Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO [68] and RLOO [1] that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark [78], while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates. 1

Vision-language models (VLMs) like CLIP exhibit strong zero-shot capabilities but often fail to generalize under distribution shifts. Test-time adaptation (TTA) allows models to update at inference time without labeled data, typically via entropy minimization. However, this objective is fundamentally misaligned with the contrastive image-text training of VLMs, limiting adaptation performance and introducing failure modes such as pseudo-label drift and class collapse. We propose CLIPTTA, a new gradient-based TTA method for vision-language models that leverages a soft contrastive loss aligned with CLIP's pre-training objective. We provide a theoretical analysis of CLIPTTA's gradients, showing how its batchaware design mitigates the risk of collapse. We further extend CLIPTTA to the open-set setting, where both in-distribution (ID) and out-of-distribution (OOD) samples are encountered, using an Outlier Contrastive Exposure (OCE) loss to improve OOD detection. Evaluated on 75 datasets spanning diverse distribution shifts, CLIPTTA consistently outperforms entropy-based objectives and is highly competitive with state-of-the-art TTA methods, outperforming them on a large number of datasets and exhibiting more stable performance across diverse shifts. Source code is available at: CLIPTTARepository.

Vision-Language Navigation (VLN) policies trained on offline datasets often exhibit degraded task performance when deployed in unfamiliar navigation environments at test time, where agents are typically evaluated without access to external interaction or feedback. Entropy minimization has emerged as a practical solution for reducing prediction uncertainty at test time; however, it can suffer from accumulated errors, as agents may become overconfident in incorrect actions without sufficient contextual grounding. To tackle these challenges, we introduce ATENA (Active TEst-time Navigation Agent), a test-time active learning framework that enables a practical human-robot interaction via episodic feedback on uncertain navigation outcomes. In particular, ATENA learns to increase certainty in successful episodes and decrease it in failed ones, improving uncertainty calibration. Here, we propose mixture entropy optimization, where entropy is obtained from a combination of the action and pseudo-expert distributions--a hypothetical action distribution assuming the agent's selected action to be optimal--controlling both prediction confidence and action preference. In addition, we propose a selfactive learning strategy that enables an agent to evaluate its navigation outcomes based on confident predictions. As a result, the agent stays actively engaged throughout all iterations, leading to well-grounded and adaptive decision-making. Extensive evaluations on challenging VLN benchmarks--REVERIE, R2R, and R2R-CE--demonstrate that ATENA successfully overcomes distributional shifts at test time, outperforming the compared baseline methods across various settings.

Test-time adaptation (TTA) aims to adapt a source model to a target domain using only test data. Existing methods predominantly rely on unsupervised entropy minimization or its variants, which suffer from degeneration, leading to trivial solutions with low-entropy but inaccurate predictions. In this work, we identify entropy-deceptive (ED) samples, instances where the model makes highly confident yet incorrect predictions, as the underlying cause of degeneration. Further, we reveal that the gradients of entropy minimization in TTA have an intrinsic lowdimensional structure, driven primarily by entropy-truthful (ET) samples whose gradients are highly correlated. In contrast, ED samples have scattered, less correlated gradients. Leveraging this observation, we show that the detrimental impact of ED samples can be suppressed by constraining model updates within the principal subspace of backward gradients. Building on this insight, we propose LCoTTA, a lifelong continual TTA method that tracks the principal subspace of gradients online and utilizes their projections onto this subspace for adaptation. Further, we provide theoretical analysis to show that the proposed subspace-based method can enhance the robustness against detrimental ED samples. Extensive experiments demonstrate that LCoTTA effectively overcomes degeneration and significantly outperforms existing methods in long-term continual adaptation scenarios.

In addition, we introduce a simple baseline, "RDumb", that periodically resets the