Can Gradient Descent Simulate Prompting?

There are two primary ways of incorporating new information into a language model (LM): changing its prompt or changing its parameters, e.g. via fine-tuning. Parameter updates incur no long-term storage cost for model changes. However, for many model updates, prompting is significantly more effective: prompted models can generalize robustly from single examples and draw logical inferences that do not occur under standard fine-tuning. Can models be modified so that fine-tuning does emulate prompting? This paper describes a method for meta-training LMs such that gradient updates emulate the effects of conditioning on new information. Our approach uses tools from gradient-based meta-learning but uses an LM's own prompted predictions as targets, eliminating the need for ground-truth labels. Subsequent gradient descent training recovers some (and occasionally all) of prompted model performance -- showing improvement on the ``reversal curse'' tasks, and answering questions about text passages after a single gradient update. These results suggest that, with appropriate initialization, gradient descent can be surprisingly expressive. Our results suggest new avenues for long-context modeling and offer insight into the generalization capabilities of gradient-based learning.

Sequential-Parallel Duality in Prefix Scannable Models

Modern neural sequence models are designed to meet the dual mandate of parallelizable training and fast sequential inference. Recent developments have given rise to various models, such as Gated Linear Attention (GLA) and Mamba, that achieve such ``sequential-parallel duality.'' This raises a natural question: can we characterize the full class of neural sequence models that support near-constant-time parallel evaluation and linear-time, constant-space sequential inference? We begin by describing a broad class of such models -- state space models -- as those whose state updates can be computed using the classic parallel prefix scan algorithm with a custom associative aggregation operator. We then define a more general class, Prefix-Scannable Models (PSMs), by relaxing the state aggregation operator to allow arbitrary (potentially non-associative) functions such as softmax attention. This generalization unifies many existing architectures, including element-wise RNNs (e.g., Mamba) and linear transformers (e.g., GLA, Mamba2, mLSTM), while also introducing new models with softmax-like operators that achieve O(1) amortized compute per token and log(N) memory for sequence length N. We empirically evaluate such models on illustrative small-scale language modeling and canonical synthetic tasks, including state tracking and associative recall. Empirically, we find that PSMs retain the expressivity of transformer-based architectures while matching the inference efficiency of state space models -- in some cases exhibiting better length generalization than either.

Line of Sight: On Linear Representations in VLLMs

Language models can be equipped with multimodal capabilities by fine-tuning on embeddings of visual inputs. But how do such multimodal models represent images in their hidden activations? We explore representations of image concepts within LlaVA-Next, a popular open-source VLLM. We find a diverse set of ImageNet classes represented via linearly decodable features in the residual stream. We show that the features are causal by performing targeted edits on the model output. In order to increase the diversity of the studied linear features, we train multimodal Sparse Autoencoders (SAEs), creating a highly interpretable dictionary of text and image features. We find that although model representations across modalities are quite disjoint, they become increasingly shared in deeper layers.

Log-Augmented Generation: Scaling Test-Time Reasoning with Reusable Computation

While humans naturally learn and adapt from past experiences, large language models (LLMs) and their agentic counterparts struggle to retain reasoning from previous tasks and apply them in future contexts. To address this limitation, we propose a novel framework, log-augmented generation (LAG) that directly reuses prior computation and reasoning from past logs at test time to enhance model's ability to learn from previous tasks and perform better on new, unseen challenges, all while keeping the system efficient and scalable. Specifically, our system represents task logs using key-value (KV) caches, encoding the full reasoning context of prior tasks while storing KV caches for only a selected subset of tokens. When a new task arises, LAG retrieves the KV values from relevant logs to augment generation. Our approach differs from reflection-based memory mechanisms by directly reusing prior reasoning and computations without requiring additional steps for knowledge extraction or distillation. Our method also goes beyond existing KV caching techniques, which primarily target efficiency gains rather than improving accuracy. Experiments on knowledge- and reasoning-intensive datasets demonstrate that our method significantly outperforms standard agentic systems that do not utilize logs, as well as existing solutions based on reflection and KV cache techniques.

Self-Steering Language Models

While test-time reasoning enables language models to tackle complex tasks, searching or planning in natural language can be slow, costly, and error-prone. But even when LMs struggle to emulate the precise reasoning steps needed to solve a problem, they often excel at describing its abstract structure--both how to verify solutions and how to search for them. This paper introduces DisCIPL, a method for "self-steering" LMs where a Planner model generates a task-specific inference program that is executed by a population of Follower models. Our approach equips LMs with the ability to write recursive search procedures that guide LM inference, enabling new forms of verifiable and efficient reasoning. When instantiated with a small Follower (e.g., Llama-3.2-1B), DisCIPL matches (and sometimes outperforms) much larger models, including GPT-4o and o1, on challenging constrained generation tasks. In decoupling planning from execution, our work opens up a design space of highly-parallelized Monte Carlo inference strategies that outperform standard best-of-N sampling, require no finetuning, and can be implemented automatically by existing LMs.

ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning

We present ThinkPrune, a simple yet effective method for pruning the thinking length for long-thinking LLMs, which has been found to often produce inefficient and redundant thinking processes. Existing preliminary explorations of reducing thinking length primarily focus on forcing the thinking process to early exit, rather than adapting the LLM to optimize and consolidate the thinking process, and therefore the length-performance tradeoff observed so far is sub-optimal. To fill this gap, ThinkPrune offers a simple solution that continuously trains the long-thinking LLMs via reinforcement learning (RL) with an added token limit, beyond which any unfinished thoughts and answers will be discarded, resulting in a zero reward. To further preserve model performance, we introduce an iterative length pruning approach, where multiple rounds of RL are conducted, each with an increasingly more stringent token limit. We observed that ThinkPrune results in a remarkable performance-length tradeoff -- on the AIME24 dataset, the reasoning length of DeepSeek-R1-Distill-Qwen-1.5B can be reduced by half with only 2% drop in performance. We also observed that after pruning, the LLMs can bypass unnecessary steps while keeping the core reasoning process complete. Code is available at https://github.com/UCSB-NLP-Chang/ThinkPrune.

(How) Do Language Models Track State?

Transformer language models (LMs) exhibit behaviors -- from storytelling to code generation -- that appear to require tracking the unobserved state of an evolving world. How do they do so? We study state tracking in LMs trained or fine-tuned to compose permutations (i.e., to compute the order of a set of objects after a sequence of swaps). Despite the simple algebraic structure of this problem, many other tasks (e.g., simulation of finite automata and evaluation of boolean expressions) can be reduced to permutation composition, making it a natural model for state tracking in general. We show that LMs consistently learn one of two state tracking mechanisms for this task. The first closely resembles the "associative scan" construction used in recent theoretical work by Liu et al. (2023) and Merrill et al. (2024). The second uses an easy-to-compute feature (permutation parity) to partially prune the space of outputs, then refines this with an associative scan. The two mechanisms exhibit markedly different robustness properties, and we show how to steer LMs toward one or the other with intermediate training tasks that encourage or suppress the heuristics. Our results demonstrate that transformer LMs, whether pretrained or fine-tuned, can learn to implement efficient and interpretable state tracking mechanisms, and the emergence of these mechanisms can be predicted and controlled.

LM Agents for Coordinating Multi-User Information Gathering

This paper introduces PeopleJoin, a benchmark for evaluating LM-mediated collaborative problem solving. Given a user request, PeopleJoin agents must identify teammates who might be able to assist, converse with these teammates to gather information, and finally compile a useful answer or summary for the original user. PeopleJoin comprises two evaluation domains: PeopleJoin-QA, focused on questions about tabular data, and PeopleJoin-DocCreation, focused on document creation tasks. The two domains are adapted from existing NLP benchmarks for database question answering and multi-document summarization; here, however, the information needed to complete these tasks is distributed across synthetic ``organizations'' of 2--20 users, simulating natural multi-user collaboration scenarios. We implemented several popular LM agent architectures, evaluating their accuracy and efficiency at completing tasks, and highlight new research questions that can be studied using PeopleJoin.

The Surprising Effectiveness of Test-Time Training for Abstract Reasoning

Language models have shown impressive performance on tasks within their training distribution, but often struggle with novel problems requiring complex reasoning. We investigate the effectiveness of test-time training (TTT) -- updating model parameters temporarily during inference using a loss derived from input data -- as a mechanism for improving models' reasoning capabilities, using the Abstraction and Reasoning Corpus (ARC) as a benchmark. Through systematic experimentation, we identify three crucial components for successful TTT: (1) initial finetuning on similar tasks (2) auxiliary task format and augmentations (3) per-instance training. TTT significantly improves performance on ARC tasks, achieving up to 6x improvement in accuracy compared to base fine-tuned models; applying TTT to an 8B-parameter language model, we achieve 53% accuracy on the ARC's public validation set, improving the state-of-the-art by nearly 25% for public and purely neural approaches. By ensembling our method with recent program generation approaches, we get SoTA public validation accuracy of 61.9%, matching the average human score. Our findings suggest that explicit symbolic search is not the only path to improved abstract reasoning in neural language models; additional test-time applied to continued training on few-shot examples can also be extremely effective.

LoRA vs Full Fine-tuning: An Illusion of Equivalence

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 match the performance of fully fine-tuned models on various tasks with an extreme reduction in the number of trainable parameters. Even in settings where both methods learn similarly accurate models, \emph{are their learned solutions really equivalent?} We study how different fine-tuning methods change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that full fine-tuning and LoRA yield weight matrices whose singular value decompositions exhibit very different structure; moreover, the fine-tuned models themselves show distinct generalization behaviors when tested outside the adaptation task's distribution. More specifically, we first show that the weight matrices trained with LoRA have new, high-ranking singular vectors, which we call \emph{intruder dimensions}. Intruder dimensions do not appear during full fine-tuning. Second, we show that LoRA models with intruder dimensions, despite achieving similar performance to full fine-tuning on the target task, become worse models of the pre-training distribution and adapt less robustly to multiple tasks sequentially. Higher-rank, rank-stabilized LoRA models closely mirror full fine-tuning, even when performing on par with lower-rank LoRA models on the same tasks. These results suggest that models updated with LoRA and full fine-tuning access different parts of parameter space, even when they perform equally on the fine-tuned distribution. We conclude by examining why intruder dimensions appear in LoRA fine-tuned models, why they are undesirable, and how their effects can be minimized.