Multimodal contrastive learning (MCL) aims to embed data from different modalities in a shared embedding space. However, empirical evidence shows that representations from different modalities occupy completely separate regions of embedding space, a phenomenon referred to as the modality gap. Moreover, experimental findings on how the size of the modality gap influences downstream performance are inconsistent. These observations raise two key questions: (1) What causes the modality gap? (2) How does it affect downstream tasks? To address these questions, this paper introduces the first theoretical framework for analyzing the convergent optimal representations of MCL and the modality alignment when training is optimized. Specifically, we prove that without any constraint or under the cone constraint, the modality gap converges to zero. Under the subspace constraint (i.e., representations of two modalities fall into two distinct hyperplanes due to dimension collapse), the modality gap converges to the smallest angle between the two hyperplanes. This result identifies \emph{dimension collapse} as the fundamental origin of the modality gap. Furthermore, our theorems demonstrate that paired samples cannot be perfectly aligned under the subspace constraint. The modality gap influences downstream performance by affecting the alignment between sample pairs. We prove that, in this case, perfect alignment between two modalities can still be achieved via two ways: hyperplane rotation and shared space projection.

There is increasing evidence of Human Label Variation (HLV) in Natural Language Inference (NLI), where annotators assign different labels to the same premise-hypothesis pair. However, within-label variation--cases where annotators agree on the same label but provide divergent reasoning--poses an additional and mostly overlooked challenge. Several NLI datasets contain highlighted words in the NLI item as explanations, but the same spans on the NLI item can be highlighted for different reasons, as evidenced by free-text explanations, which offer a window into annotators' reasoning. To systematically understand this problem and gain insight into the rationales behind NLI labels, we introduce LITEX, a linguistically-informed taxonomy for categorizing free-text explanations in English. Using this taxonomy, we annotate a subset of the e-SNLI dataset, validate the taxonomy's reliability, and analyze how it aligns with NLI labels, highlights, and explanations. We further assess the taxonomy's usefulness in explanation generation, demonstrating that conditioning generation on LITEX yields explanations that are linguistically closer to human explanations than those generated using only labels or highlights. Our approach thus not only captures within-label variation but also shows how taxonomy-guided generation for reasoning can bridge the gap between human and model explanations more effectively than existing strategies.

Discrete diffusion models have become highly effective across various domains. However, real-world applications often require the generative process to adhere to certain constraints. To this end, we propose a Sequential Monte Carlo (SMC) framework that enables scalable inference-time control of discrete diffusion models through principled importance weighting and optimal proposal construction. Specifically, our approach derives tractable importance weights for a range of intermediate targets and characterises the optimal proposal, for which we develop two practical approximations: a first-order gradient-based approximation and an amortised proposal trained to minimise the log-variance of the importance weights. Empirical results across synthetic tasks, language modelling, biology design, and text-to-image generation demonstrate that our framework enhances controllability and sample quality, highlighting the effectiveness of SMC as a versatile recipe for scaling discrete diffusion models at inference time.

Large Language Models (LLMs) nowadays are expected to process inputs of unprecedented length, with current token limits extending to several million tokens.

Controlling undesirable Large Language Model (LLM) behaviors, such as the generation of unsafe content or failing to adhere to safety guidelines, often relies on costly fine-tuning. Activation steering provides an alternative for inference-time control, but existing methods typically lack fine-grained, adaptive mechanisms. We introduce a novel approach using a lightweight, trainable controller network integrated during inference. This controller network observes specific intermediate LLM activations and predicts both a global scaling factor and layer-specific weights. The predicted global scaling factor and layer-specific weights then dynamically modulate the intensity of a steering patch, derived from a pre-computed "refusal direction" vector, applied across the LLM's layers during generation. Trained on activations from both harmful and benign prompts, our controller learns to discriminatively apply nuanced, layer-aware interventions, activating steering primarily for harmful inputs. Experiments using safety benchmarks like ToxicChat & In-The-Wild Jailbreak Prompts demonstrate that our weighted steering controller significantly increases refusal rates compared to the base LLM, achieving targeted behavioral modification without altering the original model parameters. Our experiments with Llama-3.1-8B, Llama-3.2-1B & Mistral-7B show our approach outperforms existing methods, presenting an efficient and adaptive method for fine-grained control over LLM behavior at inference time.

Large language models (LLMs) still struggle across tasks outside of high-resource languages. In this work, we investigate cross-lingual transfer to lower-resource languages where task-specific post-training data is scarce. Building on prior work, we first validate that the subsets of model parameters that matter most for mathematical reasoning and multilingual capabilities are distinctly non-overlapping. To exploit this implicit separability between task and target language parameterization, we develop and analyze numerous modular frameworks to improve the composition of the two during fine-tuning. These methods generally employ freezing parameters or post hoc model merging to assign math and language improvement to different key parts of the LLM. In the absence of in-language math data, we demonstrate that the modular approaches successfully improve upon baselines across three languages, four models, and two fine-tuning paradigms (full and LoRA). Furthermore, we identify the most consistently successful modular method to be fine-tuning separate language and math experts and model merging via Layer-Swapping, somewhat surprisingly. We offer possible explanations for this result via recent works on the linearity of task vectors. We further explain this by empirically showing that reverting less useful fine-tuning updates after training often outperforms freezing them from the start.

Low-rank optimization has emerged as a promising direction in training large language models (LLMs) to improve running time and reduce the memory usage of adaptive optimizers by constraining learning to a lower-dimensional space. Prior work typically projects gradients of linear layers using approaches based on Singular Value Decomposition (SVD) or QR-decomposition. Applying these techniques individually to each layer in large models is computationally expensive and incurs additional memory costs due to storing the projection matrices. In this work, we propose a computationally efficient and conceptually simple, two-step procedure to approximate SVD/QR-based gradient projections into lower-dimensional spaces by using a predefined orthogonal matrix of the Discrete Cosine Transform (DCT). We dynamically select columns from the DCT matrix based on their alignment with the gradient of each layer. The effective projection matrices are obtained via a simple matmul with the DCT matrix in $O(n^3)$ time, followed by a lightweight sorting step to identify the most relevant basis vectors. For large layers, DCT can be computed via Makhoul's $N$-point algorithm based on Fast Fourier Transform (FFT) in $O(n^2 \log(n))$ time. Due to the predefined nature of the orthogonal bases, they are computed once at the start of training. Our numerical experiments on both pre-training and fine-tuning tasks demonstrate the effectiveness of our dual strategy in approximating optimal low-rank projections, obtaining an approach with rank-independent running time that matches the performance of costly SVD/QR-based methods while achieving faster runtime and reduced memory usage by up to $25\%$ across different model sizes. Our code is available at \href{https://github.com/IST-DASLab/ISTA-DASLab-Optimizers}{\texttt{https://github.com/IST-DASLab/ISTA-DASLab-Optimizers}}.

Large Language Models (LLMs) are increasingly deployed in multi-turn conversational applications, where the management of the Key-Value (KV) Cache presents a significant bottleneck. The linear growth of the KV Cache with dialogue history imposes substantial computational costs, and existing eviction strategies often degrade performance by repeatedly compressing early conversational context, leading to information loss and context forgetting. This paper introduces FlowKV, a novel \textbf{multi-turn isolation mechanism} for KV Cache management, which can be applied to any KV Cache compression method without training. FlowKV's core innovation is a multi-turn isolation mechanism that preserves the accumulated compressed KV cache from past turns. Compression is then strategically applied only to the newly generated KV pairs of the latest completed turn, effectively preventing the re-compression of older context and thereby mitigating catastrophic forgetting. Our results demonstrate that FlowKV consistently and significantly outperforms baseline strategies in maintaining instruction-following accuracy and user preference retention from 10.90\% to 75.40\%, particularly in later conversational turns.

Temporal reasoning is pivotal for Large Language Models (LLMs) to comprehend the real world. However, existing works neglect the real-world challenges for temporal reasoning: (1) intensive temporal information, (2) fast-changing event dynamics, and (3) complex temporal dependencies in social interactions. To bridge this gap, we propose a multi-level benchmark TIME, designed for temporal reasoning in real-world scenarios. TIME consists of 38,522 QA pairs, covering 3 levels with 11 fine-grained sub-tasks. This benchmark encompasses 3 sub-datasets reflecting different real-world challenges: TIME-Wiki, TIME-News, and TIME-Dial. We conduct extensive experiments on reasoning models and non-reasoning models. And we conducted an in-depth analysis of temporal reasoning performance across diverse real-world scenarios and tasks, and summarized the impact of test-time scaling on temporal reasoning capabilities. Additionally, we release TIME-Lite, a human-annotated subset to foster future research and standardized evaluation in temporal reasoning. The code is available at https://github.com/sylvain-wei/TIME , the dataset is available at https://huggingface.co/datasets/SylvainWei/TIME , and the project page link is https://sylvain-wei.github.io/TIME/ .

Corporate LLMs are gaining traction for efficient knowledge dissemination and management within organizations. However, as current LLMs are vulnerable to leaking sensitive information, it has proven difficult to apply them in settings where strict access control is necessary. To this end, we design AC-LoRA, an end-to-end system for access control-aware corporate LLM chatbots that maintains a strong information isolation guarantee. AC-LoRA maintains separate LoRA adapters for permissioned datasets, along with the document embedding they are finetuned on. AC-LoRA retrieves a precise set of LoRA adapters based on the similarity score with the user query and their permission. This similarity score is later used to merge the responses if more than one LoRA is retrieved, without requiring any additional training for LoRA routing. We provide an end-to-end prototype of AC-LoRA, evaluate it on two datasets, and show that AC-LoRA matches or even exceeds the performance of state-of-the-art LoRA mixing techniques while providing strong isolation guarantees. Furthermore, we show that AC-LoRA design can be directly applied to different modalities.