Daily Papers

Existing text-to-image models often rely on parameter fine-tuning techniques such as Low-Rank Adaptation (LoRA) to customize visual attributes. However, when combining multiple LoRA models for content-style fusion tasks, unstructured modifications of weight matrices often lead to undesired feature entanglement between content and style attributes. We propose QR-LoRA, a novel fine-tuning framework leveraging QR decomposition for structured parameter updates that effectively separate visual attributes. Our key insight is that the orthogonal Q matrix naturally minimizes interference between different visual features, while the upper triangular R matrix efficiently encodes attribute-specific transformations. Our approach fixes both Q and R matrices while only training an additional task-specific Delta R matrix. This structured design reduces trainable parameters to half of conventional LoRA methods and supports effective merging of multiple adaptations without cross-contamination due to the strong disentanglement properties between Delta R matrices. Experiments demonstrate that QR-LoRA achieves superior disentanglement in content-style fusion tasks, establishing a new paradigm for parameter-efficient, disentangled fine-tuning in generative models.

We give explicit low-rank bilinear non-commutative schemes for multiplying structured n times n matrices with 2 leq n leq 5, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic complexity. Our schemes are discovered over F_2 or F_3 and lifted to Z or Q. Using a flip graph search over tensor decompositions, we derive schemes for general, upper-triangular, lower-triangular, symmetric, and skew-symmetric inputs, as well as products of a structured matrix with its transpose. In particular, we obtain 4 times 4 rank-34 schemes: (i) multiplying a general matrix by its transpose using 10 recursive calls, improving the factor from 26/41 (0.634) to 8/13 (0.615); and (ii) multiplying an upper-triangular matrix by a general matrix using 12 recursive calls, improving the factor from 8/13 (0.615) to 22/37 (0.595). Additionally, using F_3 flip graphs, we discover schemes over Q that fundamentally require the inverse of 2, including a 2 times 2 symmetric-symmetric multiplication of rank 5 and a 3 times 3 skew-symmetric-general multiplication of rank 14 (improving upon AlphaTensor's 15).

Causal disentanglement seeks a representation of data involving latent variables that relate to one another via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement that accurately recovers a latent causal model.

The fine-tuning of Large Language Models (LLMs) is pivotal for achieving optimal performance across diverse downstream tasks. However, while full fine-tuning delivers superior results, it entails significant computational and resource costs. Parameter-Efficient Fine-Tuning (PEFT) methods, such as LoRA, address these challenges by reducing the number of trainable parameters, but they often struggle with rank adjustment efficiency and task-specific adaptability. We propose Triangular Adaptive Low-Rank Adaptation (TriAdaptLoRA), a novel PEFT framework inspired by neuroscience principles, which dynamically optimizes the allocation of trainable parameters. TriAdaptLoRA introduces three key innovations: 1) a triangular split of transformation matrices into lower and upper triangular components to maximize parameter utilization, 2) a parameter importance metric based on normalized Frobenius norms for efficient adaptation, and 3) an adaptive rank-growth strategy governed by dynamic thresholds, allowing flexible parameter allocation across training steps. Experiments conducted on a variety of natural language understanding and generation tasks demonstrate that TriAdaptLoRA consistently outperforms existing PEFT methods. It achieves superior performance, enhanced stability, and reduced computational overhead, particularly under linear threshold-driven rank growth. These results highlight its efficacy as a scalable and resource-efficient solution for fine-tuning LLMs.

This paper gives three formulas for the pseudoinverse of a matrix product A = CR. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse A^+_r may be very useful when A is a very large matrix. 1. A^+ = R^+C^+ when A = CR and C has independent columns and R has independent rows. 2. A^+ = (C^+CR)^+(CRR^+)^+ is always correct. 3. A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+ only when rank(P^TA) = rank(AQ) = rank(A) with A = CR.

In the applications of proxy-SU(3) model in the context of determining (beta,gamma) values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with Z ge 30, it is seen that one needs not only the highest weight (hw) or leading SU(3) irreducible representation (irrep) (lambda_H, mu_H) but also the lower SU(3) irreps (lambda ,mu) such that 2lambda + mu =2lambda_H + mu_H-3r with r=0,1 and 2 [Bonatsos et al., Symmetry {\bf 16}, 1625 (2024)]. These give the next highest weight (nhw) irrep, next-to-next highest irrep (nnhw) and so on. Recently, it is shown that for nuclei with 32 le Z,N le 46, there will be not only proxy-SU(3) but also proxy-SU(4) symmetry [Kota and Sahu, Physica Scripta {\bf 99}, 065306 (2024)]. Following these developments, presented in this paper are the SU(3) irreps (lambda ,mu) with 2lambda + mu =2lambda_H + mu_H-3r, r=0,1,2 for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with 32 le N le 46) assuming good proxy-SU(4) symmetry. A simple method for obtaining the SU(3) irreps is described and applied. The tabulations for proxy-SU(3) irreps provided in this paper will be useful in further investigations of triaxial shapes in these nuclei.

CONTEXT The R programming language has a huge and active community, especially in the area of statistical computing. Its interpreted nature allows for several interesting constructs, like the manipulation of functions at run-time, that hinder the static analysis of R programs. At the same time, there is a lack of existing research regarding how these features, or even the R language as a whole are used in practice. OBJECTIVE In this paper, we conduct a large-scale, static analysis of more than 50 million lines of real-world R programs and packages to identify their characteristics and the features that are actually used. Moreover, we compare the similarities and differences between the scripts of R users and the implementations of package authors. We provide insights for static analysis tools like the lintr package as well as potential interpreter optimizations and uncover areas for future research. METHOD We analyze 4230 R scripts submitted alongside publications and the sources of 19450 CRAN packages for over 350000 R files, collecting and summarizing quantitative information for features of interest. RESULTS We find a high frequency of name-based indexing operations, assignments, and loops, but a low frequency for most of R's reflective functions. Furthermore, we find neither testing functions nor many calls to R's foreign function interface (FFI) in the publication submissions. CONCLUSION R scripts and package sources differ, for example, in their size, the way they include other packages, and their usage of R's reflective capabilities. We provide features that are used frequently and should be prioritized by static analysis tools, like operator assignments, function calls, and certain reflective functions like load.