Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to effectively fine-tune LLMs with an extreme reduction in trainable parameters. But, are their learned solutions really equivalent? We study how LoRA and full-finetuning change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that LoRA and full fine-tuning yield weight matrices whose singular value decompositions exhibit very different structure: weight matrices trained with LoRA have new, high-ranking singular vectors, which we call intruder dimensions, while those trained with full fine-tuning do not. Further, we extend the finding that LoRA forgets less than full fine-tuning and find its forgetting is vastly localized to the intruder dimension - by causally intervening on the intruder dimensions by changing their associated singular values post-fine-tuning, we show that they cause forgetting. Moreover, scaling them down significantly improves modeling of the pre-training distribution with a minimal drop in downstream task performance. Given this, we should expect accumulating intruder dimensions to be harmful and lead to more forgetting. This will be amplified during continual learning because of sequentially fine-tuning, and we show that LoRA models do accumulate intruder dimensions here tend to perform worse in this setting, emphasizing the practicality of our findings.

Neural network architectures have a large impact in machine learning. However, in the specific case of reinforcement learning, network architectures have remained notably simple, as changes often lead to small gains in performance. This work introduces a novel encoder architecture for pixel-based model-free reinforcement learning. The Hadamax (Hadamard max-pooling) encoder achieves state-of-the-art performance by max-pooling Hadamard products between GELU-activated parallel hidden layers. Based on the recent PQN algorithm, the Hadamax encoder achieves state-of-the-art model-free performance in the Atari-57 benchmark. Specifically, without applying any algorithmic hyperparameter modifications, Hadamax-PQN achieves an 80% performance gain over vanilla PQN and significantly surpasses Rainbow-DQN. For reproducibility, the full code is available on GitHub.

The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points. No existing work has defined a measurable RG order parameter, tested it under controlled variation of the input distribution, or made quantitative predictions that are empirically verified. We study the simplest architecture for which the analogy is tractable: a pure MLP residual stack trained on masked token prediction over synthetic Markov chain sequences with known spectral properties. We report three findings. (i) The effective rank of the residual stream decreases monotonically with depth after training, consistent with progressive integration of irrelevant degrees of freedom. (ii) This rank collapse is selective: it occurs for chains with short correlation length approximately 1 but is absent for chains with long correlation length approximately 7, measured at the position level to control for mean-pooling artifacts. The network preserves exactly the degrees of freedom relevant to the prediction task, the content of the RG relevance criterion. (iii) Inter-layer kernel drift is concentrated at one or two specific transitions, with the remainder of the network near a fixed point, consistent with a discrete fixed-point plateau. Together these findings constitute the first quantitative, position-level evidence that MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.

Adaptive stochastic gradient methods such as ADAGRAD have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by accumulating past gradients which are used to tune the step size adaptively. In certain situations the full-matrix variant of ADAGRAD is expected to attain better performance, however in high dimensions it is computationally impractical.

Despite its potential, 3DGS encounters challenges such as needle-like artifacts, suboptimal geometries, and inaccurate normals caused by the Gaussians converging into anisotropic shapes with one dominant variance.

While Low-Rank Adaptation (LoRA) has proven beneficial for efficiently fine-tuning large models, LoRA fine-tuned text-to-image diffusion models lack diversity in the generated images, as the model tends to copy data from the observed training samples.

For extreme low-bit quantization of large language models (LLMs), Double Binary Factorization (DBF) is attractive as it enables efficient inference without sacrificing accuracy. However, the scaling parameters of DBF are too restrictive; after factoring out signs, all rank components share the same magnitude profile, resulting in performance saturation. We propose Multi-envelope DBF (MDBF), which retains a shared pair of 1-bit sign bases but replaces the single envelope with a rank-$l$ envelope. By sharing sign matrices among envelope components, MDBF effectively maintains a binary carrier and utilizes the limited memory budget for magnitude expressiveness. We also introduce a closed-form initialization and an alternating refinement method to optimize MDBF. Across the LLaMA and Qwen families, MDBF enhances perplexity and zero-shot accuracy over previous binary formats at matched bits per weight while preserving the same deployment-friendly inference primitive.

Modern deep networks are heavily overparameterized yet often generalize well, suggesting a form of low intrinsic complexity not reflected by parameter counts. We study this complexity at initialization through the effective rank of the Neural Tangent Kernel (NTK) Gram matrix, $r_{\text{eff}}(K) = (\text{tr}(K))^2/\|K\|_F^2$. For i.i.d. data and the infinite-width NTK $k$, we prove a constant-limit law $\lim_{n\to\infty} \mathbb{E}[r_{\text{eff}}(K_n)] = \mathbb{E}[k(x, x)]^2 / \mathbb{E}[k(x, x')^2] =: r_\infty$, with sub-Gaussian concentration. We further establish finite-width stability: if the finite-width NTK deviates in operator norm by $O_p(m^{-1/2})$ (width $m$), then $r_{\text{eff}}$ changes by $O_p(m^{-1/2})$. We design a scalable estimator using random output probes and a CountSketch of parameter Jacobians and prove conditional unbiasedness and consistency with explicit variance bounds. On CIFAR-10 with ResNet-20/56 (widths 16/32) across $n \in \{10^3, 5\times10^3, 10^4, 2.5\times10^4, 5\times10^4\}$, we observe $r_{\text{eff}} \approx 1.0\text{--}1.3$ and slopes $\approx 0$ in $n$, consistent with the theory, and the kernel-moment prediction closely matches fitted constants.