We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate functions of feature vectors in the corresponding nodes. Those classes of graphs include several prominent examples, such as: ε-neighborhood graphs, used on regular basis in machine learning. Rather than conducting walks on graphs' nodes, those methods rely on walks in continuous spaces, in which those graphs are embedded. To accurately and efficiently approximate original combinatorial calculations, SWING applies customized Gumbel-softmax sampling mechanism with linearized kernels, obtained via random features coupled with importance sampling techniques. This algorithm is of its own interest. SWING relies on the deep connection between implicitly defined graphs and Fourier analysis, presented in this paper. SWING is accelerator-friendly and does not require input graph materialization. We provide detailed analysis of SWING and complement it with thorough experiments on different classes of i-graphs.

We propose (GRFs++), a new class of (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase our claims and complement our results with theoretical analysis.

Concept erasure is the task of erasing information about a concept (e.g., gender or race) from a representation set while retaining the maximum possible utility -- information from original representations. Concept erasure is useful in several applications, such as removing sensitive concepts to achieve fairness and interpreting the impact of specific concepts on a model's performance. Previous concept erasure techniques have prioritized robustly erasing concepts over retaining the utility of the resultant representations. However, there seems to be an inherent tradeoff between erasure and retaining utility, making it unclear how to achieve perfect concept erasure while maintaining high utility. In this paper, we offer a fresh perspective toward solving this problem by quantifying the fundamental limits of concept erasure through an information-theoretic lens. Using these results, we investigate constraints on the data distribution and the erasure functions required to achieve the limits of perfect concept erasure. Empirically, we show that the derived erasure functions achieve the optimal theoretical bounds. Additionally, we show that our approach outperforms existing methods on a range of synthetic and real-world datasets using GPT-4 representations.

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides exact translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods.

Efficient neural networks are essential for scaling machine learning models to real-time applications and resource-constrained environments. Fully-connected feedforward layers (FFLs) introduce computation and parameter count bottlenecks within neural network architectures. To address this challenge, in this work, we propose a new class of dense layers that generalize standard fully-connected feedforward layers, Efficient, Unified and General dense layers (EUGens). EUGens leverage random features to approximate standard FFLs and go beyond them by incorporating a direct dependence on the input norms in their computations. The proposed layers unify existing efficient FFL extensions and improve efficiency by reducing inference complexity from quadratic to linear time. They also lead to the first unbiased algorithms approximating FFLs with arbitrary polynomial activation functions. Furthermore, EuGens reduce the parameter count and computational overhead while preserving the expressive power and adaptability of FFLs. We also present a layer-wise knowledge transfer technique that bypasses backpropagation, enabling efficient adaptation of EUGens to pre-trained models. Empirically, we observe that integrating EUGens into Transformers and MLPs yields substantial improvements in inference speed (up to 27%) and memory efficiency (up to 30%) across a range of tasks, including image classification, language model pre-training, and 3D scene reconstruction. Overall, our results highlight the potential of EUGens for the scalable deployment of large-scale neural networks in real-world scenarios.

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or downweighting attention depending on the relationship between the query and keys in the graph. In this paper, we propose to parameterise topological masks as a learnable function of a weighted adjacency matrix -- a novel, flexible approach which incorporates a strong structural inductive bias. By approximating this mask with graph random features (for which we prove the first known concentration bounds), we show how this can be made fully compatible with linear attention, preserving $\mathcal{O}(N)$ time and space complexity with respect to the number of input tokens. The fastest previous alternative was $\mathcal{O}(N \log N)$ and only suitable for specific graphs. Our efficient masking algorithms provide strong performance gains for image and point cloud data, including with $>30$k nodes.

Sequence-based deep learning models have emerged as powerful tools for deciphering the cis-regulatory grammar of the human genome but cannot generalize to unobserved cellular contexts. Here, we present EpiBERT, a multi-modal transformer that learns generalizable representations of genomic sequence and cell type-specific chromatin accessibility through a masked accessibility-based pre-training objective. Following pre-training, EpiBERT can be fine-tuned for gene expression prediction, achieving accuracy comparable to the sequence-only Enformer model, while also being able to generalize to unobserved cell states. The learned representations are interpretable and useful for predicting chromatin accessibility quantitative trait loci (caQTLs), regulatory motifs, and enhancer-gene links. Our work represents a step toward improving the generalization of sequence-based deep neural networks in regulatory genomics.

We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The previous fastest methods for general RWKs were of cubic time complexity and not applicable to labelled graphs. Our method samples dependent random walks to compute novel graph embeddings in ℝ^d whose dot product is equal to the true RWK in expectation. It does so without instantiating the direct product graph in memory, meaning we can scale to massive datasets that cannot be stored on a single machine. We derive exponential concentration bounds to prove that our estimator is sharp, and show that the ability to approximate general RWKs (rather than just special cases) unlocks efficient implicit graph kernel learning. Our method is up to 27× faster than its counterparts for efficient computation on large graphs and scales to graphs 128 × bigger than largest examples amenable to brute-force computation.

Machine unlearning is the process of efficiently removing the influence of a training data instance from a trained machine learning model without retraining it from scratch. A popular subclass of unlearning approaches is exact machine unlearning, which focuses on techniques that explicitly guarantee the removal of the influence of a data instance from a model. Exact unlearning approaches use a machine learning model in which individual components are trained on disjoint subsets of the data. During deletion, exact unlearning approaches only retrain the affected components rather than the entire model. While existing approaches reduce retraining costs, it can still be expensive for an organization to retrain a model component as it requires halting a system in production, which leads to service failure and adversely impacts customers. To address these challenges, we introduce an exact unlearning framework -- Sequence-aware Sharded Sliced Training (S3T), which is designed to enhance the deletion capabilities of an exact unlearning system while minimizing the impact on model's performance. At the core of S3T, we utilize a lightweight parameter-efficient fine-tuning approach that enables parameter isolation by sequentially training layers with disjoint data slices. This enables efficient unlearning by simply deactivating the layers affected by data deletion. Furthermore, to reduce the retraining cost and improve model performance, we train the model on multiple data sequences, which allows S3T to handle an increased number of deletion requests. Both theoretically and empirically, we demonstrate that S3T attains superior deletion capabilities and enhanced performance compared to baselines across a wide range of settings.

Recent efforts to scale Transformer models have demonstrated rapid progress across a wide range of tasks (Wei at. al 2022). However, fine-tuning these models for downstream tasks is quite expensive due to their large parameter counts. Parameter-efficient fine-tuning (PEFT) approaches have emerged as a viable alternative, allowing us to fine-tune models by updating only a small number of parameters. In this work, we propose a general framework for parameter efficient fine-tuning (PEFT), based on *structured unrestricted-rank matrices* (SURM) which can serve as a drop-in replacement for popular approaches such as Adapters and LoRA. Unlike other methods like LoRA, SURMs give us more flexibility in finding the right balance between compactness and expressiveness. This is achieved by using *low displacement rank matrices* (LDRMs), which hasn't been used in this context before. SURMs remain competitive with baselines, often providing significant quality improvements while using a smaller parameter budget. SURMs achieve: **5**-**7**% accuracy gains on various image classification tasks while replacing low-rank matrices in LoRA and: up to **12x** reduction of the number of parameters in adapters (with virtually no loss in quality) on the GLUE benchmark.

Chromosome analysis is essential for diagnosing genetic disorders. For hematologic malignancies, identification of somatic clonal aberrations by karyotype analysis remains the standard of care. However, karyotyping is costly and time-consuming because of the largely manual process and the expertise required in identifying and annotating aberrations. Efforts to automate karyotype analysis to date fell short in aberration detection. Using a training set of ~10k patient specimens and ~50k karyograms from over 5 years from the Fred Hutchinson Cancer Center, we created a labeled set of images representing individual chromosomes. These individual chromosomes were used to train and assess deep learning models for classifying the 24 human chromosomes and identifying chromosomal aberrations. The top-accuracy models utilized the recently introduced Topological Vision Transformers (TopViTs) with 2-level-block-Toeplitz masking, to incorporate structural inductive bias. TopViT outperformed CNN (Inception) models with >99.3% accuracy for chromosome identification, and exhibited accuracies >99% for aberration detection in most aberrations. Notably, we were able to show high-quality performance even in "few shot" learning scenarios. Incorporating the definition of clonality substantially improved both precision and recall (sensitivity). When applied to "zero shot" scenarios, the model captured aberrations without training, with perfect precision at >50% recall. Together these results show that modern deep learning models can approach expert-level performance for chromosome aberration detection. To our knowledge, this is the first study demonstrating the downstream effectiveness of TopViTs. These results open up exciting opportunities for not only expediting patient results but providing a scalable technology for early screening of low-abundance chromosomal lesions.

We present an embodied AI system which receives open-ended natural language instructions from a human, and controls two arms to collaboratively accomplish potentially long-horizon tasks over a large workspace. Our system is modular: it deploys state of the art Large Language Models for task planning,Vision-Language models for semantic perception, and Point Cloud transformers for grasping. With semantic and physical safety in mind, these modules are interfaced with a real-time trajectory optimizer and a compliant tracking controller to enable human-robot proximity. We demonstrate performance for the following tasks: bi-arm sorting, bottle opening, and trash disposal tasks. These are done zero-shot where the models used have not been trained with any real world data from this bi-arm robot, scenes or workspace.Composing both learning- and non-learning-based components in a modular fashion with interpretable inputs and outputs allows the user to easily debug points of failures and fragilities. One may also in-place swap modules to improve the robustness of the overall platform, for instance with imitation-learned policies.

We study an auction setting in which bidders bid for placement of their content within a summary generated by a large language model (LLM), e.g., an ad auction in which the display is a summary paragraph of multiple ads. This generalizes the classic ad settings such as position auctions to an LLM generated setting, which allows us to handle general display formats. We propose a novel factorized framework in which an auction module and an LLM module work together via a prediction model to provide welfare maximizing summary outputs in an incentive compatible manner. We provide a theoretical analysis of this framework and synthetic experiments to demonstrate the feasibility and validity of the system together with welfare comparisons.

Fairness, especially group fairness, is an important consideration in the context of machine learning systems. The most commonly adopted group fairness-enhancing techniques are in-processing methods that rely on a mixture of a fairness objective (e.g., demographic parity) and a task-specific objective (e.g., cross-entropy) during the training process. However, when data arrives in an online fashion -- one instance at a time -- optimizing such fairness objectives poses several challenges. In particular, group fairness objectives are defined using expectations of predictions across different demographic groups. In the online setting, where the algorithm has access to a single instance at a time, estimating the group fairness objective requires additional storage and significantly more computation (e.g., forward/backward passes) than the task-specific objective at every time step. In this paper, we propose Aranyani, an ensemble of oblique decision trees, to make fair decisions in online settings. The hierarchical tree structure of Aranyani enables parameter isolation and allows us to efficiently compute the fairness gradients using aggregate statistics of previous decisions, eliminating the need for additional storage and forward/backward passes. We also present an efficient framework to train Aranyani and theoretically analyze several of its properties. We conduct empirical evaluations on 5 publicly available benchmarks (including vision and language datasets) to show that Aranyani achieves a better accuracy-fairness trade-off compared to baseline approaches.

Reward-based finetuning is crucial for aligning language policies with intended behaviors (e.g., creativity and safety). A key challenge is to develop steerable language models that trade-off multiple (conflicting) objectives in a flexible and efficient manner. This paper presents Conditional Language Policy (CLP), a general framework for finetuning language models on multiple objectives. Building on techniques from multi-task training and parameter-efficient finetuning, CLP learn steerable models that effectively trade-off conflicting objectives at inference time. Notably, this does not require training or maintaining multiple models to achieve different trade-offs between the objectives. Through extensive experiments and ablations on two summarization datasets, we show that CLP learns steerable language models that outperform and Pareto-dominate the existing approaches for multi-objective finetuning.

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

Extractive opinion summarization involves automatically producing a summary of text about an entity (e.g., a product's reviews) by extracting representative sentences that capture prevalent opinions in the review set. Typically, in online marketplaces user reviews accrue over time, and opinion summaries need to be updated periodically to provide customers with up-to-date information. In this work, we study the task of extractive opinion summarization in an incremental setting, where the underlying review set evolves over time. Many of the state-of-the-art extractive opinion summarization approaches are centrality-based, such as CentroidRank. CentroidRank performs extractive summarization by selecting a subset of review sentences closest to the centroid in the representation space as the summary. However, these methods are not capable of operating efficiently in an incremental setting, where reviews arrive one at a time. In this paper, we present an efficient algorithm for accurately computing the CentroidRank summaries in an incremental setting. Our approach, CoverSumm, relies on indexing review representations in a cover tree and maintaining a reservoir of candidate summary review sentences. CoverSumm's efficacy is supported by a theoretical and empirical analysis of running time. Empirically, on a diverse collection of data (both real and synthetically created to illustrate scaling considerations), we demonstrate that CoverSumm is up to 25x faster than baseline methods, and capable of adapting to nuanced changes in data distribution. We also conduct human evaluations of the generated summaries and find that CoverSumm is capable of producing informative summaries consistent with the underlying review set.

We propose a new class of linear Transformers called FourierLearner-Transformers (FLTs), which incorporate a wide range of relative positional encoding mechanisms (RPEs). These include regular RPE techniques applied for sequential data, as well as novel RPEs operating on geometric data embedded in higher-dimensional Euclidean spaces. FLTs construct the optimal RPE mechanism implicitly by learning its spectral representation. As opposed to other architectures combining efficient low-rank linear attention with RPEs, FLTs remain practical in terms of their memory usage and do not require additional assumptions about the structure of the RPE mask. Besides, FLTs allow for applying certain structural inductive bias techniques to specify masking strategies, e.g. they provide a way to learn the so-called local RPEs introduced in this paper and give accuracy gains as compared with several other linear Transformers for language modeling. We also thoroughly test FLTs on other data modalities and tasks, such as image classification, 3D molecular modeling, and learnable optimizers. To the best of our knowledge, for 3D molecular data, FLTs are the first Transformer architectures providing linear attention and incorporating RPE masking.

We present Self-Adaptive Robust Attention for Robotics Transformers (SARA-RT): a new paradigm for addressing the emerging challenge of scaling up Robotics Transformers (RT) for on-robot deployment. SARA-RT relies on the new method of fine-tuning proposed by us, called up-training. It converts pre-trained or already fine-tuned Transformer-based robotic policies of quadratic time complexity (including massive billion-parameter vision-language-action models or VLAs), into their efficient linear-attention counterparts maintaining high quality. We demonstrate the effectiveness of SARA-RT by speeding up: (a) the class of recently introduced RT-2 models, the first VLA robotic policies pre-trained on internet-scale data, as well as (b) Point Cloud Transformer (PCT) robotic policies operating on large point clouds. We complement our results with the rigorous mathematical analysis providing deeper insight into the phenomenon of SARA.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular *low displacement rank*) for integrating tensor fields defined on weighted trees. Several applications of the resulting *fast tree-field integrators* (FTFIs) are presented, including: (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) *Topological Transformers* (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as **three** extra learnable parameters per Transformer layer, leading to **1.0-1.5\%+** accuracy gains. Importantly, most of FTFIs are **exact** methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide **5.7-13x** speedups. We also provide an extensive theoretical analysis of our methods.