The success of large language models in real-world applications relies on parameter-efficient fine-tuning methods such as Low-Rank Adaptation (LoRA), which inserts compact, trainable adapters into selected layers. In this paper, we propose SimplexLoRA, a LoRA variant that adaptively adjusts adapter ranks during fine-tuning based on their learned importance. Unlike standard LoRA, which employs a fixed rank across all layers, SimplexLoRA optimizes per-adapter importance weights on the n-scaled simplex during a short warm-up and then freezes them, dynamically allocating capacity where it is most beneficial without increasing the overall parameter budget or inference cost. We evaluate SimplexLoRA across 12 language understanding, summarization, and reasoning tasks using DeBERTaV3, BART-large, Llama 3.1 8B, and Qwen3-8B. Our results show that SimplexLoRA consistently matches or outperforms standard LoRA and recent adaptive baselines, with the largest gains at low ranks. Our code is available at https://github.com/brain-lab-research/SimplexLoRA.

Aligned large language models are trained to comply with benign requests while refusing harmful ones. However, recent work shows that this refusal behavior is fragile and can often be disrupted by simple activation- or weight-space interventions. In particular, refusal has been shown to be largely mediated by a single residual-stream direction, typically computed as a difference-of-means vector between harmful and harmless prompts. However, this standard construction aggregates heterogeneous harmful prompts into one uniform average, potentially conflating distinct refusal-related phenomena. In this work, we study whether refusal interventions can be strengthened by learning how to combine prompt-specific refusal directions. We propose Weighted Refusal Direction Optimization (WRDO), a procedure that constructs a composite refusal direction from a bank of per-prompt directions using learned aggregation weights. This approach allows different harmful prompts to contribute unequally to the final intervention direction. We evaluate WRDO against prior single-direction methods on three open-weight language models using three guard judges and HarmBench as an external evaluator. We further measure the effect of the intervention on general model capability through standard utility benchmarks. Finally, we investigate a defense-oriented setting in which the same optimization machinery is used in reverse to restore refusal behavior in an abliterated model checkpoint. Our results show that weighted aggregation provides a more effective and flexible mechanism for manipulating refusal representations. Code is available at https://github.com/brain-lab-research/WRDO.

Post-training compression is essential for deploying large language models (LLMs) under tight resource constraints. Tensor decompositions have emerged as a promising direction, offering compact parameterizations well suited to Transformer weight structures. However, existing studies evaluate these methods in narrow settings, leaving unclear whether tensorization is effective at large-scale deployment. We systematically evaluate tensor compression across dense and MoE architectures, establishing performance trade-offs grounded in both empirical analysis and theoretical analysis. % We identify a fundamental mismatch between the shared subspaces assumed by tensor decompositions and the heterogeneous representations learned by modern LLMs, thereby delineating their practical limits and clarifying their viable role in large-scale deployment. We identify a fundamental mismatch between the shared subspaces assumed by tensor decompositions and the heterogeneous representations learned by modern LLMs, thereby delineating their practical limits that persist across an extensive range of mainstream dense and MoE deployment settings evaluated in this work. The code is available at https://github.com/brain-lab-research/TT-LLM.

Post-training quantization (PTQ) is essential for deploying LLMs under memory and bandwidth constraints. However, extreme low-bit quantization remains highly sensitive to activation outliers and anisotropic weight curvature. Existing incoherence-based PTQ methods mitigate this issue with fixed randomized Hadamard transforms (RHTs), which improve quantization robustness but cannot adapt the rotated basis to the layer, calibration distribution, or quantizer. We introduce HARP (Hadamard-preconditioned Adaptive Rotation Processor), a learnable structured two-sided orthogonal processor that replaces fixed Hadamard mixing while preserving exact full-precision equivalence. HARP represents each rotation as a product of sparse butterfly-like block-orthogonal stages, supports non-power-of-two dimensions through Mixed-Radix schedules, and initializes to the RHT processor up to a fixed permutation. Fitted only on calibration data, HARP adapts the quantization basis to each layer and backend. Across 2-4 bit settings on Llama models from 1B to 70B, HARP consistently improves perplexity and yields its clearest zero-shot gains at 2 bits; a 2-bit Qwen3-8B experiment shows the same transfer beyond the Llama family. HARP also preserves deployment efficiency: on Llama 2 7B at 2 bits, it reaches 128 tok/s, retaining 90% of RHT throughput (142 tok/s) and running approximately 2.1× faster than FP16 (61 tok/s).

The widespread utilization of language models in modern applications is inconceivable without Parameter-Efficient Fine-Tuning techniques, such as low-rank adaptation (LoRA), which adds trainable adapters to selected layers. Although LoRA may obtain accurate solutions, it requires significant memory to train large models and intuition on which layers to add adapters. In this paper, we propose a novel method, WeightLoRA, which overcomes this issue by adaptive selection of the most critical LoRA heads throughout the optimization process. As a result, we can significantly reduce the number of trainable parameters while maintaining the capability to obtain consistent or even superior metric values. We conduct experiments for a series of competitive benchmarks and DeBERTa, BART, Llama and Qwen models, comparing our method with different adaptive approaches. The experimental results demonstrate the efficacy of WeightLoRA and the superior performance of WeightLoRA+ in almost all cases. The source code is available at https://github.com/brain-lab-research/WLoRA

Modern mathematical reasoning benchmarks primarily focus on answer finding rather than proof verification, creating a gap in evaluating the proving capabilities of large language models (LLMs). We present a methodology for generating diverse mathematical proof tasks using formal tools. Our approach combines Lean-based synthetic problem generation with a Tool-Integrated Reasoning (TiR) framework for partial (sampling-based) proof validation, and it uses contrastive preference optimization to align the model’s proof outputs. Experiments on the Qwen-2.5 family of models demonstrate meaningful improvements in mathematical reasoning, particularly for smaller models. Our aligned models achieve up to a 57% higher success rate than baselines on the MiniF2F benchmark (across 0.5B, 1.5B, and 7B parameter models). These results highlight the potential of synthetic data and integrated validation for advancing LLM-based mathematical reasoning.