Computer Science (arXiv)

Quantization is a fundamental technique to handle the growing sizes of embeddings generated by modern models. Existing quantization schemes are largely embedding agnostic and allocate bits uniformly across dimensions. However, recent models produce embeddings with significant geometric structure. In this work, we investigate whether a variable bit allocation scheme can improve quantization quality under a fixed memory budget. We propose a simple variable bit allocation framework that partitions an embedding into contiguous buckets and allocates storage non-uniformly across them. Using a greedy allocation strategy, we instantiate this framework for both Product Quantization (PQ) and Scalar Quantization (SQ). We perform a series of experiments on embeddings known to have the Matryoshka property (MRL), and consistently observe that non-uniform allocations outperform uniform baselines at identical storage budgets. The largest improvements occur in the low-bit regime, where uniform allocation is particularly inefficient for MRL embeddings. At the same compression rates, variable allocation improves recall by up to 8\% for PQ and up to 18\% for SQ. Our results suggest a new direction for structure-aware compression and indexing techniques for large-scale retrieval systems.

A YARA rule is easy to distribute, but the malware sample used to demonstrate a positive match is not. This complicates storage, continuous integration, disaster-recovery exercises, and reproducible scanner validation. Constructing a replacement fixture requires more than embedding literals: YARA conditions can combine alternatives, counts, offsets, integer reads, and executable-container constraints, while the resulting file should not reproduce malware behavior. Positive validation is existential: it requires one file-level member of a rule's match set, not reconstruction of the originating sample. We present Aray, a deterministic-first YARA interpreter and positive-fixture synthesizer. Models may propose constructive normalizations or typed extraction fallbacks, but never backend source or binary structure. Conventional code validates normalized rules, derives string and integer witnesses, and performs extraction, routing, collision-checked layout, and ELF, PE, or generic serialization. Only residual normalization semantics reach a bounded model judge. We evaluated Aray over 416 public-rule entries. Normalization accepted 182 entries without model assistance and 234 after model normalization. Constructibility preflight admitted 406 entries, and every admitted fixture matched its upstream original rule. This yields 406/416 (97.6%) overall and 406/406 among constructible rules, with ten expected preflight dispositions and no scanner mismatches or construction failures. An unreachable endpoint confirmed zero model invocations during realization. The original-rule oracle validates generated fixtures against their source rules; proving implication for all possible files is a separate, stronger objective. Two anchored-regex failures were repaired before the final run, so these are post-fix systems results, not a held-out estimate.

Historical Arabic manuscript transcription is not only a recognition problem. A usable scholarly system must cope with shifting hands and layouts, preserve uncertain readings, distinguish visual evidence from linguistic plausibility, and record the researcher's final decision. We present Phoenix, a 4.99-million-parameter CNN-BiLSTM-CTC recognizer, and Athar, an evidence-aware review workflow built around it. Phoenix is adapted across archival, Maghrebi, and historical manuscript domains using document-aware replay, an expanded 81-symbol codec, and forgetting guards that reject checkpoints that improve a new domain at unacceptable cost to previous domains. In a pre-specified held-out comparison against the preceding checkpoint, frozen before evaluation and scored with greedy decoding and raw references, Phoenix reduced CER from 22.12% to 17.86% on 10,594 Agapet lines and from 17.72% to 11.84% on 11,684 Omar lines, while regressing from 10.39% to 10.72% on 164 TariMa lines. Across the two large held-out sets, character-weighted CER fell from 19.98% to 14.93%, a 25.3% relative error reduction. A separate same-protocol development diagnostic found the lowest CER for Phoenix on four of four comparable domains (9.59% unweighted macro CER). An N-best diagnostic revealed a 2.15-point oracle gap between beam decoding and Oracle@25, while neural text rerankers, consensus MBR, CTC-posterior quality estimation, and local pre-CTC hidden-state quality estimation recovered less than 4% of this gap. Athar therefore preserves the visual reading, exposes bounded alternatives, uses local language models conservatively, retrieves source parallels with unique, ambiguous, or abstain states, and exports auditable TEI and PAGE-XML records. The results support evaluating manuscript HTR as auditable evidence management rather than silent text replacement.

Network embedding methods learn low-dimensional representations of graph-structured data to support downstream tasks such as node classification, link prediction, and influence maximization. However, real-world networks often reflect structural inequalities arising from demographic imbalances, homophily, and other societal biases, which fairness-agnostic embedding methods can encode and amplify. To address this issue, numerous fairness-aware network embedding methods have been proposed to mitigate bias while preserving embedding utility. This survey presents a comprehensive overview of fairness-aware network embeddings for complex networks. We propose a taxonomy that categorizes existing methods along three main complementary dimensions: underlying embedding approach (spectral, random walk, graph neural network, Bayesian, and method-agnostic), fairness intervention strategy (pre-processing, in-processing, and post-processing), and fairness objective criterion (embedding- or task-level). We further compare methods with respect to group versus individual fairness and assumptions regarding sensitive attributes. Finally, we discuss current limitations and highlight promising future research directions. This survey provides a unified perspective on fairness-aware network embedding and serves as a reference for developing fair and trustworthy network representation learning methods.

While modern autonomous driving systems excel at perception tasks such as object detection and trajectory prediction, they lack the high-level causal reasoning required to interpret traffic accidents. In particular, determining responsibility, such as identifying who is at fault and which traffic rule was violated, remains largely unexplored in current benchmarks. To this end, we introduce CAViAR (Causal Accident Video and Incident Analysis Repository), a human-annotated dashcam benchmark comprising 2,249 real-world accident videos collected from CarCrashDataset (CCD) and Nexar. Each video is annotated with structured labels spanning environmental conditions, accident type, causal explanation, apparent At-Fault Agent, affected agent, and apparent rule-violation category. We benchmark state-of-the-art vision-language models (VLMs), including Cosmos-Reason2, Qwen3-VL, and InternVL3. Once class imbalance is accounted for with majority/random baselines and balanced metrics, perceptual competence is uneven--lighting is nearly solved, whereas weather and road-condition accuracy fall at or below the majority-class baseline---and all models degrade sharply on accident type and responsibility reasoning. Overall, CAViAR exposes a practical Perception--Reasoning Gap: current VLMs may recognize salient context, but do not reliably map visible agent actions to annotated rule-relevant responsibility categories in safety-critical driving scenarios. Code, annotation schema, prompts, and evaluation scripts are available at: https://github.com/nec-labs-ma/CAViAR

K-12 students often possess creative engineering ideas but lack technical skills to build them, while undergraduates have coding expertise but few opportunities to lead real-world projects or mentor others. The rapid development of AI-assisted tools offers a potential bridge to connect these groups, yet the structure for effective K-12 and university collaborations remains underexplored. This paper introduces a multi-tiered mentorship framework enabling high school students to engage in authentic engineering through AI-assisted development using large language models and AI agents, while undergraduate mentors provide architectural oversight. We test this framework through LuckyTag, a privacy-preserving NFC-based lost-and-found system. The model positions high schoolers as product leads, undergraduates as technical architects, and faculty as minimal-intervention advisors. A pilot with four high school students, three undergraduates and two faculty yielded survey data showing high perceived barrier removal and gains in system architecture understanding. Thematic analysis reveals that AI amplifies rather than supplants mentoring demands, requiring human oversight for logic and security. These findings suggest a hybrid model for equitable K-12 and university collaboration on computing integration that emphasizes "AI micromanagement" and architectural reasoning over traditional syntax.

Bayesian inference via Markov Chain Monte Carlo (MCMC) provides effective parameter estimation, but its real-time application in complex physical systems is hindered by heavy computational bottlenecks and extreme sensitivity to statistical noise. We address this by proposing a neural-network-based probabilistic surrogate framework for rapid and robust MCMC inference. Using fusion plasma Thomson scattering diagnostics as a challenging, noise-dominated testbed, our approach employs a dual-head architecture to simultaneously estimate the expected physical emission spectrum and the channel-wise intrinsic measurement noise variance. By optimizing a Gaussian Negative Log-Likelihood (GNLL) objective, the learned aleatoric uncertainty dynamically buffers the sampler against pathological shot noise. Evaluations demonstrate that this surrogate framework achieves > 1500x acceleration over exact physical forward models, while simultaneously reducing inference error (RMSE) by >20% compared to standard homoscedastic neural baselines, offering a highly promising paradigm for real-time physical analysis.

Split-conformal prediction provides marginal coverage under exchangeability and is increasingly used as an abstention layer for zero-shot vision-language models (VLMs). We audit this practice under deployment shift for CLIP, OpenCLIP, and SigLIP across ImageNet and non-ImageNet settings. Marginal coverage can remain relatively high while class-conditional tail coverage collapses: on ImageNet-Sketch, worst-class coverage falls to $\approx 0$ and 10-12% of classes lie below a finite-sample null floor, despite marginal coverage of about 0.86. The failure is aligned with target-domain class accuracy but is not predicted by the source-domain diagnostics we test. Source-side Mondrian calibration improves the in-distribution tail but does not transfer, while clustered conformal and Conf-OT improve marginal or average metrics without recovering the worst-class tail. Target-side class calibration substantially lifts the tail, but requires labels for every class and remains set-size-intensive. We further identify a 2-3$\times$ cross-family efficiency gap and show that native SigLIP sigmoid scores remove APS's probability-mass interpretation. The findings persist across the tested model scale, pretraining corpus, prompt, miscoverage level $α$, and shifted non-ImageNet settings. Marginal conformal coverage should therefore be treated as an average reliability statistic, not as a safety guarantee for the class tail.

High-fidelity embodied AI simulators provide realistic evaluation of complex robotic systems, but their computational cost limits their direct use for large-scale reinforcement learning campaigns. We advocate the use of less accurate but more expeditious simulations, which might draw on data-driven, e.g., neural dynamics, models. This contribution argues that the practical value of a neural dynamics model for complex robot control lies in learning the \emph{right abstraction}: a reduced state that preserves the control-relevant physics of the high-fidelity system while enabling high-throughput policy learning. We develop a neural reduced dynamics (NRD) framework that separates the state the model propagates from what can be supplied as an input or recovered analytically, trains policies entirely inside the frozen learned model, and validates them back in the high-fidelity simulator. Two case studies instantiate it across three control tasks: terrain-aware HMMWV trajectory tracking on rigid, bumpy and deformable Continuum Representation Model (CRM) terrain; and goal reaching for a stock tracked vehicle and its front-mounted articulated arm. Every policy transfers back to the high-fidelity simulator. A single policy trained inside the terrain-conditioned dynamics model, and given no terrain input of its own, attains lower median and mean tracking error than both single-terrain specialists on all three terrains, including zero-shot bumpy terrain. Quantitatively, the tracked vehicle reaches 100 of 100 goals and the arm 97 of 100, with zero contacts or joint-limit violations. The NRD models advance roughly four orders of magnitude faster in simulated time than the high-fidelity simulator scenes they replace, making iterative on-policy learning practical and supporting neural reduced dynamics as a bridge between accurate but expensive physics simulation and scalable robot learning.

A fundamental challenge in robotic teleoperation is enabling an operator to control a remote robot as effortlessly and intuitively as their own hands. Despite the growing use of teleoperation to collect demonstration data for training autonomous robot policies, teleoperated robot performance still falls significantly short of human dexterity, even for basic tasks. Here, we present evidence that a key factor contributing to this performance gap is the absence of spatially distributed tactile feedback. Using a two-degree-of-freedom (DoF) bilateral force-feedback telemanipulator paired with a 32-DoF tactile fingertip display, we show that operator performance improves significantly when localized deformations on the remote manipulator are faithfully reproduced on the operator's fingertip. In a series of teleoperation tasks, reproducing distributed contact information not only accelerated task performance but also brought teleoperated movements closer to natural human behavior by minimizing corrective actions and task completion steps, thereby reducing the deviation between teleoperated and natural trajectories by 29$\unicode{x2013}$79%. Furthermore, we found that increasing the resolution of the tactile feedback$\unicode{x2014}$by refining how finely the measured displacements were quantized for reproduction$\unicode{x2014}$compressed the state-space distribution of teleoperated motions, which has been associated with improved training outcomes for autonomous robot policies. Together, these results suggest that spatially distributed tactile feedback is essential for closing the gap between human and teleoperated dexterity and training the next generation of autonomous robots.

These notes develop four interconnected ways of reading a quantum circuit. A circuit for us begins as an operational composition of gates; then, it becomes a diagram whose local equalities may be used as calculations; next, it becomes a protected process once errors, syndromes, and logical degrees of freedom are separated; and finally, it becomes geometric when its connectivity, topology, and boundary data are treated as physical design parameters. The development begins at the level of bits and qubits before appealing to Deutsch's and Grover's algorithms as basic examples of quantum circuits. With the basics in hand, we interpret quantum circuits diagramatically, leading us to compact closed string diagrams and the ZX-calculus. After that, we consider how to correct quantum circuits by introducing the Knill--Laflamme condition, homological surface codes, and related concepts with a view towards thinking of these as operations on diagrams. The lectures eventually arrive at the properties of hyperbolic quantum codes and the prospect of physical superconducting circuits emulating the negatively-curved lattices needed to support those codes. These mathematical ideas and physical experiments, taken together, represent one way to impart a geometric layer onto quantum circuits. By the very end, we bring the ideas nearly full circle by assessing the extent to which these device physics experiments operationalize the basic ZX diagrams encountered much earlier in the story. While the later material reports on original research, and while the discussion becomes increasingly mathematical as the sections progress, no prior knowledge of quantum information, quantum computing, or quantum error correction is actually assumed.

Statistical watermarks for language models live in the freedom of the signifier: they choose among tokens that are nearly equivalent in meaning, and they are therefore eroded by exactly those transformations which move the form of a text while leaving its content in place. The literature measures such transformations by their endpoint, through the semantic similarity between the original and the rewritten text. We show that the endpoint is the wrong statistic. Adapting the formalism of linguistic loops, we prove that the invariant of a chain of meaning-preserving transformations factorises canonically into an endpoint part and a holonomy in the stabiliser of the initial state, the second of which the semantic deficit cannot see; the loop rotation is parallel transport on the unit sphere of the embedding space, so that the analogy with the Wilson loop becomes a theorem rather than a figure of speech. On the side of the detector we prove an exact identity: the residual statistic is proportional to the number of positions whose seeding window survived intact, from which the decay law $ρ^{h+1}$ follows as the independent-edit corollary. The identity has a disconcerting consequence, which we confirm to three decimal places: at one and the same retention rate the surviving signal may be one half of the original, one quarter of it, or exactly nothing, according only to where the edits fall.

Mission-critical intelligent systems often operate under time-varying limitations that reduce control authority and change the admissible safe operating envelope. In such settings, a safety certificate learned under nominal conditions may become invalid as system capability changes. To address this challenge, this paper proposes a degradation-aware, data-driven safety-filtering framework that learns a safe set from data, updates it online, and enforces the resulting learned barrier through a time-varying control barrier function (CBF). A nominal safe envelope is first learned from operational data using a radial basis function (RBF)-kernel support vector machine (SVM), whose decision function serves as the initial CBF candidate. To capture capability-induced safe-set contraction, a continuous-time decremental SVM update law is developed so that selected support-vector coefficients are reduced according to a degradation signal. A homotopy-smoothed SVM-CBF is then introduced to avoid discontinuous changes in the learned barrier during active-set transitions. The resulting time-varying learned barrier is enforced using a quadratic-program-based safety filter under degraded input constraints. Forward invariance of the learned time-varying safe set and recursive feasibility of the safety filter are established. Simulation results on a vertical takeoff and landing (VTOL) model show that the proposed method maintains safety under reduced control authority and avoids abrupt barrier-switching effects during safe-set contraction.

This study reports the development of an Automatic Speech Recognition (ASR) system in Mizo, a low-resource language. The development included collecting 17.62 hours of speech data, curating it, and fine-tuning the Mizo ASR system with three Whisper multilingual models and with the SraVaani 1.0 Indic multilingual model. Whisper-large-v3 achieved the lowest conventional WER (18.08%), while morphology-aware evaluation yielded a WER of 7.22%. Zero-shot evaluation of the SraVaani 1.0 Indic multilingual model yielded a WER of 58.27%, while Mizo-specific fine-tuning reduced the conventional WER to 29.45% and the morphology-aware WER to 17.93%. The results demonstrate that the Whisper model can achieve a substantially low WER, even when adapted to an unseen language. In contrast, SraVaani 1.0 supports the Mizo language in its multilingual model; however, fine-tuning with carefully curated Mizo speech data substantially improves its performance.

A finite-dimensional two-field system for divergence-free edge cochains is introduced. Its MHD-type designation refers only to a quadratic exchange pattern and exact total-energy cancellation; it is not a physical MHD discretization. A general cancellation class is separated from a corrected explicit realization: the anticommutator $D(a)J+JD(a)$ is skew-symmetric for diagonal $D(a)$ and skew-symmetric $J$, and its projected bilinear map has the required trilinear antisymmetry. The central result is a Hodge coercivity criterion: the full divergence-free space admits the Poincaré-type estimate needed for dissipativity if and only if its harmonic $1$-cochain space is trivial. Under this condition, global existence, an exact energy identity, an absorbing ball, and a compact global attractor follow. When harmonic modes are present, a harmonic-decoupled interaction class yields invariant harmonic affine fibres and fibre-wise attractors. Deterministic disk, annular, and two-hole examples illustrate the spectral criterion, energy law, and distinction between general harmonic exchange and harmonic-fibre invariance.

Educational visual question answering, or VQA, requires models to solve curriculum-oriented multiple-choice questions using both language and visual evidence. Compared with conventional open-ended VQA, educational examples often include structured assessment metadata, diagrams or image contexts, and semantically close answer options, creating strong opportunities for question-option shortcuts. We develop and evaluate a parameter-efficient adaptation framework for a frozen multimodal large language model in this setting. We introduce GRACE, Grounded Reasoning via Adapter Composition and Evidence-Aware Calibration, a framework that uses the pedagogical state of each question to specialize lightweight language and vision adaptation. The state combines inference-visible subject, grouped skill, grade, visual-context, question-intent, and option-structure cues. GRACE uses factor-specific prompts and lightweight visual adapters, then applies evidence-aware option calibration to score all candidates under a shared multimodal context. On ScienceQA, GRACE improves a shared-adapter baseline from 90.5 percent to 93.1 percent overall accuracy and from 88.7 percent to 91.2 percent on image-context questions. Removing pedagogical composition, option calibration, or the visual adapter reduces overall accuracy by 1.4, 1.0, and 1.5 points, respectively. These controlled results show that structured educational state is an effective routing signal for parameter-efficient multimodal adaptation.

Robustness verification of neural networks is increasingly important, due to their use in many critical domains. In certain scenarios, proof sharing has been shown to accelerate incomplete verification techniques by reusing intermediate-layer abstract states, or templates, across queries. However, questions remain as to the robustness of template-based acceleration across varying network architectures, properties, datasets, and training methods. In this work, we perform a systematic study of the effectiveness of template-based acceleration and its limits. Our study shows that template subsumption rates can vary widely across scenarios. We present a novel metric of jointly stable neurons to explain this variation, showing that in some cases template-based techniques are very unlikely to provide any speedup. Then, we present FastCert, a novel technique for automatically distributing templates across neural network layers to increase performance impact, eschewing templates entirely if they are unlikely to produce a speedup. Across a large set of covering-design based $L_0$-verification tasks, FastCert achieved an average speedup of 1.13x over an extant template-based reuse technique.

Generative AI may enable new forms of context-aware creative expression by dynamically tailoring media content to its consumption context. For instance, AI systems could adapt song lyrics to the listener and their current activity. However, existing media adaptation systems primarily optimize for audience experience, often neglecting artists' intent, style, and preference. We address this challenge by introducing a novel creator-centered approach to adaptive media authoring and present MultiVerse, a system that instantiates this approach for steering adaptive lyrics. Our approach allows creators to explicitly author controls based on their intent, lyric structure, and audience context, and uses rule-based validations to ensure controls are followed. We conducted a study with 10 songwriters, comparing MultiVerse with a prompting-based workflow for composing adaptive lyrics. The comparison revealed that creators preferred to author how lyrics adapt by explicitly specifying relevant context and adaptation constraints, while recognizing trade-offs in flexibility and iteration speed. Interviews further revealed that creators viewed adaptive media as enabling new forms of audience connection, introducing a distinct creative process, favoring new compositional strategies, and reshaping notions of authorship.

Search-based Automated Program Repair (APR) techniques rely on carefully designed mutation operators to explore the space of candidate fixes. Recent advances in Large Language Models (LLMs) suggest that generative models could replace such operators by dynamically proposing repairs. In this paper, we investigate this hypothesis in the context of Cyber-Physical Systems (CPSs) modeled in Simulink/Stateflow. We extend the state-of-the-art FlowRepair approach by replacing a subset of its mutation operators with LLM-generated mutations, enabling more flexible and expressive patch generation. We evaluate the approach on a benchmark of 19 real-world faulty Stateflow models across four CPS domains, using the same experimental setup as FlowRepair for controlled comparison under the same wall-clock budget. Contrary to expectations, in this controlled evaluation, the LLM-based mutation substantially degrades repair performance under the FlowRepair experimental setup. Across the tested LLM variants, the LLM-based repair produced plausible patches for 4-6 models and valid patches for 4 models, compared to 18 and 16, respectively, with the original approach. Our analysis reveals that, in this integration, LLMs struggle with precise symbolic edits, lack behavioral feedback, and generate a noisy search space that hinders effective exploration. Rather than showing a general limitation of LLMs for APR, these findings highlight fundamental limitations of naively integrating LLMs into search-based APR and motivate hybrid approaches that combine structured mutation with generative guidance.

Mechanistic interpretability seeks quantities that models do not expose directly: represented states, component effects, interactions, and responses to interventions. Patching, gradients, Hessian-vector products, and subset interventions provide different measurements under different access assumptions and may target different quantities. We formulate their shared measurement structure as mechanistic tomography: designed measurement for recovering internal mechanisms and intervention effects. For a chosen basis and intervention family, measurements take the form y = Ax + w, where A describes the interventions, x is the target map, and w contains nonlinear response, sampling error, and basis misspecification. This language gives a practical procedure: start with the least costly measurements, test on held-out interventions at the intended scale, calibrate simple mismatch, and expand the measurement family when structured residuals remain. Control provides a demanding validation setting because an estimate that guides an intervention acts as an observer. In a two-HMM model, control error rises with observer error, while target improvement can hide nuisance-state movement. Under forward-only access, sparse aggregate measurements recover a finite-effect map with fewer interventions than coordinate patching. With gradient access, finite probes improve a local attribution map. Lifted measurements and Hessian-vector products recover interactions missed by first-order maps, while Tracr shows that the required family depends on the basis. On GPT-2-small IOI, the Name Mover-Negative Name Mover interaction is the largest held-out predictive term among three tested cross-group pairs. On Qwen-2.5-7B, finite calibration makes an additive refusal-response map adequate, so held-out error does not support pairwise lifting.

We modify the NN/QFT duality [1] to incorporate the layerwise permutation symmetry of the network, resulting in a $(0\!+\!1)$-dimensional lattice gauge theory, in which each layer of $N$ neurons acts as an $N$-component lattice site, and the weight matrices play the role of gauge fields living on the links. In this framework, we compute the tree-level neuron-neuron propagator which describes the evolution of layer variance in the network, and develop the Feynman diagram machinery to compute interactions in the perturbative expansion in $1/N$. In particular, we obtain a recursive expression for all corrections to the exact propagator at $O(1)$, representing statistical fluctuations in the ensemble of networks, including infinitely-many loop diagrams mediating the interactions from previous layers. We also present a preliminary analysis of neuron scattering amplitudes that contribute order-by-order in $1/N$, which provides a field-theoretic framework for studying higher-point correlations, and by extension information propagation, in deep networks. We remark on some interesting directions for future work at the intersection of neural networks and quantum field theory.

Uncertainty quantification (UQ) is essential for the safe deployment of large language models (LLMs). Existing methods, from verbalized confidence to ones requiring multiple generations, are often zero-shot and produce scores quantifying uncertainty without the need for labelled data. Nonetheless, in practice one must always evaluate their performance on a dataset of interest before deployment. In this work we show that, by leveraging this dataset, we consistently outperform these existing scores. Specifically, we build simple classifiers that predict LLM response correctness by using these scores and the correctness of similar queries as features. Our method produces minimal computational overhead, making it a cheap and straightforward enhancement for UQ in LLMs for real-world applications.

Gaussian boson sampling (GBS) is a sampling task proposed to demonstrate quantum advantage. We consider Gaussian boson sampling on $M$ optical modes, with $K$ equally squeezed input modes and $N$ observed photon counts. We complete the proof of the hiding conjecture for Gaussian boson sampling with an arbitrary number of squeezers $K$, which is a part of the argument for classical hardness of GBS. In particular, we show that for any $K$ and $N=o(\sqrt{K})$, the symmetric product $MK^{-1/2}U_{NK}U_{NK}^T$, for $U_{NK}$ the top left $N\times K$ submatrix of an $M\times M$ Haar random unitary $U$, is close in total variation distance to both an $N\times N$ symmetric complex Gaussian matrix $\mathbf G$ with independent entries, and the symmetric product $GG^T/\sqrt{K}$ for $G$ an $N\times K$ matrix of iid standard complex Gaussians. We show however that the density-based instance generating method of [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013), Lemma 5.8] used to efficiently implement a hiding procedure fails for Gaussian boson sampling with $K=cM$ if $c<1/2$. Instead we use approximate instance generating to implement the hiding for the usual classical hardness reduction.

Given a set of input states, we consider the task of predicting the expectation value of a Pauli observable at the output of an unknown quantum evolution, using only a limited number of measurements. Recently, quantum Gaussian process (QGP) regression was introduced for this task across various classes of unitary evolution. Here, we extend the QGP framework beyond unitary dynamics. In particular, we prove convergence of the channel's outputs to a QGP and derive the associated closed-form kernel under a uniform (Lebesgue measure) prior over quantum channels. The kernel's dimensional factor, however, dictates the required observation precision. While manageable when the channel and observable are restricted to small subsystems, exponential suppression precludes learning when the subsystem grows extensively with the system size. Since the Lebesgue prior is overly broad for many applications, we propose an empirical Bayes heuristic that replaces the dimensional factor with a learnable scale parameter while retaining the kernel's state-overlap correlation structure. In numerical simulations of up to 64 qubits, channel QGP regression with the Lebesgue kernel exhibits a strong inductive bias for local channels, enabling faithful extrapolation. For global 64-qubit channels, the rescaled kernel restores learnability, with predictions improving systematically with the shot budget. Results from a noisy quantum computer further demonstrate the robustness of QGP regression under experimental conditions. Beyond regression, we validate QGPs as Bayesian-optimization surrogates for state preparation under noisy XXZ dynamics.

Continuous self-improvement requires an ever-expanding pool of self-generated, diverse, adaptive goals. For language agents, existing training environment pools (hand-curated, statically synthesized, or frozen-verifier) keep the goal distribution fixed as the learner scales. We introduce SPADE (Self-Play in Adaptive Synthetic Executable Environments), a self-play RL framework in which a single LLM plays two roles: an Environment Designer that writes complete, long-horizon training environments as executable code with an OpenAI Gym-style reset()/step() interface, and a Reasoning Agent that learns to act in them. Each is a stateful, multi-turn environment (state transitions, reward functions, and verification code), so one interface spans reasoning problems and multi-step agentic tool use. The Reasoning Agent's regret is estimated using the gap between its reward with and without privileged hints; in optimizing this regret signal the Environment Designer learns to target environments at the edge of the agent's capabilities while keeping them feasible. Through extensive experimentation, we find several components critical to success: grounding the Environment Designer on documents sampled from a large pretraining corpus, and giving it an accumulated environment memory. Scaling to 30B-parameter models, SPADE improves over the strongest fixed-environment baseline by +5.3 on average across eight held-out math, science, code, and reasoning benchmarks, and lifts the tool-use setting by +5.7 on BFCL-v4 multi-turn and +13.9 on ACEBench-Agent; on the games setting, the margin over the strongest baseline grows with model scale. By making environment design itself a learnable component, SPADE takes a concrete step toward open-ended self-improvement.