Papers

Hardware-aware neural architecture search (NAS) is dominated by evaluation cost: every architecture must be trained before its reward is known. Conformal-prediction filters cut this cost by pruning candidates whose predicted-reward upper bound misses a threshold, with a distribution-free guarantee that at most a fraction $\delta$ are wrongly discarded. That guarantee assumes exchangeability between calibration and test candidates, which the surrounding reinforcement-learning (RL) loop violates: the policy's proposals improve as search proceeds and, in layer-by-layer construction, shift within every episode. We replace one-shot quantile estimation with online feedback control (Adaptive Conformal Inference, with tuning-free, locally-adaptive, and group-conditional variants), restoring steerable coverage: dialing the target delivers it, monotonically and reproducibly, for arbitrary sequences. Across three neural-network architecture families and both single-step and sequential search (three seeds), it tracks every requested level to within ${\sim}10^{-3}$ while pruning 25-50% of evaluations at no measured accuracy cost, whereas static calibration loses control of its coverage and a Gaussian-process baseline stays conservative regardless of the request. Finally, used as an acquisition function on one constrained testbed, the same optimistic bound beats random search, a gain that fixed optimism already carries and online calibration sharpens. The source code is available at https://github.com/Vicomtech/rl-hw-nas.

Reeb Transforms offer a compact representation of how shapes in $\mathbb{R}^n$ change when sliced along varying directions. We define the Reeb Transform as the family of Reeb graphs induced by height functions along all directions in the unit sphere. In this paper, we develop a rigorous treatment of Reeb Transforms for o-minimal definable sets, with particular emphasis on one-dimensional stratified spaces embedded in $\mathbb{R}^d$ and on surfaces in $\mathbb{R}^3$. We establish injectivity of the Reeb Transform in multiple settings, including compact surfaces in $\mathbb{R}^3$, capturing the essential topological features needed to uniquely reconstruct such surfaces. However, in dimensions above three, the Reeb Transform ceases to be injective, indicating the limitations of this descriptor in higher-dimensional settings.

Speech delivery varies with both the requested paralinguistic attribute and the linguistic content. We introduce ParaGeo, a matched-content decomposition of paralinguistic variation in a frozen speech language model. Synthesized audio tokens are replayed with a fixed listening prompt; pooled key/value (K/V) representations are centered and projected into a shared low-dimensional space. Our GLM-4-Voice probe spans 80 requested controls from 12 benchmark families across eight sentences. With a globally fitted calibration basis, content-held-out centroid accuracy using this basis is 9.49% versus a 1.25% permutation baseline; same-label cross-content cosine similarity is 0.285 versus 0.017, and both conditional permutation tests yield p = 0.001. A separate ten-scenario, six-style probe reveals reproducible contrast directions across scenarios. Static, additive, and temporal interventions produce attribute-, layer-, and schedule-dependent response profiles. These results provide a shared coordinate representation for measuring paralinguistic structure and an empirical starting point for latent speech control. Code is available at https://github.com/yuhanlydia/ParaGeo.

Open-weight language models can be downloaded, modified, and deployed beyond their developers' control, limiting the effectiveness of centrally enforced safeguards. Recent work has therefore proposed trigger-tag mechanisms that produce a detectable signal when a model is used under a target condition, such as generating phishing contents. Although these mechanisms borrow from established techniques, their use for conditional misuse detection in open-weight LLMs is relatively new. Therefore, existing research works have not systematically studied the robustness of trigger-tag mechanisms under adversarial attacks. To close this gap, (i)~we formalize trigger-tags and distinguish token-level trigger-tags, which introduce watermark-inspired signals during decoding, from weight-level trigger-tags, which learn backdoor-inspired associations between target conditions and detectable model behavior. Furthermore, (ii)~we introduce \Untag, a unified attack framework that organizes their mechanism-specific attack surfaces into a common taxonomy. We evaluate representative token-level and weight-level trigger-tags using phishing as a case study. We find that while trigger-tags may provide useful evidence in controlled settings, our attacks render the existing trigger-tag mechanisms to be entirely ineffective. Consequently, we argue that these mechanisms should not be treated as robust misuse detectors when attackers can transform outputs or modify open weights.

Existing streaming vision-language models (VLMs) continuously perceive and reason over visual streams, but their computational pathways remain fixed throughout inference. Consequently, they cannot adapt computation to evolving scene dynamics, where different future events demand different levels and forms of perception. We show that streaming VLMs inherently possess the ability to anticipate the immediate future, and leverage this capability to dynamically configure future computation in a training-free manner. Realizing such anticipatory computation, however, is very challenging: future anticipation must be sufficiently reliable to guide computation, planning must run concurrently with streaming inference, and online reconfiguration must incur negligible overhead. To address these challenges, we introduce FORESIGHT, a dual-stream architecture comprising two Siamese LLMs with shared weights, input encoders, and KV cache. The first LLM continuously processes incoming tokens, while the second runs ahead of the stream to anticipate future context, plan future computation, and generate task responses without interrupting streaming inference. Each plan decides when to reason next, what to check then, and how densely to sample, keeping transient evidence separate from persistent control. The resulting computation plan is executed online through an efficient reconfiguration protocol with schemaguided decoding and lightweight diff-based updates, enabling dynamic adaptation with low overhead. With a frozen Qwen3-VL-8B backbone, FORESIGHT achieves 23.0 mean joint F1 on OmniPro Online evaluation beating strongest trained baseline by 9.5%, while improving the backbone by 6.7 on StreamingBench and 15.4 on OVO-Bench, with the largest gain of 18.7 when evidence arrives later in the video stream. Our source code will be made publicly available.

We prove Ehrhart positivity for series-parallel matroids and extend this result to all series-parallel extensions of multi-path matroids. A formula for the Ehrhart coefficients of series-parallel matroids is derived and used to prove strict positivity. An extension criterion based on weighted lattice-point counts is established. Recursive formulas for lattice-point counts are derived, and the recursion is shown to preserve a class of polynomials with nonnegative coefficients. We finally construct a connected transversal matroid with a negative Ehrhart coefficient, disproving the conjecture of Ferroni, Morales, and Panova that every connected matroid whose base polytope admits a subdivision into series-parallel matroid base polytopes is Ehrhart positive.

We record a finite-field census of the split-cubic elliptic curves $E_{a,b,c}^{(n)}:y^2=(ax+n)(bx+n)(cx+n)$ attached to positive integral $D(n)$-triples. For $n\in\{-3,3,5,8,12,20\}$ there are $164$ such triples with $1\le a<b<c\le100$, allowing zero squares. Their reductions at the ten primes $\operatorname{NextPrime}(10^k)$, $3\le k\le12$, give $1640$ records, of which $45$ have cofactor four relative to the largest prime divisor of the group order. We collect the standard split-cubic and quadratic-twist identities in the explicit normalization $\lambda=b(c-a)/(c(b-a))$ and $\delta=cn(b-a)$, and use them to audit the point counts. The archive records group orders, factorizations, cofactors, embedding degrees and transfer-field bit lengths. A worked example compares the main curve with its nonsquare twist. The census is deterministic and descriptive; it provides neither an asymptotic density estimate nor cryptographic parameter recommendations.

Modern autoregressive (AR) video diffusion models excel at short-horizon video generation, yet generating long videos remains challenging due to drifting, where colors and textures shift, and motion dynamics decay. Existing works primarily rely on KV conditioning, which selects or modifies cached key-value (KV) entries to mitigate drifting. However, we observe that KV conditioning alone is insufficient as it assumes cached KV entries remain in-distribution. This assumption fails beyond the training horizon: nothing constrains the construction of KV entries during rollout, giving rise to the KV-provenance problem where cached entries themselves become out-of-distribution (OOD). To address this, we propose In-Distribution Forcing (ID-Forcing), a test-time framework that aligns both KV caching and KV conditioning with training configurations. Its key mechanism, self-caching, prevents OOD KV entries at their source. Each chunk is cached without attending to prior KV entry, keeping the rolling window exactly in-distribution. Consequently, ID-Forcing seamlessly extends short-horizon models to minute-scale video generation. Extensive evaluations show that our method remains competitive on standard video generation benchmark while substantially outperforming prior work in mitigating drifting, as validated by both our drift metrics and a user study.

In lifelong reinforcement learning, retaining previously learned policies is not sufficient for effective transfer to a new task. Useful knowledge may be distributed across several prior policies, and its relevance may change as the learner acquires experience. One hypothesis is that task similarity can be effectively used in a continual learning setting to find and combine previously learned policies. To test it, Adaptive Mask Selection and Composition (AMSC) is designed to estimate similarity from online experience via non-parametric Wasserstein task embeddings from state-action-reward samples. The z-score-normalized sparsemax of the similarity scores are used to derive a variable-size support to periodically choose and weight policies to form a prior when learning a new task. On CT-graph and MiniGrid, AMSC achieves higher mean performance and forward transfer than the evaluated modular composition baselines while exhibiting no forgetting. Results on Continual World suggest that identifying relevant prior knowledge and determining its layer-specific composition may require additional layer-specific tuning. Ablations show that selecting relevant sources and determining how strongly to reuse them are central to these gains. Independently measured pairwise transfer is also positively associated with task-embedding similarity. These results indicate that task similarity can be an effective criterion to select and weight specific knowledge for reuse in lifelong reinforcement learning.

We identify an entropy-mediated mechanism underlying the spatiotemporal organization of the chromosome in the bacterial cell Caulobacter crescentus. Effective entropic interactions between replicating DNA segments emerge from their topological modifications of daughter DNA polymers caused by transient ParA-ParB binding. Enthalpic contributions arising from the ParABS system further influence their dynamics. In C. crescentus, chromosome replication and segregation occur concurrently before cell division. The origin of replication oriC of the mother chromosome of C. crescentus is tethered to the old cell pole. Replication generates two daughter oriCs, one of which remains anchored at the old pole. The other oriC is actively transported toward the new pole by the ParABS system of proteins even as replication of the rest of the chain is in progress. How ParABS generates a directed force to transport a daughter oriC to the opposite pole during chromosome replication remains unclear. Furthermore, the two daughter chromosomes get neatly segregated into two halves of the cell. In a bead-spring polymer model of the replicating C. crescentus chromosome, we model transient ParA-ParB contacts that generate DNA loops and an effective entropic repulsion. This repulsion drives chromosome segregation and produces oriC trajectories consistent with experiments, aided by the ParA concentration gradient near the new pole. This minimal framework, incorporating the physics of topologically modified (ToMo) polymers, allows us to quantitatively reproduce the time-dependent spatial organization of different tagged loci and replisomes observed in multiple experiments. Incorporating a minimal model of extrusion also allows us to recover the linear arrangement of the chromosome arms, as is inferred from the characteristic diagonals of Hi-C maps.

Deep Neural Networks (DNNs) inherently exhibit a degree of robustness to bit-level faults due to their distributed representation of information. As a model increases in width, this information becomes more dispersed, theoretically reducing the impact of any single bit fault. In this paper, we empirically investigate the relationship between model width and robustness to Single Event Upsets (SEUs). We conduct a comprehensive experiment in which baseline models undergo iterative structured pruning to reduce their width while preserving task performance as much as possible. At each pruning stage, we run a targeted fault-injection campaign to evaluate the model's performance under simulated bit-flip scenarios. Our results show that, although structured pruning increases per-inference sensitivity to faults by reducing redundancy, this effect is effectively counterbalanced by shorter execution time, which lowers the probability of encountering an SEU. These findings suggest that structured pruning can yield significant energy and latency savings without compromising overall reliability, providing useful guidance for designing robust AI systems for space applications.

We show that the conformal class of a compact spin manifold with boundary is uniquely determined by its boundary values of harmonic spinors if the metric is locally conformal to a real-analytic metric in some coordinates. More precisely, we consider the boundary conjugation (BC) map for the Dirac operator corresponding to MIT boundary conditions, and prove that if two locally conformally real-analytic (LCRA) metrics have equivalent BC maps over an open subset of the boundary, then the two manifolds are conformally equivalent. The class of LCRA manifolds includes conformally Einstein manifolds, as well as all smooth surfaces. We also show that a real-analytic unitary connection on an LCRA manifold is uniquely determined up to local gauge equivalence by the BC map of its twisted Dirac operator in dimensions greater than 2.

We study the scaling limit of the collision measure of two i.i.d. discrete-time random walks on $\mathbb Z^2$, which records their collision sites and times. This is a critical regime for collisions: the walks collide infinitely often, whereas the limiting Brownian motions do not collide at positive times. Hence, existing general results on the convergence of collision measures do not apply. Assuming that the jump distribution has mean zero and finite second moment, we prove that, under a logarithmic scaling, the collision measure converges in distribution to a non-trivial random measure. We also give an explicit representation of the limiting measure in terms of a Poisson point process. To prove convergence, we introduce a new cluster decomposition of the Laplace transform of the collision measure, revealing the cluster structure of collisions.

Predicting many molecular properties requires accurate ground-state energies of molecular Hamiltonians. Quantum-selected configuration interaction (QSCI) obtains such energies by measuring an input state to select important electronic configurations and classically diagonalizing the Hamiltonian in the subspace they span. ADAPT-QSCI, an adaptive extension of QSCI, improves the input state through iterative circuit growth. For single-reference molecules, the sampling distribution is dominated by the Hartree-Fock (HF) configuration, so most measurements reproduce a configuration already known. We reduce this redundancy by placing the HF configuration in the diagonalization subspace classically, before any measurement. This invalidates the operator-selection criterion of ADAPT-QSCI, and we derive a consistent replacement with energy and gradient in closed form, adding no query to the quantum device. At the per-iteration shot budgets previously used for ADAPT-QSCI, the proposed scheme reaches chemical accuracy with approximately $63\%$ and $43\%$ of the CNOT gates for $\mathrm{H}_4$ and $\mathrm{H}_6$, and $44\%$ and $40\%$ of the total shots. The advantage depends on the budget, however: in the infinite-shot limit the $\mathrm{H}_4$ CNOT count increases to $125\%$ of that of ADAPT-QSCI. These results identify the per-iteration shot budget as a key design variable governing resource savings in QSCI-based algorithms.

The dimensionality of entanglement in high-dimensional quantum systems is quantified by the Schmidt number, whose large value signals potential advantages for quantum communication and quantum computation. A commonly used approach to practical Schmidt-number detection in finite-dimensional systems is based on the estimation of fidelities to pure states with large entanglement dimensionality or lower bounds to these fidelities. However, for mode-entangled continuous-variable systems, the corresponding measurements are typically difficult to realize. Here, we introduce and assess fidelity bounds for Schmidt-number detection based on practically more accessible measurements of the first and second statistical moments of arbitrary continuous-variable quantum states. We provide analytical formulas that allow evaluating these bounds and test them for families of Gaussian and non-Gaussian states, including two-mode squeezed thermal states and photon-added displaced two-mode squeezed vacuum states. We compare our bounds to other methods for the certification of high-dimensional entanglement based on the same measurements.

Matching candidates to vacancies is central to recruitment, and a recruiter needs to see why a candidate fits, not only a single opaque relevance score. We provide this evidence as named, interpretable matching dimensions recruiters can act on - eight in our current deployment. We propose a two-part approach. The first is an LLM-based labeler whose prompts and feature definitions were refined from recruiter feedback while it served as an earlier production matching stage. In the current architecture, it is used only for offline labeling and is not called on online requests. The second is a feature bi-encoder distilled from it: a LoRA-adapted embedding backbone with compact per-dimension heads that runs on CPU and serves all online requests. Both parts keep improving: prompts are revised as feedback arrives, and the bi-encoder is retrained on the updated labels. The model is trained on 168,772 labeled vacancy-resume pairs (17,921 vacancies and 180,030 resumes). Recruiters using the service can confirm or revise surfaced feature predictions. On 927 recruiter-recorded values from this selected production-feedback subset, the deployed student agrees with the recorded decisions in 888 cases (95.79%). This is operational, non-blinded agreement rather than an independent human evaluation.

In this paper, we first expand fixed diagonals of the Jacobi-Stirling numbers in a binomial basis. For the second kind, the expansion coefficients are polynomials in $z+1$ with nonnegative integer coefficients. We give a recurrence and a signed-partition interpretation for these coefficients. The same holds for the differences between corresponding unsigned first-kind and second-kind coefficients. We then prove that every nonzero nonnegative linear combination of the descent polynomials over Jacobi-Stirling permutations with a fixed number of deleted barred letters has only simple negative zeros when that number is one, two, or three. The same holds when exactly one or two barred letters are retained. Thus we verify five infinite families in a conjecture of Gessel, Lin and Zeng. Finally, using insertion operators, we find that every descent polynomial over Jacobi-Stirling permutations with a fixed number of deleted barred letters is top heavy and has an increasing left half.

Supervised AI-text detectors report high benchmark accuracy, but it is not clear what their decisions are based on. We analyze a RoBERTa-based detector under semantic, structural, and tokenizer-level perturbations, using the M4 dataset (N = 10,000) and controlled generations (N = 300). When Mistral-7B-Instruct was asked to make machine text sound more human, Verb Diversity rose from 0.77 to 0.92 and the outputs became easier to detect. Detection scores appear to track statistical complexity, which also leads to a 76.3% false-positive rate on formal human writing. As a control, we evaluate event-based Latent Space detection. Paraphrasing changed 87% of its event sequences (Jaccard = 0.067), and homoglyphs altered 70% of the extracted verbs even though extraction still ran (Jaccard = 0.30). Its best domain AUC was 0.577. RoBERTa's robustness seems specific to the features it uses, and structural abstraction did not make detection more robust.

While representation similarity across independently trained language models is well-documented, how internal mechanics such as attention behave across models remains far less characterized. Inspired by this gap, we examine the structure of post-softmax attention weights by marginalizing over query positions, mapping them into a joint token-head "marginal attention space". Evaluating across 60+ diverse LLMs, we find that different properties emerge when reducing this space along its token and head axes. When reduced token-wise, marginal attention yields a text-intrinsic signal robustly conserved across models. To explain this property, we empirically connect marginal attention to the input-output Jacobian of the network, and prove theoretically that under a smoothness assumption, models with similar next-token distributions are guaranteed to have similar input-output Jacobian statistics. When reduced head-wise, it forms a model-private signature conserved across documents. Practically, this provides a natural way to estimate a per-head budget for key-value (KV) cache eviction, effectively decoupling model-specific budget allocation from text-intrinsic token scoring. On standard eviction benchmarks, a per-head budget precomputed offline on pretraining text, combined with a training-free token score, shows competitive performance with methods that recompute the budget on every document or train it per target. Code available at https://github.com/Flegyas/marginal-attention

The spectral fluctuations in complex quantum systems are modeled in terms of spectra from random matrices. Quantitative agreement with random matrices holds only when the quantum spectrum is a pure sequence, and not a composite spectrum that mixes levels from different symmetry sectors. It was shown earlier that discrete symmetries in composite spectra can be detected using higher-order spacing ratio statistics provided the symmetry sectors are of equal dimensions. The general case is when the symmetry sectors have unequal dimensions, and the symmetries of the Hamiltonian system are unknown or only partially known. In this work, we address how the number of symmetry sectors can be determined from a composite spectrum arising in Hermitian and non-Hermitian settings. A Best Subset Technique is proposed for determining the number of the symmetry sectors by comparing the spectral fluctuations to that of an appropriate random matrix ensemble without requiring de-symmetrization. It is demonstrated using spectra from Gaussian, Wishart and Ginibre ensembles, and also for spectra drawn from many-body quantum systems.

We establish a weak type $(1,1)$ estimate for the Bochner–Riesz mean operator at the critical index $\delta=\frac{d-1}{2}$ on the quantum torus $\mathbb{T}^d_\theta$, where the associated kernel is rough.

The subseasonal-to-seasonal (S2S) timescale, roughly from two weeks to two months ahead, is a critical forecast window for sectors such as agriculture, energy, and water management. Yet, it is widely known as the `predictability desert'. Recent AI weather models excel up to two weeks ahead but deteriorate beyond, largely because they are trained to predict fine-scale details that are neither predictable nor essential at S2S timescales. We argue that a more physically grounded objective is to forecast only the slowly varying components that remain predictable. Computer vision reached the same conclusion with the Joint-Embedding Predictive Architecture (JEPA), which predicts in latent space, discarding unpredictable details. In this work, we introduce S2S-JEPA, which brings the JEPA paradigm to S2S forecasting. It is tailored to this task through design elements from state-of-the-art AI weather models. S2S-JEPA achieves comparable skill to the gold-standard ECMWF physics-based ensemble and surpasses it on multiple metrics at weeks 5 to 6.

Communication in shared space interweaves verbal and non-verbal signals, and pointing gestures anchor language to the environment: "put the cup on that one" is uninterpretable without the gesture that fixes the referent. Yet no common framework exists for evaluating whether generated gestures indicate their intended referent; distributional metrics reward a gesture aimed at the wrong object as long as it looks natural. We introduce a benchmark for spatially grounded gesture generation, comprising ~2K pointing-annotated clips from naturalistic VR dialogue with ground-truth 3D referents, a task in which systems must decide when, how and where to point within conversational speech, and a protocol that separates temporal alignment, spatial grounding and perceived naturalness. We also provide a flow-matching baseline, MM-Conv-Flow. Evaluating it alongside an independent retrieval-based system and captured human motion, we find that geometric grounding can exceed that of human pointing without any gain in perceived naturalness, showing that referential gesture quality must be measured along separate dimensions.

We develop a finite-state geometric framework based on third-order Bargmann invariants for evaluating Chern numbers and characterizing local quantum-state geometry. Using gauge-invariant state overlaps, the framework evaluates the Chern number directly on discretized parameter spaces while retaining local geometric information through the phase-derived density and the complementary amplitude density, as well as signatures associated with changes in topological character. We apply the construction to the Qi–Wu–Zhang, $1/3$- and $1/4$-flux Hofstadter, SSH, and Rice–Mele models, including a rank-$2$ extension for isolated composite subspaces and applications to closed-loop and parameter-space topology. The resulting framework organizes Chern topology and local geometric information directly from finite-state data, providing a compact state-based description without relying on dynamical evolution.

Quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) is a promising route to using quantum computers for strongly correlated electronic structure problems, but its scalability is limited by a classical post-processing bottleneck: the measured quantum trial state must be used to evaluate overlaps, force biases, and local energies for many walkers throughout the AFQMC propagation. Existing matchgate-shadow approaches avoid the exponential cost of generic classical shadows, but their post-processing remains expensive for large systems. In this work, we show that particle-number-preserving fermionic shadows, implemented as orbital-rotation shadows, are able to drastically reduce QC-AFQMC post-processing costs. We derive efficient estimators for overlaps and their derivatives, giving $O(N^3)$ scaling for overlaps and force biases and $O(N^4)$ scaling for local energies per shadow and walker and with $O(N)$ Cholesky vector. For fixed normalized target determinants, we also prove that the overlap estimator is unbiased with variance upper bounded by $O(\eta)$, where $\eta$ is the particle number, yielding a sufficient budget of $O(\eta/\epsilon^2)$ ideal independent measurements for additive overlap error $\epsilon$. We combine these estimators with a novel virtual-correlation-energy treatment and a GPU implementation and demonstrate QC-AFQMC using orbital-rotation shadows. Performance projections for $\pi$-conjugated molecules up to pentacene with a (22e, 22o) active space and 356 total orbitals show that the full classical post-processing workflow can be completed in slightly more than two days on 8$\times$A100 graphics processing units (GPUs). These results significantly reduce classical post-processing costs for QC-AFQMC and motivate further improvements in preparation and measurement of the trial state on quantum hardware.

An LLM agent can recognize uncertainty yet still choose the wrong next step: asking when action is already justified, or seeking clarification when the constraints must change. We formalize actionable indeterminacy: act when an accepted action is shared across all admissible preferences or objectives, clarify when each possibility is feasible but no action is shared, and propose a minimum-cost permitted constraint repair when the request is infeasible. We construct a solver-grounded benchmark spanning object allocation, meeting scheduling, apartment choice, and stable matching. Matched pairs retain the same source while changing whether intervention is necessary, and evaluation separates decision correctness, matched-pair reliability, and fully correct responses. Our findings reveal a recurring difficulty in recognizing when intervention is unnecessary: models can identify situations requiring clarification or repair yet still intervene when a justified action already exists. Correct decision labels also fail to guarantee usable actions, questions, or repairs. Crucially, response requirements shape not only how decisions are expressed but also which decisions are made. Making the required content explicit substantially improves fully correct responses and can change intervention decisions, even when outputs are already parseable. These findings highlight that reliable agency requires more than recognizing uncertainty: it requires intervening only when necessary and translating the chosen next step into a verifiable response.

Clustering variables in causal graphs reduces the size of the graph and simplifies causal inference. However, arbitrary clustering can alter crucial causal relations among variables and lead to erroneous conclusions. While the identifiability of a causal effect in the clustered graph implies the identifiability in the original graph under mild conditions, nonidentifiability in clustered graph does not imply nonidentifiability in the original graph without further assumptions. When both identifiability and nonidentifiability are preserved, the clustering operation is called identification invariant. We present a broad class of clustering operations that are identification invariant based on conditions related to the c-components of the original graph. Finally, we demonstrate use of the results in practical settings.

We construct degree-three isogenies of Hesse elliptic curves over an arbitrary field of characteristic different from three, which correspond to a step of the cubic arithmetic-geometric mean. As an application, we describe the Serre-Tate canonical lift of an ordinary elliptic curve in characteristic three by the 3-adic cubic arithmetic-geometric mean. We also discuss the relations of the Hesse curves with complex and finite hypergeometric functions.

E-commerce videos are information-dense and frequently compared by consumers evaluating products and merchants assessing marketing strategies. However, existing multimodal models mainly focus on single-video understanding and have limited ability to compare information across videos. We introduce AdsCVR, the first e-commerce cross-video reasoning benchmark, containing 2,483 videos and 6,110 question-answer pairs across six reasoning dimensions. Cross- video reasoning requires models to locate fine-grained evidence among many redundant frames and integrate visual details, speech, and on-screen text. We therefore propose AdSeek, an agentic framework that dynamically selects visual and audio tools during multi-turn exploration, replacing static uniform sampling with active evidence acquisition. To address the sparse credit assignment of reinforcement learning, we develop an offline trajectory rectification mechanism that identifies reasoning errors and missing multimodal evidence in RL-generated trajectories. The corrected trajectories provide supervised fine-tuning signals that reduce biases learned during RL. This mechanism supports a rectified bootstrapping pipeline in which initial RL exposes reasoning bottlenecks, supervised fine-tuning corrects them, and a final RL stage further improves the policy. AdSeek achieves 74.30 percent accuracy on the AdsCVR test split, outperforming its Qwen3-VL-8B-Instruct backbone by 27.90 percentage points. It also generalizes to the open- domain CrossVid benchmark, demonstrating effective active evidence gathering.

Codon optimization, the process of selecting synonymous codons to improve mRNA translation efficiency and protein expression, is central to therapeutic protein production and mRNA vaccines, yet it remains a hard problem. The design space is discrete and combinatorially large, precluding gradient-based methods, and existing tools rely on heuristic proxies (e.g., Codon Adaptation Index or GC-content) that poorly capture true expression. We introduce Latent-Space Codon Optimization (LSCO), which recasts this discrete problem as a continuous one by mapping sequences into the latent space of a pretrained mRNA language model, enabling efficient gradient-based search. LSCO combines four components: a data-driven expression objective from an uncertainty-aware predictor, a Minimum-Free-Energy regularizer for structural stability, a naturalness prior from a protein-to-codon back-translation model, and constrained decoding for protein fidelity. On a real-world, wet-lab antibody expression dataset, LSCO outperforms simple frequency-based, as well as modern deep generative baselines in predicted expression, while retaining suitable biophysical properties.