Papers

Domain shift remains a key challenge in deploying machine learning models to the real world. Unsupervised domain adaptation (UDA) aims to address this by minimising domain discrepancy during training, but the discrepancy estimates suffer from high variance in stochastic settings, which can stifle the theoretical benefits of the method. This paper proposes Optimal Reordering of Data for Error-Reduced Estimation of Discrepancy (ORDERED), a novel unbiased stochastic variance reduction technique which reduces the discrepancy estimation error by optimising the order in which the training data are sampled. We consider two specific domain discrepancy losses (correlation alignment and the maximum mean discrepancy), formulate their stochastic estimation error as a function of the data sampling order, and propose a practical optimisation algorithm. Our simulations demonstrate reduced variance compared to related methods, and experiments on two domain shift image classification benchmarks show improved target domain accuracy.

We consider the stabilization of Vlasov–Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy may rely on the full phase-space state, practical feedback is typically limited to sparse macroscopic diagnostics. We therefore study imitation learning methods that distill a fully observed expert policy into controllers operating only on macroscopic measurements. We show the stability guarantees of the learned policy, where the error floor depends on the minimal behavior cloning loss achievable under the observation constraints. We further characterize this minimal loss in terms of a notion of entropy that quantifies the complexity of the initial distribution. Our results demonstrates the theoretical feasibility of learning stabilizing feedback policies for kinetic plasma dynamics from macroscopic observations, and exhibits the adaptivity of the learning approach to low-complexity structures. Through extensive numerical experiments, we validate our theory and show that the learned policies can stabilize the system using only macroscopic observations, within a significantly longer time horizon than non-adaptive baseline controllers.

We identify and prove a fundamental trade-off governing long-sequence models: no model can simultaneously achieve (i) per-step computation independent of sequence length (Efficiency), (ii) state size independent of sequence length (Compactness), and (iii) the ability to recall a number of historical facts proportional to sequence length (Recall). We formalize this trade-off within an Online Sequence Processor abstraction that unifies Transformers, state space models, linear recurrent networks, and their hybrids. Using the Data Processing Inequality and Fano's Inequality, we prove that any model satisfying Efficiency and Compactness can recall at most O(poly(d)/log V) key-value pairs from a sequence of arbitrary length, where d is the model dimension and V is the vocabulary size. We classify 52 architectures published before March 2026 into the triangle, showing that each achieves at most two of the three properties and that hybrid architectures trace continuous trajectories in the interior. Experiments on synthetic associative recall tasks with five representative architectures validate the theoretical bound: empirical recall capacity lies strictly below the information-theoretic limit, and no architecture escapes the triangle.

As time-to-market is crucial in the Integrated Circuit (IC) industry, speeding up layout manufacturability verifi-cation is essential. Chemical-Mechanical Polishing (CMP) plays a vital role in IC fabrication but is significantly influenced by Layout-Dependent Effects (LDE). An accurate and efficient CMP model enables design teams to correct surface unevenness before fabrication, reducing costs and accelerating the design phase. However, existing models often rely on Density Step Height (DSH) modeling, which is time-consuming for calibration and requires substantial hardware resources for fine-grained predictions. In this paper, we propose combining the advantages of two surface analysis techniques, White Light Interfer-ometry (WLI) and Atomic Force Microscopy (AFM), to train a deep learning model. This model aims to predict full-chip post-CMP nanotopography with nanometer-scale accuracy. Our deep learning model is based on a Convolutional Neural Network (CNN) and follows a two-step pipeline. The model is trained on each technique separately, resulting in a detailed full-chip CMP model.

Localization in 5G and 6G networks is essential for important use cases such as intelligent transportation, smart factories, and smart cities. Although deep learning has enabled improving localization accuracy, depending on the deployment scenario and the effort required for dataset collection campaigns on a given infrastructure, the training process for localization models can vary significantly. Furthermore, with respect to feature selection, recent works have demonstrated the robustness of angle-of-arrival (AoA) based localization. In view of these two points, we propose an adaptive framework for AoA-based localization that consists of two alternative learning strategies, each suited either for large or small training datasets. The proposed framework is evaluated on a real, massive multiple input multiple output (mMIMO) orthogonal frequency division multiplexing (OFDM) outdoor channel state information (CSI) dataset. First, we investigate offline learning when large training datasets are available; we propose a hierarchical framework that first distinguishes between line of sight (LoS) and non line of sight (NLoS) regions and then moves to more fine grained localization in the respective region. This approach provides high-performance localization through accumulated batch retraining and an integrated hyperparameter optimization mechanism. Second, when only a small training dataset is available, an online learning framework is proposed, using incremental tree-based and ensemble-based models for handling streaming data and continuously updating mode, as well as an online few-shot learning model for rapidly initializing new classes from a limited labeled support set. These results showcase that highly accurate robust localization can be achieved incrementally during network operation by exploiting online learning, alleviating the need for large dataset collection campaigns.

Recent flow matching (FM) methods improve the few-shot adaptation of vision-language models, by modeling cross-modal alignment as a continuous multi-step flow. In this paper, we argue that existing FM methods are inherently constrained by incompatible geometric priors on pre-trained cross-modal features, resulting in suboptimal adaptation performance. We first analyze these methods from a polar decomposition perspective (i.e., radial and angular sub-manifolds). Under this new geometric view, we identify three overlooked limitations in them: 1) Angular dynamics distortion: The radial-angular coupling induces non-uniform speed on the angular sub-manifold, leading to regression training difficulty and extra truncation errors. 2) Radial dynamics neglect: Feature normalization discards modality confidence, failing to distinguish out-of-distribution and in-distribution data, and abandoning crucial radial dynamics. 3) Context-agnostic unconditional flow: Dataset-specific information loss during pre-trained cross-modal feature extraction remains unrecovered. To resolve these issues, we propose warped product flow matching (WP-FM), a unified Riemannian framework that reformulates alignment on a warped product manifold. Within this framework, we derive direct product flow matching (DP-FM) by introducing a constant-warping metric, which yields a decoupled cylindrical manifold (i.e., direct product manifold). DP-FM enables independent radial evolution and constant-speed angular geodesic transport, effectively eliminating angular dynamics distortion while preserving radial consistency. Meanwhile, we incorporate classifier-free guidance by conditioning the flow on the pre-trained VLMs' hidden states to inject missing dataset-specific information. Extensive results across 11 benchmarks have demonstrated that DP-FM achieves a new state-of-the-art for multi-step few-shot adaptation.

Gap-closing rate and visual looming swap discriminative dominance depending on deceleration intensity - a finding that reconciles a long-standing conflict in the car-following literature and challenges spacing-centered assumptions in traditional driver behavior models. This study presents a two-stage analytical framework that distinguishes between information availability (kinematic variables measurable in the environment) and information utilization (variables that demonstrably separate driver behavioral patterns), applied to 1,060,119 valid car-following observations from the NGSIM trajectory dataset (2,932 vehicles). Six kinematic features are extracted, and deceleration events are detected under two threshold conditions (-0.5 m/s^2 and -0.3 m/s^2). K-means clustering identifies behavioral modes, and one-way ANOVA with eta-squared effect sizes ranks each feature's discriminative power. Three key findings emerge: (1) threshold selection fundamentally shapes behavioral inference - the stricter threshold yields three interpretable modes while the permissive threshold collapses these to two; (2) hard braking prioritizes gap-closing rate (eta^2 = 0.715) while moderate braking emphasizes visual looming (eta^2 = 0.574); and (3) spacing headway is negligible (eta^2 <= 0.014) across both thresholds. These findings provide empirically grounded candidates for perceptual cue prioritization and have direct implications for ADAS warning system design and autonomous vehicle control.

Frontier models increasingly adopt Mixture-of-Experts (MoE) architectures to achieve large-model performance at reduced cost. However, training MoE models on HPC platforms is hindered by large memory footprints, frequent large-scale communication across heterogeneous networks, and severe workload imbalance. To characterize these challenges, we develop a mathematical model that quantifies memory, compute, and communication requirements for MoE configurations under various parallelization schemes, verified through micro-benchmarking, code instrumentation, and hardware profiling. Our analysis identifies performance bottlenecks: all-to-all latency at scale from expert parallelism, insufficient compute-communication overlap, low GPU utilization from imbalanced skinny GEMMs, and the absence of platform-aware hybrid parallelization strategies. To address these, we introduce Piper, a framework that leverages resource modeling to identify efficient training strategies for MoE models on target HPC platforms, applying pipeline parallelism with optimized schedules. Piper achieves 2-3.5X higher MFU than state-of-the-art frameworks such as X-MoE, and a novel all-to-all algorithm delivers 1.2-9X bandwidth over vendor implementation.

On-policy distillation is an efficient alternative to reinforcement learning, offering dense token-level training signals. However, its reliance on a stronger external teacher has driven recent work on on-policy self-distillation, where the same model serves as both teacher and student under different prompt contexts. Yet, existing self-distillation methods largely reduce learning to KL matching toward the context-augmented teacher model. This approach often suffers from training instability and can degrade reasoning performance over time. Moreover, self-distillation from the same model with prompt augmentation lacks the exploratory diversity provided by a genuine external teacher. To address these limitations, we move beyond fixed-teacher KL matching and propose Preference-Based Self-Distillation (PBSD), which revisits on-policy self-distillation through a reward-regularized perspective. Instead of directly matching the teacher distribution, we derive a reward-regularized objective whose analytic optimum is a reward-reweighted teacher distribution, yielding a target policy provably superior to the original teacher under this objective. Practically, PBSD optimizes preference gaps between teacher and student samples while maintaining on-policy student sampling. We support this framework with a statistical analysis of the induced preference-learning problem, formally establishing when on policy self-distillation is preferable to learning from an external teacher in our setting. Experiments on mathematical reasoning and tool-use benchmarks across multiple model scales demonstrate that PBSD consistently achieves the strongest average performance among comparable baselines, showing improved training stability over prior self-distillation baselines while preserving token efficiency.

We report a systematic failure mode in predictive representation learning. Across 2695 neural network configurations trained to predict linear-Gaussian dynamics, the optimal encoder tracks the environment rather than the system it is meant to model. The mean causal fidelity – the fraction of encoder sensitivity allocated to system degrees of freedom – is 0.49, and only 2.5% of configurations exceed 0.70. The failure intensifies with dimension: at N=100, the optimal encoder becomes causally blind (fidelity ~10^{-8}) while achieving 92% lower prediction error than the causal representation. We prove this is not an optimization artifact but a structural property of the predictive objective: when environment modes are slower or less noisy than system modes, every minimizer of the population risk encodes the former. The set of dynamics exhibiting this predictive-causal gap is open and of positive measure in parameter space. In a nonlinear Duffing-GRU sweep, unconstrained predictors learn environment-dominant representations in 55% of tasks (95% CI 41–68%) versus 24% under operational grounding (p=2.3e-3); the median out-of-distribution MSE inflation under environment shift is 1.82x versus 1.00x. Operational grounding – restricting the loss to system observables – partially suppresses the gap, but causal fidelity is never recovered without an explicit system-environment boundary. The results identify the predictive-causal gap as a structural limit of learning, with implications for self-supervised representation learning, world models, and the scaling paradigm.

Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose \HEDGE, a generative model defined directly on relaxed incidence matrices via a structured stochastic diffusion. The forward process combines a hypergraph-specific two-sided heat operator with an Ornstein–Uhlenbeck component, preserving structure-aware noising near the data while yielding an explicit Gaussian terminal law. Conditional on an observed hypergraph, this forward process is linear-Gaussian, so conditional means, covariances, scores, and reverse-drift targets are available in closed form. We therefore learn a permutation-equivariant state-only reverse-drift field in incidence space by regressing onto exact conditional targets, and generate samples by simulating a learned reverse-time SDE from the Gaussian base law. We establish exactness in the ideal state-only setting together with finite-horizon stability guarantees, and empirically show improved hypergraph generation quality relative to strong baselines.

Efficient CUDA implementations of attention mechanisms are critical to modern deep learning systems, yet supporting diverse and evolving attention variants remains challenging. Existing frameworks and compilers trade performance for flexibility, while expert-written kernels achieve high efficiency but are difficult to adapt. Recent work explores large language models (LLMs) for GPU kernel generation, but prior studies report unstable correctness and significant performance gaps for complex operators such as attention. We present CuBridge, an LLM-based framework that adapts expert-written attention kernels through a structured lift-transfer-lower workflow. CuBridge starts from expert-written CUDA attention kernels and lifts them into an executable intermediate representation that makes execution orchestration explicit while abstracting low-level CUDA syntax. Given a user-provided PyTorch specification, CuBridge generates and verifies a target IR program, then reconstructs optimized CUDA code via reference-guided lowering. Across diverse attention variants and GPU platforms, CuBridge consistently produces correct kernels and substantially outperforms general frameworks, compiler-based approaches, and prior LLM-based methods.

System Neural Diversity (SND) measures behavioral heterogeneity in multi-agent reinforcement learning by averaging pairwise distances over all $\binom{n}{2}$ agent pairs, making each call quadratic in team size. We introduce Graph-SND, which replaces this complete-graph average with a weighted average over the edges of an arbitrary graph $G$. Three regimes follow: $G=K_n$ recovers SND exactly; a fixed sparse $G$ defines a localized diversity measure at $O(|E|)$ cost; and random edge samples yield an unbiased Horvitz-Thompson estimator and a normalized sample mean with $O(1/\sqrt{m})$ concentration in the sampled edge count $m$. For fixed sparse graphs we prove forwarding-index distortion bounds for expanders and a spectral refinement under low-rank distance structure; for random $d$-regular graphs we prove an unconditional probabilistic $\widetilde{\mathcal{O}}(D_{\max}/\sqrt{n})$ bound. On VMAS we verify recovery, unbiasedness, concentration, and wall-clock scaling, with a PettingZoo TVD panel checking non-Gaussian transfer. In a 500-iteration $n=100$ PPO run, Bernoulli-$0.1$ Graph-SND tracks full SND while reducing per-call metric time by about $10\times$, and frozen-policy GPU timing up to $n=500$ follows the predicted $\binom{n}{2}/|E|$ speedup. Random $d$-regular expanders empirically achieve $\mathrm{SND}_{G}^{\mathrm{u}}/\mathrm{SND} \in [0.9987, 1.0013]$ at $\Theta(n \log n)$ edges. In DiCo diversity control at $n=50$, Bernoulli-$0.1$ Graph-SND preserves set-point tracking with paired reward differences indistinguishable from zero across nine matched cells while cutting per-call metric cost by ${\sim}9.5\times$. Together, these results show that the SND aggregation bottleneck can be removed without changing the metric's semantics, yielding a drop-in sparse alternative that scales beyond complete-graph SND and supports both passive measurement and closed-loop diversity control.

Many decentralized distillation methods are designed around training-time coordination, yet deploy each node in isolation even when more capable neighbors remain available at inference time. This is an incomplete objective for settings such as IoT, where devices are heterogeneous, data is scarce and skewed, and a node's strongest neighbors may far exceed its own local capacity. We study how nodes should train so that their predictions compose well at deployment, and how each node should learn whom to trust. Under a server-free, model-agnostic protocol where nodes exchange only queries and soft predictions, we propose Learned Neighbor Trust (LNTrust) wherein each node learns a compact trust function over its neighborhood from local validation evidence. This trust function gates auxiliary distillation during training and defines a deployment ensemble at inference, so that collaboration learned during training transfers directly to deployment. Across datasets and topologies, LNTrust improves deployed accuracy over the strongest output-only baseline by large margins while using significantly less communication than previous methods.

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.

LLM agents have been increasingly adopted for solving security tasks. However, existing evaluations usually require source code access, while commercial off-the-shelf (COTS) binaries dominate deployed software and require reasoning from stripped, optimized machine code. This discrepancy raises an important question: can modern LLM agents reason about vulnerabilities in critical COTS binaries? Motivated by this question, we build SLYP, a REACT-style pipeline for end-to-end vulnerability discovery and validation of COTS binaries. SLYP combines extensible MCP servers for binary exploration and dynamic debugging, and validates candidate vulnerabilities by synthesizing debugger-verified proof-of-concept (PoC) crashes. We evaluate SLYP and production coding agents, including Claude Code and Codex, on COTS Windows binaries centered on a 20-object COM benchmark. SLYP uncovers all 64 vulnerable entry functions while default production agents miss up to 15; SLYP also surfaces more true vulnerabilities than the state-of-the-art static analyzer, which discovers at most 35 with a large number of false positives. For validation, SLYP generates debugger-verified PoCs for 67.5% of cases, while default production agents generate none. Further ablations show that tool sets and model choice materially affect COTS binary reasoning. Our additional evaluation also demonstrates the generalizability of SLYP on Windows kernel targets. To date, SLYP has uncovered 39 zero-day vulnerabilities, 31 in COM/RPC services and 8 in kernel drivers, all disclosed to the Microsoft Security Response Center (MSRC), with 23 assigned CVEs and $203,000 bounty awards.

This paper treats chord progression generation as a standalone task and asks how much old-domain data must be retained in fine-tuning to acquire a new genre without forgetting the old. I study jazz fine-tuning of a pop-pretrained 25M-parameter Music Transformer (84.21% top-1 next-token accuracy on a held-out pop test set). The jazz corpus is over two orders of magnitude smaller than the pop corpus, so every run uses all 1,513 jazz training sequences, and the swept variable is the volume of pop "rehearsal" data mixed alongside: 0, 1K, 2.5K, 5K, or 10K. At the tabulated best epochs every fine-tuned run gains 7 to 9 points of jazz top-1 (the released F1 checkpoint equals the Phase 0 baseline, as the paper's Correction explains), and pop top-1 falls by 2.11 points under jazz-only fine-tuning but by at most 1.19 with rehearsal. Top-1 also scores the three header tokens of each sequence, and two of them shift whole runs: the jazz-majority runs predict the jazz genre marker even for pop songs, and most test songs carry a placeholder C-major key that a checkpoint predicts for every such song or for none, as the best epochs of F1 and F3 happen to do. Scored without the header tokens, every run gains 7.2 to 7.8 jazz points, jazz-only fine-tuning loses 1.48 pop points, and the four rehearsal volumes lose pop at nearly one rate, within 0.11 points of each other at every epoch and 0.73 to 0.90 points below baseline by their last epoch. The smallest volume tested (0.66x the jazz volume) already gives nearly all the measured protection, and no volume stops a slow decline. In informal listening the author more often selects the 10K and 1K endpoints, which carry more committed stylistic identities, than the middle of the sweep, but no formal listening study has been conducted. All six checkpoints and the selection-corrected F1 retrain ft-pop80-v2 are released at https://huggingface.co/PearlLeeStudio.

DualTCN is the first deep-learning framework for inverting time-domain marine controlled-source electromagnetic (MCSEM) transient data. Moving away from traditional subsurface discretization, the framework regresses four earth-model parameters – $\sigma_1$, $\sigma_2$, $d_1$, $d_2$ – and reconstructs conductivity-depth profiles using a differentiable soft-step decoder. The optimized architecture (379K parameters) features a Temporal Convolutional Network (TCN) encoder paired with a late-time branch and an auxiliary seafloor-depth head. This design achieves a 25.3% loss reduction over baseline models, with high predictive accuracy ($R^2 = 0.898$ for $\sigma_2$) and an inversion speed of 3.5~ms per sample on an A100 GPU. The framework demonstrates high robustness to noise through curriculum-based amplitude augmentation, maintaining a mean $\bar{R}^2$ of 0.858 at $\pm2\%$ random amplitude error, compared to $0.363$ without augmentation. DualTCN generalizes effectively to three-layer extensions (seawater/resistive layer/basement), accurately resolving basement conductivity ($R^2 \approx 0.88$), though thin-layer resolution remains a physical limitation ($R^2 \approx 0.23$). In comparative benchmarks, DualTCN significantly outperforms traditional local optimization methods like Levenberg-Marquardt and L-BFGS-B, yielding a mean $\bar{R}^2 = 0.877$ versus 0.129-0.439 for multi-start baselines, while operating at up to 21,000$\times$ lower computational cost. Finally, the framework incorporates uncertainty quantification via Monte Carlo (MC) Dropout. While well-calibrated for $\sigma_1$ (PICP90 = 0.944), inherent signal limitations at short offsets (200m) lead to under-coverage for $d_2$ (PICP90 = 0.572), which can be mitigated through post-hoc temperature scaling or split conformal prediction.

We compare in-context learning with fixed queries and agentic learning with adaptive queries for uniform approximation of task families. We consider two settings: an unrestricted regime, where querying and approximation are arbitrary functions, and a realizable regime, where we require these operations to be implemented by ReLU neural networks. In both settings, adaptivity never hinders approximation performance. However, this advantage can change when one passes from the unrestricted regime to the realizable regime. We identify four distinct approximation scenarios, each witnessed by an explicit task family: (a) no advantage of adaptivity; (b) an advantage in the unrestricted regime that persists under ReLU realizability; (c) an advantage that arises only under realizability; and (d) an advantage that disappears under realizability. This demonstrates that representational constraints interact profoundly with the effect of adaptivity.

Accurate forecasting of electric vehicle (EV) charging demand is critical for grid stability, infrastructure planning, and real-time charging optimization. In this work, we study the problem of early prediction of charging demand, where the total energy of a session is estimated using only information available at plug-in time and during the first minutes of charging. This enables actionable decisions while the session is still in progress, which is of direct importance for EV network operators. We construct a session-level dataset from the Adaptive Charging Network (ACN), combining session metadata with early-window charging measurements, and derive tabular features capturing user intent, temporal patterns, and initial charging behavior. We focus on a single operational depot, Caltech, and model intra-depot heterogeneity through station-level client partitions while evaluating multiple model families in a federated learning (FL) setting. Our results show that federated models can approach centralized predictive performance while keeping data in-depot, enabling privacy-enhanced training across distributed charging infrastructures. Overall, we demonstrate that reliable demand estimates can be obtained early in the session with minimal data, and that FL provides a practical pathway toward scalable and privacy-aware analytics for EV charging networks. Code is available at https://github.com/Indigma-Innovations/federated-learning-ev-charging-demand.

Long-horizon LLM agents depend on intermediate information-gathering turns, yet training feedback is usually observed only at the final answer, because process-level rewards require high-quality human annotation. Existing turn-level shaping methods reward turns that increase the likelihood of a gold answer, but they require answer supervision or stable task-specific verifiers. Conversely, label-free RL methods extract self-signals from output distributions, but mainly at the answer or trajectory level and therefore cannot assign credit to intermediate turns. We propose Self-Induced Outcome Potential (SIOP), which treats semantic clusters of final answers as latent future outcome states for potential-based turn-level credit assignment. For each query, SIOP samples multiple rollouts, clusters final answers into semantic outcome modes, and builds a reliability-aware target distribution over these states. It then rewards turns for increasing posterior support for reliable future states using a tractable cluster-level approximation. The objective generalizes information-potential shaping from gold-answer supervision to settings without task-specific gold verifiers while avoiding the broadcasted rollout-level advantages used by standard GRPO. We formalize the framework, characterize its supervised gold-answer limit, and show that SIOP improves average performance over verifier-free outcome-level baselines on seven search-augmented agentic reasoning benchmarks while approaching a gold-supervised outcome baseline. Code is available at https://github.com/dl-m9/SIOP.git.

Activation-based steering provides control of LLM behavior at inference time, but the dominant paradigm reduces each concept to a single direction whose geometry is left largely unexamined. Rather than selecting a single steering direction, we use conceptors: soft projection matrices estimated from activations pooled across both poles of a bipolar concept, which preserve the concept's full multidimensional subspace. A geometric analysis shows the bipolar subspace strictly subsumes the single-vector baseline. We further show that the conceptor quota provides a parameter-free layer-selection diagnostic, predicting concept separability with Pearson correlations up to r=0.96 across three instruction-tuned models and three semantic dimensions. Beyond selection, conceptors admit a closed-form Boolean algebra (AND, OR, NOT): we evaluate conceptor compositionality on thematically related sub-concepts. Across a systematic five-axis design-space evaluation, conceptors match or outperform additive baselines at layers where concept subspaces are multi-dimensional while producing substantially fewer degenerate outputs. Conceptor steering is a geometrically principled, compositional, and practically safer alternative to single-direction steering from a limited number of contrastive pairs.

A Tree Markov Decision Problem (T-MDP) is a finite-horizon MDP with a starting state $s_{1}$, in which every state is reachable from $s_{1}$ through exactly one state-action trajectory. T-MDPs arise naturally as abstractions of decision making in sequential games with perfect recall, against stationary opponents. We consider the problem of on-line learning in T-MDPs, both in the PAC and the regret-minimisation regimes. We show that well-known bandit algorithms – Lucb and Ucb – can be applied on T-MDPs by treating each policy as an arm. The apparent technical challenge in this approach is that the number of policies is exponential in the number of states. Our main innovation is in the design of confidence bounds based on data shared by the policies, so that the bandit algorithms can yet be implemented with polynomial memory and per-step computation. We obtain instance-dependent upper bounds on sample complexity and regret that sum a “gap term” from every terminal state, rather than every policy. Empirically, our algorithms consistently outperform available alternatives on a suite of hidden-information games.

Weight matrices in deep networks exhibit geometric continuity—principal singular vectors of adjacent layers point in similar directions. While this property has been widely observed, its origin remains unexplained. Through experiments on toy MLPs and small transformers, we identify two mechanisms: residual connections create cross-layer gradient coherence that aligns weight updates across layers, and symmetry-breaking nonlinearities constrain all layers to a shared coordinate frame, preventing the rotation drift that would otherwise destabilize weight structure. Crucially, a nonlinear but rotation-equivariant activation reaches less than half of ReLU's continuity, isolating symmetry breaking—not nonlinearity alone—as the active ingredient. Activation and normalization play distinct roles: activation concentrates continuity in the leading singular direction, while normalization distributes it across multiple directions. In transformers, continuity is projection-specific: Q, K, Gate, and Up (which read from the residual stream) develop input-space ($\mathbf{v}_1$) continuity; O and Down (which write to it) develop output-space ($\mathbf{u}_1$) continuity; V alone, lacking an adjacent nonlinearity, develops only low continuity.

Modern LLMs show mastery over an ever-growing range of skills, as well as the ability to compose them flexibly. However, extending model capabilities to new skills in a scalable manner is an open problem: fine-tuning and parameter-efficient variants risk catastrophic forgetting, while context-based approaches have limited expressiveness and are constrained by the model's effective context. We explore skill neologisms–soft tokens integrated in the model's vocabulary and optimized to improve capabilities over a specific skill–as a way to selectively acquire new skills without weight updates. We first observe that pretrained LLMs already exhibit tokens associated with procedural knowledge. We then show on a controlled synthetic task that skill neologisms can be learned to improve model capabilities on specific skills while being composable with out-of-distribution skills, and that independently trained skill neologisms can be composed zero-shot. Finally, we validate zero-shot composition of independently learned skill neologisms on the more realistic natural language setting of the Skill-Mix benchmark. These results suggest that skill neologisms may provide a scalable path towards skill-based continual learning.

Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not violate the true geometry of change. We propose Displacement-Reshaped Optimal Transport (ReshapeOT), a method that reshapes the ground metric by integrating observed sample displacements as an additional source of knowledge. Technically, ReshapeOT replaces the Euclidean metric with a Mahalanobis distance estimated from displacement second moments. This effectively carves expressways through the input space, inviting transport solutions that better align with observed displacements. Our method is computationally lightweight, integrates seamlessly into any OT solver that operates on a cost matrix, and can be kernelized for further flexibility. Experiments on synthetic and real-world data show that ReshapeOT achieves substantial gains in transport reliability. We further demonstrate our method's usefulness in two practical use cases.

Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), has advanced LLM reasoning. However, GRPO suffers from three credit assignment failures: uniform token-level granularity that ignores heterogeneous informational value, uniform polarity that penalizes correct steps and rewards incorrect ones, and zero-variance collapse that erases outcome-driven gradients. We systematically quantify these failures, revealing highly non-uniform token informativeness, widespread step-level polarity misalignment, and substantial training waste. To address these limitations, we propose Entropy-Progress Aligned GRPO (EP-GRPO), a framework that mines the model's intrinsic information flow for dense, self-supervised guidance. EP-GRPO integrates entropy-gated modulation to prioritize high entropy decision pivots, implicit process signals from policy divergence anchored to outcome advantages for directional token-level feedback without external reward models, and cumulative entropy mapping that enables progress-aligned advantage normalization, naturally maintaining gradient flow under zero reward variance. Extensive experiments on mathematical reasoning benchmarks demonstrate that EP-GRPO achieves superior accuracy and efficiency compared to GRPO and its variants. The code will be available.

Point forecasting for graph-structured multivariate time series is a fundamental problem, but rigorous uncertainty quantification for such predictions is still underexplored. Conformal prediction (CP) offers uncertainty estimation with a solid coverage guarantee under the exchangeability assumption, which requires the joint data distribution to be unchanged under permutation. However, in graph-structured time series, inherent cross-node coupling can violate the exchangeability condition, making direct application of CP unreliable. Inspired by the spectral graph theory, such coupling resides in global trends and can be characterized by the low-frequency components, while high-frequency components are nearly exchangeable. Therefore, we propose a novel concept named Spectral Graph Conditional Exchangeability (SGCE), which conditions exchangeable high-frequency components on low-frequency ones to preserve global trends and enable effective CP in the spectral domain. Based on SGCE, we further propose Spectral Conformal prediction via wAveLEt transform (SCALE). SCALE uses graph wavelets to decompose low/high-frequency components and conformalizes high-frequency residuals via adaptive gating over a low-frequency embedding. Experimental results on real-world traffic datasets show that SCALE not only achieves valid coverage but also consistently improves the coverage-efficiency trade-off over the state-of-the-art CP methods.

LLM-based Triton kernel generation has attracted significant interest, yet a fundamental empirical question remains unanswered: where does this capability break down, and why? We present KernelBenchX, a benchmark designed to answer this question through category-aware evaluation of correctness and hardware efficiency across 176 tasks in 15 categories. Our systematic comparison of five representative methods yields three main findings. First, task structure determines correctness more than method design. Category explains nearly three times more variance in semantic correctness than method (9.4% vs 3.3% explained deviance), and 72% of Fusion tasks fail across all five methods while Math tasks are solved consistently. Second, iterative refinement improves correctness, but not performance. Across GEAK iterations, compile rate rises from 52.3% to 68.8% while average speedup declines from $1.58\times$ to $1.44\times$; newly rescued kernels consistently underperform persistently correct ones ($1.16\times$ vs $1.58\times$ speedup in round~0$\to$1). Third, correctness does not imply efficiency. 46.6% of correct kernels are slower than the PyTorch eager baseline, and cross-hardware speedup variance reaches $21.4\times$. Besides, quantization remains completely unsolved (0/30 successes) despite non-trivial compilation rates, revealing systematic misunderstanding of numerical computation contracts rather than surface-level syntax errors. These findings suggest that future progress depends on handling global coordination, explicitly modeling numerical precision, and incorporating hardware efficiency into generation. The code is available at https://github.com/BonnieW05/KernelBenchX

When a machine learning (ML) model forecasts an undesired event, one often seeks a decision to avoid it, known as the avoiding undesired future (AUF) problem. Many rehearsal learning methods have been proposed for AUF, but they rely on an underlying graph structure; learning such a graph from observational data is challenging and can incur substantial estimation error. In this work, we demonstrate that the order structure can be sufficient for AUF decision-making, and propose the first order-based rehearsal learning method. Although an order is less informative than a graph, it can be sufficient to identify the influence of decisions from observational data, suggesting that learning the entire graph is not always necessary. To learn the order, we develop an information-theoretic method that imposes no restrictions on the form of structural functions or the type of noise distributions. For AUF decision-making, we construct an order-based sampler to approximate the influence of decisions and, combined with a surrogate objective for maximizing the post-decision success probability, reduce the AUF task to a differentiable optimization problem. Experiments show that our order learning method outperforms existing methods, and that our AUF approach not only surpasses methods relying on learned graphs or learned orders, but also matches or even exceeds oracle baselines that are given the true graph.