Computer Science (arXiv)

Among $n+1$ equiprobable equal-energy signals in $\R^n$ under additive white Gaussian noise with maximum-likelihood decoding, which arrangement maximizes the probability of correct decoding? The question is Shannon's, recorded by Rice in 1950. Mulgund proved in 2026 that the regular-simplex value bounds the correct-decoding probability of every signal set at every signal-to-noise ratio, leaving open whether the simplex is the only maximizer. This paper determines the equality cases in a form stronger than uniqueness. A signal set other than a regular simplex falls strictly below the bound at every positive signal-to-noise ratio. Hence a code meeting the bound at one positive operating point is already a regular simplex, up to vertex relabeling and an orthogonal map. In probabilistic form, among the correlation matrices that signal sets induce, any matrix other than the identity gives a lower-orthant probability strictly above its independent counterpart at every finite threshold, leaving no room for a nontrivial equality. No code of ambient dimension below $n$ attains the bound. Under an energy budget $E$ with unrestricted blocklength the optimal codebook is uniquely the regular simplex of circumradius $\sqrt{E}$. Every optimal codeword therefore exhausts its allowance. Equality in the Simplex Mean Width Conjecture likewise occurs only at the regular simplex. The proof strengthens the first self-convolution step of Mulgund's argument with Royen's correlation theorem. The single-parameter rigidity is machine-checked in Lean 4.

For any tripartite relation $R\subseteq \mathbb{Z}^3$, the $R$-Triangle problem asks, given an edge-weighted graph, whether it contains a triangle whose weights form a triple in $R$. The All-Edge $R$-Triangle problem asks to determine for every edge whether it is contained in such a triangle. It is known that $R$-Triangle and All-Edge $R$-Triangle are subcubically fine-grained equivalent for every $R$ [Vassilevska W.-Williams'10]. However, while it is conjectured that these problems are tightly equivalent, this reduction only shows that if $R$-Triangle has an $O(n^{3-ε})$-time algorithm for some $ε>0$, then All-Edge $R$-Triangle has an $O(n^{3-ε/3})$-time algorithm. This paper provides a strong unconditional barrier to a tight equivalence: the reduction of [Vassilevska W.-Williams'10] is optimal for black-box reductions that work for arbitrary $R$. We give further results about black-box reductions between a variety of $R$-triangle problems. Our positive results yield new reductions between several classes of triangle and matrix problems --- for instance, we demonstrate that an $O(n^{2.53})$-time algorithm for computing equality or dominance product would imply an improvement on known algorithms for computing boolean $(\min, +)$-product, giving the first conditional lower bound for dominance and equality product. Our negative results can be thought of as barriers against natural fine-grained proof techniques. Besides the result that a tighter equivalence between $R$-Triangle and All-Edge $R$-Triangle is not possible, we also show that no appropriately "black-box" reductions are capable of demonstrating a subcubic equivalence between triangle counting and binary integer matrix multiplication, or a tight equivalence between boolean matrix multiplication and listing $n^2$ triangles, and more, despite the fact that all of these equivalences are conjectured to hold.

Object detection models deployed in safety-critical applications remain vulnerable to backdoor attacks that cause targeted misbehaviors when a hidden trigger is present. Existing detection methods either rely on trigger inversion or exploit architecture-specific assumptions, and critically, representative existing methods fail to generalize reliably to scene-level attacks, where a single trigger induces anomalous behavior across all objects in the scene simultaneously. We present DistScan, a backdoor detection framework based on a simple but previously unexploited observation: backdoor injection systematically shifts a model's pre-NMS prediction class distribution away from its training class frequencies, even on clean inputs without any trigger present. DistScan aggregates intermediate class predictions over a clean validation set and flags a model as backdoored if the resulting distribution deviates significantly from the training class frequencies, requiring no model weight access, no trigger knowledge, and no additional training. Extensive experiments on MS-COCO and PASCAL VOC across two architectures and three scene-level attack scenarios demonstrate that DistScan substantially outperforms existing methods, improving average detection accuracy over the best-performing applicable baseline by 27.32 percentage points.

Anticipating how scenes evolve under ego actions is fundamental to safe autonomous driving, yet the full potential of world models for decision-making remains unrealized. The critical challenge lies in ensuring that future modeling is not merely predictive, but decision-informative: the predicted future must directly shape which trajectory is selected. Existing approaches decouple future representation learning from planning optimization, or share predicted states across trajectory candidates, thereby diluting the action-specific consequences that ought to guide selection. To bridge this gap, we propose DA-WAM, a framework that unifies predictive representation learning, action-conditioned future modeling, and trajectory scoring under a single decision-making objective. DA-WAM maintains predictive supervision throughout planner optimization via an online encoder and a stable momentum target, allowing future representations to co-evolve with the driving task. An action-conditioned predictor generates a distinct future latent state per trajectory candidate, which is then evaluated by a future-latent-conditioned factorized scorer. For the expert-matched trajectory, the predicted future latent is supervised by the observed future representation, while safety-critical hard negatives provide additional supervision near planning boundaries. Extensive experiments on NAVSIM-v1 and NAVSIM-v2 demonstrate state-of-the-art performance, while ablations and diagnostic analyses validate the key components.

S-JEPA uses soft Gaussian mixture model (GMM) posteriors instead of hard cluster labels to preserve uncertainty. It remains unclear whether the probability values alone are sufficient, or whether it also matters which GMM components receive the non-maximal probabilities. We test this with two matched controls. FIXED-RANDPERM keeps the top-1 component and probability together with the multiset of non-maximal probability values, but reassigns those non-maximal values using a mapping fixed for each physical frame. UNIFORM-TAIL keeps the top-1 component, its probability, and total non-maximal mass but distributes that mass uniformly. Across three independent seeds, REAL SOFT outperforms both controls on two frozen Encoder readouts. It provides better recovery of the original GMM tail and greater accessibility of spectral dynamics over short time scales after controlling for the complete spectrum of the current frame. In two exposure experiments, both readouts improved overall as more frames retained the original mapping. We also descriptively follow one Phase 2 trajectory after the switch to the online GMM. These results show that the numerical probability structure of the soft target does not fully determine the learned Encoder representation. The mapping of non-maximal probabilities to GMM components also matters.

Readable AI output can leave an evaluability gap: even when the source is shown, an overall-quality judgment may not reflect what an output preserves. We investigated how source-text condition and output rendering relate to perceived translation quality, and how output and system appraisals relate to trust and stated disclosure willingness in a plain-text interface. A focal 2 * 2 comparison (N=306) using TransLingo examined simple generated narratives and complex literary-philosophical prose alongside LLM-generated readability-oriented outputs and researcher-revised fidelity-oriented outputs. A descriptive stimulus audit indicated greater source retention in fidelity-oriented outputs in both source-text conditions. Factorial analyses showed a significant rendering-by-source-text-condition interaction in perceived quality. Participants rated fidelity-oriented outputs higher than readability-oriented outputs for the simple narratives, whereas no reliable rendering difference emerged for the complex prose. A corresponding source-condition-dependent pattern was observed for perceived intelligence, agency-oriented anthropomorphic attribution, and task-performance trust. A separate theory-ordered appraisal-structure SEM characterized concurrent associations among perceived quality, perceived intelligence, agency-oriented anthropomorphic attribution, task-performance trust, and stated disclosure willingness across six domains, with task-performance trust as the proximal correlate of stated willingness. The observed rating pattern distinguishes source access from source evaluability: for the complex stimuli, displaying the source did not ensure that one overall-quality rating reflected differences in retained content. It also separates support for evaluating translation output from data-handling support for decisions about what personal text to entrust to a system.

We present a new data-driven learning of a Random Geometric Graph (RGG) of a multivariate dataset, where the graph is drawn in a probabilistic metric space. This graph learning works for generic datasets, irrespective of the type of the observables; their probability distributions; or size of the data. We identify a metric of the space that the graph is drawn in, as a probability distribution of a random variable that we introduce, namely, a variable that represents the disparity between the connectedness of two vertices of the graph, and the correlation between the two random variables that are attached to the respective vertex. It is the closed-form {\it{cdf}} of this disparity variable that we advance as the distance function of the host space of the learnt RGG, such that the edge exists between any two nodes, if this inter-nodal distance falls short of a chosen cutoff probability. Drawing the RGG in this probabilistic space leads to the graph being an Soft RGG, such that any edge - if it exists - exists with an identified probability. We forward a simple Rejection Sampling-based technique for learning the probability of any edge. The expected degree distribution of a vertex of this RGG is identified as local, and dependent on the inter-observable correlation matrix. If said correlation matrix is not known, it can be learnt given the data, using its closed-form posterior probability density function, that we forward. We illustrate our graph learning method by learning multiple RGGs of highly multivariate real datasets.

We present a simple linear-time algorithm that outputs an Eulerian tour of an undirected multigraph with $n$ vertices and $m$ edges, if one exists, in $O(m)$ time and using $O(n)$ words of working memory. The input is given as read-only adjacency lists, and the output is written to an append-only stream in traversal order. Our algorithm first finds a sparse spanning circuit (a skeleton), then traverses the circuit step-by-step, repeatedly outputting further circuits rooted at the current vertex. This solves a problem left open by Ismaili Alaoui, Plump, and Wild (SOSA 2026): their space-efficient variant of Hierholzer's algorithm handles general directed multigraphs, but it is unclear how to generalize it to general undirected multigraphs. Our result completes the picture in the read-only model for space-efficient output of Eulerian tours.

While multimodal large language models (MLLMs) excel in medical applications, most of them favor static images or short-term signals. In the critical field of dynamic electrocardiograms (ECG), models struggle with complex temporal reasoning and diagnostic report generation due to a lack of high-quality datasets and benchmarks. To address this, we introduce (i) Holtercare-23K, a large-scale multimodal dynamic ECG dataset comprising 22,980 QA pairs derived from 788 clinical Holter records and featuring a novel signal-video-text tri-modal alignment. Based on this dataset, we present (ii) Holtercare-Bench, a multimodal benchmark that evaluates models on temporal localization, clinical diagnosis, and global summarization. Zero-shot evaluations of leading MLLMs reveal a significant performance gap in processing ultra-long pathological sequences. However, fine-tuning representative models yields substantial improvements. This work illuminates the limitations of current MLLMs in electrophysiology and provides a foundational benchmark for long-term medical MLLMs. Our project is available at https://github.com/ZJU4HealthCare/Holtercare-Bench.

Object detectors often produce over-confident predictions for objects outside their training categories, leading to so-called out-of-distribution (OoD) hallucinations. Existing approaches for detecting or mitigating such hallucinations typically either construct scoring functions directly over learned object detector representations or modify the object detector itself to suppress hallucination emergence. However, the latent priors implicitly encoded in these representations remain largely unexplored and have not been explicitly decoded for OoD detection. To uncover and exploit these latent priors, we propose Structured Prior Knowledge (SPK), a hallucination-oriented framework that explicitly elicits OoD-relevant priors from pretrained object detectors. Specifically, SPK leverages in-distribution data and hallucination-inducing samples as diagnostic supervision to elicit part-level semantic concepts underlying object detector decision-making, rather than using them merely for rejection or object detector adaptation. The elicited semantic priors are further integrated with geometric and contextual priors to form a compact five-dimensional SPK representation for OoD detection. Extensive experiments across diverse object detector architectures and multiple OoD benchmarks demonstrate that SPK achieves state-of-the-art OoD detection. Our findings reveal that pretrained object detectors already encode substantially richer latent knowledge than is typically exploited for OoD detection. More importantly, this knowledge can be explicitly elicited and organized into a compact, structured, and interpretable knowledge space for prediction reliability analysis. This suggests a promising proactive route for improving object detector reliability by explicitly uncovering and leveraging latent priors. Code and data are available at: https://gricad-gitlab.univ-grenoble-alpes.fr/dnn-safety/spk

Foundation models are increasingly adapted for downstream medical imaging tasks, yet the influence of the chosen adaptation strategy on subgroup fairness remains poorly understood. We investigate how three parameter-efficient adaptation techniques, including linear heads on the raw CLS token, an MLP, and an attention-pooling module over multi-layer patch features, affect both pathology classification performance and subgroup disparities when applied to the frozen Rad-DINO chest X-ray encoder. Using MIMIC-CXR, we evaluate eight pathologies across race, sex, and imaging-view subgroups on a prevalence-preserving, demographically balanced test set, and additionally probe how strongly each adapter encodes protected attributes. We find that attention pooling achieves the strongest overall discriminative performance and encodes attributes, particularly race, most strongly, but that improved overall performance does not consistently reduce subgroup disparities. Notably, stronger attribute encoding did not correspond to larger disparities: early network layers encoded race most weakly yet produced the largest subgroup performance gaps. Exploring different attention-pooling layer combinations further revealed no consistent relationship between the layers pooled, attribute encoding strength, and subgroup fairness. Our results indicate that richer, more expressive representations can improve accuracy while leaving fairness implications task-dependent and unpredictable, which must be assessed directly and per-task rather than inferred from encoding strength or overall performance alone.

Large vision-language models (LVLMs) often hallucinate, generating content that the input image does not support. Preventing such content during decoding calls for a candidate-specific measure of how strongly the image supports the token under consideration. The model's visual-token states offer a natural source of this evidence because projecting each state through the output head reveals which vocabulary items that position favors. These position-wise readouts cannot be pooled directly because their probability magnitudes are not comparable across visual positions. Vocabulary ranks provide a scale-invariant basis for pooling, but tokens still differ systematically in their typical rank-based evidence. We propose ReWEIGH, a training-free decoding intervention that aggregates these ranks across visual positions and compares each candidate with a token-specific reference estimated from unlabeled images. At inference, ReWEIGH caches the image evidence during prefill and applies a bounded penalty only to candidates that fall below their reference. On four 7B backbones, ReWEIGH reduces hallucinated object mentions by up to 21.3% while largely preserving or improving descriptive and general performance. With evidence cached, the average added latency is 1.33% per token, and the reductions extend across six architecture families to 32B parameters.

An agent still learning its environment should be cautious while ignorant and bold once confident. The entropic value-at-risk captures this through a robust-optimization identity---a confidence level fixes the radius of a relative-entropy ball of alternative models---but that ball cannot reach catastrophes the nominal deems impossible, precisely what a safe agent must hedge. We instead use an optimal-transport ball and study the coherent risk measure it induces, the Wasserstein entropic value-at-risk. It has a variational dual mirroring the entropic formula (an inverse temperature becomes a transport price), occupies a definite place in the risk hierarchy, and provably accounts for the reachable catastrophes the entropic measure ignores; we verify both dualities numerically. Driving the transport radius by belief entropy then yields a closed-form robust dynamic-programming operator whose caution contracts as the belief sharpens, with a certified safety sandwich and a sharp safety switch.

Large language model (LLM) agents can now post-train an LLM end-to-end. They can write code, launch training, evaluate checkpoints, and improve downstream performance, raising the prospect of AI-for-AI. We argue that this picture conflates two distinct capabilities: execution-level capability, iterating within a selected training strategy; and strategy-level capability, revising the high-level judgment as experimental evidence accumulates. Analyzing a large corpus of publicly released post-training trajectories, we find that across different tasks, the agent's training strategy is locked in at the very beginning, and the entire remaining budget is spent on local adjustments within the selected strategy. We then examine three natural explanations--missing experience, missing guidance, and insufficient reasoning--with escalating interventions. Extensive experiments show that (1) an experience-driven scaffold improves execution across the board (+12.6 points on GSM8K and +40.8 on HumanEval) but leaves the strategy static; (2) human guidance effectively redirects the initial strategy, yet the agent falls back into local adjustment loops once training starts; and (3) additional inference compute pays off on easier tasks but yields almost no gain on the hardest one. In conclusion, what agents lack is neither experience, guidance, nor reasoning compute, but a mechanism for spontaneously reevaluating their strategy during execution.

As deep neural networks (DNNs) continue to scale, inter-layer scheduling, which orchestrates the spatial allocation of compute resources and the temporal execution order across layers, has become a decisive factor in sustaining high utilization and energy efficiency on tiled accelerators. However, existing inter-layer schedulers defer cost feedback until a complete fine-grained intra-layer scheduling has been resolved. The resulting decoupled flow repeatedly explores sub-optimal or even infeasible inter-layer schedules, and the absence of early pruning during the inter-layer phase remains a critical bottleneck for design-space exploration (DSE) in DNN compilers. Our key observation is that the cost of an intra-layer scheduling can be tightly upper-bounded once the inter-layer cut fixes the sub-mesh shape, which lets us cost every inter-layer candidate without solving the intra-layer problem. Hence, we propose a hierarchical partitioning-and-mapping framework, HyperCut, that enables early filtering of inter-layer schedules based on hypergraph partitioning. Based on the directed hypergraph (DHG) abstraction of DNN, we introduce a unified representation, State, that jointly encodes the DHG partition, tile mesh allocation and tensor batch splitting. Thereby, partitioning and mapping are coupled into a union optimization object. For a DNN with N layers, the resulting theoretical design space is bounded by O(N), compared with O(9.899^N) for the state-of-the-art open-source scheduler SET. Across 10 evaluated cases, HyperCut achieves 2.0x performance improvement and 80.47% exploration time reduction over the SET baseline, measured by geometric mean.

The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising. We bring these two areas together by studying the adaptivity of diffusion models to the structured geometry of multimodal high-dimensional data that consists of multiple clusters in $\mathbb{R}^D$, each with its own low-dimensional structure, and inter-cluster separation depending on $D$. We employ $K$-mixture Gaussian distributions as a canonical framework to capture this geometry and establish two theoretical results. First, we interpret denoising as a dynamical Bayesian classifier: the mixture score is a posterior-weighted average of cluster-wise scores, and we show that, with high probability, the posterior class probabilities concentrate on a single cluster once the signal-to-noise ratio reaches the scale $Θ(\log (KD)/D)$. Second, by separately analysing the denoising process in its mixing and cluster-commitment phases, we prove that the KL error bound depends linearly on the maximum intrinsic dimension of a cluster, up to a logarithmic factor, even when $K$ grows polynomially with $D$. This improves on ambient-dimensional bounds and extends existing low-dimensional adaptivity analyses to multimodal distributions with heterogeneous, approximately low-rank covariances.

This paper proposes a lightweight, plug-and-play framework that improves robustness to viewpoint shifts in Vision-Language-Action (VLA) policies without policy retraining. To our knowledge, this is the first approach to directly leverage 3D Gaussian-based novel-view synthesis for observation-space adaptation in VLA policies. Current VLA performance relies on the implicit assumption that training and deployment camera configurations are identical. Our experiments show that even a small displacement of the camera mount can reduce the success rate on the LIBERO benchmark from about 90% to about 10% in the worst case. Prior approaches, such as large-scale fine-tuning or generative data augmentation, are computationally expensive and risk catastrophic forgetting. To address this, viewpoint shifts are reformulated as a localized novel-view synthesis problem. Under a Locality assumption, that camera perturbations remain within a small bounded region relative to the workspace, viewpoint normalization reduces to a scene- and policy-independent disocclusion task. Our work implements this idea with a 4M-parameter 3D-Gaussian canonicalizer prepended to a frozen VLA policy. Without modifying policy weights, GS-VLA improves performance across three orthogonal axes: (1) Policy architectures, (2) Unseen task suites, and (3) Perturbation scales. These results show that a lightweight visual module can recover a large fraction of the performance lost under viewpoint shift, without policy retraining.

PSMA and FDG PET/CT visualise complementary biological information in prostate cancer. Combining both tracers could capture heterogeneous tumour phenotypes that may be missed by either alone, yet there is no consensus on effective deep learning architectures for fusing these modalities. We evaluated multimodal image-fusion strategies for automatic whole-body PET/CT lesion segmentation to estimate total tumour burden. Using the public DEEP-PSMA Challenge dataset, we trained tracer-specific 3D nnU-Net baselines and compared (i) early fusion with a single encoder and one decoder (OEOD) or two decoders (OETD), and (ii) intermediate fusion via a dual-encoder cross-attention U-Net (DECA-UNet). Tracer-specific baselines performed strongly (PSMA Dice = 0.93; FDG = 0.81). Fusion yielded mixed results: OEOD produced a combined Dice of 0.90 (on an easier, non-tracer-specific task), whilst the tracer-specific fusion models reached PSMA/FDG = 0.69/0.64 (OETD) and 0.76/0.57 (DECA-UNet). Whilst fusion often provided reasonable PSMA segmentation, FDG performance degraded and no strategy consistently exceeded the single-tracer baselines. Under the evaluated setting, tracer-specific models remain the stronger baseline; clinically useful gains from multimodal fusion will likely require architectures that better preserve tracer specific representations. Our code is available at: https://github.com/JackJ3636/DEEP_PSMA_code

This paper addresses the general problem of extracting music-theoretic and psychological features from symbolically encoded melodies. We review existing melodic feature extraction toolboxes, enumerate their features, and organise them into a common taxonomy. We then describe a new software library that provides implementations of all of these features in a straightforward Python package. We then demonstrate the combined feature set on the Essen Folksong Collection, using the dataset to produce a series of style classification models. These models help us answer key questions about the interpretability and dimensionality of the feature set. Our results show excellent classification accuracy using the full feature set, and promising performance for an eight-dimensional factor-analytic solution that improves the interpretability of the classifier. We distribute our new toolbox as an open-source Python package, $\mathtt{melody-features}$, which can easily be used in various applications within music analysis, music psychology, and music information retrieval.

Long-term robot operation in evolving environments requires object-level understanding that persists across repeated revisits. Existing systems either overwrite history to maintain an up-to-date map or store semantic snapshots without consistent cross-session object identity, resulting in temporal amnesia: the systematic loss of object history that prevents answering queries such as "Where has the green chair been across all sessions?" We propose LT-Mem, a volatility-aware memory evolution framework that unifies spatially aligned instance-level 3D perception with volatility-conditioned temporal reasoning. First, a multi-session SLAM backbone provides spatially aligned per-object observations across sessions. Second, a reasoning layer governs how object memory evolves: deterministic evidence scoring preserves cross-session identity, and a volatility-aware policy selects among overwrite, hold, and multi-hypothesis actions based on each object's dynamics. Third, the resulting Tri-Memory structure (Live, Delta, Meta) preserves both current states and event histories, enabling longitudinal object-centric reasoning. We further introduce LT-VQA, a dataset and evaluation suite comprising multi-session recordings, persistent identity annotations, and temporal QA pairs. Experiments show that LT-Mem consistently outperforms baselines across all metrics while consuming an order of magnitude fewer tokens, and ablations confirm that gains are driven by the structured memory architecture rather than LLM capacity.

Music-driven character animation enables and enhances transformative applications in entertainment and interactive education. However, synthesizing realistic drumming motion from audio remains challenging due to the inherent tension between high-acceleration dynamics and the need for extreme spatial-temporal precision. Existing approaches, often reliant on motion matching or MIDI input, struggle with generalizing to diverse real-world audio. Moreover, the field lacks standardized evaluation metrics capable of distinguishing precise drumming from noisy motion. In this paper, we introduce a generative diffusion framework featuring a dual-objective loss function that decouples skeletal integrity from drumstick precision, thus enabling centimeter-level stick precision without sacrificing natural body dynamics. Additionally, leveraging our own dataset and data augmentation strategy, the model generalizes to non-curated, in-the-wild audio. To rigorously evaluate performance, we propose two novel metrics: an impact-to-target distance to quantify spatial precision and an audio-motion correlation score to assess temporal alignment. Our quantitative analysis and user studies demonstrate that our system generates high-quality motion that is often indistinguishable from ground-truth performances.

Traditional malware detection systems that rely on a single representation of malware often fail to identify novel threats. These representations of malware binaries, also known as modalities, do not provide the models with sufficient information to discriminate among all samples. Additionally, individual representations introduce new failure modes, with some modality extraction being dependent upon the success of disassembling. Past works have integrated either additional modalities or more discriminative representations for classification. In this work, we present Malformer, a quadrimodal malware detection model that incorporates text, image, graph, and audio representations of Windows executables. We demonstrate that multimodal transformer fusion can enhance the performance of Windows malware detectors over that of unimodal and bimodal detectors. Malformer employs a combination of two RoBERTa encoders paired with a modified Vision Transformer for image data, WavLM for audio data, and an adaptive loss-weighting scheme to fuse modality-specific representations. Evaluated on a dataset of 201,549 binary samples, Malformer achieved 98.3% accuracy and an F1 score of 0.9833, outperforming both unimodal baselines and bimodal detectors by 4.6-17.6 percentage points. Malformer demonstrates that multimodal fusion provides a promising foundation for countering the growing scale of malware threats, equipping defenders with generalized and resilient detection capabilities.

We study optimal online algorithms for embedding a permutation $π$ of $[k]$ into an iid stream of uniform $[0,1]$ random variables. This problem is a broad generalization of the classical online monotone subsequence selection problem, recovered in the special case $π=\mathrm{Id}_k$. Our first contribution is an efficiently solvable dynamic program for the optimal embedding time of any $k$-permutation $π$. This dynamic program also yields an explicit optimal online embedding algorithm. We then investigate the asymptotic scaling of the optimal embedding time for uniformly random target permutations, as well as the extremal problem of identifying the permutations with largest expected online embedding time. Our second main result shows that, to first order, random permutations are strictly faster to embed than monotone permutations, which in turn are strictly faster to embed than the extremal permutations. This separation stands in sharp contrast to prevailing conjectures and heuristics in the offline theory of permutation embeddings.

Deep reinforcement learning (DRL) has recently gained a great attention due to its real-time adaptation and effectiveness in complex optimization problems. This paper investigates the optimal deployment of millimeter-wave (mmWave) base stations (BSs) in a realistic, non-convex campus topology. The optimization problem is NP-hard, due to the non-convex, non-smooth nature of the max-min fairness objective. To overcome these constraints, we formulate the BS placement as a Markov Decision Process (MDP) and systematically benchmark four DRL schemes: a discrete single-agent Deep Q-Network (DQN), a spatially partitioned Multi-Agent DQN, a continuous single-agent Deep Deterministic Policy Gradient (DDPG), and a geographically partitioned multi-agent DDPG framework. Numerical evaluations reveal that the multi-agent DDPG approach substantially outperforms single-agent in dense scenarios. Additionally full coverage is achieved, and a fairness Jain's index of 0.94 is obtained. Finally, the multi-agent demonstrates highly efficient computational convergence of dense scenarios with $400$ users.

Implantable neural interfaces require low-power real-time signal processing to remain within strict thermal and bandwidth constraints, motivating lightweight feature extraction methods for on-chip spike sorting. This work presents the Walsh-Hadamard Transform (WHT) as a hardware-efficient feature extraction method for neural spike classification. WHT can be implemented using only adders, subtractors, and registers without coefficient memory. WHT performance is compared against the Compressed Hadamard Transform (CHT) and Principal Component Analysis (PCA), improving mean F1-scores from 55-60% to 70-75% on difficult high-noise datasets and from 90-95% to 95-99% on all other simulated datasets. In addition to improved classification performance, WHT demonstrates greater robustness to noise, downsampling, reduced training size, and distance metric selection, maintaining standard deviations typically below 5%, while CHT and PCA reach up to 10% under high-noise conditions.