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Deep Learning · Attention Mechanisms

Saeed Amizadeh, Sara Abdali, Yinheng Li, Kazuhito Koishida

Transformers and their attention mechanism have been revolutionary in the field of Machine Learning. While originally proposed for the language data, they quickly found their way to the image, video, graph, etc. data modalities with various signal geometries. Despite this versatility, generalizing the attention mechanism to scenarios where data is presented at different scales from potentially different modalities is not straightforward. The attempts to incorporate hierarchy and multi-modality within transformers are largely based on ad hoc heuristics, which are not seamlessly generalizable to similar problems with potentially different structures. To address this problem, in this paper, we take a fundamentally different approach: we first propose a mathematical construct to represent multi-modal, multi-scale data. We then mathematically derive the neural attention mechanics for the proposed construct from the first principle of entropy minimization. We show that the derived formulation is optimal in the sense of being the closest to the standard Softmax attention while incorporating the inductive biases originating from the hierarchical/geometric information of the problem. We further propose an efficient algorithm based on dynamic programming to compute our derived attention mechanism. By incorporating it within transformers, we show that the proposed hierarchical attention mechanism not only can be employed to train transformer models in hierarchical/multi-modal settings from scratch, but it can also be used to inject hierarchical information into classical, pre-trained transformer models post training, resulting in more efficient models in zero-shot manner.

Deep Learning · Graph Neural Networks

GUOGUO AI, Hezhe Qiao, Hui Yan, Guansong Pang

Current semi-supervised graph anomaly detection (GAD) methods utilizes a small set of labeled normal nodes to identify abnormal nodes from a large set of unlabeled nodes in a graph. These methods posit that 1) normal nodes share a similar level of homophily and 2) the labeled normal nodes can well represent the homophily patterns in the entire normal class. However, this assumption often does not hold well since normal nodes in a graph can exhibit diverse homophily in real-world GAD datasets. In this paper, we propose RHO, namely Robust Homophily Learning, to adaptively learn such homophily patterns. RHO consists of two novel modules, adaptive frequency response filters (AdaFreq) and graph normality alignment (GNA). AdaFreq learns a set of adaptive spectral filters that capture different frequency components of the labeled normal nodes with varying homophily in the channel-wise and cross-channel views of node attributes. GNA is introduced to enforce consistency between the channel-wise and cross-channel homophily representations to robustify the normality learned by the filters in the two views. Experiments on eight real-world GAD datasets show that RHO can effectively learn varying, often under-represented, homophily in the small labeled node set and substantially outperforms state-of-the-art competing methods. Code is available at \url{https://github.com/mala-lab/RHO}.

Deep Learning · Generative Models and Autoencoders

Li Liang, Bo Miao, Xinyu Wang, NAVEED AKHTAR, Jordan Vice, Ajmal Mian

Outdoor 3D semantic scene generation produces realistic and semantically rich environments for applications such as urban simulation and autonomous driving. However, advances in this direction are constrained by the absence of publicly available, well-annotated datasets. We introduce SketchSem3D, the first large‑scale benchmark for generating 3D outdoor semantic scenes from abstract freehand sketches and pseudo‑labeled annotations of satellite images. SketchSem3D includes two subsets, Sketch-based SemanticKITTI and Sketch-based KITTI-360 (containing LiDAR voxels along with their corresponding sketches and annotated satellite images), to enable standardized, rigorous, and diverse evaluations. We also propose Cylinder Mamba Diffusion (CymbaDiff) that significantly enhances spatial coherence in outdoor 3D scene generation. CymbaDiff imposes structured spatial ordering, explicitly captures cylindrical continuity and vertical hierarchy, and preserves both physical neighborhood relationships and global context within the generated scenes. Extensive experiments on SketchSem3D demonstrate that CymbaDiff achieves superior semantic consistency, spatial realism, and cross-dataset generalization. The code and dataset will be available at here.

Social Aspects · Trustworthy Machine Learning

Soroush H. Zargarbashi, Mohammad Sadegh Akhondzadeh, Aleksandar Bojchevski

For any black-box model, conformal prediction (CP) returns prediction *sets* guaranteed to include the true label with high adjustable probability. Robust CP (RCP) extends the guarantee to the worst case noise up to a pre-defined magnitude. For RCP, a well-established approach is to use randomized smoothing since it is applicable to any black-box model and provides smaller sets compared to deterministic methods. However, smoothing-based robustness requires many model forward passes per each input which is computationally expensive. We show that conformal prediction attains some robustness even with *a single forward pass on a randomly perturbed input*. Using any binary certificate we propose a single sample robust CP (RCP1). Our approach returns robust sets with smaller average set size compared to SOTA methods which use many (e.g. $\sim 100$) passes per input. Our key insight is to certify the conformal procedure itself rather than individual conformity scores. Our approach is agnostic to the task (classification and regression). We further extend our approach to smoothing-based robust conformal risk control.

Deep Learning · Attention Mechanisms

Difan Deng, Marius Lindauer

We present Neural Attention Search (NAtS), an end-to-end learnable sparse transformer that automatically evaluates the importance of each token within a sequence and determines if the corresponding token can be dropped after several steps. To this end, we design a search space that contains three token types: (i) Global Tokens will be preserved and queried by all the following tokens. (ii) Local Tokens survive until the next global token appears. (iii) Sliding Window Tokens have an impact on the inference of a fixed size of the next following tokens. Similar to the One-Shot Neural Architecture Search approach, this token-type information can be learned jointly with the architecture weights via a learnable attention mask. Experiments on both training a new transformer from scratch and fine-tuning existing large language models show that NAtS can efficiently reduce the KV cache and the inference costs for the transformer-based models while maintaining the models' performance.

Deep Learning · Everything Else

Sheng Huang, Lele Fu, Fanghua Ye, Tianchi Liao, Bowen Deng, zhangchuanfu, Chuan Chen

Federated learning enables collaborative training while preserving the privacy of all participants. However, the heterogeneity in data distribution across multiple training nodes poses significant challenges to the construction of federated models. Prior studies were dedicated to mitigating the effects of data heterogeneity by using global information as a blueprint and restricting the local update of the model for reaching a "hard consensus". But this practice makes it difficult to balance local and global information, and it neglects to negotiate amicably between local and global models to reach mutually agreeable results, called ``soft consensus". In this paper, a multiple-path solving method is proposed to balance global and local features and combine these two feature preference paths to reach a soft consensus. Rather than relying on global information as the sole criterion, a negotiation process is employed to address the same objective by accommodating diverse feature preferences, thereby facilitating the discovery of a more plausible solution through multiple distinct pathways. Considering the overwhelming power of local features during local training, a swapping strategy is applied to weaken them to balance the solution paths. Moreover, to minimize the additional communication cost caused by the introduction of multiple paths, the solution of the task network is converted into data adaptation to reduce the amount of parameter transmission. Extensive experiments are conducted to demonstrate the advantages of the proposed method.

Applications · Language, Speech and Dialog

Weixiang Zhao, Jiahe Guo, Yang Deng, Tongtong Wu, Wenxuan Zhang, Yulin Hu, Xingyu Sui, Yanyan Zhao, Wanxiang Che, Bing Qin 等

Multilingual reasoning remains a significant challenge for large language models (LLMs), with performance disproportionately favoring high-resource languages. Drawing inspiration from cognitive neuroscience, which suggests that human reasoning functions largely independently of language processing, we hypothesize that LLMs similarly encode reasoning and language as separable components that can be disentangled to enhance multilingual reasoning. To evaluate this, we perform a causal intervention by ablating language-specific representations at inference time. Experiments on 10 open-weight LLMs spanning 11 typologically diverse languages show that this language-specific ablation consistently boosts multilingual reasoning performance. Layer-wise analyses further confirm that language and reasoning representations can be effectively disentangled throughout the model, yielding improved multilingual reasoning capabilities, while preserving top-layer language features remains essential for maintaining linguistic fidelity. Compared to post-training methods such as supervised fine-tuning or reinforcement learning, our training-free language-reasoning disentanglement achieves comparable or superior results with minimal computational overhead. These findings shed light on the internal mechanisms underlying multilingual reasoning in LLMs and suggest a lightweight and interpretable strategy for improving cross-lingual generalization.

Deep Learning · Graph Neural Networks

Bowen Deng, Lele Fu, Sheng Huang, Tianchi Liao, Jialong Chen, Zhang Tao, Chuan Chen

Graph classification has long assumed a closed-world setting, limiting its applicability to real-world scenarios where new categories often emerge. To address this limitation, we introduce Graph-Level Novel Category Discovery (GLNCD), a new task aimed at identifying unseen graph categories without supervision from novel classes. We first adapt classical Novel Category Discovery (NCD) methods for images to the graph domain and evaluate these baseline methods on four diverse graph datasets curated for the GLNCD task. Our analysis reveals that these methods suffer a notable performance degradation compared to their image-based counterparts, due to two key challenges: (1) insufficient utilization of structural information in graph self-supervised learning (SSL), and (2) ineffective pseudo-labeling strategies based on ranking statistics (RS) that neglect graph structure. To alleviate these issues, we propose ProtoFGW-NCD, a framework consisting of two core components: ProtoFGW-CL, a novel graph SSL framework, and FGW-RS, a structure-aware pseudo-labeling method. Both components employ a differentiable Fused Gromov-Wasserstein (FGW) distance to effectively compare graphs by incorporating structural information. These components are built upon learnable prototype graphs, which enable efficient, parallel FGW-based graph comparisons and capture representative patterns within graph datasets. Experiments on four GLNCD benchmark datasets demonstrate the effectiveness of ProtoFGW-NCD.

Deep Learning · Theory

Peter Ochieng

Contrastive learning thrives—or fails—based on how we construct \emph{positive} and \emph{negative} pairs. In the absence of explicit labels, models must infer semantic structure from these proxy signals. Early work on Siamese networks \citep{chopra2005learning,hadsell2006dimensionality} already showed that pair construction directly shapes learned representations. In modern contrastive frameworks, poor pair selection remains a primary failure mode: it either causes collapse, where all embeddings converge to a point, or wastes the representational capacity of the space \citep{chen2020simple,tian2020makes,khosla2020supervised}. Contemporary methods typically generate positives via semantic-preserving augmentations (crop, jitter, view transform), while negatives are drawn from other elements in the mini-batch under the assumption that different images are semantically dissimilar. But this assumption breaks down in fine-grained, low-diversity, or high-resolution settings \citep{kalantidis2020hard,robinson2020contrastive,chuang2020debiased}, motivating techniques such as hard-negative mining and debiased losses \citep{bachman2019learning,tian2020makes}. \paragraph{Beyond pairs: batch-level diversity.} While most prior work focuses on \emph{which} individual negatives to select, we study the geometry of the entire batch. Our central observation is this: the overall \emph{diversity} of the batch embedding space strongly governs both training dynamics and representational quality. If diversity is too low, the model sees nearly identical negatives and gradients vanish—leading to collapse. If diversity is too high, negatives become almost orthogonal, but the resulting gradients shrink in magnitude, and learning slows. Optimal training thus occurs within a \emph{moderate diversity window}: high enough to avoid collapse, low enough to preserve update strength.

General Machine Learning · Representation Learning

Zhuang Qi, Yu Pan, Lei Meng, Sijin Zhou, Han Yu, Xiaoxiao Li, Xiangxu Meng

Federated Prompt Learning (FPL) enables communication-efficient adaptation by tuning lightweight prompts on top of frozen pre-trained models. Existing FPL methods typically rely on global information, which is only available after the second training round, to facilitate collaboration among client models. Therefore, they are inherently dependent on multi-round communication to fully exhibit their strengths. Moreover, existing one-shot federated learning methods typically focus on fitting seen tasks, but lack cross-task generalization. To bridge this gap, we propose the global prompt refinement with non-interfering attention masking (GPR-NIAM) method for one-shot FPL. The core idea is to design a masking mechanism that restricts excessive interaction between the original text embeddings and the learnable prompt embeddings. GPR-NIAM achieves this through the collaboration of two key modules. Firstly, the attention isolation module suppresses attention from the learnable prompt tokens to the original text tokens, and reweights the reverse attention which preserves generalization across tasks. Secondly, the cross-silo collaborative refinement module integrates decentralized visual knowledge into a unified base and calibrates the global prompt through multi-source cross-modal knowledge alignment, further mitigating the inconsistency caused by data heterogeneity. Extensive experiments conducted on ten benchmark datasets under two tasks show that GPR-NIAM outperforms eight state-of-the-art methods in both class-level and domain-level generalization.

General Machine Learning · Representation Learning

Shuangyi Chen, Yuanxin Guo, Yue Ju, Hardik Dalal, Zhongwen Zhu, Ashish Khisti

Parameter-Efficient Fine-Tuning (PEFT) methods like Low-Rank Adaptation (LoRA) optimize federated training by reducing computational and communication costs. We propose RoLoRA, a federated framework using alternating optimization to fine-tune LoRA adapters. Our approach emphasizes the importance of learning up and down projection matrices to enhance expressiveness and robustness. We use both theoretical analysis and extensive experiments to demonstrate the advantages of RoLoRA over prior approaches that either generate imperfect model updates or limit expressiveness of the model. We provide a theoretical analysis on a linear model to highlight the importance of learning both the down-projection and up-projection matrices in LoRA. We validate the insights on a non-linear model and separately provide a convergence proof under general conditions. To bridge theory and practice, we conducted extensive experimental evaluations on language models including RoBERTa-Large, Llama-2-7B on diverse tasks and FL settings to demonstrate the advantages of RoLoRA over other methods.

Optimization · Optimization and Learning under Uncertainty

Gongwei Chen, Lirong Jie, Lexiao Zou, Weili Guan, Miao Zhang, Liqiang Nie

Benefiting from the availability of extensive navigation trajectories, both manually and automatically annotated, current graphical user interface (GUI) agents have achieved remarkable advancements in performance. However, these annotated datasets often contain substantial noise, which impedes effective agent training and underscores the necessity for rigorous trajectory quality assessment. In contrast to existing prompting-based evaluators that rely on proprietary multimodal large language models (MLLMs), we propose an Uncertainty-aware Reinforced Self-Training (URST) framework to train lightweight MLLMs for efficient and reliable trajectory evaluation. URST iteratively fine-tunes MLLMs using their own generated thoughts and judgments to enable self-improvement, while its uncertainty-aware sampling strategy ensures the selection of the most informative training examples. To further enhance reasoning and judgment capabilities, we propose a simplified group policy optimization approach that effectively leverages diverse positive and negative samples for evaluator learning. Our evaluator demonstrates superior judgment performance across both in-domain and out-of-domain datasets. When used to filter navigation datasets, it consistently leads to performance improvements in training GUI agents.

Social Aspects · Fairness, Equity, Justice and Safety

Yi Liu, Dianqing Liu, Mingye Zhu, Junbo Guo, Yongdong Zhang, Zhendong Mao

The widespread adoption of large language models (LLMs) across industries has increased the demand for high-quality and customizable outputs. However, traditional alignment methods often require retraining large pretrained models, making it difficult to quickly adapt and optimize LLMs for diverse applications. To address this limitation, we propose a novel \textit{Residual Alignment Model} (\textit{RAM}) that formalizes the alignment process as a type of importance sampling. In this framework, the unaligned upstream model serves as the proposal distribution, while the alignment process is framed as secondary sampling based on an autoregressive alignment module that acts as an estimator of the importance weights. This design enables a natural detachment of the alignment module from the target aligned model, improving flexibility and scalability. Based on this model, we derive an efficient sequence-level training strategy for the alignment module, which operates independently of the proposal module. Additionally, we develop a resampling algorithm with iterative token-level decoding to address the common first-token latency issue in comparable methods. Experimental evaluations on two leading open-source LLMs across diverse tasks, including instruction following, domain adaptation, and preference optimization, demonstrate that our approach consistently outperforms baseline models.

Deep Learning · Algorithms

Ningfeng Yang, Tor Aamodt

We study the problem of training neural networks with quantized parameters. Learning low-precision quantized parameters by enabling computation of gradients via the Straight-Through Estimator (STE) can be challenging. While the STE enables back-propagation, which is a first-order method, recent works have explored the use of zeroth-order (ZO) gradient descent for fine-tuning. We note that the STE provides high-quality biased gradients, and ZO gradients are unbiased but can be expensive. We thus propose First-Order-Guided Zeroth-Order Gradient Descent (FOGZO) that reduces STE bias while reducing computations relative to ZO methods. Empirically, we show FOGZO improves the tradeoff between quality and training time in Quantization-Aware Pre-Training. Specifically, versus STE at the same number of iterations, we show a 1-8% accuracy improvement for DeiT Tiny/Small, 1-2% accuracy improvement on ResNet 18/50, and 1-22 perplexity point improvement for LLaMA models with up to 0.3 billion parameters. For the same loss, FOGZO yields a 796$\times$ reduction in computation versus n-SPSA for a 2-layer MLP on MNIST. Code is available at [https://github.com/1733116199/fogzo](https://github.com/1733116199/fogzo).

Social Aspects · Trustworthy Machine Learning

Sahar Abdelnabi, Ahmed Salem

Reasoning-focused LLMs sometimes alter their behavior when they detect that they are being evaluated—which can lead them to optimize for test-passing performance or to comply more readily with harmful prompts if real-world consequences appear absent. We present the first quantitative study of how such “test awareness” impacts model behavior, particularly its performance on safety-related tasks. We introduce a white-box probing framework that (i) linearly identifies awareness-related activations and (ii) steers models toward or away from test awareness while monitoring downstream performance. We apply our method to different state-of-the-art open-weight reasoning LLMs across both realistic and hypothetical tasks (denoting tests or simulations). Our results demonstrate that test awareness significantly impacts safety alignment (such as compliance with harmful requests and conforming to stereotypes) with effects varying in both magnitude and direction across models. By providing control over this latent effect, our work aims to provide a stress-test mechanism and increase trust in how we perform safety evaluations.

Computer Vision · Vision Models & Multimodal

Chuhao Zhou, Jianfei Yang

Embodied agents operating in smart homes must understand human behavior through diverse sensory inputs and communicate via natural language. While Vision-Language Models (VLMs) have enabled impressive language-grounded perception, their reliance on visual data limits robustness in real-world scenarios with occlusions, poor lighting, or privacy constraints. In this paper, we introduce HoloLLM, a Multimodal Large Language Model (MLLM) that integrates uncommon but powerful sensing modalities, such as LiDAR, infrared, mmWave radar, and WiFi, to enable seamless human perception and reasoning across heterogeneous environments. We address two key challenges: (1) the scarcity of aligned modality-text data for rare sensors, and (2) the heterogeneity of their physical signal representations. To overcome these, we design a Universal Modality-Injection Projector (UMIP) that enhances pre-aligned modality embeddings with fine-grained, text-aligned features from tailored encoders via coarse-to-fine cross-attention without introducing significant alignment overhead. We further introduce a human-VLM collaborative data curation pipeline to generate paired textual annotations for sensing datasets. Extensive experiments on two newly constructed benchmarks show that HoloLLM significantly outperforms existing MLLMs, improving language-grounded human sensing accuracy by up to 30\%. This work establishes a new foundation for real-world, language-informed multisensory embodied intelligence.

Deep Learning · Graph Neural Networks

Yujie Xing, Xiao Wang, Bin Wu, Hai Huang, Chuan Shi

Graph Transformers (GTs) have emerged as a powerful paradigm for graph representation learning due to their ability to model diverse node interactions. However, existing GTs often rely on intricate architectural designs tailored to specific interactions, limiting their flexibly. To address this, we propose a unified hierarchical mask framework that reveals an underlying equivalence between model architecture and attention mask construction. This framework enables a consistent modeling paradigm by capturing diverse interactions through carefully designed attention masks. Theoretical analysis under this framework demonstrates that the probability of correct classification positively correlates with the receptive field size and label consistency, leading to a fundamental design principle: An effective attention mask should ensure both a sufficiently large receptive field and a high level of label consistency. While no single existing mask satisfies this principle across all scenarios, our analysis reveals that hierarchical masks offer complementary strengths—motivating their effective integration. Then, we introduce M$^3$Dphormer, a Mixture-of-Experts based Graph Transformer with Multi-Level Masking and Dual Attention Computation. M$^3$Dphormer incorporates three theoretically grounded hierarchical masks and employs a bi-level expert routing mechanism to adaptively integrate multi-level interaction information. To ensure scalability, we further introduce a dual attention computation scheme that dynamically switches between dense and sparse modes based on local mask sparsity. Extensive experiments across multiple benchmarks demonstrate that M$^3$Dphormer achieves state-of-the-art performance, validating the effectiveness of our unified framework and model design.

General Machine Learning · Transfer, Multitask and Meta-learning

Chaoyang Li, Runze Ye, Jianyang Qin, Jinhao Cui, Lingzhi Wang, Ning Hu, Qing Liao

Current parameter-efficient fine-tuning (PEFT) methods have shown superior performance in continual learning. However, most existing PEFT-based methods focus on mitigating catastrophic forgetting by limiting modifications to the old task model caused by new tasks. This hinders backward knowledge transfer, as when new tasks have a strong positive correlation with old tasks, appropriately training on new tasks can transfer beneficial knowledge to old tasks. Critically, achieving backward knowledge transfer faces two fundamental challenges: (1) some parameters may be ineffective on task performance, which constrains the task solution space and model capacity; (2) since old task data are inaccessible, modeling task correlation via shared data is infeasible. To address these challenges, we propose CaLoRA, a novel \textbf{c}ausal-\textbf{a}ware \textbf{lo}w-\textbf{r}ank \textbf{a}daptation framework that is the first PEFT-based continual learning work with backward knowledge transfer. Specifically, we first propose \textbf{p}ar\textbf{a}meter-level \textbf{c}ounterfactual \textbf{a}ttribution (PaCA) that estimates the causal effect of LoRA parameters via counterfactual reasoning, identifying effective parameters from a causal view. Second, we propose \textbf{c}ross-t\textbf{a}sk \textbf{g}radient \textbf{a}daptation (CaGA) to quantify task correlation by gradient projection and evaluate task affinity based on gradient similarity. By incorporating causal effect, task correlation, and affinity, CaGA adaptively adjusts task gradients, facilitating backward knowledge transfer without relying on data replay. Extensive experiments across multiple benchmarks and continual learning settings show that CaLoRA outperforms state-of-the-art methods. In particular, CaLoRA better mitigates catastrophic forgetting by enabling positive backward knowledge transfer.

Mingyang Liu, Xinyang Chen, Xiucheng Li, Weili Guan, Liqiang Nie

Unsupervised domain adaptation has emerged as a pivotal paradigm for mitigating distribution shifts in time series analysis. The fundamental challenge in time series domain adaptation arises from the entanglement of domain shifts and intricate temporal patterns. Crucially, the latent continuous-time dynamics, which are often inaccessible due to sensor constraints, are only partially observable through discrete time series from an explicit sensor-limited single view. This partial observability hinders the modeling of intricate temporal patterns, impeding domain invariant representation learning. To mitigate the limitation, we propose **EDEN** (multiple **E**xplicit **D**omain **E**nhanced adaptation **N**etwork), expanding the raw dataset to multi-scale explicit domains, multi-subspace explicit domains and multi-segment explicit domains. EDEN enhances domain adaptation with three coordinated modules tailored to integrate multiple explicit domains: (1) Multi-Scale Curriculum Adaptation implements progressive domain alignment from coarse-scale to fine-scale. (2) Quality-Aware Feature Fusion evaluates feature quality in multi-subspace explicit domains and adaptively integrates temporal-frequency features. (3) Temporal Coherence Learning enforces segment-level consistency with multi-segment explicit domains. The representation enriched by multiple explicit domains bridges the gap between partially observed discrete samples and the underlying implicit temporal dynamics, enabling more accurate approximation of implicit temporal patterns for effective cross-domain adaptation. Our comprehensive evaluation across 6 time series benchmarks demonstrates EDEN's consistent superiority, achieving average accuracy improvements of 4.8% over state-of-the-art methods in cross-domain scenarios. Code is available at the anonymous link: .

General Machine Learning · Transfer, Multitask and Meta-learning

Tim Genewein, Kevin Li, Jordi Grau-Moya, Anian Ruoss, Laurent Orseau, Marcus Hutter

Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven, with less emphasis on a conceptual understanding of prompting. In this paper we discuss how optimal prompting can be understood through a Bayesian view, which also implies some fundamental limitations of prompting that can only be overcome by tuning weights. The paper explains in detail how meta-trained neural networks behave as Bayesian predictors over the pretraining distribution, whose hallmark feature is rapid in-context adaptation. Optimal prompting can be studied formally as conditioning these Bayesian predictors, yielding criteria for target tasks where optimal prompting is and is not possible. We support the theory with educational experiments on LSTMs and Transformers, where we compare different versions of prefix-tuning and different weight-tuning methods. We also confirm that soft prefixes, which are sequences of real-valued vectors outside the token alphabet, can lead to very effective prompts for trained and even untrained networks by manipulating activations in ways that are not achievable by hard tokens. This adds an important mechanistic aspect beyond the conceptual Bayesian theory.