Polynomial-based learnable spectral graph neural networks (GNNs) utilize polynomial to approximate graph convolutions and have achieved impressive performance on graphs. Nevertheless, there are three progressive problems to be solved. Some models use polynomials with better approximation for approximating filters, yet perform worse on real-world graphs. Carefully crafted graph learning methods, sophisticated polynomial approximations, and refined coefficient constraints leaded to overfitting, which diminishes the generalization of the models. How to design a model that retains the ability of polynomial-based spectral GNNs to approximate filters while it possesses higher generalization and performance?

Per-example gradient norms are a vital ingredient for estimating gradient noise scale (GNS) with minimal variance. Observing the tensor contractions required to compute them, we propose a method with minimal FLOPs in 3D or greater tensor regimes by simultaneously computing the norms while computing the parameter gradients. Using this method we are able to observe the GNS of different layers at higher accuracy than previously possible. We find that the total GNS of contemporary transformer models is predicted well by the GNS of only the normalization layers. As a result, focusing only on the normalization layer, we develop a custom kernel to compute the per-example gradient norms while performing the LayerNorm backward pass with zero throughput overhead. Tracking GNS on only those layers, we are able to guide a practical batch size schedule that reduces training time by 18% on a Chinchilla-optimal language model.

Vehicle Routing Problems (VRPs) can model many real-world scenarios and often involve complex constraints. While recent neural methods excel in constructing solutions based on feasibility masking, they struggle with handling complex constraints, especially when obtaining the masking itself is NP-hard. In this paper, we propose a novel Proactive Infeasibility Prevention (PIP) framework to advance the capabilities of neural methods towards more complex VRPs. Our PIP integrates the Lagrangian multiplier as a basis to enhance constraint awareness and introduces preventative infeasibility masking to proactively steer the solution construction process. Moreover, we present PIP-D, which employs an auxiliary decoder and two adaptive strategies to learn and predict these tailored masks, potentially enhancing performance while significantly reducing computational costs during training. To verify our PIP designs, we conduct extensive experiments on the highly challenging Traveling Salesman Problem with Time Window (TSPTW), and TSP with Draft Limit (TSPDL) variants under different constraint hardness levels. Notably, our PIP is generic to boost many neural methods, and exhibits both a significant reduction in infeasible rate and a substantial improvement in solution quality.

Safety fine-tuning helps align Large Language Models (LLMs) with human preferences for their safe deployment. To better understand the underlying factors that make models safe via safety fine-tuning, we design a synthetic data generation framework that captures salient aspects of an unsafe input by modeling the interaction between the task the model is asked to perform (e.g., "design") versus the specific concepts the task is asked to be performed upon (e.g., a "cycle" vs. a "bomb"). Using this, we investigate three well-known safety fine-tuning methods--supervised safety fine-tuning, direct preference optimization, and unlearning--and provide significant evidence demonstrating that these methods minimally transform MLP weights to specifically align unsafe inputs into its weights' null space. This yields a clustering of inputs based on whether the model deems them safe or not. Correspondingly, when an adversarial input (e.g., a jailbreak) is provided, its activations are closer to safer samples, leading to the model processing such an input as if it were safe.

We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to diffusions, such Markov processes admit time reversals that turn out to be PDMPs as well. We apply this observation to three PDMPs considered in the literature: the Zig-Zag process, Bouncy Particle Sampler, and Randomised Hamiltonian Monte Carlo. For these three particular instances, we show that the jump rates and kernels of the corresponding time reversals admit explicit expressions depending on some conditional densities of the PDMP under consideration before and after a jump. Based on these results, we propose efficient training procedures to learn these characteristics and consider methods to approximately simulate the reverse process. Finally, we provide bounds in the total variation distance between the data distribution and the resulting distribution of our model in the case where the base distribution is the standard $d$-dimensional Gaussian distribution. Promising numerical simulations support further investigations into this class of models.

Past analyses of reinforcement learning from human feedback (RLHF) assume that the human evaluators fully observe the environment. What happens when human feedback is based only on partial observations? We formally define two failure cases: deceptive inflation and overjustification. Modeling the human as Boltzmann-rational w.r.t. a belief over trajectories, we prove conditions under which RLHF is guaranteed to result in policies that deceptively inflate their performance, overjustify their behavior to make an impression, or both. Under the new assumption that the human's partial observability is known and accounted for, we then analyze how much information the feedback process provides about the return function. We show that sometimes, the human's feedback determines the return function uniquely up to an additive constant, but in other realistic cases, there is irreducible ambiguity. We propose exploratory research directions to help tackle these challenges and experimentally validate both the theoretical concerns and potential mitigations, and caution against blindly applying RLHF in partially observable settings.

This paper explores the weakly-supervised referring image segmentation (WRIS) problem, and focuses on a challenging setup where target localization is learned directly from image-text pairs. We note that the input text description typically already contains detailed information on how to localize the target object, and we also observe that humans often follow a step-by-step comprehension process (\ie, progressively utilizing target-related attributes and relations as cues) to identify the target object. Hence, we propose a novel Progressive Comprehension Network (PCNet) to leverage target-related textual cues from the input description for progressively localizing the target object.Specifically, we first use a Large Language Model (LLM) to decompose the input text description into short phrases. These short phrases are taken as target-related cues and fed into a Conditional Referring Module (CRM) in multiple stages, to allow updating the referring text embedding and enhance the response map for target localization in a multi-stage manner.Based on the CRM, we then propose a Region-aware Shrinking (RaS) loss to constrain the visual localization to be conducted progressively in a coarse-to-fine manner across different stages.Finally, we introduce an Instance-aware Disambiguation (IaD) loss to suppress instance localization ambiguity by differentiating overlapping response maps generated by different referring texts on the same image. Extensive experiments show that our method outperforms SOTA methods on three common benchmarks.

Bayesian optimization (BO) is an attractive machine learning framework for performing sample-efficient global optimization of black-box functions. The optimization process is guided by an acquisition function that selects points to acquire in each round of BO. In batched BO, when multiple points are acquired in parallel, commonly used acquisition functions are often high-dimensional and intractable, leading to the use of sampling-based alternatives. We propose a statistical physics inspired acquisition function that can natively handle batches. Batched Energy-Entropy acquisition for BO (BEEBO) enables tight control of the explore-exploit trade-off of the optimization process and generalizes to heteroskedastic black-box problems. We demonstrate the applicability of BEEBO on a range of problems, showing competitive performance to existing acquisition functions.

Gene therapies have the potential to treat disease by delivering therapeutic genetic cargo to disease-associated cells. One limitation to their widespread use is the lack of short regulatory sequences, or promoters, that differentially induce the expression of delivered genetic cargo in target cells, minimizing side effects in other cell types. Such cell-type-specific promoters are difficult to discover using existing methods, requiring either manual curation or access to large datasets of promoter-driven expression from both targeted and untargeted cells. Model-based optimization (MBO) has emerged as an effective method to design biological sequences in an automated manner, and has recently been used in promoter design methods. However, these methods have only been tested using large training datasets that are expensive to collect, and focus on designing promoters for markedly different cell types, overlooking the complexities associated with designing promoters for closely related cell types that share similar regulatory features. Therefore, we introduce a comprehensive framework for utilizing MBO to design promoters in a data-efficient manner, with an emphasis on discovering promoters for similar cell types. We use conservative objective models (COMs) for MBO and highlight practical considerations such as best practices for improving sequence diversity, getting estimates of model uncertainty, and choosing the optimal set of sequences for experimental validation. Using three leukemia cell lines (Jurkat, K562, and THP1), we show that our approach discovers many novel cell-type-specific promoters after experimentally validating the designed sequences. For K562 cells, in particular, we discover a promoter that has 75.85\% higher cell-type-specificity than the best promoter from the initial dataset used to train our models.

Efficient transfer learning has shown remarkable performance in tuning large-scale vision-language models (VLMs) toward downstream tasks with limited data resources. The key challenge of efficient transfer lies in adjusting image-text alignment to be task-specific while preserving pre-trained general knowledge. However, existing methods adjust image-text alignment merely on a set of observed samples, e.g., data set and external knowledge base, which cannot guarantee to keep the correspondence of general concepts between image and text latent manifolds without being disrupted and thereby a weak generalization of the adjusted alignment. In this work, we propose a Homology Consistency (HC) constraint for efficient transfer on VLMs, which explicitly constrains the correspondence of image and text latent manifolds through structural equivalence based on persistent homology in downstream tuning. Specifically, we build simplicial complex on the top of data to mimic the topology of latent manifolds, then track the persistence of the homology classes of topological features across multiple scales, and guide the directions of persistence tracks in image and text manifolds to coincide each other, with a deviating perturbation additionally. For practical application, we tailor the implementation of our proposed HC constraint for two main paradigms of adapter tuning. Extensive experiments on few-shot learning over 11 datasets and domain generalization demonstrate the effectiveness and robustness of our method.