Papers

Analog computing with microwave signals can perform linear transformations directly in the analog domain, as the signals propagate through a microwave network. A fundamental question is which transformations can be computed with a given set of microwave components. In our previous work, we answered this question for networks of hybrid couplers and phase shifters by deriving a necessary and sufficient condition on the transformations these networks can compute, and we showed that the discrete Fourier transform (DFT) satisfies it. In this paper, we take a first step toward the formalization of analog computing with microwaves in Lean, a programming language and proof assistant that is increasingly adopted in mathematics. We formalize the considered components, their series and parallel connections, and the class of networks they can implement. Then, we formally prove the necessary and sufficient condition characterizing these networks, as well as the implementability of the DFT of any size power of two. All proofs are checked by the Lean kernel, and the code is openly available at: https://github.com/matteonerini/formalizing-analog-computing.

Sampling from a probability distribution with access only to its log-density is a foundational problem in statistics, machine learning, and the physical sciences. This problem is studied in the data-free score-based diffusion literature, which samples the target density via estimating scores of densities produced by convolution with Gaussian random variables and implementing a reverse SDE. In this framework, score estimators are constructed via Markov chain Monte Carlo, importance sampling, or rejection sampling. The estimators often operate far beyond the regime where mixing time and error control can be established and have large bias and variance when estimating the underlying score. In our method we propose post-processing: splitting a fixed computation budget across multiple evaluations, querying the estimator at different points, and fitting a single pooled estimate via linear combination to minimize bias and variance at a target location. The final value is an affine map of a vector of multiple score estimates. We show this reduces score estimation error when compared to the computation-matched base estimator queried at a single point. We demonstrate improved sample quality over other score estimation methods matched for computation cost on difficult target densities such as log-concave densities with large condition number, multimodal densities, and high-dimensional densities.

We prove two supercongruence statements proposed by Z.-W. Sun for Domb numbers. The first concerns the unweighted truncated sum $$S_p=\sum_{n=0}^{p-1}D_n$$ and is governed by the two proper ideal classes of the order of discriminant $-60$ in $\mathbb{Q}(\sqrt{-15})$. We prove Sun's conjectured congruences modulo $p^2$ and obtain stronger formulas modulo $p^3$ in the split cases. The second concerns Domb sums weighted by the Lucas sequences associated with $X^2-11X+1$. Sun's original formulation has the exceptional counterexample $p=3$; after excluding this prime, we prove the corrected statement, including its modulo-$p^3$ refinement when both relevant quadratic characters are $+1$. Both results arise from one modular mechanism. The twisted Domb series is a modular period on $\Gamma_0(6)+\langle 3\rangle$ and is related by a quadratic pullback to Zagier's sporadic $C$-sequence. At primes inert in the imaginary quadratic field underlying the relevant complex multiplication, the truncated $C$-period is the Hasse invariant and vanishes at supersingular reduction; a finite pullback then gives divisibility modulo $p^2$. At split primes, explicitly constructed determinant-$1$ or determinant-$3$ matrices identify the Beukers unit root, yielding congruences modulo $p^3$. The two applications correspond respectively to orders of complex multiplication of discriminants $-60$ and $-156$.

Long-horizon mobile manipulation requires a task plan and the motion that executes it. Generative planners trained on demonstration produce both in one pass, requiring neither a symbolic domain nor search. To date, however, they have relied on thousands of scripted demonstrations of fixed-base arms and executed open loop. This paper presents a hybrid flow matching planner: a single network generates the symbolic plan with masked discrete flow matching and the motion trajectory with continuous flow matching. Unlike prior generative planners, we aim to learn from a much smaller set of demonstrations and to execute the plan in closed loop. Two properties of the data compensate for the small dataset. A demonstration resumed from any of its intermediate actions is itself a demonstration, which multiplies the training samples and enables replanning after every action. Objects of the same kind are interchangeable, which turns demonstrations of one goal into demonstrations of every permuted goal. Our base implementation produces valid plans on 68% of held-out scenes; a training and generation scheme for the discrete plan raises this to 76%, and replanning after every action raises the task completion rate from 40% to 53% in a kinematic simulation. The planner matches the task completion rate of motion-only flow matching policies while additionally providing the symbolic plan, and it outperforms previous hybrid diffusion formulations on both task completion and plan validity. We validate the planner on a real mobile manipulator. Videos and project page: https://andreumatoses.github.io/research/hybrid-flow-planning

We prove ten conjectures of Z.-W. Sun on Ramanujan-type series for $1/\pi^4$ and $\pi^4$ with harmonic numbers. They follow by comparing Taylor coefficients in new Borwein-Bradley-type identities, whose products depend only on $x^3$, $x^4$, $x^6$ or $x^8$. These identities come from parametric extensions of the series of Cullen and Zhao. We derive the extensions from K. C. Au's Wilf-Zeilberger (WZ) seeds, and their sums are trigonometric. Our proofs use Guillera's periodicity argument and give new proofs of the original series. In the same way, Dougall's $_5F_4$ sum gives half-integer analogues of the identities of Koecher, Borwein-Bradley and Cohen, whose Taylor coefficients are Apéry-like series for products of zeta values.

Future integrated sensing and communication (ISAC) networks require wireless platforms that can adapt not only their signals but also the physical locations from which they radiate and observe. This article presents pinching-antenna systems (PASS) as a spatially adaptive platform for ISAC. PASS adopts dielectric waveguides as signal-transport media and reconfigurable dielectric pinching antennas to realize programmable radiation and observation points along these waveguides. This unique architecture introduces new spatial degrees of freedom, allowing the network to dynamically reconfigure its interaction geometry with users, targets, and the surrounding environment, rather than solely optimizing signals over a fixed antenna geometry. Leveraging a terahertz testbed, we experimentally validate the spatial control and spatially selective reception capabilities of PASS and demonstrate constructive field combining between two coherent radiation points. We further explore how such spatial reconfigurability can enable radio-map-assisted communication, environment division multiple access, and closed-loop active radio perception. Finally, we identify key challenges and research directions toward practical PASS-ISAC networks.

We study a one-parameter three-dimensional quadratic flow, denoted ETM-3D, on the benchmark domain $\rho\geq0$. Its homogeneous quadratic triad preserves Euclidean quadratic energy, while the full vector field has constant divergence -8. A shifted quadratic Lyapunov function yields an explicit positively invariant absorbing set and therefore global ultimate boundedness. The equilibria reduce generically to a scalar quartic, with a separate singular case at $\rho=\sqrt{5}$. Continuation reveals two saddle-node bifurcations, a generic transcritical bifurcation, a supercritical Hopf bifurcation, and a fold of limit cycles. Stable and unstable period-one branches meet at the fold with their nontrivial Floquet multipliers approaching +1. Just beyond this point, a 25-point logarithmic parameter study gives a laminar-length scaling exponent of -0.551 (95% confidence interval [-0.621,-0.481]), consistent with type-I intermittency. At larger $\rho$, a chaotic attractor coexists with an asymptotically stable equilibrium and periodic windows occur. Structural invariants are used to distinguish the flow from several classical quadratic chaotic families.

Latent world models enable robots to plan by predicting the consequences of actions. Planning long tasks with control-rate actions requires many prediction steps, which enlarges the search space and accumulates error. Skill-level actions shorten these sequences, but a symbolic skill vocabulary requires domain knowledge and labeled demonstrations. We construct skill-level actions from the inputs of a flow-matching policy trained on demonstrations segmented into complete skills. The policy maps a noise seed and an observation, optionally with a code or label, to a complete skill execution, so one execution is one world-model transition. On this mechanism we propose four action abstractions with increasing task knowledge: a compressed seed, two discrete codes learned from the demonstrations, and a symbolic label. We evaluate them with a common world-model training procedure and planning framework on simulated block rearrangement tasks that require up to 14 sequential skills. The symbolic label succeeds in over 90% of the tasks that require up to six skills and degrades beyond. Without any label, an object-centric learned code matches it on single-skill tasks and retains half to three quarters of its success on tasks of two to five skills. Ablations attribute much of the label's advantage to its planner knowing which actions are applicable, rather than to the label itself. Beyond six skills the search, not the world model, limits success. Project page: https://andreumatoses.github.io/research/flow-skill-wm

Modern models increasingly learn through black-box oracles such as humans, optimization solvers, and external tools that provide feedback without exposing their internal mechanisms. A common remedy is to learn an (action-)value function as a control variate. In this paper, we first observe that even an exact action-value function can be arbitrarily far from variance-optimal. We show that this gap arises because the value function minimizes the noise in each action's own gradient term, while an action can still affect the rest of the gradient estimator through shared parameters. A simple unbiased correction, at no extra oracle cost, can still reduce its variance by an arbitrarily large factor. Motivated by this, we then prove that the residual variance can be decomposed exactly by actions with no cross terms. This decomposition yields a closed-form variance-minimizing correction for neural-network parameters, which can be computed by a simple projection. Empirically, our correction consistently reduces the variance left by the value function and improves learning across all tasks. The source code for all experiments is available at https://github.com/Zihao-Kevin/black_box_opt.

In this paper, we develop a method that enables bimanual dexterous hands to manipulate articulated objects with a high success rate without suffering from an embodiment gap. We observe that the correlation between hand motions and object motions is dictated by the object rather than the hands and can be learned from human-object demonstrations. Based on this observation, we propose PatternDex, a method that learns this correlation and represents it as a token sequence, which we call an interaction pattern. From this pattern, PatternDex estimates the wrist motions and contact points that fit the target robot, and then trains a reinforcement learning policy that exploits these estimates as guidance. Since the guidance fits the target embodiment, the policy explores only the actions that the target robot can execute and thus achieves high success rates. PatternDex also requires only simple fine-tuning to train a new robot, since it can reuse the learned interaction pattern. We evaluate PatternDex with bimanual dexterous hands on human demonstrations from the ARCTIC dataset. PatternDex achieves, on average, a 92.8% success rate with Allegro hands, while the state-of-the-art baseline achieves 52.2%. Also, it achieves success rates above 70% with three other robot hands after fine-tuning alone. Furthermore, we verify that the learned policy transfers well to a real-world task of opening a microwave. Videos and additional results are available at https://patterndex.github.io/PatternDex/

This letter proposes DNPush, a Distributed Nonparallel Pushing force controller for cooperative object transport without inter-robot communication. Each robot uses local force measurements, a preassigned force weight, and a locally expressed desired transport direction, without requiring an object model, contact locations, a CoM estimate, or moment arm magnitudes online. DNPush regulates nonparallel force magnitudes from local force direction misalignments through a reciprocal-sine law. Under the stated contact conditions, Lyapunov analysis with LaSalle's invariance principle proves convergence to a unique rotational equilibrium, where perpendicular force contributions cancel and the net torque from normal forces is zero. Object velocity converges to the desired transport direction, and suitable contact regions exist for convex polygons. Simulations isolate the reciprocal-sine scaling mechanism, five-robot coordination, and active rotational damping. Hardware experiments with soft tactile differential-drive robots achieve a velocity direction error of 0.61 deg +/- 0.79 deg over five trials with a fixed transport direction and demonstrate object transport through waypoints with three robots.

Genomic language models can write synthetic DNA that carries no record of its origin. A generation-time watermark could provide a provenance signal, if a verifier can detect it using only the DNA sequence, a key, and published detector settings, without knowing where the generated region starts, which strand it lies on, or how it was divided into six-base tokens. We embed the SynthID tournament watermark in two genomic language models, Carbon and GENERator-v2. The verifier searches both strands, every start position, and four window lengths, and corrects its decision for the whole search. In a detection cohort of 1,544 held-out prompts, it found all 3,088 marked sequences per model, unedited and after one substituted, inserted, or deleted base. For ordinary sequences, the one-sided 95% upper confidence bound on the false-positive rate was at most 0.850%; one bound for the wrong-key control reached 1.015% (Carbon, after a deletion). In a development cohort, neither model showed a detectable change in likelihood or in predefined sequence measures. Under random edits placed without reference to the detector, detection stayed complete or nearly complete up to a 2% per-base edit rate. These results show statistical detection, not biological function, secret-key security, or robustness to an editor who sees the detector.

Objective: To assess trends in family physicians' (FPs) electronic health record (EHR) satisfaction and their experience of interoperability across organizations. Materials and Methods: Serial cross-sectional analysis of five waves of the American Board of Family Medicine's Continuous Certification Questionnaire (2022-26). Adjusted logistic regression compared odds of being very satisfied across 11 EHRs; Cochran-Armitage tests assessed vendor trends. Ease of using outside information was analyzed separately for same- and different-vendor sources. Results: Across 36,785 FPs, adjusted odds of being very satisfied relative to Epic ranged from 0.91 (95% CI, 0.74-1.11) for Elation Health to 0.17 (95% CI, 0.15-0.20) for Oracle Health/Cerner. Only Epic's users became significantly more satisfied (Benjamini-Hochberg adjusted P < .001), widening the vendor satisfaction gap. Within comparable periods, ease of using different-vendor information did not improve; fewer than 13% rated it very easy. Epic's interoperability advantage reversed by exchange type: non-Epic users had less than half the odds of Epic users of rating same-vendor interoperability very easy (adjusted OR, 0.41; 95% CI, 0.38-0.44) but 1.54 times the odds for different-vendor interoperability (95% CI, 1.35-1.75). Discussion: Rising national exchange volume has not yielded easier use of outside information. Epic's advantage is confined to its own network, so market concentration may shift, rather than solve, the different-vendor problem. Conclusion: The ABFM data are already informing EHR policy but also have utility for the EHR marketplace. While EHR satisfaction has known implications for burden and burnout, poor interoperability is a quality and safety threat that may be compounded by artificial intelligence.

Gaussian elimination with partial pivoting is the standard algorithm for solving a dense $n\times n$ system of linear equations $Ax=b$. The “growth factor” $\rho\,$ for this process may be as large as $2^{n-1}$, and when $\rho$ is large, the algorithm is unstable. Nevertheless, long experience has shown that Gaussian elimination is resoundingly stable in practice. Experiments indicate that among random matrices with independent normally distributed entries, growth factors $\rho \gg n^{1/2}$ are in a precise sense exponentially rare. Here we take a step toward confirming this observation by proving it not for the full growth factor, which depends on all the entries of the upper-triangular factor $U$, but for the corner entry $u_{nn}^{}$.

The epitaxial graphene grown on SiC interface has been the subject of tremendous research efforts to control its electronic transport properties in the quest for graphene electronic applications. The electronic structure of the epitaxial graphene buffer layer on SiC(0001) is investigated at the atomic scale using monochromated electron energy loss spectroscopy (EELS) in an aberration-corrected scanning transmission electron microscope (STEM). The C $K$-edge reveals spectral fine structures distinctly different from free-standing graphene layer, providing direct experimental evidence of a modified bonding environment. Ab initio calculations providing a site-resolved probe of orbital character to elucidate the origin of these spectral features: covalent bonding between one-quarter of the buffer-layer carbon atoms and the substrate silicon atoms induces partial $\mathrm{sp}^3$ hybridization, quenching the out-of-plane $\pi$ states and disrupting $\pi$-conjugation across the interfacial layer. Substrate-imposed symmetry breaking further lifts the in-plane orbital degeneracy. This orbital-engineering framework, rooted in $\pi$-state quenching and site-specific symmetry breaking, establishes a quantitative basis for tailoring graphene-substrate interfaces toward next-generation low-energy transistor applications.

Segment routing (SR) involves routing requests through shortest paths or a limited number of segments, which are themselves the shortest paths between their endpoints. While this flexibility makes segment routing attractive for traffic engineering (TE) in IP/MPLS networks, it becomes challenging to update when some links become unavailable (e.g., maintenance) and routing decisions must adapt while limiting the number of configuration changes between two consecutive periods. We address the problem of dynamically selecting SR-TE configurations for multiple traffic demands with the objective of minimizing the maximum link utilization (MLU). In addition, a reconfiguration budget is imposed in order to limit the number of segments modified. Based on this representation, we develop a MLU column-generation optimization framework. It allows to jointly consider traffic distribution, SR configuration complexity, and temporal reconfiguration costs in time-varying IP/MPLS networks. The numerical results are obtained using realistic datasets provided by Orange, with topologies containing up to 1,263 nodes and 15,000 traffic demands. The optimality gap (i.e., accuracy) is below 5% in 80.45% of the 133 instance-time evaluations.

Machine-learning classification is now used across medicine, the social sciences, economics, education and engineering, very often by researchers who do not program. Two errors recur in such work: preprocessing learned on all rows before cross-validation (data leakage), and reporting the cross-validation score of the classifier that won a comparison (selection bias). Both make published scores optimistic. We present EasyClassifier, an open-source Python package that guides a user from a CSV or Excel file to a finished analysis through a sequence of plain-language, multiple-choice questions, with no code. It makes the correct procedure the default rather than an option: every preprocessing step is learned inside each training fold; the selected classifier receives a separate final score from nested cross-validation (up to 2,000 rows), or an untouched 20% test set; classifiers run with fixed default parameters and fixed random seeds; and every run writes a report with a ready-to-adapt Methods paragraph, the references to cite, and figures prepared for publication. On ten public datasets from seven fields and a random-label control, split in half so that one half served as an untouched external test, the common practice overstated balanced accuracy by 2.9 percentage points on average (up to 9.9 on small data), whereas the score EasyClassifier reports had a mean signed bias of +0.7 points and a mean absolute error of 2.3 points (one-sided Wilcoxon p = 3.2 x 10^{-4}, 30 runs). On random labels it reported 48.8% balanced accuracy against a chance level of 50%. EasyClassifier is available under the MIT license from PyPI (pip install easyclassifier), GitHub, and Zenodo.

In recent years, flow-matching models have produced significant improvements in zero-shot text-to-speech synthesis. Conditioned on an audio prompt and text, these models learn a velocity field and generate speech by iteratively solving an ODE. During inference, the solver evolves a single state spanning both the prompt and the region to be generated, although only the generated region is ultimately retained. The discarded prompt state, however, still matters; its intermediate values influence generation through the velocity field that couples the two regions. As sampling continues, this state can drift away from the prescribed conditional path, introducing a discrepancy into subsequent generation updates. Unlike the unknown generated trajectory, the prompt path is available in closed form from the reference audio and the initial noise. We exploit this observation with Prompt-Consistency Inference (PCI), a training-free rule that restores the prompt block to its analytic value before each velocity evaluation, while leaving the generated block unchanged. PCI improves speaker similarity and intelligibility across the evaluated flow-matching TTS backbones without additional network evaluations. Our ablation studies further show that PCI keeps post-step prompt discrepancies smaller and that corrections covering the later sampling stages recover much of the observed similarity gain.

Self-evolving large language model (LLM) systems repeatedly propose, evaluate, and incorporate updates to prompts, skills, or other persistent artifacts. Despite their growing effectiveness, these systems typically operate under a predetermined iteration or compute budget, without a principled criterion to determine when further evolution is no longer worthwhile. This can lead to two undesirable consequences: unnecessary computation after performance has saturated and the risk of returning late updates that overfit or exploit the evaluation signal. These issues motivate us to study two fundamental questions: when should a self-evolving system stop, and what should it output once it stops? We address the first by formulating an online sequential testing problem and constructing an anytime-valid restart detector using the per-item paired evaluation outcomes already produced by self-evolving LLM systems. We address the second by formulating a change-point estimation problem and using the estimated transition to select an earlier artifact for output. The resulting procedure is plug-and-play and requires no modification of the underlying self-evolving algorithms. Across two self-evolving frameworks, three LLM model families, and five benchmarks, our method substantially reduces computation costs while maintaining comparable unseen-test performance. For example, on SearchQA with SkillOpt and DeepSeek V4 Flash, our method stops at round 4 rather than the full budget of 40, reducing token usage by 91.6% while achieving 82.43% unseen-test accuracy versus 82.00% under the full-budget run.

We study mixed-integer quadratic fractional optimization problems with binary and continuous box-constrained variables. The objective is the ratio of two quadratic functions, a structure that arises naturally in portfolio selection, signal processing, and data analytics. We propose an exact algorithm based on Dinkelbach's parametric reformulation. At each Dinkelbach iteration, the fractional problem is replaced by a nonconvex mixed-integer quadratic subproblem with box constraints. This subproblem is solved globally by a specialized branch-and-bound solver. To accelerate the outer scheme, we use a Variable Neighborhood Search heuristic to provide an initial feasible solution to the Dinkelbach scheme. The heuristic alternates between continuous local searches and a binary-space exploration phase in which the continuous variables of a feasible incumbent are fixed. Numerical results show that the proposed approach outperforms general-purpose exact algorithms based on Dinkelbach's parametric reformulation.

Even a few action perturbations can substantially degrade the performance of a deployed decision policy. Certifying the resulting return loss is challenging in stochastic environments, where returns vary even without an attack. We introduce FoSeRL, a framework for certifying deployed RL policies against precommitted, temporally sparse action attacks. The deployed policy is unchanged, with no smoothing or retraining. Certification requires a resettable simulator supporting shared randomness and independent one-step successor queries, but no analytical dynamics model. FoSeRL certifies that an attacked episode loses no more than a prescribed amount of return relative to the same episode unattacked, with at least a target probability and at a user-specified confidence level. Both runs share the initial state and randomness, so the measured loss reflects the attack, not the episode; carrying the running return gap as a state coordinate makes it the terminal value, reducing trajectory-level certification to terminal safety. Time-dependent barrier conditions on the augmented state bound the terminal failure probability: satisfied exactly, they certify every admissible precommitted attack; learned from sampled trajectories and verified on held-out data, they certify the same guarantee under a specified attack-episode setting. Across six stochastic continuous-control environments and three RL policy families (TD3, SAC, and PPO), FoSeRL certifies non-trivial cardinality–magnitude robustness frontiers, achieves substantially larger certified budgets than policy smoothing, and reveals marked robustness differences among policies with comparable nominal performance.

Autoregressive generation in Large Language Models (LLMs) is constrained by the memory and computational demands of attention mechanisms. Sparse attention methods mitigate this cost by selecting only high-probability entries of the attention matrix. We observe that in many such methods, this renders the probability-value multiplication negligible, shifting the bottleneck to the query-key step. Key heads can therefore be reduced to accelerate inference, while retaining more value heads preserves capacity with limited additional decoding cost. We introduce Sparse Asymmetric Group-Query Attention (SAGA), which decouples key and value head counts to exploit this principle, and pair it with approximate top-N (Atop-N) attention, a simple sparse attention method designed to study the interaction between sparsity and head-count asymmetry. We formalize the benefits of this asymmetry theoretically and validate them empirically through latency measurements and quality evaluations on models up to 1.5B parameters. Together, SAGA and Atop-N achieve end-to-end decoding speedups exceeding $2\times$ over our full-attention GQA baseline at long contexts. Models trained from scratch with SAGA nearly match the quality of comparable GQA variants on the evaluated benchmarks. To facilitate adoption, we introduce an efficient fine-tuning method that converts pretrained models to the SAGA architecture, enabling practitioners to benefit from our approach without costly retraining.

We study model-free online reinforcement learning (RL) for episodic tabular Markov decision processes, focusing on both gap-dependent regret and policy switching cost. While fine-grained gap-dependent analysis has been established for model-free RL algorithms using Hoeffding-type exploration bonuses, such results for model-free algorithms with variance-based exploration bonuses remain unknown, despite their superior worst-case and coarse-grained gap-dependent guarantees. In this paper, we resolve this open problem by establishing the first fine-grained gap-dependent regret upper bound for UCB-Bernstein+, a refined UCB-Bernstein algorithm, in variance-aware model-free online RL. Moreover, by integrating a stage-wise policy update design into our fine-grained framework and using refined variance-based bonuses, we achieve the best-known gap-dependent local switching cost to date. In addition, our analysis yields improved worst-case guarantees for both regret and local switching cost over the original UCB-Bernstein algorithm. Numerical experiments further demonstrate that UCB-Bernstein+ achieves favorable empirical performance in both regret and local switching cost.

Beyond scaling their parameters and data, large language models currently gain versatility on new problems along a single axis: the tokens they spend on chain-of-thought (CoT). We investigate whether dynamic routing programs, which execute a subset of the model's layers or iterate some of them, can open a second axis of test-time adaptation, complementary to CoT and free of any gradient update. Prior work showed that such programs exist and bring accuracy and efficiency gains on problems similar to those they were trained on; we ask whether they can also be identified rapidly, from a handful of demonstrations (3 or 10), by a strategy that transfers across models and tasks without training. First, we find that strategies that select programs by the probability they assign to the demonstrations' labels, arbitrated by the model's own confidence, bring consistent gains: on average over the 49 tasks of MMLU and substantially on four of seven models, and most of all on far out-of-distribution tasks such as ARC-AGI, where programs double the accuracy of a 7B model whose CoT fails. Second, on MMLU across the seven post-trained models, routing complements CoT in practice: the two succeed on different queries, and their composition exceeds CoT alone. Despite these gains, our analyses show that confidence-based selection leaves much of the potential untapped, in two places in particular: (1) in surfacing the routing potential that is already present early in pre-training but becomes harder to select after post-training, and (2) in making models robust to the refinements routing introduces, since unsuccessful routes tend to drive the residual stream out of the distribution that the following layers expect. Together, our results point to dynamic routing as a paradigm for extending the plasticity of existing and future LLMs in rapid test-time adaptation.

We prove a complexity dichotomy theorem for $\mathrm{Holant}^*$ problems over complex-valued symmetric constraint functions $\mathcal{F}$ on domain size $3$. We give a decidable tractability criterion and prove that if $\mathcal{F}$ satisfies the criterion, then $\mathrm{Holant}^*(\mathcal{F})$ is solvable in polynomial time, and otherwise it is #P-hard. This is the first Holant dichotomy for a set of complex-valued constraint functions on higher domains. We show that complex-valued constraint functions have a rich structure not observed in real-valued constraint functions. This structure is only revealed when we analyze them in a bipartite Holant setting with a non-standard bilinear form and provides the backbone to the proof of the dichotomy. We use group actions and the spin representation of $\mathrm{SL}(2, \mathbb{C})$ in $\mathrm{SO}(3, \mathbb{C})$ and the generalized orthogonal group to facilitate this analysis. We also introduce $\textit{frames}$ and $\textit{shells}$. Frames linearize the group action and provide a unified framework for proving #P-hardness when used in conjunction with shells. Furthermore, we characterize the lower dimensional constraint functions by $\textit{annihilators}$, which makes it possible to analyze $\textit{essentially Boolean domain}$ functions in domain size $3$.

Routine complete blood counts (CBCs) could yield new biomarkers, but the private records needed to evaluate candidates cannot be shared with frontier language model agents that excel at discovery. We distilled the evidence held in the Clalit Health Services panel of over 5.4 million patients into a released scoring tool: for each of 13 immune-mediated diseases, a graph attention network was trained inside the data boundary to predict the case-control AUC of candidate CBC expressions, and only the trained weights were released. The tool grounds an agent's propose-score-refine loop in real-world data without exposing any patient data. In external validation, agent-discovered expressions improved on their literature-seeded starting points by a median of 4.18 AUC percentage points, and across three independent cohorts, reranking the candidates of three frontier research tools improved on their first choices in most comparisons, with gains that varied by cohort. The released scorer supports privacy-preserving biomarker hypothesis generation.

The log predictive density score (LPDS) and related estimators of the expected log predictive density (ELPD) have become the de facto standard for Bayesian model comparison. The LPDS is a natural out-of-sample measure of predictive density performance that accounts for parameter uncertainty, is less dependent on the prior than the marginal likelihood, and is easily computed sequentially using standard Monte Carlo from posterior draws. Our article demonstrates, however, that the standard Monte Carlo estimate of the LPDS can be extremely variable and severely biased when the test data has outliers, leading to misleading conclusions and suboptimal model choices. Estimating the LPDS as the difference between the log marginal likelihood of the full dataset and the training data is shown to be a dramatically more efficient approach. This estimator is also shown to be a much more effective fallback for observations that have been flagged as problematic by the widely used PSIS-LOO model comparison framework in Stan.

In life-or-death situations, a benevolent lie may appear more moral than telling the truth. Yet such lies can backfire, producing unintended and sometimes fatal consequences. This tension, famously disputed by Kant and Constant in 1797, applies not only to lying but to assertive speech acts in general, raising the question of which utterance should be chosen when moral stakes are high. We present a logical framework for the ethical evaluation of speech-act utterances based on agents' beliefs. Implemented in Answer Set Programming (ASP), the framework assesses utterances under deontologism, consequentialism, and principialism, and is illustrated on Sartre's The Wall (1939), a reworking of that controversy in which lying leads alternately to rescue and to death. Our setting is general by design: as two variants show, accommodating a new moral situation amounts to adjusting parameters, not rules.

Simulation is a fundamental computational primitive in reinforcement learning (RL), yet conventional simulation explicitly generates individual trajectories even when downstream procedures use only aggregate statistics. To address this, we develop an exact fast-simulation framework for finite-horizon tabular Markov decision processes. Our framework has two complementary modes. In direct batch simulation, a batch is represented by its aggregate Markov flow. With sufficient parallel simulation resources, this flow can be obtained by trajectory aggregation; when such simulation is unavailable or costly but the initial state and transition distributions are directly accessible, we instead generate an identically distributed flow through forward Markov-flow sampling without materializing individual trajectories. The latter reduces the simulator-side computational dependence on batch size $m$ from $O(m)$ to $O(1)$. In adaptive batch simulation, when batch length is determined by a data-dependent condition, exact multivariate-hypergeometric splitting recursively refines a candidate Markov flow while preserving the conditional law, reducing the cost dependence on $m$ from $O(m)$ to $O(\log m)$. Together, these modes accelerate simulation by keeping trajectories aggregated whenever possible and refining flows only when required to locate data-dependent boundaries. The framework applies broadly across simulator-based, offline, and online batch or stage-based RL, as illustrated with representative algorithms from each setting.

In a companion article \cite{RJnodyn} the present authors proved a form of the Rudolph–Johnson theorem which is effective at finite resolution, bounding the low-frequency Fourier coefficients of a $\times 2 \times 3$-invariant measure by its normalized entropy. Here we read that bound in the other direction, as a constraint on eigenfunction behavior in potential counterexamples to Furstenberg's $\times 2 \times 3$ conjecture. We show that a near return of the coordinate function $x \mapsto e^{2\pi ix}$ to itself under the semigroup generated by $2$ and $3$ forces the resolution entropy to be small, and that adherence of the coordinate function to eigenfunctions of $x \mapsto 2x$ forces it to decay. These rates are explicit in the rate of adherence and in the arithmetic of the eigenvalues.