Papers

Barzilai–Borwein (BB) method has shown strong practical performance in continuous optimization, yet its convergence dynamics remains poorly understood. In particular, a central unresolved question is whether BB converges superlinearly for almost every strictly convex quadratic problem and initialization. We provide a negative answer to this question. Specifically, for every finite dimension $n\geq4$, we construct a nonempty open, hence positive-Lebesgue-measure, family of strictly convex quadratic problems and initial points for which the long Barzilai–Borwein method (BB1) converges but cannot converge root-superlinearly. More precisely, with the explicit constants $\rho_{\min}=10^{-6},\rho_{\max}=0.61$, every spectral component of the gradient is bounded above and below by the corresponding geometric sequence. Consequently, the gradient norm and the energy norm of the error satisfy two-sided geometric estimates with the same rates, while the objective gap satisfies the corresponding estimates with squared rates. In particular, all three quantities are bounded below by geometric sequences, ruling out superlinear convergence. The construction is highly nontrivial, based on a computer-assisted proof of a nonresonant, attracting seven-cycle of the projectivized BB dynamics in dimension four.

Quality control in printing, particularly in rotogravure printing, still depends on slow, costly, and subjective manual inspection. Automated surface defect detection is critical for maintaining high-quality standards in rotogravure printing. Deep learning models give prospects for automation. However, training robust deep learning models, such as YOLO or Vision Transformers, is heavily hindered by the extreme scarcity of real-world industrial defects images. To overcome this limitation, this paper introduces a novel synthetic data generation framework tailored for rotogravure printing quality control. The proposed pipeline automatically generates high-fidelity images of specific printing defects (creases, streaks, misregistration, etc.) and outputs corresponding bounding boxes and annotations. To validate the framework, a synthetic dataset of 7533 images was generated and used to train the state-of-the-art object-detection model RFDETR. Experimental results demonstrate that the model trained on our synthetic data achieves a Mean Average Precision (mAP) of 80.9% on real industrial testing samples. This framework provides a zero-cost, rapid-deployment solution for automating defect inspection in printing lines without requiring massive manual data collection.

Faithful explanations of time-series classifiers should identify subsequences that are not only sufficient to preserve a black-box model's prediction, but also necessary for maintaining it. However, existing sufficiency-oriented methods can assign high importance to spurious subsequences that support the prediction without being essential to the model's decision. We introduce TimePNS, a necessity-aware framework for time-series explanation. Inspired by Pearl's counterfactual notion of necessity, TimePNS assesses whether a temporal factor is necessary by intervening on it and measuring whether the original prediction is disrupted. The framework adopts a two-stage design. Stage I learns an identifiable causal generative process together with a sufficiency-oriented explanation mask. Stage II performs counterfactual interventions on temporal factors to derive necessity signals, which supervise a temporal gate that refines the initial explanation by suppressing non-essential components and emphasizing counterfactually necessary ones. Experiments on synthetic and real-world time-series benchmarks show that TimePNS more accurately identifies decision-critical subsequences and consistently improves sufficiency-necessity trade-offs over strong baselines.

Molecular graph encoding often relies on a single, static structure, ignoring the thermodynamic ensemble of molecules that are present in solution. Here, we introduce EnsembleEGNN, a foundation model that encodes structural ensembles by processing individual conformers through shared equivariant graph neural network layers, pooled with a set attention block, to make property predictions from the whole ensemble. Pretrained on the CREMP cyclic peptide dataset using multi-task self-supervision, the model is trained to encode the conformational variability of each molecule. When predicting membrane permeability from the CycPeptMPDB benchmark, EnsembleEGNN achieves an $R^2$ of $0.477$ under random cross-validation, outperforming a sequence-only BERT baseline ($R^2=0.439$). This representation advantage persists under rigorous out-of-distribution Butina splits ($R^2=0.401$ versus $0.354$). Finally, a hybrid architecture co-training EnsembleEGNN with the BERT model achieves the highest overall accuracy across both random ($R^2=0.538$) and structural holdout evaluations ($R^2=0.444$). These results demonstrate that encoding conformational ensembles into latent representations improves predictions for properties governed by thermodynamics.

Vision-language models (VLMs) can behave very differently depending on whether the same underlying problem is presented textually or visually. This inconsistency suggests that different views expose different reasoning paths and failure modes that standard multimodal post-training does not fully exploit. To study and exploit this phenomenon, we construct ODA-Data, a high-quality paired multimodal geometry dataset with text-dominant, image-dominant, and combined image+text views of the same problems, together with splits for training and evaluating view dependent reasoning behaviors. We then develop Modality-Informed Reciprocal Reasoning Optimization (MIRROR), a reinforcement learning approach that derives a cross-view self-distillation signal from the model's own modality-dependent capabilities. For each problem, MIRROR evaluates the model under all views, selects the best-performing view as a teacher, and trains the remaining views using a GRPO task-reward objective augmented with a reverse-KL regularizer toward that teacher. Across reasoning benchmarks that evaluate on multimodal mathematics problems, MIRROR improves over standard RL and yields more accurate and consistent behavior across different input modality representations.

While large audio-language models have achieved remarkable progress in auditory perception, they still lag behind text-based large language models in deep logical reasoning, primarily due to the scarcity of high-quality audio reasoning data. To bridge this gap, we propose X$^3$-OPD, a cross-modal on-policy distillation framework that transfers reasoning capabilities from a powerful text teacher to an audio-language student. During training, the student generates reasoning trajectories conditioned on its own acoustic perception, while the teacher provides token-level guidance using matched textual inputs and verified answers. We further construct a three-tier symmetric corpus covering textual reasoning rendered into speech, audio-event reasoning grounded in complex acoustic scenes, and spoken-dialogue reasoning involving paralinguistic cues. This design extends cross-modal distillation beyond textually recoverable content to reasoning grounded in non-linguistic events, prosody, and conversational context. Experiments on MMSU, MMAU, BIG Bench Audio, and MMAR demonstrate that X$^3$-OPD substantially improves audio-grounded reasoning and chain-of-thought quality while largely preserving the model's existing capabilities under domain shift.

The coupled ghost and gluon Dyson–Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang–Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.

The rapid progress of AI has intensified the long-standing pursuit of automation: replacing human participation with algorithms wherever possible. Implicit in this pursuit is the assumption that humans remain in the loop only because current AI systems are not yet sufficiently capable. This paper challenges that assumption. Rather than asking how far automation can extend, we ask where its conceptual limits lie and argue that human participation may persist even with highly capable AI systems for three distinct reasons. Technical or complementarity grounds arise when humans contribute capabilities or perspectives unavailable to AI. Normative or developmental grounds arise when participation itself is valuable for human agency or learning. Most importantly, emergence grounds arise from target emergence: in some activities, the target is not fully specified in advance but instead emerges through the interaction itself. In these cases, human participation is not merely a means of improving execution but is constitutive of the target being produced. Human–AI co-construction, understood as the joint production of outcomes by humans and AI systems, is therefore not simply a temporary response to imperfect AI, but a persistent feature of activities whose objectives emerge through participation. This perspective has important implications for the limits of automation and for the design, evaluation, and ethics of future AI systems.

Motivated by the success of modern flow-based generative models in modeling complex data, we study two-sample testing through the lens of flow-based methods. We propose the Zero-Flow Two-Sample Test (ZF2ST), built on the zero-flow criterion, which characterizes distributional equality through a time-reversal antisymmetry of a learnable velocity field. We extend this criterion and further develop the Zero-Flow Discrepancy, an identifying discrepancy that controls the Wasserstein distance, and derive a variational representation in terms of a witness function. This representation naturally leads to a witness-based test whose power is governed by the signal-to-noise ratio (SNR), allowing direct power maximization for witness learning. ZF2ST learns the witness on one data split and performs testing on held-out samples, thereby maintaining Type-I error control and admitting a simple asymptotic null distribution. Experimentally, ZF2ST performs competitively across various synthetic and real-world benchmarks, while showing particularly strong performance in distinguishing image distributions from different sources.

Speculative decoding accelerates autoregressive generation by having a draft propose tokens that a target verifies in parallel. Frontier models increasingly ship a built-in Multi-Token-Prediction (MTP) draft head, assumed to be cheap beside verification. A shipped full-attention MTP head can become disproportionately expensive beside a hybrid target at long context. The head attends over the full KV cache for each of $\gamma$ draft forwards per decode step, while only 9-25% of target layers retain full attention, so a single draft layer can issue context reads at a rate comparable to the whole target. On hard, low-acceptance workloads, deep native MTP becomes net-negative: slower than no speculation. We apply a StreamingLLM-style window plus attention sink to the draft only (Windowed-MTP); target verification remains full-context, so the target distribution is preserved. The intervention is training-free and drop-in. On three models from two hybrid families (Gated DeltaNet and Mamba2) at 1M context on one GPU in SGLang, it provides an acceptance-free 1.28-1.44x per-decode-step speedup over native MTP. The speedup grows with context; at matched acceptance, TPOT improves by the same factor. The window removes most of the draft's working set, and a compact ring buffer converts that reduction into physical capacity: it reclaims the otherwise dead draft pool, a measured 7.7-11.1% of total KV at 1M, making room for one additional concurrent 1M request in the Qwen-35B batch sweep.

Cognitive impairment (CI) is a growing public health concern. Early and accurate diagnosis is critical for enabling timely intervention and improving patient outcomes. Speech-based CI detection has emerged as a promising non-invasive approach, as speech signals encode both linguistic and acoustic markers associated with cognitive decline. Recent advances in large language models (LLMs) further strengthen the potential of speech-based assessment by enabling more expressive representation learning and improved generalization across diverse speakers, recording devices, and clinical environments. Moreover, multimodal learning by jointly modeling linguistic and acoustic features allows for a more comprehensive characterization of cognitive and behavioral changes related to CI, leading to more reliable detection. In this work, we propose a multimodal CI detection framework based on open-source LLMs that integrates speech audio and corresponding transcripts while preserving patient privacy. Acoustic embeddings are extracted directly from speech signals, while textual embeddings are generated from automatically transcribed speech. These modality-specific embeddings are then concatenated to create a combined feature vector and used for downstream classification, without requiring access to raw or sensitive patient data. The proposed approach is evaluated on the ADReSS20 and ADReSSo21 benchmark datasets. Experimental results show that the proposed multimodal framework achieves an CI classification accuracy of 92.4% and consistently outperforms single-modality baselines. Our work establishes a new state-of-the-art for CI identification, with the proposed method demonstrating superior cross-dataset generalization. This advance highlights the power of an LLM-based multimodal framework that fuses linguistic and acoustic data to enable robust, scalable, and non-invasive screening.

Do independently trained language models come to represent the same thing in the same way? We answer for code, extending a recently introduced concept-circuit extraction method to a 2x2 design – Python and Rust crossed with Qwen2.5-Coder-7B and DeepSeek-Coder-V1-6.7B – and measuring a complete inventory of grammatical concepts (58 Python, 57 Rust) identically in all four cells: the smallest design that separates what depends on the task, the language, and the model. The answer splits into three parts. What earns dedicated circuitry is set by the task: the models agree on which concepts receive circuits (Spearman $\rho$ = 0.638 for Python, 0.673 for Rust, both p < $10^{-7}$). Where those circuits sit is set by the model: Qwen processes concepts in a late band (~L17-19), DeepSeek at L6-7, for both languages. How circuits grow across layers is also set by the model: Qwen gives its atomic concepts an early spike that DeepSeek does not. "Are circuits universal?" thus has no single answer: yes for What, no for Where and How – universality is a property of representational content, not of computational organisation. None of this structure was fixed in advance. The agreement could have landed anywhere between independence and identity; it lands at $\rho \approx 0.65$. Rust constructs receive 2-3x more concept-specific circuitry than their Python equivalents, in both models. Both models share neurons between the languages (6/7 and 7/7 paired constructs), DeepSeek 1.94x more than Qwen – a direction no prior result predicts. And Qwen binds nine keywords of Rust's type-and-trait machinery into one tight neuron cluster (Jaccard 0.535 vs null 0.112, p < 0.001), a semantic dimension invisible in surface syntax. Ablation and linear probes confirm the circuits are functional. All claims are scoped to this 2x2; whether the per-model profile predicts a third model is the designed next test.

Coordinating autonomous vehicles at unsignalized intersections remains a critical challenge for multi-agent reinforcement learning (MARL) systems, which typically struggle with combinatorial action spaces, reliance on privileged information, or rigid agent designs. We propose Master-Agent Proto-plan System (MAPS), a hierarchical deep reinforcement learning (DRL) architecture in which a centralized Master agent generates a compact, continuous embedding, denoted as proto-plan, that encodes a global coordination strategy. Decentralized Worker agents integrate this embedding with local observations to execute vehicle-specific control, decoupling strategic intent from tactical execution and enabling independent optimization of each module. As a proof-of-concept evaluation of this coordination mechanism, we test MAPS across 72 intersection configurations in HighwayEnv. MAPS achieves collision-free navigation while significantly reducing average travel time, outperforming state-of-the-art baselines. The learned proto-plans further exhibit robust generalization: a system trained with three agents achieves a 94% success rate when deployed zero-shot to five-agent scenarios, confirming that proto-plan-based hierarchical learning provides a promising framework for multi-vehicle coordination.

An initial high-recall stage in an empirical pipeline decides which items pass to later review, labelling, or modelling, and relevant items it misses are lost to every subsequent stage. We study how many audit labels are needed to certify, with finite-sample validity, that this missed relevant mass is small, and our main results characterise the label complexity of this problem. We first show that no procedure using only labels from inside the candidate set can certify any non-trivial bound on the missed mass: the audit must sample the excluded pool, the only region where unrecovered relevant items can lie. We then prove a matching finite-corpus lower bound. Any valid audit that certifies fewer than $m$ missed relevant items with high probability when none are present, even if adaptive and permitted to label the entire included pool, must inspect on the order of $N_0/m$ excluded-pool labels. Excluded-pool auditing is therefore minimax rate-optimal, not merely convenient, for missed-mass certification in the zero-miss regime. Building on this characterisation, we develop an exact finite-sample toolkit, using binomial and hypergeometric inversion rather than asymptotic approximation, that certifies missed mass, converts it to recall through a two-pool design, certifies pre-specified families of nested candidate generators simultaneously, and produces stress-test certificates against declared perturbation mechanisms. These certificates can be paired with observable review burden to select the least burdensome pre-specified candidate generator meeting a missed-mass target. Every guarantee holds under one discipline: the candidate generator, or the pre-specified family from which it is selected, and the audit rule are fixed before the certification labels are examined.

Deterministic KV-cache eviction keeps the top-$k$ tokens under an importance score and deletes the rest, and after the deletion the serving system cannot know what the eviction cost it on the current query. We replace the deterministic tail with Poisson sampling at known inclusion probabilities, which makes the eviction error identifiable and turns a survey-sampling variance estimator over the retained set into a per-step error certificate at one extra scalar per retained token. On a thirty-turn assistant compressed to a 10% cache budget, the certificate-gated system answers 0.97 of recall questions against 0.09 for top-$k$, and for facts stated 26 to 30 turns earlier it recalls 97% against 2%. We prove that no estimator computable from the information a deterministic scheme retains is consistent for its own eviction error: evicted values can be altered so that everything retained is unchanged while the true attention-output error grows without bound. Under the Poisson design the certificate covers the realized attention error in 96.9–97.7% of 12{,}096 replay cells and in 98.1–99.7% on twelve further architectures. Randomization buys attribution, not prediction: a pre-registered study on LongBench at 6k and 16k tokens (about 74{,}000 generations) finds question-aware eviction at 25–50% budgets nearly free and output log-probability the better failure predictor, while the certificate answers the question confidence cannot, separating eviction-induced from inherent failures at AUC 0.65–0.75 against 0.47–0.54, and schedules recomputation at 1.7–1.8 times the gain of random gating. On real long-term conversations the gated system returns the full-cache score inside the heavy-damage regime, and the rule that triggers it is the same across five model families.

Scaling inference-time computation has emerged as a reliable method to improve the performance of large language models on complex reasoning and programming tasks. However, standard approaches such as independent sampling and sequential multi-turn refinement operate without token-level credit assignment, resulting in computational inefficiency, since valid reasoning prefixes are frequently discarded. In this work, we introduce Test-Time Scaling via Error Localization (TTEL), an inference-time algorithm that utilizes fixed or environment feedback to perform token-level error localization. By comparing conditional probabilities under informed feedback against a null-context baseline, TTEL isolates the step at which an error occurred. The algorithm then truncates the trajectory and branches a new generation, maximally reusing the valid prefix. Extensive evaluations demonstrate that TTEL establishes strictly dominating Pareto frontiers across sequential reasoning domains, measured by pass-at-k vs. generated-token cost. With Qwen3-8B on LiveCodeBench, TTEL attains a pass@64 of 71.0% while generating approximately half as many tokens as independent sampling (360.4k vs. 735.0k). Generalizing to math benchmarks AIME-2025 and HMMT-2025, TTEL cleanly outperforms competing test-time baselines across both Qwen3-8B and Qwen3-4B-Thinking-2507.

Post-training quantization (PTQ) of diffusion transformers (DiTs) to W4A4 severely degrades output quality, because activations entering each linear layer contain outliers that 4-bit formats cannot represent. The standard fix applies an invertible linear transform to the activations and its inverse to the weights before quantizing both. Normalization layers between blocks force this transform to run online at every denoising step, making its inference computation cost the binding design constraint. Existing options trade quantization quality for inference cost: per-channel scaling (SmoothQuant) is computationally cheap but impacts the magnitude of the channels, which can harm quantization accuracy; fixed Hadamard transforms yield better quantization accuracy but require large block sizes that incur a high online cost; learned full-$d$ invertible transforms calibrate best but entail a prohibitive dense $d \times d$ matrix multiplication (GEMM) per layer per step. We propose KroQuant, a PTQ method that applies a learned Kronecker-structured invertible transform to each 32-element block of the activation, storing less than half the parameters of per-channel scaling. The block-local structure runs as small tensor-core GEMMs, and on an MI350 GPU the KroQuant quantizer kernel is up to $14\%$ faster than the SmoothQuant kernel. Offline LoRaQ weight calibration then absorbs the residual per-weight quantization error. On PixArt-$\Sigma$, SANA, and FLUX.1-schnell at W4A4 (MXFP4e2), KroQuant produces outputs closer to the FP reference than SVDQuant and LoRaQ on MJHQ-30K and SDCI, while preserving or improving image quality.

Reliable electric vehicle (EV) charging infrastructure is a cornerstone of sustainable, low-carbon cities, yet urban climate stress such as extreme heat, heavy precipitation, and humidity increasingly raises equipment fault risk and undermines the resilience of urban energy and mobility services. Shifting operation from reactive repair to preventive maintenance depends on accurate, forward-looking fault-risk prediction, a task complicated by the heterogeneous time scales of physical, behavioral, contextual, and historical signals and by forecasting over a multi-week horizon. We develop FGDSE, a feature-governed dynamic stacking ensemble that forms an interpretable decision-support system for climate-resilient charging-asset management. It partitions heterogeneous signals into four feature families, assigns each to a domain expert whose inductive bias matches the data, and adds two deep temporal experts for short-term pulses and long-term degradation; a horizon-wise gating mechanism then learns adaptive weights to forecast daily fault risk over 1 to 30 days. SHAP attribution and an X-learner extend the probabilistic output into causal decision support with post-level treatment effects. On 25 months of data from 13 stations, FGDSE surpasses twelve baselines beyond the ten-day horizon, sustains about 85% macro-recall at 30 days with an AUC decay of only 3.2 points, and reveals a shift of dominance from fault history toward climate stress. It identifies extreme heat as the sole exposure whose causal effect amplifies over time, flagging roughly 30% of posts as heat-sensitive and yielding quantitative thresholds for climate-adaptive maintenance that strengthens urban mobility resilience and sustains low-carbon travel.

Chain-of-thought reasoning models such as DeepSeek-R1-Distill-Qwen-7B exhibit a bimodal convergence pattern: generations either terminate within a token budget (converged) or exhaust it without reaching a conclusion (non-converged). We characterize this phenomenon empirically, showing that converged generations achieve 90.3% accuracy on AIME 1983-2024 while non-converged ones achieve only 6.6%, with an overall convergence rate of 62.0%. We then ask whether this outcome is detectable early in the thinking chain using internal model representations. Training linear probes on hidden-state activations at token positions 50-300, we find that layer-20 activations at token 150 achieve AUC 0.608 (+-0.080, 5-fold CV), reliably above chance even at token 50. Activation probes consistently outperform behavioral baselines derived from token entropy and repetition statistics. A sweep-level permutation test yields p=0.063 (100,000 permutations), consistent with a modest signal that our sample size cannot confirm at conventional thresholds. These findings suggest that convergence fate is partially encoded in intermediate representations well before the generation ends, opening a path toward early-exit inference and adaptive compute allocation.

Discrete flow matching provides a flexible framework for generative modeling on discrete structures. However, the standard factorized training objective exposes the model to targets of varying difficulty, mixing well-conditioned, predictable tokens with ambiguous, high-entropy ones. We empirically demonstrate that the uncertainty over the value of each token is closely related to the density of available context in its neighborhood. Motivated by this observation, we propose a simple modification to the underlying continuous-time Markov chain (CTMC) that incorporates local context information. Our context-weighted sampler improves generation quality with negligible computational overhead, while our scaled cross-entropy loss function reweights the training signal from different tokens and reduces generative perplexity by up to 63% on OpenWebText. Moreover, our approach matches a strong semi-autoregressive block diffusion baseline in quality while retaining the ability to perform generation in any order. These results highlight the role of local context as an important factor in discrete generative modeling and show that simple context-aware modifications can significantly improve both sampling and training efficiency.

Cooperative multi-task semantic communication (CMT-SemCom) improves task execution performance by leveraging shared representations. However, as we demonstrated in [1], cooperative multi-tasking can be either constructive or destructive, depending on the semantic relationships among tasks. To ensure constructive cooperation, we propose a semantic-aware task clustering method for CMT-SemCom. We have formulated a sequential multi-stage optimization problem in which semantically aligned tasks are clustered once after a short initial training phase, and then end-to-end (E2E) joint training is conducted exclusively within the discovered groups. Specifically, the problem decomposes into two stages: (i) a semantic clustering problem leveraging hierarchical density-based spatial clustering, and (ii) an intra-cluster E2E CMT-SemCom learning problem. Simulation results demonstrate that the proposed framework effectively mitigates destructive cooperation and negative transfer, yielding accuracy gains compared to unclustered multi-tasking and individual training baselines.

Quantum transfer learning (QTL) is often evaluated by replacing a classical classifier with a fixed variational quantum head, but this hides a key question: when is the quantum branch actually useful? We propose QSTAR: Quantum Selective Transfer with Adaptive Routing, a selective QTL framework that keeps high-confidence classical predictions and routes only low-confidence samples to a fallback branch. Using a frozen ResNet18 backbone on Fashion-MNIST, we compare manually designed QTL heads, KetGPT-designed quantum heads, and parameter-matched classical baselines under a common data split and optimization schedule. Standard QTL heads reach at most 57.0% accuracy, while the strongest KetGPT head in the main filtered sweep reaches 78.5% accuracy and 0.785 F1-score. Although the strongest fixed classical head remains higher at 81.6%, selective routing gives the quantum branch a clearer role. On low-confidence samples, KetGPT #180 improves accuracy over a parameter-matched MLP fallback by 6.82, 4.31, and 3.03 percentage points at thresholds of 0.70, 0.80, and 0.90. At the full-system level, Adaptive KetGPT-QTL reaches 80.9% accuracy and 0.807 F1-score, outperforming the adaptive classical baseline. A separate compact-circuit ablation identifies KetGPT #160 as a stronger fixed-head candidate, reaching 81.9% accuracy with only 10 quantum parameters and 9 gates. These results suggest that architecture-searched quantum heads are most useful as targeted fallback branches for uncertain inputs rather than uniform replacements for classical classifiers.

A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.

Mobile-health interventions increasingly use online learning and decision making algorithms to personalize when to nudge users toward healthier behavior, but a poorly designed algorithm can burden and disengage participants. New algorithm design decisions should therefore be vetted against realistic simulated users before each real-life deployment. We propose a method to develop “JITAI-Twins”: digital twins of a target subpopulation for comparing candidate online algorithms before a just-in-time adaptive intervention (JITAI) deployment. The method builds on a conditional time-series diffusion model that is temporally consistent (future actions do not affect the generated past), and it supports repeated updating from three sources of information, in three steps: pre-training on a large observational dataset, fine-tuning on small prior intervention deployments in related populations, and inference-time calibration to the next target population from domain-scientist expertise. We validate the twin at each pre-deployment stage of the long-running HeartSteps series (v2 through v4) of physical-activity suggestion intervention deployments, treating each successive deployment as an upcoming study. The proposed method reproduces the target subpopulation's temporal and between-participant structure better than simpler simulators. These results suggest that our twin can be used to simulate a target deployment before it runs, the prerequisite for testing and informing online algorithm design decisions.

Score Entropy Discrete Diffusion (SEDD) parameterizes discrete reverse processes with unconstrained positive score ratios. While positivity guarantees nonnegative reverse jump rates, it does not ensure Bayes realizability: ratios at a noisy state need not be jointly induced by any clean-token posterior under the forward kernel. The score-entropy loss has the correct population optimum but does not enforce this constraint away from it. In a trained pure-uniform SEDD checkpoint, roughly one quarter of complete score vectors violate the coordinate box, while more than half lie inside it yet remain materially incompatible with any valid posterior. Such violations can produce negative pre-normalization weights in finite-step sampling. Projecting raw scores onto the bridge polytope removes all observed negative weights and improves external generative PPL from $203.6$ to $175.1$ without changing the sampler. We introduce mean-to-score (M2S), which predicts a clean-token posterior mean and converts it to the score through an exact kernel-dependent linear map. The construction applies to any known coordinate-wise continuous-time Markov chain (CTMC) satisfying a mild support condition. For uniform corruption, it maps the probability simplex onto the bridge polytope; for absorbing-mask corruption, the resulting objective recovers MD4 exactly. In a controlled 28.4M-parameter CIFAR-10 comparison, M2S lowers test BPD from $3.173$ to $3.129$ and FID-50k from $\CifarSEDDFID$ to $\CifarMtwoSFID$. A 170M-parameter M2S model trained on about 262B OpenWebText token slots outperforms the evaluated pure-uniform SEDD, GIDD, and Neural CTMC checkpoints at every tested sampling budget, reaching generative PPL $143.3$ at 128 steps versus $183.6$ for the strongest pure-uniform baseline.

Deep neural networks encode complex representations, but deconstructing this internal knowledge remains a challenge. Given the link between learning and compression, network compression offers a promising lens to analyze this knowledge. However, standard compression heuristics often suffer from scale symmetries and architectural biases. To resolve these, we introduce Hilbert Operator for Progressive Encoding (HOPE), a mathematical framework to gradually deconstruct the representations in trained network weights. HOPE shifts network compression from the discrete domain into a Hilbert space of continuous functions. By modeling individual neurons as rank-1 Hilbert-Schmidt operators, HOPE unifies pruning and neuron merging as low-rank subspace projection. Extending this formulation, HOPE introduces macro block eviction to encompass multi-layer structures like entire residual pathways under the same unified metric. This unified approach enables unbiased architectural decisions across layers with different types and sizes. HOPE is a data-free and hyperparameter-free framework. We present proof-of-concept experiments in model compression and fine-tuning to highlight the practical potential of our theory.

Fine-tuning an aligned language model on a narrow stream of bad advice can make it broadly misaligned on questions unrelated to the training data, a phenomenon called emergent misalignment. We ask why the narrow lesson generalizes at all, and we find that narrow fine-tuning recruits a persona structure that is present in the model before the fine-tune exists. From a frozen instruction-tuned model (Qwen2.5-14B-Instruct) we extract per-domain persona subspaces by contrastive teacher forcing and find that 4 unrelated domains share one low-rank core at 657x a random-subspace null, with 82% of that core lying outside a style core built at matched diversity. The literal first optimizer step of fine-tuning on insecure code climbs a broad-misalignment margin harder than the same code framed as educational, and forecasts realized margin movement out to 375 steps. Projecting the subspace out of the residual stream throughout fine-tuning prevents broad misalignment (27.7% to 0.0% of judged generations) while a matched-rank random subspace changes nothing; injecting it into the never-fine-tuned model induces misalignment that grows with dose to 45.4%, past the fine-tuned model it is measured against. The same projection applied to the weight gradient is inert, and three post-hoc weight edits leave the disposition in place: the sharpest edit suppresses the behavior rather than removing it, and the ablated structure re-forms inside the subspace the edit cleared. Spreading a fixed budget of bad data across 4 domains produces more broad misalignment than mechanical weight superposition and matched diversity jointly account for. All measurements come from one model at 14B; the extraction is from an aligned instruction-tuned checkpoint, which leaves the structure's provenance open; and the intervention that prevents misalignment also abolishes the narrow trained behavior.

Machine unlearning aims to remove the influence of specific training data while preserving model utility. Many state-of-the-art approaches pursue this goal by restricting the forgetting update to a subset of parameters selected through gradient-based saliency. Although such methods are widely adopted, the actual contribution of saliency-based weight selection to representation-level forgetting remains unclear. In this work, we perform the first controlled ablation of the saliency masking mechanism used by SalUn. Using a matched-compute experimental design on CIFAR-10 and CIFAR-100 with ResNet-18, we compare saliency-based masking against random masks of equal sparsity and unconstrained updates, while keeping the unlearning objective, optimization schedule, and computational budget fixed. Across multiple representation-level evaluations, including linear probing, prototype recovery, and layer-wise CKA, the three configurations exhibit statistically equivalent representation-level recoverability. We find that forget gradients are strongly concentrated in the final network layers (approximately 92% of the squared gradient energy on CIFAR-10) before any mask is applied, causing all masking strategies to operate within the same representational subspace. Furthermore, saliency masks show limited class specificity (specificity index 0.09-0.11), selecting highly overlapping parameter subsets across different forget classes. Our findings suggest that, in the studied setting, representation-level forgetting is primarily governed by gradient concentration and representation geometry rather than by the specific identity of saliency-selected weights. More broadly, the results support a growing body of evidence indicating that effective representation-level unlearning requires objectives that act directly on latent representations rather than on increasingly sophisticated weight-selection strategies.

LoRA adapters are often shared on their own, and the amount of information they can hold about their training data bounds what sharing them can reveal. Following Morris et al. (2026), we measure this amount in bits by training adapters on frozen language models to memorize random token sequences. LoRA adapters store 2 to 3.4 bits per trainable parameter, less than full fine-tuning of the same model. The number of parameters alone does not set this amount: at equal size, adapters on MLP layers store more than adapters on attention layers, and a randomly initialized frozen model supports as much storage as a pretrained one once the scale of its output logits can be trained. We then train the same adapter on a task with supervised fine-tuning (SFT) and with GRPO. At the same accuracy, SFT stores about three times as much information specific to its training examples, and it stores most of the bits of secrets planted in the training data, which GRPO does not store because it rarely samples them.

Integrating heterogeneous biomedical data, including clinical metadata, histopathology images, and molecular profiles, is crucial for comprehensive disease understanding. However, gene expression data acquisition remains constrained by high costs and privacy concerns, limiting its use in multimodal research and AI-driven applications. We present MultiModal Molecular Generation (M$^3$-Gen), a novel framework for the generation of gene expression profiles by conditioning a Generative Adversarial Network on histopathology images and clinical metadata. M$^3$-Gen learns a unified latent representation from the clinical variables and the images, leveraging contrastive learning, and exploits the embeddings of the two modalities to guide a generative model in producing biologically coherent gene expression profiles. Evaluations on the TCGA dataset demonstrate that M$^3$-Gen generates realistic and functionally meaningful gene expression data. Importantly, by integrating multiple modalities in an attention-based mechanism, M$^3$-Gen provides intrinsic explainability: it allows the identification of which regions of the histopathology images most strongly influenced the generation of specific gene expression profiles, making the model's decisions interpretable by design.