In the lower-star filtration (LSF), simplices are assigned filtration values according to the maximum-vertex rule, with each simplex entering the filtration when its highest-valued vertex appears. A limitation of this construction is that some higher-dimensional simplices may enter simultaneously with their boundary faces, causing certain topological features to be filled immediately upon formation and thus not appear in the resulting persistence diagram. To address this limitation, we propose three alternative filtration methods: the \(\varepsilon\)-lower-star filtration (ELSF), the \(L_p\) filtration (LpF), and the softmax filtration (SMF). {ELSF introduces a dimension-dependent delay to the maximum-vertex rule,} allowing higher-dimensional simplices to enter the filtration after their boundary faces, whereas {LpF and SMF use aggregation functions that depend on all vertex values rather} than solely on their maximum. By modifying how filtration values are assigned, these methods allow simplices to enter the filtration more progressively, so that topological features such as loops and voids may persist over longer filtration intervals rather than being filled immediately. Consequently, the resulting persistence diagrams may include persistence features that are not observed under LSF, potentially providing useful information for distinguishing data populations. Experimental results on simulated and real-world datasets demonstrate that the proposed filtration methods are computationally efficient and can provide greater sensitivity to structural differences in the data than LSF.
Global solar photovoltaic (PV) capacity is rapidly growing, helping decrease our emissions and dependence on fossil fuels. However, optimally siting a solar plant remains challenging, requiring anticipation of geographical, urban, and infrastructure needs. Current methods rely on multi-criteria decision analysis (MCDA) using hand-picked geophysical layers and solar-resource products, however these strategies are not geographically transferable and do not capture the practical requirements of solar sites. We use geospatial embeddings, dense vectors representing geophysical properties of a location, to analyse 38,591 existing solar sites and the land they were built on to learn the latent solar suitability signal. We assess a set of linear and non-linear models and select a soft-voting ensemble of a random forest and a multilayer perceptron (RF+MLP ensemble), chosen for accuracy and large scale deployability. Validated against future installations in thirteen countries, the ensemble separates existing solar sites from random land with a median ROC-AUC of 0.90. Compared with published MCDA strategies, the ensemble increases ROC-AUC by 0.06-0.30 in every country. The ranking also concentrates real deployment: the most-suitable 20% of land holds 84% of estimated generation (annual energy yield) and 67% of installed capacity (potential power output). After applying standard siting constraints, 5.6% of global land (9.8% if cropland is permitted) remains highly suited to solar. The global 10 m resolution solar suitability dataset and code can be found here: https://github.com/Abdullahr29/Global-Solar-Siting.
Partial occlusions challenge object recognition in both human and computer vision (CV), but the impact is largely dependent on the occlusion and model design. Properties relating to color are particularly important in biological recognition and frequently leveraged for camouflage, however there are still open questions about what makes them effective and how they translate to CV. This work studies partial occlusions that create camouflage, including those that blend in with target objects or with scenes, which alter object representations in distinct ways. Experiments evaluate recognition performance on both human participants and models ranging from convolutional neural networks (CNNs) to transformers, and additional analysis is performed on models to uncover trends in processing and object representations under multiple occlusion types. Novel metrics offer explainability of model behavior under occlusion: non-occlusion precision (NOP) and non-occlusion recall (NOR) measure alignment of model activations with and without occlusion, and activation in occlusion (AIO) measures the percentage of activations that occur in occluded regions. Findings show that human recognition, and most transformers, are negatively impacted by generated camouflaging occluders, with scene-based camouflage performing worse than object-based. Classical CNNs show a strong opposite trend, performing the worst on neutral-colored occlusions, suggesting that contextually-related colors, particularly scene-based, benefit object recognition rather than disrupting shape or boundary cues. Additionally, generated camouflaging occluders for training augmentation improves robustness to unseen camouflage for selected CNN model, and occlusion metrics suggest trends about learned mechanisms. Findings have interesting implications for alignment in human and computer vision, model vulnerabilities, and explainability.
Latent diffusion models rely on pretrained autoencoders that introduce lossy compression and constrain spatial granularity. Pixel-space diffusion avoids this bottleneck and enables flexible tokenization at multiple spatial scales, yet existing approaches largely adopt two-level coarse-to-fine architectures with limited cross-scale interaction. We introduce MS-pDiT, a multi-scale pixel-space diffusion transformer that treats spatial scale as a modality. MS-pDiT tokenizes the same noisy image at multiple patch sizes, processes each scale in a dedicated transformer stream, and enables bidirectional information exchange through compacted MM-DiT-style joint attention, with attention cost independent of the finest patch size. This design establishes the number of scales as a new architectural scaling dimension. On ImageNet $256\times256$, increasing the number of scales from two to five consistently improves FID from 4.39 to 2.31, 2.26, and 2.19, while adding an intermediate scale substantially outperforms increasing depth under comparable parameter budgets. Further analysis highlights the importance of bidirectional cross-scale interaction and late introduction of fine-grained streams. MS-pDiT achieves FID scores of 1.43 and 1.44 on ImageNet $256\times256$ and $512\times512$, respectively, and naturally extends to text-to-image generation, achieving 0.86 on GenEval and 83.9 on DPG-Bench.
The limited supervision available for the few-shot adaptation of vision-language models makes gradient estimation particularly noisy. We find that the gradient magnitudes are severely miscalibrated, while the signs of a small top-magnitude subset remain informative. This motivates SignSparseSGD and DynSignSparseSGD, two state-free optimizers that use gradient magnitudes only to select where to update and fixed-magnitude signs to decide how to update. The static variant fixes the support after the first minibatch. The dynamic variant refreshes it at every step. Across 11 datasets, three CLIP backbones, and five shot levels, the proposed methods are competitive with or outperform parameter-efficient and optimization-based baselines on average, while exhibiting markedly lower sensitivity to long training schedules. They introduce no task-specific modules, maintain no first- or second-moment optimizer states, and use one shared configuration across datasets, backbones, and shot levels. Our code is included in the supplementary materials and will be released upon publication.
Predicting outcomes from spatiotemporal data, such as assessing Parkinson's severity from human motion, often requires explainability in addition to accuracy. Practitioners need to know what drove the prediction, whether it be spatial (a body joint), temporal (a specific window), or both. Shapley values are attributions computed by treating input features as players in a cooperative game and measuring how the model output changes as coalitions of players are removed. Computing them involves choosing what counts as players, how absent players are imputed, and how the game is evaluated. How these choices affect explanation quality is poorly understood for spatiotemporal data, and real data carries no ground-truth attributions to check against. We present MotionBench-XAI, a benchmark built on i) five synthetic spatiotemporal datasets with exact ground-truth Shapley values, ii) three real datasets across clinical gait, electrocardiogram, and audio, iii) ten attribution methods across three player sets, and iv) three trained architectures. We show that grouping features into players, across time, space, or both, matters more than the choice of imputer. Generative imputers improve explanations only when their conditional models are accurate. On real data, the standard proxy metrics select contradictory best methods. We distill these findings into practical insights and provide an open-source pipeline.
Reward models used for off-policy evaluation (OPE) are commonly selected using held-out data. When sample size and context dimension grow proportionally, the difference in test risk between models fitted on the full sample and on a fixed fraction of it need not vanish. Held-out evaluation can therefore consistently estimate the test risk of the model trained on the smaller sample, but because the relative ranking of candidate reward models can change after full-data refitting, held-out selection can be suboptimal. We develop an Onsager-corrected, target-policy-weighted criterion that estimates the full-data reward model's out-of-sample risk under the target policy using only its training observations. This enables early stopping along the full-data gradient-descent trajectory without sample splitting. For neural networks with fixed depth and hidden width under Gaussian contexts, single-index rewards, context-dependent multi-index target policies, and known context-independent logging, we prove uniform consistency of our criterion over a fixed finite set of gradient-descent iterates and a near-oracle guarantee for the selected reward model. The same correction yields a doubly robust estimator that consistently estimates the true policy value without sample splitting, even when reward-model prediction error does not vanish. Experiments show decreasing risk-estimation error as dimension grows at a fixed sample-to-dimension ratio, and improved reward-model selection relative to held-out baselines. Empirically, our correction also reduces the root mean squared error of doubly robust value estimates computed from the same data used to fit and select the reward models.
Topological deep learning (TDL) extends learning on graphs, such as molecules or social networks, to higher-order structures, such as rings in a molecule or groups in a social network. Explaining which of these structures drive a model's predictions, and which architectural components matter most for its performance, remains challenging. We introduce TopoSHAP, an efficient and general explanation framework that addresses both questions across topological domains and model architectures. TopoSHAP-cell assigns Shapley values to topological data cells and extracts compact explanations. These explanations match or outperform graph-based counterparts on GraphXAI benchmark data while running up to 112$\times$ faster. They also reveal advantageous topological feature design, leading to measured improvements in explanation recovery and predictive accuracy. On the architecture side, TopoSHAP-neighbor explains how neighborhoods contribute to model performance, and turns these evaluations into a backward-elimination search that identifies smaller, competitive architectures early in training. This is up to $11.3\times$ cheaper than traditional TDL training sweeps.
Graph generation has shown tremendous effectiveness in modeling complex scientific tasks ranging from molecule generation to optimized circuit design. Most recent advancements have developed models that learn to denoise noisy graphs using either discrete diffusion or flow matching. However, discrete graph diffusion scales quadratically with the number of nodes, making it difficult to use such models on larger graphs. On the other hand, latent graph generation instead seeks to denoise noisy graph latents, which scale better to more nodes due to their lower dimension. However, in practice, latent graph generation models lag behind their discrete counterparts in performance. We study this problem, finding that it is caused by the unequal distribution of that different latent dimensions have on graph reconstruction. the impact. We observe that the vast majority of impact is contained in only a smaller number of latent dimensions. Since equal emphasis is placed on reconstructing the entire latent in the loss function, existing models are optimized to reconstruct information irrelevant to the downstream task. To tackle this problem, we propose Latent Importance Reweighting ({\bf LIR)} which weights each latent dimensions via it's importance to final graph reconstruction. Importance is calculated as the relative influence of a single latent unit on graph reconstruction, which is represented via the Jacobian of the decoder relative to the latent. Our method is model-agnostic and requires no additional model parameters or hyperparameters. Experiments show that LIR can boost performance and lead to faster training convergence when applied to two different autoencoders on various benchmark datasets. Code: https://github.com/biraaj/GraphGenLatentReweight
Unsupervised Environment Design (UED) approaches train reinforcement learning (RL) agents on diverse curricula that may evolve with their capabilities. While prior work has largely focused on how these curricula are constructed, we study whether their students remain trainable under the resulting distributions. Across multiple UED mechanisms, environment complexities, and extended training horizons, we identify recurring learner-side pathologies, including parameter growth, degraded value--outcome ordering, and loss of representational diversity, that accompany stagnation and performance degradation. These findings connect limitations in UED to optimization failures previously identified in conventional deep RL, while showing how adaptive curricula couple the learner's optimization state to its future training distribution. Controlled interventions show that mitigating selected pathologies improves learning. Stabilizing the learner improves long-horizon performance and zero-shot generalization without changing the curriculum rule or increasing environment interaction. Our results establish learner trainability as a complementary design principle for UED. Effective curricula require students that remain capable of learning from the distributions they produce.
Low-rank approximation is a basic tool for inference from large and noisy data matrices. However, when noise variances differ across entries, a setting known as heteroskedasticity, the noise can distort the observed spectrum, producing spurious components and obscuring weak signals. To address these challenges, we develop BRINE (Blind Resolvent-based Iterative Noise Equalizer), a data-driven procedure that iteratively rescales rows and columns to equalize the average noise variance across both dimensions. Under suitable conditions, this procedure restores the Marchenko-Pastur law for the noise spectrum and can amplify signal components without prior knowledge of the signal or noise structure. A key idea underlying our approach is to equalize the diagonal entries of the data resolvent as a proxy for equalizing the unknown noise variances. At the population level, we identify a potential function that characterizes this equalization and motivates an iterative minimization procedure. We prove convergence of the iterations to the true equalizer for arbitrary positive variance profiles, with a geometric rate under mild conditions. The updates can be estimated directly from noisy data, and we establish probabilistic error bounds for the scaling factors. Simulations and experiments across diverse biological data modalities and preprocessing pipelines illustrate the effectiveness of our approach.
Extrapolation beyond LiDAR coverage is an important yet under-evaluated challenge of depth completion. In real camera--LiDAR systems, partial sensor overlap, occlusions, and limited field coverage often leave large image regions weakly observed or completely unobserved by LiDAR. Thus, we investigate depth completion in this beyond-coverage regime using only sparse supervision from raw single-sweep LiDAR, without dense depth labels, LiDAR accumulation, or pseudo-LiDAR generation. Our approach leverages a frozen monocular depth foundation model, lightweight per-frame alignment to sparse LiDAR geometry, and a refinement module that fuses the aligned prior with sparse LiDAR anchors to predict dense metric depth. To regularize learning under raw sparse supervision, we introduce a high-frequency normal-consistency loss defined as the image-space gradient of the per-pixel normal cosine discrepancy. This term penalizes spatial variation in scalar angular error; it does not directly match changes in neighboring normal vectors. We further introduce an evaluation protocol that explicitly separates LiDAR-supported and beyond-coverage regions, revealing extrapolative behavior that conventional depth-completion metrics can obscure. Our method achieves strong depth accuracy beyond LiDAR coverage while remaining competitive in LiDAR-covered regions, providing a practical way to deploy monocular foundation priors in multi-sensor systems.
The number of domain fine-tuned models, particularly in the biomedical domain, is rapidly expanding. Fine-tuning promises high-performing models at a fraction of the cost of training a base model, but it can also produce unintended behavioral changes. Multiple studies have shown that safety guardrails can erode with fine-tuning, yet large-scale studies across model architectures, data mixtures, and fine-tuning methodologies remain limited. Where prior work in this space has studied value-centric refusal, this work focuses on knowledge-centric abstention. We audit 25 biomedical domain fine-tuned large language models against 11 paired base checkpoints on MedAbstain and ClinDet-Bench to evaluate the impact of fine-tuning on knowledge-centric abstention. We find that defined appropriate abstention measured by these benchmarks, already low in base models (median 8.3% on MedAbstain), falls further after fine-tuning (median 4.2%, decreasing in 21 of 25 pairs on MedAbstain), and that the magnitude and direction of change are heterogeneous across pairs. These results motivate fine-tuning methods that improve domain-specific capability while preserving appropriate caution.
Semantic Textual Similarity (STS) operates on document pairs, returning a single scalar per comparison. In a multi-document setting where several sources may have contributed to one or more targets, pairwise STS cannot disentangle each source's marginal semantic contribution from their shared vocabulary. In this paper, Semantic Conditional Similarity (SCS) is introduced as a conditional form of STS that computes similarity between two documents after eliminating semantic elements shared with a third via set-theoretic operations. SCS makes four contributions: 1) it introduces directionality, partitioning pairwise relations into lateral (inter-source) and vertical (source-to-target) classes; 2) conditioning induces role-dependent asymmetry by extending the comparison domain from unordered pairs to ordered, conditioned triples of a target, a reference, and a conditioning document; 3) SCS introduces inter-document conditioning by subtracting shared content from a third document, complementing the intra-document conditioning in recent C-STS work; and 4) the set-theoretic decomposition achieves threshold-free partitioning of shared and residual content, requiring no arbitrary similarity cutoff. Although developed for the $n \to 1$ configuration, the framework extends to $1 \to n$ via vertical role reversal and to $m \to n$ via independent composition of source- and target-side conditioning. With the established $1 \to 1$ case, these span the full spectrum of document cardinality. SCS scores should be interpreted ordinally, as rankings of marginal contributions rather than absolute measurements. The broader implication is that metric space axioms commonly assumed in similarity formalizations constrain expressiveness in role-differentiated multi-document settings, and that extending the domain to conditioned triples can recover information that pairwise-symmetric comparisons suppress.
Can a network look stable at every layer and still be exponentially unstable as a whole? The Lipschitz constant of a neural network is a basic stability quantity appearing in optimization guarantees, generalization bounds, and robustness certificates. Deep networks naturally admit two such notions, input Lipschitzness, measuring sensitivity to data perturbations, and parameter Lipschitzness, measuring sensitivity to weight perturbations. We prove that, for deep networks with normalization layers, with batch normalization as the canonical example, both Lipschitz constants can grow exponentially with depth and hence with parameter dimension, even under strong per-layer norm control such as $\|W_\ell\|_2\le 1$, and already for linear activations. Thus, a mechanism widely used to stabilize training can create severe worst-case instabilities that are invisible locally, i.e., from layerwise norm bounds alone. Parameter-Lipschitz explosion turns Lipschitz-dependent nonsmooth optimization guarantees into exponential-in-dimension bounds for deep normalized networks, while input-Lipschitz explosion makes worst-case Lipschitz-based generalization and robustness certificates vacuous. The latter also yields a concrete rank-separation mechanism for adversarial vulnerability. The theory predicts that perturbations introducing new singular directions should be amplified much more strongly than perturbations at the same noise level that remain within the input's original singular subspace. Experiments on MNIST, Fashion-MNIST, and CIFAR-10 support this prediction, showing that rank-creating perturbations cause substantially sharper drops in accuracy, confidence, and margins than same-subspace perturbations.
Generative models of brain MRI are useful to understand brain conditions, and to enrich scarce and imbalanced neuroimaging data. However, training these models requires large, multi-site training sets, which is challenging. Federated learning (FL) allows for training deep learning models without sharing data. We show that training a 3D conditional latent model federatedly (where data is kept private at each site) performs similarly to centralized training (where all the data have been copied to a single site). We evaluate three metrics: conditional fidelity (how well generated MRIs perform in classification), diversity (how the generated images match the real data distribution, using MultiScale-SSIM), and realism (how close generated images are to real images, using Fr\'{e}chet Inception Distance). Our results show that federated training is a viable route to develop multi-site generative models of brain MRI.
Dimensionality reduction is widely used to visualize high-dimensional data and guide scientific discovery, yet interpreting which original features contribute to low-dimensional representations remains challenging, particularly for black-box methods such as t-SNE and UMAP. We introduce \textbf{MEDALLION} (Manifold Embedding Distillation and Attributions for Low-dimensional Latent InterpretatiON), a novel framework for interpreting low-dimensional embeddings through knowledge distillation and neural feature attribution. MEDALLION distills any given embedding with a neural encoder which we explain via a broad range of existing neural feature attribution methods. Through experiments on MNIST and applications in single-cell transcriptomics, we show MEDALLION provides informative feature attributions that cast additional insights into the underlying embedding and compare its performance with existing interpretability approaches.
Vision-Language Models (VLMs) have achieved strong performance on static visual understanding benchmarks, yet their ability to act in dynamic environments remains less well understood. We introduce AtariBench, a controlled benchmark that evaluates VLMs across 20 Atari 2600 games, requiring models to make sequential decisions from high-temporal-resolution gameplay streams. By decoupling fast in-game dynamics from wall-clock inference speed, AtariBench focuses on whether models can perceive rapid visual state changes, reason over spatiotemporal dynamics, and ground actions in the current observation. Our experiments reveal substantial limitations in state-of-the-art VLMs: models often fail to infer object motion and direction, exhibit brittle sequential decision-making, and over-rely on textual interaction history despite newly appended visual feedback. We further introduce a separability analysis to identify which in-game scores provide reliable signals of model competence, and use the benchmark to study how memory design and prompting strategies affect performance. Overall, AtariBench exposes a persistent gap between passive visual perception and active decision-making, providing a lightweight and rigorous testbed for developing VLMs that can reason and act in dynamic environments.
Symbolic models offer interpretability, but their construction through generational evolution can be computationally expensive. This article presents Random Symbolic Boosting (RSB), a method that constructs explicit additive symbolic models via boosting over populations of randomly generated syntax trees, eliminating the need for generational evolution. The idea combines two observations: high-dimensional spaces can be spanned by enough linearly independent vectors, and the semantics of syntax trees can be directly manipulated as such vectors. It is shown that, for Ordinary Least Squares, the boosting process guarantees a monotonic reduction of the training error for both regression and classification. Furthermore, an adaptive geometric early stopping mechanism is introduced. It is based on the angle between the prediction and target vectors, is independent of the problems scale, and requires no adjustments across tasks. Evaluated on a standard benchmark for symbolic regression, the method is located at the Pareto-optimal point between predictive accuracy and training time, ranking first on the real-world datasets. Additionally, it was tested on a large tabular classification benchmark with 200 problems, achieving competitive results.
We study the classic least-squares linear regression problem under differential privacy (DP) in the batch and the continual observation setting. In the latter setting, the mechanism receives a stream of $n$ data points $(x_i,y_i)$ ($x_i\in\mathbb{R}^d$ and $y_i\in\mathbb{R}$) and must output an estimate of the optimal parameters at each time step $i$. Although differentially private linear regression has been extensively studied in the batch setting, the problem remains underexplored for the continual setting, with prior work being restricted to constrained linear regression and update time polynomial in $n$. In this work, we introduce ContinualAdaSSP, the first mechanism for unconstrained linear regression under continual differential privacy. Our mechanism's suboptimality gap is proportional to $\sqrt{d}\operatorname{polylog}(n)$. It requires $O(d^2\log{n})$ space and $O(d^2\log{n}+d^{\omega})$ update time, where $d$ is the dimension of the input space. We also study fundamental limits of differentially private linear regression by showing the first lower bounds for the box-constrained least-squares linear regression problem. Our lower bounds are proportional to $\min(n,\frac{\sqrt{d}}{\log^{1.5}d})$ for $(1,O(\frac{1}{n}))$-DP, and $\min(n,\frac{d}{\epsilon})$ for $\epsilon$-DP, and are derived using a reduction from a fingerprinting code problem from [Peter et al., 2024], providing new insights into the inherent hardness of this canonical task. Our experimental evaluation on real-world datasets shows that the accuracy of our continual observation mechanism clearly outperforms any other known differentially private mechanism for this problem such as rerunning the batch algorithm at each time step.