Papers

In networks, effective dynamic treatment allocation requires deciding both whom to treat and also when, so as to amplify policy impact through spillovers. An early intervention at a well-connected node can trigger cascades that change which nodes are worth targeting in the next period. Existing treatment strategies under network interference are largely static while dynamic treatment frameworks typically ignore network structure altogether. We integrate these perspectives and propose Q-Ising, a three-stage pipeline that (i) estimates network adoption dynamics via a Bayesian dynamic Ising model from a single observed panel, (ii) augments treatment adoption histories with continuous posterior latent states, and (iii) learns a dynamic policy via offline reinforcement learning. The Bayesian mechanism enables uncertainty quantification over dynamic decisions, yielding posterior ensemble policies with interpretable spillover estimates. We provide a finite-sample regret upper bound that decomposes into standard offline-RL uncertainty, network abstraction error, and first stage error in Ising state estimation. We apply our method to data from Indian village microfinance networks and synthetic stochastic block models under simulated heterogeneous susceptible-infected-susceptible (SIS) dynamics and demonstrate that adaptive targeting outperforms static centrality benchmarks.

It has been known for a long time that initializing weight matrices to be orthogonal instead of having i.i.d. Gaussian components can improve training performance. This phenomenon can be analyzed using finite-width corrections, where the infinite-width statistics are supplemented by a power series in $1/\mathrm{width}$. In particular, recent empirical results by Day et al. show that the tensors appearing in this treatment stabilize for large depth, as opposed to the tensors of i.i.d.-initialized networks. In this article, we derive explicit layer-wise recursion relations for the tensors appearing in the finite-width expansion of the network statistics in the case of orthogonal initializations. We also provide an extension of recently-introduced Feynman diagrams for the corresponding recursions in the i.i.d.-case which are valid to all orders in $1/\mathrm{width}$. Finally, we show explicitly that the recursions we derive reproduce the stability of the finite-width tensors which was observed for activation functions with vanishing fixed point. This work therefore provides a theoretical explanation for the stability of nonlinear networks of finite width initialized with orthogonal weights, closing a long-standing gap in the literature. We validate our theoretical results experimentally by showing that numerical solutions of our recursion relations and their analytical large-depth expansions agree excellently with Monte-Carlo estimates from network ensembles.

Accurate classification of breast cancer subtypes from gene expression data is critical for diagnosis and treatment selection. However, such datasets are characterized by high dimensionality and limited sample size, posing challenges for machine learning models. In this study, we evaluate the impact of model complexity and feature selection on subtype classification performance using TCGA-BRCA gene expression data. Logistic regression, random forest, and support vector machine (SVM) models were trained using varying numbers of highly variable genes (50 to 20,518). Performance was evaluated using stratified 5-fold cross-validation and assessed with accuracy and macro F1 score. While all models achieved high accuracy, macro F1 analysis revealed substantial differences in subtype-level performance. Logistic regression demonstrated the most stable and balanced performance across subtypes, including improved detection of rare classes. Random forest underperformed on minority subtypes despite strong overall accuracy, while SVM showed sensitivity to feature dimensionality. These findings highlight the importance of model simplicity, evaluation metrics, and feature selection in high-dimensional biological classification tasks.

Trust in counterfactual explanations depends critically on whether their recommended changes are truly minimal: suboptimal explanations may vastly overshoot the actual changes needed to alter a decision, and heuristic errors can affect individuals unevenly, giving some users relevant recourse while assigning others unnecessarily costly recommendations. Consequently, we study the problem of computing optimal counterfactual explanations for tree ensembles under plausibility and actionability constraints. This is a combinatorial problem: for a fixed model, counterfactual search boils down to selecting consistent branching decisions and threshold-defined regions under a distance objective. We exploit this structure through CPCF, a constraint programming (CP) formulation in which numerical features are encoded as interval domains induced by split thresholds, while discrete features retain native finite-domain representations. This yields a compact finite-domain formulation that supports multiple distance objectives without continuous split-boundary search. We then place CPCF in a broader comparison across mathematical programming paradigms: we extend a maximum Boolean satisfiability (MaxSAT) formulation, originally designed for hard-voting random forests, to soft-voting ensembles, and compare against the current state-of-the-art mixed-integer linear programming (MILP) optimal approach. Across ten datasets and three types of tree ensembles, we analyze scalability, anytime performance, and sensitivity to distance metrics. We observe that CP achieves the best overall performance. More importantly, our results identify regimes in which the specific strengths of each paradigm make it best suited: CP is most versatile overall, MaxSAT handles hard-voting ensembles particularly well, and MILP remains competitive in amortized inference settings with a moderate number of split levels.

Cooperative multi-agent reinforcement learning (MARL) benchmarks commonly emphasize aggregate outcomes such as return, success rate, or completion time. While essential, these metrics can obscure how agents coordinate and fail to distinguish policies that achieve similar outcomes through different interaction processes. We propose a process-aware evaluation framework that complements aggregate performance with diagnostics of interference, coordinated task completion, participation, and coordination efficiency. We evaluate the framework in STAT, a controlled spatial task-allocation testbed, and examine its broader applicability in two established cooperative MARL benchmarks. Across diverse value-based and actor-critic methods, we find policies with nearly identical return can exhibit substantial differences in coordination behavior. Controlled scaling in STAT reveals distinct process signatures for spatial, task, and agent scaling, while a reward-shaping ablation shows that explicitly penalizing assignment conflicts can alter coordination behavior with little change in task return. Results in the established benchmarks further show that the framework remains informative under different coordination mechanisms. These findings support process-aware evaluation as a complement to outcome-based benchmarking. The framework provides a common structure for selecting and interpreting environment-specific diagnostics that characterize not only what cooperative policies achieve, but how they coordinate to achieve it.

Modern generative models can produce high-quality samples, but independent samples under the same condition often yields highly similar outputs. Particle-based methods increase diversity by letting the samples in a batch interact, typically through a repulsive force. These forces, however, also push each sample away from the data distribution and produce visible artifacts. We introduce EDDY, a training-free particle guidance method designed to avoid this failure mode. Instead of a repulsive gradient, EDDY couples particles through anti-symmetric matrix fields passed through a Stein operator, a family of drift perturbations that leaves the Fokker–Planck equation invariant. Unlike repulsive guidance, these interactions do not alter a particle's distribution while the batch is independent. For the same reason they cannot create diversity on their own, so EDDY pairs them with a negatively correlated initialization that keeps each particle's prior exact. To use EDDY with perceptual kernels such as DINOv2, we approximate its second-order terms with finite differences and Hutchinson estimates. Across FLUX.1-dev, FLUX.2-klein and SDXL, EDDY achieves higher image quality and prompt alignment than existing particle guidance methods at matched diversity.

The design of biological systems is hindered by uncertainty arising from both intrinsic stochasticity of biomolecular reactions and variability across laboratory or experimental conditions. In this work, we present a sequential framework to optimize genetic circuits under both forms of uncertainty. By employing simulator models based on differential equations or Markov jump processes alongside a reinforcement learning (RL) policy-based approach, our method suggests experiments that adapt to unknown laboratory conditions while accounting for inherent stochasticity. While previous Bayesian methods address uncertainty through iterative experiment-inference-optimization cycles, they typically require computationally expensive inference and optimization steps after each experimental round, leading to delays. To overcome this bottleneck, we propose an amortized approach trained up-front across a distribution of possible uncertain parameters. This strategy sidesteps the need for explicit parameter inference during the design cycle, enabling immediate, observation-based adaptation. We demonstrate our framework on models for heterologous gene expression and a repressilator circuit, showing that it efficiently handles both molecular noise and cross-laboratory variability.

We study online prediction under distribution shift, where inputs arrive chronologically and outcomes are revealed only after prediction. In this setting, predictors must remain stable in quiet regimes yet adapt when regimes shift, and the right adaptation memory is unknown in advance. We propose MELO (Memory-hedged Exponentially Weighted Least-Squares Online aggregation), a model-agnostic method that hedges across adaptation scales: it wraps any non-anticipating base-predictor pool with exponentially weighted least-squares (EWLS) adaptation experts at multiple forgetting factors, and aggregates raw and EWLS-adapted forecasts with MLpol, a parameter-free online aggregation rule. Under boundedness conditions, we establish deterministic oracle inequalities showing that it competes with both the best raw predictor and the best bounded, time-varying affine combinations of the base predictions, up to a path-length-dependent tracking cost and a sublinear aggregation overhead. We evaluate MELO on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. MELO reduces overall RMSE by 34.7% relative to base-only MLpol and achieves lower overall RMSE than a TabICL reference supplied with an external COVID policy-response covariate. Moreover, MELO requires only lightweight per-step recursive updates without model retraining.

Diffusion-based posterior samplers draw from measurement- or reward-conditioned posteriors using pretrained diffusion priors. Though widely used for inverse problems, their output is biased even with exact prior scores. First, we quantify this bias for the DPS algorithm, the base method for a family of samplers, by introducing a surrogate curve of probability densities which interpolates between the true posterior and the standard Gaussian. The ratio of sampler to surrogate densities solves a parabolic PDE, and its Feynman–Kac formula yields an explicit representation of this ratio as the expectation of a path functional. This representation reveals which posterior regions are over- or under-sampled. This framework also provides a design principle for bias reduction that includes STSL, a related sampler. Second, in hard-constraint problems (e.g. the low measurement noise regime) these samplers are known to be numerically unstable. We find that this instability of discretized DPS arises from an effective guidance update whose strength scales inversely with step size, inevitably violating the forward-Euler stability criterion near the constraint. This finding motivates implicit (backward-Euler) guidance updates. Finally, we show that the standard practice of early guidance-stopping, used to avoid oscillations, introduces a secondary bias which we characterize through our framework.

Outcome metrics can certify the wrong behavior. We study this failure in a two-hotel revenue-management simulator where Hotel A trains an agent against a fixed rule-based revenue-management competitor, Hotel B. A standard learning agent can obtain near-reference revenue per available room (RevPAR) while failing to learn market-like yield management: it sells too aggressively, undercuts, or collapses to modal price buckets. We diagnose this as a Goodhart-style failure under partial observability. Hotel A cannot observe the competitor's remaining inventory, booking curve, or pricing rule, so the same Hotel A-visible state maps to multiple plausible Hotel B prices. Deterministic value-based RL and deterministic copying collapse this unresolved uncertainty into shortcut behavior. We introduce a trace-level diagnostic protocol using RevPAR, occupancy, ADR, full price-bucket distributions, L1/JS distances, and seed-level confidence intervals. The verified repair is Trace-Prior RL: learn a distributional market prior from lagged market traces, then train a stochastic pricing policy with a RevPAR reward and a KL penalty to the learned prior. The final policy matches Hotel B's RevPAR, occupancy, ADR, and price distribution within seed-level uncertainty, while still optimizing Hotel A's own reward. We argue that the contribution is not a new optimizer and not a hotel-pricing leaderboard, but a reproducible failure-and-repair recipe for agentic systems where scalar rewards are easy to game and the intended behavior is only visible in traces. A key finding is that higher exact action accuracy can worsen aggregate trace alignment when the target is distributional.

Recent extensive research has demonstrated that the enhanced reasoning capabilities acquired by models through Reinforcement Learning with Verifiable Rewards (RLVR) are primarily concentrated within the rank-1 components. Predicated on this observation, we employed Periodic Rank-1 Substitution and identified a counterintuitive phenomenon: RLVR may exhibit implicit reward overfitting to the training dataset. Specifically, the model can achieve satisfactory performance on the test set even when its rewards remain relatively low during the training process. Furthermore, we characterize three distinct properties of RL training: (1) The effective rank-1 component in RLVR don't maintain other model knowledge except mathematical reasoning capability. (2) RLVR fundamentally functions by optimizing a specific singular spectrum. The distribution of singular values of almost all linear layers in RLVR-trained model behaves like heavy-tailed distribution. (3) the left singular vectors associated with rank-1 components demonstrate a stronger alignment tendency during training, which echoes the discovery that RLVR is optimizing sampling efficiency in essence. Taken together, our findings and analysis further reveal how RLVR shapes model parameters and offer potential insights for improving existing RL paradigms or other training paradigms to implement continual learning.

Foundation models (FMs) are increasingly deployed in open-world settings where distribution shift is the rule rather than the exception. The out-of-distribution (OOD) phenomena they face – knowledge boundaries, capability ceilings, compositional shifts, and open-ended task variation – differ in kind from the settings that have shaped prior OOD research, and are further complicated because the pretraining and post-training distributions of modern FMs are often only partially observed. Our position is that OOD for foundation models is a structurally distinct problem that cannot be solved within the prevailing model-centric paradigm, and that agentic systems constitute the missing paradigm required to address it. We defend this claim through four steps. First, we give a stage-aware formalization of OOD that accommodates partially observed multi-stage training distributions. Second, we prove a parameter coverage ceiling: there exist practically relevant inputs that no model-centric method (training-time or test-time) can handle within tolerance $\varepsilon$, for reasons intrinsic to parameter-based representation. Third, we characterize agentic OOD systems by four structural properties – perception, strategy selection, external action, and closed-loop verification – and show that they strictly extend the reachable set beyond the ceiling. Fourth, we respond to seven counterarguments, conceding two, and outline a research agenda. We do not claim that agentic methods subsume model-centric ones; we argue that the two are complementary, and that progress on FM-OOD requires explicit recognition of the agentic paradigm as a first-class research direction.

Regulatory approval of products in high-stakes domains such as drug development requires statistical evidence of safety and efficacy through large-scale randomized controlled trials. However, the high financial cost of these trials may deter developers who lack absolute certainty in their product's efficacy, ultimately stifling the development of `moonshot' products that could offer high social utility. To address this inefficiency, in this paper, we introduce a statistical protocol for experimentation where the product developer (the agent) conducts a randomized controlled trial sequentially and the regulator (the principal) partially subsidizes its cost. By modeling the protocol using a belief Markov decision process, we show that the agent's optimal strategy can be found efficiently using dynamic programming. Further, we show that the social utility is a piecewise linear and convex function over the subsidy level the principal selects, and thus the socially optimal subsidy can also be found efficiently using divide-and-conquer. Simulation experiments using publicly available data on antibiotic development and approval demonstrate that our statistical protocol can be used to increase social utility by more than $35$$\%$ relative to standard, non-sequential protocols.

Data reconstruction attacks on trained neural networks aim to recover the data on which the network has been trained and pose a significant threat to privacy, especially if the training dataset contains sensitive information. Here, we propose a unified optimization formulation of the data reconstruction problem based on initial and trained parameter values, incorporating state-of-the-art proposals. We show that in the random feature model, this formulation provably leads to training data reconstruction with high probability, provided the network width is sufficiently large; this unprecedented finite-width result uses PAC-style bounds. Furthermore, when the data lies in a low-dimensional subspace, we show that the network width requirement for successful reconstruction can be relaxed, with bounds depending on the subspace dimension rather than the ambient dimension. For general neural network models and unknown data orientations, we propose an efficient reconstruction algorithm that approximates the low-dimensional data subspace through the change in the first-layer weights during training and uses only the last-layer weights for reconstruction, thus reducing the search space dimension and the required network width for high-quality reconstructions. Our numerical experiments on synthetic datasets and CIFAR-10 confirm that our subspace-aware reconstruction approach outperforms standard full-space techniques.

Transformer-based tabular foundation models (TFMs) dominate small to medium tabular predictive benchmark tasks, yet their inference mechanisms remain largely unexplored. We present the first large-scale mechanistic study of layerwise dynamics in 6 state-of-the-art tabular in-context learning models. We explore how predictions emerge across depth, identify distinct stages of inference and reveal latent-space dynamics that differ from those of language models. Our findings indicate substantial depthwise redundancy across multiple models, suggesting iterative refinement with overlapping computations during inference stages. Guided by these insights, we design a proof-of-concept, looped single-layer model that uses only 20% of the original model's parameters while achieving comparable performance. The code is available at https://github.com/amirbalef/is_one_layer_enough.

Reinforcement learning fine-tuning has become the dominant approach for aligning diffusion models with human preferences. However, assessing images is intrinsically a multi-dimensional task, and multiple evaluation criteria need to be optimized simultaneously. Existing practice deal with multiple rewards by training one specialist model per reward, optimizing a weighted-sum reward $R(x)=\sum_k w_k R_k(x)$, or sequentially fine-tuning with a hand-crafted stage schedule. These approaches either fail to produce a unified model that can be jointly trained on all rewards or necessitates heavy manually tuned sequential training. We find that the failure stems from using a naive weighted-sum reward aggregation. This approach suffers from a sample-level mismatch because most rollouts are specialist samples, highly informative for certain reward dimensions but irrelevant for others; consequently, weighted summation dilutes their supervision. To address this issue, we propose MARBLE (Multi-Aspect Reward BaLancE), a gradient-space optimization framework that maintains independent advantage estimators for each reward, computes per-reward policy gradients, and harmonizes them into a single update direction without manually-tuned reward weighting, by solving a Quadratic Programming problem. We further propose an amortized formulation that exploits the affine structure of the loss used in DiffusionNFT, to reduce the per-step cost from K+1 backward passes to near single-reward baseline cost, together with EMA smoothing on the balancing coefficients to stabilize updates against transient single-batch fluctuations. On SD3.5 Medium with five rewards, MARBLE improves all five reward dimensions simultaneously, turns the worst-aligned reward's gradient cosine from negative under weighted summation in 80% of mini-batches to consistently positive, and runs at 0.97X the training speed of baseline training.

Differentially private (DP) zeroth-order (ZO) fine-tuning of large language models (LLMs) inherits DP's harsh utility-privacy trade-off. PAC Privacy, an instance-based notion, offers an alternative. It bounds the mutual information (MI) between the secret input and the output, and calibrates the noise to the stability of the output under the input distribution. We introduce PACZero, a family of ZO fine-tuning mechanisms under PAC Privacy. For stability, PACZero quantizes each update to a single bit, the sign of the ZO update aggregated over the secret subset of the training data. On many steps all candidate subsets agree on this sign, so the bit can be released at no cost in MI. On the remaining steps the bit passes through a noisy channel calibrated to a per-step MI budget. We study two channels, the standard additive Gaussian channel of PAC Privacy (PACZero-AGC) and a binary asymmetric channel with optimal bit flipping (PACZero-BAC), along with their zero-budget versions at $\mathrm{MI} \to 0$, PACZero-AGC$_0$ and PACZero-BAC$_0$. At zero MI, nothing released during training, including the fine-tuned model, carries any information about which secret subset was sampled, so no adversary inferring that subset can do better than its prior. In particular, the success rate of any membership inference attack (MIA) is bounded by 50% under a balanced prior. To our knowledge, this is the first such guarantee for LLM fine-tuning, and DP matches the MIA bound only at $\varepsilon = \delta = 0$ and infinite noise. We evaluate on SST-2 and SQuAD with models from 1.3B to 8B parameters, under LoRA and full fine-tuning. Both channels retain high utility under tight MI budgets, and even PACZero-BAC$_0$, which guarantees zero MI, stays within 2 points of non-private ZO fine-tuning with the same number of steps. To our knowledge no DP method achieves usable utility matching this MIA-resistance level.

Since its introduction in 2017, the Transformer has become one of the most widely adopted architectures in modern deep learning. Despite extensive efforts to improve positional encoding, attention mechanisms, and feed-forward networks, the core token-mixing mechanism in Transformers remains attention. In this work, we show that the attention module in Transformers can be interpreted as performing Nadaraya-Watson regression, where it computes similarities between tokens and aggregates the corresponding values accordingly. Motivated by this perspective, we propose Cubit, a potential next-generation architecture that leverages Kernel Ridge Regression (KRR), while the vanilla Transformer relies on Nadaraya-Watson regression. Specifically, Cubit modifies the classical attention computation by incorporating the closed-form solution of KRR, combining value aggregation through kernel similarities with normalization via the inverse of the kernel matrix. To improve the training stability, we further propose the Limited-Range Rescale (LRR), which rescales the value layer within a controlled range. We argue that Cubit, as a KRR-based architecture, provides a stronger mathematical foundation than the vanilla Transformer, whose attention mechanism corresponds to Nadaraya-Watson regression. We validate this claim through comprehensive experiments. The experimental results suggest that Cubit may exhibit stronger long-sequence modeling capability. In particular, its performance gain over the Transformer appears to increase as the training sequence length grows.

Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve learning. Most existing approaches focus on special cases, such as prescribed symmetries and exact equivariance, without addressing how to discover more general structures that require nonlinear operators to transform and map between continuous state/action systems with isomorphic value functions. We propose VPSD-RL (Value-Preserving Structure Discovery for Reinforcement Learning). It models continuous RL as a controlled diffusion with value-preserving mappings defined through Lie-group actions and associated pullback operators. We show that a value-preserving structure exists exactly when pulling back the value function and pushing forward actions commute with the controlled generator and reward functional. Further, approximate value-preserving structures with rigorous guarantees can be found when the Hamilton–Jacobi–Bellman mismatch is small. This framework discovers exact and approximate value-preserving structures by searching for the associated Lie group operators. VPSD-RL fits differentiable drift, diffusion, and reward models; learns infinitesimal generators via determining-equation residual minimization; exponentiates them with ODE flows to obtain finite transformations; and integrates them into continuous RL through transition augmentation and transformation-consistency regularization. We show that bounded generator/reward mismatch implies quantitative stability of the optimal value function along approximate orbits, with sensitivity governed by the effective horizon, and observe improved data efficiency and robustness on continuous-control benchmarks.

In many scientific domains, including experimentation, researchers rely on measurements of proxy outcomes to achieve faster and more frequent reads, especially when the primary outcome of interest is challenging to measure directly. While proxies offer a more readily accessible observation for inference, the ultimate goal is to draw statistical inferences about the primary outcome parameter and proxy data are typically imperfect in some ways. To correct for these imperfections, current statistical inference methods often depend on strict identifying assumptions (such as surrogacy, covariate/label shift, or missingness assumptions). These assumptions can be difficult to validate and may be violated by various additional sources of distribution shift, potentially leading to biased parameter estimates and miscalibrated uncertainty quantification. We introduce an estimate-level framework, inspired by domain adaptation techniques, to empirically calibrate proxy-based inference. This framework models the proxy-primary metric discrepancy as a random effect at the parameter level, estimating its distribution from aggregated historical observations across past domains (e.g., experiments, time periods, or distinct segments). This method avoids the requirement for retaining individual-level response data. Additionally, this adjustment can be layered on top of existing proxy-correction methods (such as prediction-powered inference or importance weighting) to account for additional biases not addressed by those corrections. To manage uncertainty when the number of historical domains is limited, we provide both a method-of-moments estimator and a domain bootstrap procedure. We further validate this approach using publicly available datasets and real-world experiments.

Predictive models are often deployed through existing decision policies that stakeholders are reluctant to change unless a risk constraint requires intervention. We study risk-controlled post-processing: given a deterministic baseline policy, choose a new policy that maximizes agreement with the baseline subject to a chance constraint on a user-specified loss. At the population level, we show that the optimal policy has a threshold structure: it follows the baseline except on contexts where switching to the oracle fallback policy yields a large reduction in conditional violation risk. At the finite-sample level, given a fitted fallback policy and score, we develop a post-processing algorithm that uses calibration data to select a threshold. Leveraging tools from algorithmic stability and stochastic processes, we show that under regularity conditions, in the i.i.d. setting, the expected excess risk of the post-processed policy is $O(\log n/n)$. In the special case when an exact-safe fallback policy is available, the algorithm achieves precise expected risk control under exchangeability. In this setting, we also give high-probability near-optimality guarantees on the post-processed policy. Experiments on a COVID-19 radiograph diagnosis task, an LLM routing problem, and a synthetic multiclass decision task show that targeted post-processing can meet or nearly meet risk budgets while preserving substantially more agreement with the baseline than score-blind random mixing.

We present a novel theoretical framework, Q-MMR, for off-policy evaluation in finite-horizon MDPs. Q-MMR learns a set of scalar weights, one for each data point, such that the reweighted rewards approximate the expected return under the target policy. The weights are learned inductively in a top-down manner via a moment matching objective against a value-function discriminator class. Notably, and perhaps surprisingly, a data-dependent finite-sample guarantee for general function approximation can be established under only the realizability of $Q^\pi$, with a dimension-free bound – that is, the error does not depend on the statistical complexity of the function class. We also establish connections to several existing methods, such as importance sampling and linear FQE. Further theoretical analyses shed new light on the nature of coverage, a concept of fundamental importance to offline RL.

LLM-based workflows compose specialized agents to execute complex tasks, and these agents usually share substantial context, allowing KV-Cache reuse to save computation. Existing approaches either manage KV-Cache at agent level and fail to exploit the reuse opportunities within workflows, or manage cache at the workflow level but assume that each workflow calls a static sequence of agents. However, practical workflows are typically dynamic, where the sequence of invoked agents and thus induced cache reuse opportunities depend on the context of each task. To serve such dynamic workflows efficiently, we build a system dubbed PBKV (Prediction-Based KV-Cache Management). For each workflow, PBKV predicts the agent invocations in several future steps by fusing the guidance from historical workflows and context of the target workflow. Based on the predictions, PBKV estimates the reuse potential of cache entries and keeps the high-potential entries in GPU memory. To be robust to prediction errors, PBKV utilizes the predictions conservatively during both cache eviction and prefetching. Experiments on three workflow benchmarks show that PBKV achieves up to $1.85\times$ speedup over LRU on dynamic workflows, and up to $1.26\times$ speedup over the SOTA baseline KVFlow on the static workflow.

We present a new operator-theoretic representation learning framework for offline reinforcement learning that recovers the directed temporal geometry of a controlled Markov process from hitting time observations. While prior art often produces symmetric distances or fails to satisfy the triangle inequality, our framework learns a Hilbert-space displacement geometry where expected hitting times are realized as linear functionals of latent displacements. We prove that this representation exists under latent linear closure and is uniquely identifiable up to a bounded linear isomorphism. For finite-dimensional implementations, we show that global hitting-time error is bounded by one-step transition error amplified by the environment's transient spectral radius. Furthermore, we provide finite-sample guarantees accounting for approximation, statistical complexity, and trajectory-label mismatch. Derived from this theory, we curate Isomorphic Embedding Learning (IEL) as a new goal-agnostic foundation policy learning algorithm that anchors a HILP-style consistency objective with explicit hitting-time regression to ensure that the learned geometry reflects actual decision-time progress. This asymmetric and compositional structure enables robust graph-based multi-stage planning for long-horizon navigation. Our experiments demonstrate that IEL improves the state of the art of learning foundation policy policies from offline maze locomotion data. Our code can be found on https://github.com/MagnusBoock/IEL

Self-optimizing control is a strategy for selecting controlled variables, where the economic objective guides the selection and design of controlled variables, with the expectation that maintaining the controlled variables at constant values can achieve optimization effects, translating the process optimization problem into a process control problem. Currently, self-optimizing control is widely applied to steady-state optimization problems. However, the development of process systems exhibits a trend towards refinement, highlighting the importance of optimizing dynamic processes such as batch processes and grade transitions. This paper formally introduces the self-optimizing control problem for dynamic optimization, termed the dynamic self-optimizing control problem, extending the original definition of self-optimizing control. A novel concept, "dynamic controlled variables" (DCVs), is proposed, and an implicit control policy is presented based on this concept. The paper theoretically analyzes the advantages and generality of DCVs compared to explicit control strategies and elucidates the relationship between DCVs and traditional controllers. Moreover, this paper puts forth a data-driven approach to designing self-optimizing DCVs, which considers DCV design as a mapping identification problem and employs deep neural networks to parameterize the variables. Three case studies validate the efficacy and superiority of DCVs in approximating multi-valued and discontinuous functions, as well as their application to dynamic optimization problems with non-fixed horizons, which traditional self-optimizing control methods are unable to address.

Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated by the fact that topological objects permit operations, such as structural refinements, that are not appropriate for graph data. In this work, we extend MANTRA, a benchmark dataset containing manifold triangulations, to a larger class of manifolds with more diverse homeomorphism types. We show that, contrary to prior claims, graph neural networks can saturate the benchmark, while higher-order message passing methods lag behind. However, we find that this is contingent on the right representation and feature assignment, emphasizing their importance in baseline models. Hence, we present a novel evaluation protocol based on representational diversity and triangulation refinement. Even when including refinement-like changes in the training data, existing models fail to generalize beyond the combinatorial structure of the data. This points towards a research gap in developing models that understand topological structure independent of scale. Our work thus provides the necessary scaffolding to evaluate future models and enable the development of topology-aware inductive biases.

Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging. Unsupervised tasks in particular require interpretable, scalable, and reliable size-aware graph representations. Our work addresses these issues by tracking the structural diversity of a graph across coarsening levels. The resulting graph embeddings, which we denote diversity curves, are interpretable by construction, efficient, and directly comparable across coarsening hierarchies. Specifically, we track the spread of graphs, a novel isometry invariant that is inherently well-suited for encoding the metric diversity and geometry of graphs. We utilise edge contraction coarsening and prove that this improves expressivity, thus leading to more powerful graph-level representations than structural descriptors alone. Demonstrating their utility over a range of baseline methods in practice, we use diversity curves to (i) cluster and visualise simulated graphs across varying sizes, (ii) distinguish the geometry of single-cell graphs, (iii) compare the structure of molecular graph datasets, and (iv) characterise geometric shapes.

Progress in graph learning is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard to tell whether a model actually learns from the graph, or whether it even needs to. We propose measuring this using graph invariants, i.e., permutation-invariant, task-agnostic structural descriptors. Our analysis on datasets substantiates three tacit assumptions in graph learning, namely that (i) a curated subset of invariants is more expressive than standard GNNs, (ii) benchmark datasets exhibit structural heterogeneity even when originating from the same domain, and (iii) simple models are often competitive with, and sometimes exceed, approaches based on transformers or message passing. We thus posit that graph invariants should become a standard tool for measuring graph learning task complexity and the relevance of graph structure.

Visual document retrieval has become essential for accessing information in visually rich documents. Existing approaches fall into two camps. Late-interaction retrievers achieve strong quality through fine-grained token-level matching but store hundreds of vectors per page, incurring large index footprints and high serving costs. By contrast, dense single-vector retrievers retain storage and latency advantages but consistently lag in quality because they compress all information into a single final-layer embedding. In this work, we first conduct a layerwise diagnostic on single-vector retrievers, revealing that retrieval-relevant signal resides in internal representations. Motivated by these findings, we propose MINER (Mining Multimodal Internal RepreseNtation for Efficient Retrieval), a lightweight plug-in module that probes and fuses internal signals across transformer layers into a single compact embedding without modifying the backbone or sacrificing single-vector efficiency. The first Retrieval-Aligned Layer Probing stage attaches a lightweight probe at each layer, surfacing which dimensions carry retrieval-relevant information. The subsequent Adaptive Sparse Multi-Layer Fusion stage applies performance-adaptive neuron-level masking to the selected layers and fuses the surviving signals into the final dense vector. Across ViDoRe V1/V2/V3, MINER outperforms existing dense single-vector retrievers on the majority of benchmarks, with up to 4.5% nDCG@5 improvement over its corresponding backbone. Compared to strong late-interaction baselines, in some settings MINER substantially narrows the nDCG@$5$ gap to $0.2$ while preserving the storage and serving advantages of dense retrieval.

Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local geometric framework in which semantically equivalent inputs produce representations that occupy structured regions in latent space, with paraphrastic variation along nuisance directions and semantic identity preserved in invariant subspaces. Building on this view, we make three contributions: (1) a geometric characterization of invariant latent features, (2) a contrastive subspace discovery method that separates semantic-changing from semantic-preserving variation, and (3) an application of invariant representations to zero-shot model attribution. Across models and layers, empirical results support these contributions. Invariant structure emerges in specific depth regions, semantic displacement lies largely outside the nuisance subspace, and representation-level interventions indicate a causal role of invariant components in model outputs. Invariant representations also capture model-specific geometric patterns, enabling accurate attribution. Together, these findings support a local geometric characterization of semantic invariance in language model representations.