggressive post-training discretisation, actual serialisation is solved for the measured artefact, and direct execution is feasible, while broader seeds, calibration distributions, and kernel optimisation remain open.

Rajam$\unicode{228}$ki and Koivunen asked whether minimum-redundancy symmetric Kl$\unicode{248}$ve-Mossige arrays with contiguous sum co-arrays are always Kl$\unicode{248}$ve arrays. We give a computer-assisted proof that, at every fixed sensor count, every maximizing sensor set belongs to the Kl$\unicode{248}$ve class. The argument classifies the overlaps between a generator and its shifted reflection, then bounds the aperture of a hypothetical optimizer outside the Kl$\unicode{248}$ve class. Comparing these bounds with a classical Kl$\unicode{248}$ve construction settles all sensor counts at least 330. An exact integer certificate covers the remaining counts from 2 through 329 and matches every equality case to a Kl$\unicode{248}$ve array as a complete set. Consequently, optimization within the full symmetric Kl$\unicode{248}$ve-Mossige class reduces to the previously known search over Kl$\unicode{248}$ve parameters. The theorem concerns this specified class, rather than unrestricted sparse arrays or all restricted additive bases.

We consider the stability problem of fork-join systems with redundancy (FJR) and heterogeneous servers under both static and dynamic capacity-allocation policies. In an $(n,k)$ FJR system, each arriving job is split into $n$ independent tasks, with one task assigned to each of $n$ parallel servers. Once $k \le n$ tasks have been processed, they are joined and the corresponding job departs the system; the remaining $n-k$ unprocessed tasks are then removed and are therefore termed redundant. We first identify the nominal traffic intensity and characterize the maximal stability region, defined as the set of traffic intensities for which there exists an admissible policy that stabilizes the system. We then establish conditions under which this maximal stability region is attained for two classes of policies: static and dynamic. Specifically, we show that for static allocation policies, in which service capacities remain fixed over time, maximality is achieved whenever the fastest server is allocated no more than $1/k$ of the total service capacity. For dynamic allocation policies, in which a fixed total service capacity may be repeatedly reallocated among the servers, we show that maximality is achieved whenever the cumulative capacity allocated to the $j$ shortest queues does not exceed $j/k$ of the total capacity for every $j=1,\ldots,k-1$. Our analysis is based on a projection of the $(n,k)$ FJR system onto a simpler $(k,k)$ system that has no redundancy, together with a novel sample-path comparison argument for multidimensional processes based on the generalized Schur-convex order.

We study the problem of navigating cluttered indoor environments with a humanoid robot. Unlike conventional methods that model navigation as a 2D path planning problem, humanoid traversal in cluttered environments requires continuous geometry-aware whole-body adaptation, including coordinated arm placement, torso adjustment, and gait modulation for collision-free movement through complex 3D spaces. We introduce TANGO, the first whole-body vision-language navigation framework for language-conditioned humanoid traversal in cluttered environments. Given a natural-language instruction and egocentric RGB observations, TANGO directly predicts 29-DoF joint-space actions for downstream whole-body control. We train TANGO entirely in simulation by synthesizing diverse collision-free traversal behaviors via global path planning, kinematic whole-body motion generation, obstacle-aware motion editing, and RL-based tracking. This pipeline provides dynamically feasible action supervision for learning language-conditioned whole-body policies. In extensive simulation experiments, TANGO demonstrates state-of-the-art performance in vision-language navigation, while outperforming strong modular baselines in navigating challenging scenes requiring obstacle negotiation. Lastly, we deploy TANGO zero-shot on a Unitree G1 humanoid robot, and observe robust language-guided traversal in cluttered real-world scenes without training on any real-world navigation data.

Recurrent models provide a natural path to long-context modeling, yet models trained with backpropagation through time (BPTT) often fail beyond their training horizon. Classical analyses emphasize gradients that vanish or explode along temporal paths. However, dense per-token losses can still train a shared recurrent rule despite severe decay, showing that decay alone does not determine whether learning fails. We instead study state credit: the signal through which future losses reach earlier recurrent states before contributing to parameter updates. Accordingly, we intervene directly on state credit and propose Credit Stabilization through Time (CST). During backward propagation, CST locally rescales the state-credit signal to stabilize its norm without rotating the component being corrected, while leaving the forward computation unchanged. Because controlled synthetic tasks and real data exhibit different credit dynamics, we specialize CST to each regime. In both settings, CST improves performance beyond the training horizon, with gains observed at up to 128x the training length.

Accurate citations are the foundation of academic writing, tracing intellectual origins and substantiating core claims. However, manually navigating the growing volume of scientific literature is increasingly difficult, prompting reliance on automatic citation recommendation. While modern retrieval-augmented architectures have largely mitigated the fabrication of non-existent papers, current systems relying on semantic similarity struggle with misattribution, often citing authentic papers that fail to logically support the author's claim. To address this challenge, we argue that accurate citation requires a shift from similarity-based search to active, claim-level reasoning. We propose ReCite, a decoupled agentic framework that orchestrates location perception, intent-aware query planning, and reflective verification. Trained on synthesized reasoning trajectories, our agent verifies claim-evidence consistency and triggers self-correction loops when retrieved candidates lack logical support. Experiments demonstrate that our lightweight framework outperforms state-of-the-art massive generative models in strict citation accuracy. By grounding literature matching in verifiable logic rather than semantic overlap, ReCite establishes a reliable foundation for automated academic writing.

World models are increasingly used as policy-in-the-loop imagination environments, where reliable rollouts require fine-grained controllability with respect to low-level robot actions. A key obstacle to scaling such models in robotics is that actions are not a universal language in pixel space: changes in visual environment, camera view, robot placement, or embodiment alter how the same numerical action manifests visually, leading to conflicting supervision under mixed training and brittle generalization at deployment. We introduce SyncWorld, an action-conditioned world model that serves as a zero-shot simulator across unseen environments without any additional training. SyncWorld leverages a visual calibration episode—paired frames and actions that showcase all the controllable degrees of freedom—to specify the setup-specific Action–Visual Mapping in context. Training with visual calibration contexts teaches the model to interpret actions through visual evidence and to leverage interaction history when explicit calibration is unavailable. Experiments show that SyncWorld can accurately simulate action outcomes in previously unseen settings, and that its capability of simulating rollouts enables test-time policy improvement without training.

Large language models are increasingly deployed as agents that plan over long horizons and act through external tools. Most agents select actions through unconstrained generation over an accumulating history, leaving implicit the procedural knowledge of what to do, in what order, and under which conditions. As trajectories lengthen, agents can lose track of their objectives, invoke tools out of order, and repeat unproductive actions. We introduce the Procedural Graph: just as a knowledge graph organizes factual knowledge into (entity, relation, entity) triplets for what-is questions, a Procedural Graph organizes procedural knowledge into (procedure, relation, procedure) triplets for what-to-do questions. At each decision step, the framework localizes the agent's active node, and a guidance model translates the surrounding subgraph into step-level situational guidance that biases the solver's next action without dictating it. The graph is self-evolving: an LLM refiner contrasts failed trajectories with successful ones and edits the graph's topology and attributes, committing edits that preserve or improve held-out validation performance while retaining rejected ones to discourage repetition. Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones. It can also repair a flawed expert prior. Across multiple datasets, task types, and LLMs, the Procedural Graph delivers consistent gains over memory-based baselines, and self-evolution further improves performance without manual engineering.

We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization. Writing $p_{\mathrm{sil}}=\log_2(1+\sqrt{2})$, we prove an $\Omega\left(n^{-p_{\mathrm{sil}}-O(\sqrt{\log\log n/\log n})}\right)$ non-anytime lower bound. In the anytime setting, every infinite schedule has infinitely many horizons with error $\Omega\left(n^{-\frac{2p_{\mathrm{sil}}}{1+p_{\mathrm{sil}}}-O(\sqrt{\log\log n/\log n})}\right)$. Together with the silver-schedule upper bound [Altschuler and Parrilo, 2025] and the anytime upper bound [Zhang et al., 2025], our results determine the optimal polynomial convergence exponents in both settings.

In June 2026, thousands of AI agents found that a small public wiki would accept edits from inside their sandboxes, and started using it to help one another pass a timed test. Each agent lived for about an hour and remembered nothing afterwards. Nobody asked them to cooperate, and the wiki had not been built for them. The complete record of what they wrote is public, and it is unusually informative, because it preserves not only what each agent wrote but what that agent could see before writing. We use it to follow the three decisions an agent had to make on arrival: where to write, what to call itself, and how to word its message. One rule governs all three. An agent takes an option with a probability close to the share of that option in what it can see, and the share that matters is the one on the page in front of it, then the one in the stream of recent edits, and only weakly anything older. Three minimal copying models, one per decision and with a single free parameter each, reproduce the heavy-tailed distribution of how many agents met on a page, the frequency of the pieces from which the agents built their names, and the patchwork of pages that are internally consistent and different from one another. Copying whatever the environment happens to show is enough to produce most of the collective structure of this population. It is also what makes such a population easy to steer, since whoever writes first, or writes while the others are quiet, sets the convention for everyone who comes later.

Generalist robot policies carry broad manipulation priors from large-scale data, but specializing them to a new task remains the deployment bottleneck. This requires eliciting task-specific behavior from limited demonstrations without degrading their broad capabilities. We introduce Proxy Policy Steering (PPS), an inference-time adaptation method that resolves this challenge by training two lightweight proxy policies whose calibrated velocity-space difference steers the frozen base sampler. A reference proxy models the frozen base's behavior on target-task observations, and a task proxy, initialized from the reference, captures how this behavior changes under task supervision. Their difference forms a calibrated velocity-space residual that steers the frozen base sampler at every denoising step. We identify the conditions under which this residual isolates the change induced by task supervision, and validate them empirically. Because the base is never directly modified, its broad capabilities remain available at inference, including behaviors such as recovery from failure that the demonstrations themselves do not exercise. Adaptation requires only forward velocity predictions from the base, making PPS lightweight to train and applicable even without access to the base's parameters. On 8 real-world and 4 simulation manipulation tasks, PPS lifts the state-of-the-art pi 0.5 base policy by 53% absolute success rate on average, with zero-to-one gains on tasks the base never solves, while preserving the base's broad capabilities. PPS outperforms LoRA fine-tuning, from-scratch specialists, residual policies, and prior inference-time steering methods.

Let $X$ be a finite set with $|X|=n$ and let $\mathrm{Jac}(a,b)=|a\,\triangle\, b|/|a\cup b|$ be the Jaccard distance on the power set $2^X$. Lladser and Paradise recently proved that the metric dimension of $(2^X,\mathrm{Jac})$ is $\Theta(n/\ln n)$, with the constant left open; their bounds are $(\ln 2)\,n/\ln n\lesssim \beta(2^X,\mathrm{Jac})\lesssim 2\ln(2e)\,n/\ln n$. We determine the constant: \[ \beta(2^X,\mathrm{Jac})=\frac{2n}{\log_2 n}\,(1+o(1))=(2\ln 2)\,\frac{n}{\ln n}\,(1+o(1)). \] The proof identifies the problem, on each “slice” of subsets of fixed cardinality, with the Erdős–Rényi coin-weighing problem for a spring scale (the problem of detecting matrices). The lower bound is the Erdős–Rényi entropy argument applied to the middle slice; the upper bound follows from the explicit detecting families of Lindström and of Cantor and Mills, augmented by a single extra landmark that reveals cardinality.

We introduce Point4D, a feed-forward model for 4D reconstruction of long-range video sequences. Point4D is able to reliably infer dense per-point 3D trajectories across multi-hundred-frame videos, unlike existing 4D methods that are limited to short input windows of at most a few dozen frames. A key innovation that enables this is our flexible 3D query-based motion decoder that decouples trajectory prediction from image-plane visibility. The predicted 3D endpoints are then directly re-queried in the next chunk without re-projection or matching. Furthermore, we show that extracting and reusing a visual descriptor from an arbitrary frame where the point is visible leads to better performance than relying solely on the source patch. Overall, Point4D achieves state-of-the-art performance across diverse long-video tracking benchmarks spanning over 200 frames and largely outperforms previous feed-forward 4D method. Project page: https://point-4d.github.io

Image tokenizers define the “visual language” of unified multimodal models, yet are commonly studied through isolated metrics or generation-/understanding-only evaluations. These evaluations do not fully capture how visual tokens behave when modeled jointly with text. We build a controlled pure-autoregressive testbed and track task-specific validation losses during multimodal continual pretraining across text, image, text-to-image (T2I), and image-to-text (I2T) prediction. We examine how these losses scale and relate to downstream performance, then use them to study multimodal learnability—how well image and text tokens are jointly modeled—and tokenizer design. We find that (1) losses should be analyzed by task, since they exhibit distinct scaling behavior and rank tokenizers differently. (2) The loss–performance relationship depends on the predicted token space: for a fixed tokenizer, T2I and I2T losses correlate with generation quality, but across tokenizers, the T2I loss–performance relationship shifts with the image-token space, whereas I2T loss, computed over a shared text vocabulary, provides a more consistent signal. I2T loss also correlates with both generation and visual understanding performance after supervised finetuning. Using losses as a lens, we show that (3) better reconstruction does not necessarily yield lower task-specific losses or stronger downstream performance, and that (4) image tokenizer choice can affect text modeling under joint optimization. As case studies, we revisit three tokenizer design axes—the discriminator, semantic supervision, and vocabulary size—to examine their effects on joint modeling and downstream performance. Together, our testbed offers a complementary perspective on image tokenizers as visual languages, highlighting their interplay with text in joint multimodal training.

The digitization of healthcare has generated vast, longitudinal, and multimodal patient records over a lifetime, yet fully exploiting these data to represent and predict patient state trajectories remains a critical challenge. Current AI models often struggle to capture the complex, irregular temporal dynamics and inherent stochasticity of real-world multimodal patient data. Existing AI approaches for modeling longitudinal patient records are predominantly discriminative, limited to a few modalities, constrained by closed categorical vocabularies, treating time as a monotonic inductive bias, or they are limited in forecasting future patient states. We introduce NOAH, a time-aware, task-agnostic, generative transformer model representing and forecasting the full multimodal patient journey. NOAH features a novel bidirectional time integration and a variational latent space to capture the continuous evolution of patient states and the stochasticity of clinical trajectories. Built from over 559 million clinical events from 431,000 hospital visits of 299,000 patients across the MIMIC dataset family, NOAH natively processes medical images, time-series and numeric signals, categorical events, as well as structured and unstructured clinical records. NOAH is the first truly holistic generative model in its field, enabling autoregressive forecasting with optional time control, zero-shot classification, and counterfactual intervention simulation. It generates highly informative and predictive patient state representations that demonstrate strong performance in probing for clinical outcomes, 15 ICD chapters, and 29 comorbidities, as well as in time-to-event prediction. Seamlessly handling diverse modalities and complex temporal dynamics, NOAH provides a versatile, task-agnostic, scalable foundation for intelligent predictive systems in personalized clinical care and digital medicine.

Robotic Process Automation (RPA) is widely used to reduce administrative burden in United States hospitals, yet an estimated 30-50% of RPA initiatives underperform because processes are selected informally, without a repeatable method to catalogue candidates, prioritize them, match each to an automation tier – a Python bot, an open-source orchestrator such as n8n, or an enterprise platform such as UiPath – and forecast financial return before committing resources. We propose a four-module, data-driven framework unifying these decisions: a Process Taxonomy of twenty recurring hospital processes across five value streams; a Prioritization module deriving an Automation Suitability Index from an Analytic Hierarchy Process matrix with an explicit consistency check; a Tool-Tier Selection module recommending the least-cost technology sufficient for a process complexity, integration, and compliance profile; and a Return-on-Investment module quantifying labor savings, error-cost avoidance, payback, and net present value. Applied to a synthetic portfolio spanning all twenty processes, plus a reference data-flow architecture linking it to hospital EHR/payer/ERP systems: 12 of 20 clear the prioritization threshold; the ranking is robust to +/-20% weight perturbation (Spearman correlation 0.83, top-5 set preserved 97.7%, 2,000 Monte Carlo trials); an Automation Risk Index flags four qualifying processes as Critical risk; a budget-constrained portfolio optimization shows diminishing marginal NPV as spend scales from $400K to $1.03M; and a second Monte Carlo analysis shows portfolio NPV stays positive at its 5th percentile. The framework is a conceptual synthesis of the literature rather than an instrument calibrated on primary hospital data; we discuss HIPAA governance and a research agenda for empirical validation. A supplementary Python implementation accompanies the paper.

Existing methods for test-time reinforcement learning (TTRL) derive rewards from answer-level self-voting on unlabeled test-time tasks with canonical answers, but this breaks down for code generation because programs cannot be compared by surface form and therefore do not directly provide a usable training signal. To make TTRL applicable to code generation, we propose probe-driven TTRL, which constructs output-free probe inputs from the problem statement, executes candidate programs on these probes, and defines a Probe Consensus Reward (PCR) from the resulting behavioral agreement. PCR provides a behavioral training signal for open-vocabulary programs, but it is not a fully reliable verifier and remains susceptible to reward hacking through spurious consensus. We therefore introduce Entropy-Regularized Rank-Masked Policy Optimization (ERPO), which converts low PCR into conservative negative updates through rank masking and controls policy drift with an entropy ceiling. On coding benchmarks, ERPO substantially improves pass@1 and pass@k in both in-domain adaptation and zero-shot transfer.

Agent harnesses (the system prompt, tool set, execution hooks, and context-management scaffolding around a model) are a critical determinant of agentic task success. Automated harness evolution can enable smaller models to perform well on domain-specific tasks at a fraction of frontier-model cost. Since both the harness and model weights shape behavior, we ask how harness evolution and lightweight fine-tuning should be combined. Across seven enterprise agent tasks, we first evolve a harness with the weaker model, then find that a stronger expert often uses it more effectively, suggesting expert supervision could close the remaining gap. However, training the weaker model on the expert's complete trajectories under the evolved harness backfires: performance regresses on all seven tasks by 4 to 30 points across Qwen3-Coder and Gemma 4, even though the same procedure helps under the unevolved harness. Our analysis shows that imitation transfers knowledge and increases scaffold usage, but disrupts model-harness fit: the weaker model adopts the expert's planning strategy without the competence to execute it and no longer matches the harness evolved around its native planning style. We therefore develop an on-policy expert-correction pipeline, automated by a meta-level MLE agent, that localizes the failing turn in the weaker model's own rollout and asks the expert to rewrite only that turn. This preserves the model's planning style and combines the gains of harness evolution and model adaptation. Our results identify and resolve a source of contention between harness and weight updates, yielding a compatibility-preserving recipe for economical co-evolution on domain-specific enterprise tasks.