We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm converges linearly, achieves $O(\epsilon)$ recovery error after retrieving $O(k^{3}d\log(1/\epsilon))$ training instances, consumes $O(kd)$ memory in one-pass of dataset and only requires matrix-vector product operations in each iteration. The key ingredient of our framework is a construction of an estimation sequence endowed with a so-called Conditionally Independent RIP condition (CI-RIP). As special cases of gFM, our framework can be applied to symmetric or asymmetric rank-one matrix sensing problems, such as inductive matrix completion and phase retrieval.

We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is guided by a prior distribution on random hypergraphs, a construction which generalizes the Finite Feature Model. We present a posterior inference algorithm based on Gibbs sampling, and establish posterior consistency of our regression model. Our method is evaluated with extensive experiments on simulated data and demonstrated to be able to identify meaningful interactions in applications in genetics and retail demand forecasting.

There are numerous examples where accounting for the predictors' interactions is of interest, including problems of identifying epistasis (gene-gene) and gene-environment interactions in genetics

Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition.

FMs have been found successful in many applications, such as recommendation systems [Rendle et al., 2011] and text retrieval [Hong et al., 2013].

Refusal on harmful prompts is a key safety behaviour in instruction-tuned large language models (LLMs), yet the internal causes of this behaviour remain poorly understood. We study two public instruction tuned models--Gemma-2-2B-IT and LLaMA-3.1-8B-IT using sparse autoencoders (SAEs) trained on residual-stream activations. Given a harmful prompt, we search the SAE latent space for feature sets whose ablation flips the model from refusal to compliance, demonstrating causal influence and creating a jailbreak. Our search proceeds in three stages: 1. Refusal Direction - Finding a refusal mediating direction and collecting SAE features close to that direction, followed by 2. Greedy Filtering - to prune this set to obtain a minimal set and finally 3. Interaction Discovery - a factorization-machine (FM) model that captures non-linear interactions among the remaining active features and the minimal set. This pipeline yields a broad set of jailbreak-critical features, offering insight into the mechanistic basis of refusal. Moreover, we also find evidence of redundant features which remain dormant unless earlier features are suppressed. Our findings highlight the potential for fine-grained auditing and targeted intervention in safety behaviours by manipulating the interpretable latent space.

We propose a new method for learning with multi-field categorical data.