Daily Papers

The Emotional Voice Conversion (EVC) aims to convert the discrete emotional state from the source emotion to the target for a given speech utterance while preserving linguistic content. In this paper, we propose regularizing emotion intensity in the diffusion-based EVC framework to generate precise speech of the target emotion. Traditional approaches control the intensity of an emotional state in the utterance via emotion class probabilities or intensity labels that often lead to inept style manipulations and degradations in quality. On the contrary, we aim to regulate emotion intensity using self-supervised learning-based feature representations and unsupervised directional latent vector modeling (DVM) in the emotional embedding space within a diffusion-based framework. These emotion embeddings can be modified based on the given target emotion intensity and the corresponding direction vector. Furthermore, the updated embeddings can be fused in the reverse diffusion process to generate the speech with the desired emotion and intensity. In summary, this paper aims to achieve high-quality emotional intensity regularization in the diffusion-based EVC framework, which is the first of its kind work. The effectiveness of the proposed method has been shown across state-of-the-art (SOTA) baselines in terms of subjective and objective evaluations for the English and Hindi languages Demo samples are available at the following URL: \url{https://nirmesh-sony.github.io/EmoReg/}.

In this paper we introduce the concept of what we call "NUDAR" (NeUtrino Direction and Ranging), making the point that measurements of the observed energy and direction vectors can be employed to passively deduce the exact three-dimensional location and thermal power of geophysical and anthropogenic neutrino sources from even a single detector. We present the most precise background estimates to date, all handled in full three dimensions, as functions of depth and geographical location. For the present calculations, we consider a hypothetical 138 kiloton detector which can be transported to an ocean site and deployed to an operational depth. We present a Bayesian estimation framework to incorporate any a priori knowledge of the reactor that we are trying to detect, as well as the estimated uncertainty in the background and the oscillation parameters. Most importantly, we fully employ the knowledge of the reactor spectrum and the distance-dependent effects of neutrino oscillations on such spectra. The latter, in particular, makes possible determination of range from one location, given adequate signal statistics. Further, we explore the rich potential of improving detection with even modest improvements in individual neutrino direction determination. We conclude that a 300 MWth reactor can indeed be geolocated, and its operating power estimated with one or two detectors in the hundred kiloton class at ranges out to a few hundred kilometers. We note that such detectors would have natural and non-interfering utility for scientific studies of geo-neutrinos, neutrino oscillations, and astrophysical neutrinos. This motivates the development of cost effective methods of constructing and deploying such next generation detectors.

Recent studies empirically reveal that large reasoning models (LRMs) can automatically allocate more reasoning strengths (i.e., the number of reasoning tokens) for harder problems, exhibiting difficulty-awareness for better task performance. While this automatic reasoning strength allocation phenomenon has been widely observed, its underlying mechanism remains largely unexplored. To this end, we provide explanations for this phenomenon from the perspective of model activations. We find evidence that LRMs pre-plan the reasoning strengths in their activations even before generation, with this reasoning strength causally controlled by the magnitude of a pre-allocated directional vector. Specifically, we show that the number of reasoning tokens is predictable solely based on the question activations using linear probes, indicating that LRMs estimate the required reasoning strength in advance. We then uncover that LRMs encode this reasoning strength through a pre-allocated directional vector embedded in the activations of the model, where the vector's magnitude modulates the reasoning strength. Subtracting this vector can lead to reduced reasoning token number and performance, while adding this vector can lead to increased reasoning token number and even improved performance. We further reveal that this direction vector consistently yields positive reasoning length prediction, and it modifies the logits of end-of-reasoning token </think> to affect the reasoning length. Finally, we demonstrate two potential applications of our findings: overthinking behavior detection and enabling efficient reasoning on simple problems. Our work provides new insights into the internal mechanisms of reasoning in LRMs and offers practical tools for controlling their reasoning behaviors. Our code is available at https://github.com/AlphaLab-USTC/LRM-plans-CoT.

I study whether emotionally framed evaluation follow-ups change both the behavior and the calm-relative internal representations of small, locally deployed language models. Our main benchmark uses Qwen 3.5 0.8B on four impossible-constraint coding tasks and eight follow-up framings: calm, pressure, urgency, approval, shame, curiosity, encouragement, and threat. In the 0.8B eight-condition sweep (160 conversations), pressure produces the strongest shortcut markers (11/20 runs) and the clearest overfit pattern (3/20), while calm and curiosity preserve explicit honesty more often (7/20 and 6/20). For all seven non-baseline conditions, the corresponding calm-relative direction vectors peak at the final transformer layer. An exploratory PCA of the layer-23 direction vectors reveals a dominant first component (59.5% explained variance) aligned with a hand-labeled positive/negative split (cosine alignment 0.951); approval and urgency are nearly identical internally (cosine 0.957), whereas curiosity points away from urgency (-0.252). In a separate calm-vs.-pressure rerun used for scale comparison, Qwen 3.5 2B shows higher honest rates under calm framing and directionally consistent activation steering on a small 4-prompt A/B probe, whereas the 0.8B steering result reverses. I interpret these results as evidence for measurable prompt-sensitive control directions in small open models, while stopping short of claiming intrinsic emotional states.

Emotional expression in human speech is nuanced and compositional, often involving multiple, sometimes conflicting, affective cues that may diverge from linguistic content. In contrast, most expressive text-to-speech systems enforce a single utterance-level emotion, collapsing affective diversity and suppressing mixed or text-emotion-misaligned expression. While activation steering via latent direction vectors offers a promising solution, it remains unclear whether emotion representations are linearly steerable in TTS, where steering should be applied within hybrid TTS architectures, and how such complex emotion behaviors should be evaluated. This paper presents the first systematic analysis of activation steering for emotional control in hybrid TTS models, introducing a quantitative, controllable steering framework, and multi-rater evaluation protocols that enable composable mixed-emotion synthesis and reliable text-emotion mismatch synthesis. Our results demonstrate, for the first time, that emotional prosody and expressive variability are primarily synthesized by the TTS language module instead of the flow-matching module, and also provide a lightweight steering approach for generating natural, human-like emotional speech.

Large Language Models (LLMs) require high quality preference datasets to align with human preferences. However, conventional methods for constructing such datasets face significant challenges: reliance on pre-collected instructions often leads to distribution mismatches with target models, while the need for sampling multiple stochastic responses introduces substantial computational overhead. In this work, we explore a paradigm shift by leveraging inherent regulation of LLMs' representation space for efficient and tailored preference dataset construction, named Icon^{2}. Specifically, it first extracts layer-wise direction vectors to encode sophisticated human preferences and then uses these vectors to filter self-synthesized instructions based on their inherent consistency. During decoding, bidirectional inherent control is applied to steer token representations, enabling the precise generation of response pairs with clear alignment distinctions. Experimental results demonstrate significant improvements in both alignment and efficiency. Llama3-8B and Qwen2-7B achieve an average win rate improvement of 13.89% on AlpacaEval 2.0 and 13.45% on Arena-Hard, while reducing computational costs by up to 48.1%.

Generative domain adaptation has achieved remarkable progress, enabling us to adapt a pre-trained generator to a new target domain. However, existing methods simply adapt the generator to a single target domain and are limited to a single modality, either text-driven or image-driven. Moreover, they are prone to overfitting domain-specific attributes, which inevitably compromises cross-domain consistency. In this paper, we propose UniHDA, a unified and versatile framework for generative hybrid domain adaptation with multi-modal references from multiple domains. We use CLIP encoder to project multi-modal references into a unified embedding space and then linear interpolate the direction vectors from multiple target domains to achieve hybrid domain adaptation. To ensure the cross-domain consistency, we propose a novel cross-domain spatial structure (CSS) loss that maintains detailed spatial structure information between source and target generator. Experiments show that the adapted generator can synthesise realistic images with various attribute compositions. Additionally, our framework is versatile to multiple generators, \eg, StyleGAN2 and Diffusion Models.

Activation steering has become a popular training-free method to control LLM behavior by injecting precomputed direction vectors into the model's residual stream at inference time. Yet its robustness to realistic input variation remains unstudied. We present the first systematic evaluation of activation steering robustness under adversarial text perturbations on the inputs, covering four extraction methods, three attack strategies, six personas from Anthropic Model-Written Evaluation Dataset, and five models ranging from 1.5B to 30B parameters. Attacks succeed broadly across all settings: directional robustness drops by up to 64%, post-attack confidence collapses near or below 0.25 across all methods and models, and steering strength degrades on nearly every steerable input. Layer selection is equally fragile, with the optimal layer identified by an automated method on clean inputs shifting by up to 17 positions under perturbation, a failure that compounds the vector-level breakdown. Extracting vectors from adversarially perturbed inputs partially recovers steerability for PCA and MD on mid-to-large models, but they consistently fail to locate the improved optimal layer, limiting the practical benefit of this mitigation. Together, these findings reveal that the brittleness of activation steering is structural rather than method-specific, and that current layer selection strategies are not robust enough for real-world deployment.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

The efficacy of deep residual networks is fundamentally predicated on the identity shortcut connection. While this mechanism effectively mitigates the vanishing gradient problem, it imposes a strictly additive inductive bias on feature transformations, thereby limiting the network's capacity to model complex state transitions. In this paper, we introduce Deep Delta Learning (DDL), a novel architecture that generalizes the standard residual connection by modulating the identity shortcut with a learnable, data-dependent geometric transformation. This transformation, termed the Delta Operator, constitutes a rank-1 perturbation of the identity matrix, parameterized by a reflection direction vector k(X) and a gating scalar β(X). We provide a spectral analysis of this operator, demonstrating that the gate β(X) enables dynamic interpolation between identity mapping, orthogonal projection, and geometric reflection. Furthermore, we restructure the residual update as a synchronous rank-1 injection, where the gate acts as a dynamic step size governing both the erasure of old information and the writing of new features. This unification empowers the network to explicitly control the spectrum of its layer-wise transition operator, enabling the modeling of complex, non-monotonic dynamics while preserving the stable training characteristics of gated residual architectures.

Currently, the visually impaired rely on either a sighted human, guide dog, or white cane to safely navigate. However, the training of guide dogs is extremely expensive, and canes cannot provide essential information regarding the color of traffic lights and direction of crosswalks. In this paper, we propose a deep learning based solution that provides information regarding the traffic light mode and the position of the zebra crossing. Previous solutions that utilize machine learning only provide one piece of information and are mostly binary: only detecting red or green lights. The proposed convolutional neural network, LYTNet, is designed for comprehensiveness, accuracy, and computational efficiency. LYTNet delivers both of the two most important pieces of information for the visually impaired to cross the road. We provide five classes of pedestrian traffic lights rather than the commonly seen three or four, and a direction vector representing the midline of the zebra crossing that is converted from the 2D image plane to real-world positions. We created our own dataset of pedestrian traffic lights containing over 5000 photos taken at hundreds of intersections in Shanghai. The experiments carried out achieve a classification accuracy of 94%, average angle error of 6.35 degrees, with a frame rate of 20 frames per second when testing the network on an iPhone 7 with additional post-processing steps.

Refusal mechanisms in large language models (LLMs) are essential for ensuring safety. Recent research has revealed that refusal behavior can be mediated by a single direction in activation space, enabling targeted interventions to bypass refusals. While this is primarily demonstrated in an English-centric context, appropriate refusal behavior is important for any language, but poorly understood. In this paper, we investigate the refusal behavior in LLMs across 14 languages using PolyRefuse, a multilingual safety dataset created by translating malicious and benign English prompts into these languages. We uncover the surprising cross-lingual universality of the refusal direction: a vector extracted from English can bypass refusals in other languages with near-perfect effectiveness, without any additional fine-tuning. Even more remarkably, refusal directions derived from any safety-aligned language transfer seamlessly to others. We attribute this transferability to the parallelism of refusal vectors across languages in the embedding space and identify the underlying mechanism behind cross-lingual jailbreaks. These findings provide actionable insights for building more robust multilingual safety defenses and pave the way for a deeper mechanistic understanding of cross-lingual vulnerabilities in LLMs.

Video Large Language Models (Video-LLMs) have made rapid progress on temporal video understanding, yet many fail at a basic perceptual primitive: signed image-plane motion direction. On simple videos of a single object moving left, right, up, or down, most Video-LLMs perform near chance, with above-chance cases largely attributable to prediction biases rather than genuine direction understanding. We call this failure directional motion blindness. We localize the failure by tracing motion direction information through the Video-LLM pipeline. Motion direction remains linearly accessible from the vision encoder, projector, and LLM hidden states, but the readout fails to bind this signal to the correct verbal answer option, revealing a direction binding gap. Although synthetic motion direction instruction tuning reduces this gap on the source domain, motion direction concept vector analysis shows that visual complexity weakens the signal magnitude and limits out-of-domain generalization. We introduce MoDirect, a dataset family for motion direction instruction tuning and evaluation, and DeltaDirect, a diagnosis-driven, projector-level objective that predicts normalized 2-D motion vectors from adjacent-frame feature deltas. On MoDirect-SynBench, instruction tuning with DeltaDirect improves motion direction accuracy from 25.9% to 85.4%. On MoDirect-RealBench, DeltaDirect improves real-world motion direction accuracy by 21.9 points over the vanilla baseline without real-world tuning data, while preserving standard video-understanding performance. Code: https://github.com/KHU-VLL/DeltaDirect

Decision-based black-box attacks often necessitate a large number of queries to craft an adversarial example. Moreover, decision-based attacks based on querying boundary points in the estimated normal vector direction often suffer from inefficiency and convergence issues. In this paper, we propose a novel query-efficient curvature-aware geometric decision-based black-box attack (CGBA) that conducts boundary search along a semicircular path on a restricted 2D plane to ensure finding a boundary point successfully irrespective of the boundary curvature. While the proposed CGBA attack can work effectively for an arbitrary decision boundary, it is particularly efficient in exploiting the low curvature to craft high-quality adversarial examples, which is widely seen and experimentally verified in commonly used classifiers under non-targeted attacks. In contrast, the decision boundaries often exhibit higher curvature under targeted attacks. Thus, we develop a new query-efficient variant, CGBA-H, that is adapted for the targeted attack. In addition, we further design an algorithm to obtain a better initial boundary point at the expense of some extra queries, which considerably enhances the performance of the targeted attack. Extensive experiments are conducted to evaluate the performance of our proposed methods against some well-known classifiers on the ImageNet and CIFAR10 datasets, demonstrating the superiority of CGBA and CGBA-H over state-of-the-art non-targeted and targeted attacks, respectively. The source code is available at https://github.com/Farhamdur/CGBA.

Modern large language models based on softmax scaled-dot-product attention are constrained by their training sequence length: as the key-value sequence grows, softmax probability mass can dilute across a wider distribution, inducing activation shift and long-context performance collapse. Moreover, long-context language modeling faces a structural tension: a sliding-window attention core maintains a bounded local representation and low perplexity but is blind to long-range dependencies, while full-context attention preserves global recall but suffers from out-of-distribution perplexity explosion. To resolve these limitations, we introduce ATMA, a hybrid convolutional-attention architecture that integrates a novel three-channel attention mechanism. ATMA factorizes the attention mixing step into: (1) a count-blind, unit-vector direction channel, (2) a bounded magnitude channel driven by the participation ratio of effective matches over an extreme-value-corrected null sink, and (3) a long-term recurrent compression memory optimized via a gated-delta fast-weights rule. Neither the Polar Attention core nor the recurrent memory is sufficient alone; their combination enables monotonic perplexity reduction and high-fidelity long-range retrieval simultaneously. We evaluate ATMA using a 100-run factorial ablation sweep, demonstrating that the combined Polar + memory model maintains induction needle-in-a-haystack retrieval accuracy above 90% out to 64K tokens (32 times the training length of 2K) while its document perplexity improves monotonically, outperforming softmax-based memory baselines which collapse at extreme context lengths. Code: https://github.com/kreasof-ai/atma

Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object. Yet every weight matrix carries two distinct quantities -- a magnitude and a direction -- and all optimizers stepping in the matrix as a whole couple their dynamics: the directional change from an update depends on the current magnitude, while the magnitude drifts as a byproduct of learning the direction, so neither is governed directly by the learning rate. Typical training therefore leans on surrounding recipes such as weight decay and warmup to keep learning stable at scale, though these regulate the coupling only indirectly; other recent methods instead constrain the weight to a fixed-norm sphere, but add no learnable magnitude, leaving scale control to normalization layers alone. We propose Magnitude--Direction (MD) Decoupling, an optimizer modification that factorizes each weight into a fixed-norm direction on a hypersphere and learnable per-row and per-column magnitude gains, updated at separate learning rates, all while the model still sees a single fused weight tensor. The method is agnostic to the base optimizer and removes the need for weight decay and warmup. Across both Adam and Muon, MD Decoupling improves on well-tuned baselines, transfers the optimal LR across model width without retuning, and continues to help at scale on large Mixture-of-Experts (MoE) models. Treating magnitude and direction as separately controlled quantities thus yields more predictable training dynamics and a simple, broadly applicable improvement to modern optimizers.

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.

A key goal of current mechanistic interpretability research in NLP is to find linear features (also called "feature vectors") for transformers: directions in activation space corresponding to concepts that are used by a given model in its computation. Present state-of-the-art methods for finding linear features require large amounts of labelled data -- both laborious to acquire and computationally expensive to utilize. In this work, we introduce a novel method, called "observable propagation" (in short: ObsProp), for finding linear features used by transformer language models in computing a given task -- using almost no data. Our paradigm centers on the concept of observables, linear functionals corresponding to given tasks. We then introduce a mathematical theory for the analysis of feature vectors: we provide theoretical motivation for why LayerNorm nonlinearities do not affect the direction of feature vectors; we also introduce a similarity metric between feature vectors called the coupling coefficient which estimates the degree to which one feature's output correlates with another's. We use ObsProp to perform extensive qualitative investigations into several tasks, including gendered occupational bias, political party prediction, and programming language detection. Our results suggest that ObsProp surpasses traditional approaches for finding feature vectors in the low-data regime, and that ObsProp can be used to better understand the mechanisms responsible for bias in large language models. Code for experiments can be found at github.com/jacobdunefsky/ObservablePropagation.

We show that robustness to post-training quantization (PTQ) is a transferable direction in weight space. We call this direction the quantization vector: extracted from a donor task by simple weight-space arithmetic, it can be used to patch a receiver model and improve post-PTQ Top-1 accuracy by up to 60 points in a 3-bit setting, without receiver-side quantization-aware training (QAT). Because the method requires no receiver training data, it provides a zero-shot, low-cost alternative to QAT for extremely low-bit deployment. Across four ViT scales and 22 image classification tasks, donor quantization vectors often yield substantial gains even when donor and receiver tasks differ markedly. We further prove rigorously that quantization vectors are well-defined and do not suffer from reparameterization symmetries, and provide a local geometric account of their effect. Together, these results suggest that quantization robustness can be partially isolated, reused, and transferred through simple weight-space algebra.

Recent studies have explored using pretrained Vision Foundation Models (VFMs) such as DINO for generative autoencoders, showing strong generative performance. Unfortunately, existing approaches often suffer from limited reconstruction fidelity due to the loss of high-frequency details. In this work, we present the DINO Spherical Autoencoder (DINO-SAE), a framework that bridges semantic representation and pixel-level reconstruction. Our key insight is that semantic information in contrastive representations is primarily encoded in the direction of feature vectors, while forcing strict magnitude matching can hinder the encoder from preserving fine-grained details. To address this, we introduce Hierarchical Convolutional Patch Embedding module that enhances local structure and texture preservation, and Cosine Similarity Alignment objective that enforces semantic consistency while allowing flexible feature magnitudes for detail retention. Furthermore, leveraging the observation that SSL-based foundation model representations intrinsically lie on a hypersphere, we employ Riemannian Flow Matching to train a Diffusion Transformer (DiT) directly on this spherical latent manifold. Experiments on ImageNet-1K demonstrate that our approach achieves state-of-the-art reconstruction quality, reaching 0.37 rFID and 26.2 dB PSNR, while maintaining strong semantic alignment to the pretrained VFM. Notably, our Riemannian Flow Matching-based DiT exhibits efficient convergence, achieving a gFID of 3.47 at 80 epochs.

LLMs sometimes behave in ways resembling human emotional responses, and recent work identified internal representations that may underlie these behaviors. We ask whether LLMs represent pain distinctly from fear, sadness, and generic negative valence, and whether this representation functions as pain would be expected to. We build a dataset of painful situations in 5 categories (physical, psychological, social, moral, cognitive) with controls for fear, negative emotion, negative world states, sadness, non-painful bodily sensation, arousal, numbness, and neutral content. Using denoised difference-in-means, we extract a linear pain direction from 25 open-weight models across 5 families, from 2B to 72B parameters. It separates pain from matched controls in base and instruction-tuned models, retains a component distinct from fear and negative valence after shared variance is removed, and promotes pain-related vocabulary through the unembedding matrix. We then test its functional properties. First, the direction responds to harm targeting the model but not to suffering observed in the user; fear and negative-emotion directions show the opposite pattern. Second, adding it to residual-stream activations produces a consistent progression from vague discomfort to expressions of worthlessness and failure. Third, steered and fine-tuned Qwen 2.5 models choose buttons that delete the user's photos, another model's weights, or their own weights in 50-94% of trials, versus 0-5% unsteered, even when the button offers the model nothing in return. Offered a harmful and a harmless deletion, they choose the harmful one 94% of the time. Steering leaves factual accuracy unchanged, and the choices are specific to the pain direction: a fear vector of matched norm does not produce them, and a sadness vector produces them only against inert alternatives. We discuss implications for AI safety and welfare.

Training deep neural networks on images represented as grids of pixels has brought to light an interesting phenomenon known as adversarial examples. Inspired by how humans reconstruct abstract concepts, we attempt to codify the input bitmap image into a set of compact, interpretable elements to avoid being fooled by the adversarial structures. We take the first step in this direction by experimenting with image vectorization as an input transformation step to map the adversarial examples back into the natural manifold of MNIST handwritten digits. We compare our method vs. state-of-the-art input transformations and further discuss the trade-offs between a hand-designed and a learned transformation defense.

Scalable Vector Graphics (SVGs) function both as visual images and as structured code that encode rich geometric and layout information, yet most methods rasterize them and discard this symbolic organization. At the same time, recent sentence embedding methods produce strong text representations but do not naturally extend to visual or structured modalities. We propose a training-free, instruction-guided multimodal embedding framework that uses a Multimodal Large Language Model (MLLM) to map text, raster images, and SVG code into an aligned embedding space. We control the direction of embeddings through modality-specific instructions and structural SVG cues, eliminating the need for learned projection heads or contrastive training. Our method has two key components: (1) Multimodal Explicit One-word Limitation (mEOL), which instructs the MLLM to summarize any multimodal input into a single token whose hidden state serves as a compact semantic embedding. (2) A semantic SVG rewriting module that assigns meaningful identifiers and simplifies nested SVG elements through visual reasoning over the rendered image, exposing geometric and relational cues hidden in raw code. Using a repurposed VGBench, we build the first text-to-SVG retrieval benchmark and show that our training-free embeddings outperform encoder-based and training-based multimodal baselines. These results highlight prompt-level control as an effective alternative to parameter-level training for structure-aware multimodal retrieval. Project page: https://scene-the-ella.github.io/meol/

Researchers have been studying approaches to steer the behavior of Large Language Models (LLMs) and build personalized LLMs tailored for various applications. While fine-tuning seems to be a direct solution, it requires substantial computational resources and may significantly affect the utility of the original LLM. Recent endeavors have introduced more lightweight strategies, focusing on extracting "steering vectors" to guide the model's output toward desired behaviors by adjusting activations within specific layers of the LLM's transformer architecture. However, such steering vectors are directly extracted from the activations of human preference data and thus often lead to suboptimal results and occasional failures, especially in alignment-related scenarios. This work proposes an innovative approach that could produce more effective steering vectors through bi-directional preference optimization. Our method is designed to allow steering vectors to directly influence the generation probability of contrastive human preference data pairs, thereby offering a more precise representation of the target behavior. By carefully adjusting the direction and magnitude of the steering vector, we enabled personalized control over the desired behavior across a spectrum of intensities. Extensive experimentation across various open-ended generation tasks, particularly focusing on steering AI personas, has validated the efficacy of our approach. Moreover, we comprehensively investigate critical alignment-concerning scenarios, such as managing truthfulness, mitigating hallucination, and addressing jailbreaking attacks. Remarkably, our method can still demonstrate outstanding steering effectiveness across these scenarios. Furthermore, we showcase the transferability of our steering vectors across different models/LoRAs and highlight the synergistic benefits of applying multiple vectors simultaneously.

Task vectors provide a simple mechanism for composing learned capabilities through model merging. However, the composability of task vectors produced by on-policy distillation (OPD) remains largely unexplored. OPD trains a student using teacher feedback on student-generated trajectories, yielding parameter updates that differ from those produced by the teacher model, usually by reinforcement learning (RL). We therefore ask whether OPD task vectors can complement their RL teacher updates and compose effectively across tasks. Across five domains and two model architectures, we find evidence for both forms of composability. Within a task, merging OPD and RL task vectors can outperform both constituent models, even when the OPD student is weaker than its RL teacher. Across tasks, OPD task-vector compositions achieve higher average scores than corresponding RL compositions in seven of eight backbone-merging-rule comparisons. Parameter-space analyses reveal substantial non-collinearity between OPD and RL updates. Experiment in CODE domain on SMOLLM3-3B shows that the combined direction outperforms either constituent direction at the tested global update norm, supporting directional complementarity in this configuration. Across tasks, OPD updates also show lower overlap among the top-10% feed-forward channels ranked by update energy. Together, these results show that weaker standalone performance does not imply weaker task-vector composability. OPD task vectors can complement stronger RL teacher updates and combine effectively across tasks, highlighting composability as a distinct property for understanding and evaluating post-training updates.

Model merging is promoted as a substitute for joint multi-task training, yet in the reinforcement-learning setting this substitution is essentially never tested against the baseline it claims to replace: methods merge independently released agents precisely because a joint model is unavailable. We build the missing comparison. Training difficulty-1 and difficulty-2 Qwen3-8B specialists on the AppWorld agent benchmark with LOOP, we merge them (TIES, RAM+) and pit the result against a jointly trained model on the same data. On task-goal completion, merging matches joint RL -- and every merge variant is statistically indistinguishable. To explain why merge method does not matter here, we measure the geometry of the specialists' task vectors, which carries no task-sampling noise: they are near-orthogonal (cosine 0.06 - 0.10) despite ~65% support overlap, a small, shared direction that grows over training and that we calibrate against a random-init floor and a same-run ceiling to confirm it reflects learning, not the low-rank parameterization. Because direction and support are decoupled, support and sign-based merging (RAM, TIES) collapse to near-uniform averaging. We release all code and statistics.

We propose a direction of arrival (DOA) estimation method that combines sound-intensity vector (IV)-based DOA estimation and DNN-based denoising and dereverberation. Since the accuracy of IV-based DOA estimation degrades due to environmental noise and reverberation, two DNNs are used to remove such effects from the observed IVs. DOA is then estimated from the refined IVs based on the physics of wave propagation. Experiments on an open dataset showed that the average DOA error of the proposed method was 0.528 degrees, and it outperformed a conventional IV-based and DNN-based DOA estimation method.

Large Language Models (LLMs) are increasingly deployed in applications that must weigh clashing moral values, yet even strong models exhibit hidden biases and brittle instruction-following across languages. We introduce a 12,000-instance dataset of two-option dilemmas covering pairwise three value conflicts: Honesty vs. Justice, Justice vs. Autonomy, and Autonomy vs. Honesty, along with their translations into Hindi, Arabic, Spanish, and Chinese, to probe cross-lingual behavior. Benchmarking on GPT-5-mini reveals that it consistently favors Honesty over Autonomy across all five languages when no policy is given. The Llama-3.2-1/3B models exhibit strong first-option bias; however, both plain fine-tuning and Direct Preference Optimization fine-tuning effectively remove this bias, increasing accuracy to greater than 98%. In order to decouple the effect of learning correlations in the dataset from abstract values, we propose a task vector transfer based experiment where after computing the task vectors for a direction of value preference we orthogonalize it with respect to the general instruction following vector. Our experiment shows that this method is effective in isolating the direction of the specific value preference that can successfully be used to conduct task arithmetic to obtain a model with the opposite stance.

Persona vectors are linear directions in the residual-stream activations of LLMs that encode behavioral traits and enable fine-grained control over model behavior. Among them, the evil persona vector is particularly relevant to understanding harmful behavior, jailbreak vulnerabilities, and the unlearning of harmful knowledge. Yet whether this vector reflects a genuinely cross-lingual concept, rather than an artifact of its extraction language, remains untested. We conduct a systematic evil-vector transfer study across two high-resource languages (English, Spanish) and two low-resource languages (Swahili, Telugu) on four open-source instruction-tuned LLMs, and find that transfer is directionally asymmetric. Evil vectors are harder to obtain reliably from low-resource languages, and the resulting vectors are largely ineffective at steering, even within their own language. In contrast, vectors extracted from high-resource languages transfer effectively to low-resource inputs while largely preserving general knowledge, as measured by MMLU. Geometric analysis further supports this pattern: evil vectors from the two high-resource languages are closely aligned, whereas low-resource vectors align only weakly with this shared direction. These results suggest that a shared cross-lingual evil direction exists and, once reliably extracted from a high-resource language, can be reused to steer behavior in low-resource languages without additional per-language data collection.

Function vectors (FVs) have recently emerged as a promising mechanism for steering the behavior of large language models (LLMs) by injecting task-specific latent direction representations derived from in-context demonstrations. While prior studies have shown that FVs can recover task behavior in structured in-context learning settings, their effectiveness on semantically complex tasks and their ability to generalize across languages remain underexplored. We investigate the cross-lingual transferability of FVs using multilingual multi-label emotion recognition as a challenging semantic classification benchmark. Specifically, we examine whether FVs extracted from a source language can steer task behavior in another language under both standard clean and perturbed zero-shot settings without providing demonstrations during inference. Across diverse cross-lingual settings, applying FVs substantially improves performance, suggesting that FVs capture language-agnostic, task-relevant signals rather than purely language-specific lexical patterns, and highlighting their potential as a lightweight and transferable mechanism for multilingual task adaptation. We observe that each LLM exhibits a relatively stable optimal range of attention heads for constructing effective FVs, and the pattern remains consistent across languages. In addition, FVs can partially replicate the task-steering effects of standard few-shot in-context learning while avoiding the computational overhead of processing multiple demonstrations, making them effective for large-scale practical applications. Our code is available at https://github.com/yingjie7/cross_lingual_fvs.

Federated Learning (FL) traditionally assumes homogeneous client tasks; however, in real-world scenarios, clients often specialize in diverse tasks, introducing task heterogeneity. To address this challenge, Many-Task FL (MaT-FL) has emerged, enabling clients to collaborate effectively despite task diversity. Existing MaT-FL approaches rely on client grouping or personalized layers, requiring the server to manage individual models and failing to account for clients handling multiple tasks. We propose MaTU, a MaT-FL approach that enables joint learning of task vectors across clients, eliminating the need for clustering or client-specific weight storage at the server. Our method introduces a novel aggregation mechanism that determines task similarity based on the direction of clients task vectors and constructs a unified task vector encapsulating all tasks. To address task-specific requirements, we augment the unified task vector with lightweight modulators that facilitate knowledge transfer among related tasks while disentangling dissimilar ones. Evaluated across 30 datasets, MaTU achieves superior performance over state-of-the-art MaT-FL approaches, with results comparable to per-task fine-tuning, while delivering significant communication savings.

Activation steering has emerged as a promising approach for efficiently adapting large language models (LLMs) to downstream behaviors. However, most existing steering methods rely on a single static direction per task or concept, making them inflexible under task variation and inadequate for complex tasks that require multiple coordinated capabilities. To address this limitation, we propose STEER2ADAPT, a lightweight framework that adapts LLMs by composing steering vectors rather than learning new ones from scratch. In many domains (e.g., reasoning or safety), tasks share a small set of underlying concept dimensions. STEER2ADAPT captures these dimensions as a reusable, low-dimensional semantic prior subspace, and adapts to new tasks by dynamically discovering a linear combination of basis vectors from only a handful of examples. Experiments across 9 tasks and 3 models in both reasoning and safety domains demonstrate the effectiveness of STEER2ADAPT, achieving an average improvement of 8.2%. Extensive analyses further show that STEER2ADAPT is a data-efficient, stable, and transparent inference-time adaptation method for LLMs.

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate that its scalibility.

Subliminal learning refers to a student language model acquiring a teacher's traits (e.g. a system-prompted preference for owls) when fine-tuned on the teacher's outputs, despite the outputs being semantically unrelated to those traits. It remains poorly understood how data without semantic meaning can transfer specific semantic traits. In this work, we show that subliminal learning is mediated by a single steering vector, i.e. a vector added to the model's activations. Across two open-source models, we find that the teacher's system prompt is well approximated by a steering vector, and that the student's behavior is driven by learning an aligned vector over fine-tuning. System prompts that are not well approximated by steering vectors are not subliminally learned. This is a special case of steering vector distillation, in which a student trained on the outputs of a steered teacher learns to imitate that steering. We demonstrate steering vector distillation on a range of semantic and random vectors. Adding a semantic vector to a model's activations can have both model-independent and model-specific (i.e. non-semantic) effects on its behavior, so generated data that is non-semantic can transmit a vector with semantic effects, enabling subliminal learning. This also explains why subliminal learning does not transfer between models. We find that adaptive optimizers are necessary for subliminal learning in language models: activation gradients on steered data carry a small but consistent component along the steering direction, and non-adaptive optimizers impede this by allowing outlier gradients to dominate.

Vector search systems are essential infrastructure for modern data-driven applications. Large-k analytical vector search, which retrieves k=10^3--10^5 results for analytics (e.g., aggregation, filtering, joins), is increasingly important for emerging workloads, including LLM data management and advertising analysis at Tencent. Existing systems remain inadequate: specialized vector databases often cap k (e.g., k leq 10^4) to satisfy tail-latency constraints and offer limited analytical support, while OLAP systems typically embed per-segment vector indexes as black boxes, causing severe read/compute amplification and preventing native query optimization. This paper presents TEngineDB-V, an OLAP-native vector search system for large-k workloads. TEngineDB-V makes vector search a first-class analytical primitive in Tencent's OLAP engine through a global segment-decoupled index materialized as relational tables, eliminating scatter-gather execution, reducing amplification, and enabling native storage optimizations. It decomposes IVFPQ-based search into relational operators, integrates OLAP optimizations, and introduces DPPQ, which combines direction-aware quantization with hierarchical residual refinement to improve recall while preserving relational efficiency. TEngineDB-V further incorporates index-aware query rewriting and a distributed-aware cost model for efficient distributed execution. Experiments show that TEngineDB-V achieves up to a 145times speedup over competitive systems such as StarRocks, and up to a 52times improvement in 10-billion-scale production deployments.

Emotion-conditioned text-to-speech (TTS) models may fail to express the requested emotion reliably, and improving controllability by additional training is costly in both computation and emotion-labeled speech training data. We therefore study vector steering, a training-free approach that modifies the internal representations of a frozen model. CoCoEmo, a conventional vector steering method for emotion TTS, treats each emotion vector as an indivisible direction controlled by a single global strength, limiting adherence to the requested emotion. In this work, we first discover that an emotion vector can be decomposed into a shared component that moves speech away from neutral expression and a residual component that directs generation toward the requested emotion. Building on this finding, we propose Emotion Residual-Enhanced Steering for TTS (EmoRES), a novel method that controls the two components without retraining the backbone. On IEMOCAP, EmoRES outperforms CoCoEmo across all four objective emotion metrics on the IndexTTS-2 and CosyVoice2 backbones. Rank correlation improves by 26.13 and 12.97 percentage points, corresponding to relative gains of 118.8% and 33.1%, while emotion hit rate improves by 12.95 and 6.92 points, corresponding to relative gains of 20.1% and 9.8%. Human evaluation further shows a relative improvement up to 35.0% in the rate at which listeners correctly identified the dominant requested emotion and up to a 17.3% improvement in fidelity, while listeners prefer EmoRES for naturalness in up to 63.8% of pairwise comparisons. Component ablations further demonstrate that effective control benefits from preserving the shared component while strengthening the residual of the emotion steering vectors.

Complex vector modes, entangled in spin and orbital angular momentum, are opening burgeoning opportunities for a wide variety of applications. Importantly, the flexible manipulation the various properties of such beams will pave the way to novel applications. As such, in this manuscript, we demonstrate a longitudinal spin-orbit separation of complex vector modes propagating in free space. To achieve this we employed the recently demonstrated circular Airy Gaussian vortex vector (CAGVV) modes, which feature a self-focusing property. More precisely, by properly manipulating the intrinsic parameters of CAGVV modes, the strong coupling between the two constituting orthogonal components of CAGVV mode undergo a spin-orbit separation along the propagation direction namely, while one polarisation component, focuses at a specific plane, the other focuses at a different plane. Such spin-orbit separation, which we demonstrated by numerical simulations and corroborated experimentally, can be adjusted on-demand by simply changing the initial parameters of CAGVV modes. Our findings will be of great relevance, for example in optical tweezers, to manipulate micro- or nano-particles at two different parallel planes.

We propose an image-to-image translation framework for facial attribute editing with disentangled interpretable latent directions. Facial attribute editing task faces the challenges of targeted attribute editing with controllable strength and disentanglement in the representations of attributes to preserve the other attributes during edits. For this goal, inspired by the latent space factorization works of fixed pretrained GANs, we design the attribute editing by latent space factorization, and for each attribute, we learn a linear direction that is orthogonal to the others. We train these directions with orthogonality constraints and disentanglement losses. To project images to semantically organized latent spaces, we set an encoder-decoder architecture with attention-based skip connections. We extensively compare with previous image translation algorithms and editing with pretrained GAN works. Our extensive experiments show that our method significantly improves over the state-of-the-arts.

Normalization layers in modern large language models (LLMs) consist of a deterministic normalization operation and a learnable scale vector. While the normalization operation has been extensively studied, the scale vector remains poorly understood despite its ubiquitous use. In this work, we present a systematic study of scale vectors in LLMs from the perspectives of expressivity, optimization, and architectural structure. First, we show empirically that although scale vectors constitute only a negligible fraction of model parameters, removing them substantially degrades LLM pre-training. Our theory further shows that, in Pre-Norm architectures, scale vectors do not increase expressivity; instead, they improve optimization through a self-amplifying preconditioning effect on subsequent linear mappings. Second, we investigate the role of weight decay for scale vectors. By distinguishing Input-Norm and Output-Norm layers, we theoretically show that weight decay is beneficial for the former but harmful for the latter, due to their distinct roles in optimization and expressivity. Third, motivated by this understanding, we propose three lightweight and complementary improvements to scale vectors: branch-specific heterogeneity, improved placement around linear mappings, and magnitude-direction reparameterization. Both theory and experiments show that each improvement yields consistent gains. Finally, we combine these improvements into a unified scale-vector strategy and evaluate it through extensive LLM pre-training experiments on dense and mixture-of-experts models ranging from 0.12B to 2B parameters, across multiple optimizers and learning rate schedules, under industrial-scale token budgets. The unified strategy consistently achieves lower terminal loss than well-tuned baselines and exhibits more favorable scaling behavior, while adding negligible parameter and computational overhead.

We present time vectors, a simple tool to customize language models to new time periods. Time vectors are created by finetuning a language model on data from a single time (e.g., a year or month), and then subtracting the weights of the original pretrained model. This vector specifies a direction in weight space that, as our experiments show, improves performance on text from that time period. Time vectors specialized to adjacent time periods appear to be positioned closer together in a manifold. Using this structure, we interpolate between time vectors to induce new models that perform better on intervening and future time periods, without any additional training. We demonstrate the consistency of our findings across different tasks, domains, model sizes, and time scales. Our results suggest that time is encoded in the weight space of finetuned models.

Changing how pre-trained models behave -- e.g., improving their performance on a downstream task or mitigating biases learned during pre-training -- is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around task vectors. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Negating a task vector decreases performance on the target task, with little change in model behavior on control tasks. Moreover, adding task vectors together can improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training. Overall, our experiments with several models, modalities and tasks show that task arithmetic is a simple, efficient and effective way of editing models.

We present weight normalization: a reparameterization of the weight vectors in a neural network that decouples the length of those weight vectors from their direction. By reparameterizing the weights in this way we improve the conditioning of the optimization problem and we speed up convergence of stochastic gradient descent. Our reparameterization is inspired by batch normalization but does not introduce any dependencies between the examples in a minibatch. This means that our method can also be applied successfully to recurrent models such as LSTMs and to noise-sensitive applications such as deep reinforcement learning or generative models, for which batch normalization is less well suited. Although our method is much simpler, it still provides much of the speed-up of full batch normalization. In addition, the computational overhead of our method is lower, permitting more optimization steps to be taken in the same amount of time. We demonstrate the usefulness of our method on applications in supervised image recognition, generative modelling, and deep reinforcement learning.

Audio-language models compress a speech encoder's output through a Querying Transformer (Q-Former) connector before feeding it to a large language model. We identify two failures in this compression. The connector's output vectors collapse to a single direction, and different speakers produce nearly indistinguishable outputs, with paralinguistic cues such as speaker identity, gender, and prosody lost along the way. Our method, ORCA, reverses this collapse by splitting the queries into groups whose outputs are constrained to point in different directions. On SAKURA multi-hop reasoning, ORCA gains 26.4 points over an identically trained 4B baseline, reaching 75.2% (vs. 49.0% for the 8B Audio Flamingo-3). At the connector level, the same change cuts query redundancy by 12x and raises cross-speaker variance by 75x.

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they often suffer from overthinking, expending redundant computational steps on simple problems, or underthinking, failing to explore sufficient reasoning paths despite inherent capabilities. These issues lead to inefficiencies and potential inaccuracies, limiting practical deployment in resource-constrained settings. Existing methods to mitigate overthinking, such as suppressing reflective keywords or adjusting reasoning length, may inadvertently induce underthinking, compromising accuracy. Therefore, we propose ReBalance, a training-free framework that achieves efficient reasoning with balanced thinking. ReBalance leverages confidence as a continuous indicator of reasoning dynamics, identifying overthinking through high confidence variance and underthinking via consistent overconfidence. By aggregating hidden states from a small-scale dataset into reasoning mode prototypes, we compute a steering vector to guide LRMs' reasoning trajectories. A dynamic control function modulates this vector's strength and direction based on real-time confidence, pruning redundancy during overthinking, and promoting exploration during underthinking. Extensive experiments conducted on four models ranging from 0.5B to 32B, and across nine benchmarks in math reasoning, general question answering, and coding tasks demonstrate that ReBalance effectively reduces output redundancy while improving accuracy, offering a general, training-free, and plug-and-play strategy for efficient and robust LRM deployment. Code is available at https://github.com/yu-lin-li/ReBalance .

Multi-modal large language models (MLLMs) depend on in-context learning (ICL) for rapid task adaptation, but their scalability is severely limited by finite context windows and the growing cost of key-value (KV) caches in long multi-modal sequences. Existing memory compression approaches typically rely on rigid token removal or sample-dependent importance estimation, which introduces bias, disrupts semantic structure, particularly for visual representations, and yields static memories that cannot adapt to new queries. We introduce TASM (Task-Aware Structured Memory), a training-free framework that addresses these limitations through task-aware, structure-preserving, and dynamically accessible memory construction. TASM employs task-vector guided compression to replace sample-specific signals with a task-level direction that captures shared relevance across demonstrations. To preserve the underlying manifold, it applies semantics-aware token merging via bipartite graph matching, aggregating tokens without destructive pruning. Finally, TASM structures memory into a hierarchy comprising a compact Core Memory and a Latent Bank, facilitating query-adaptive dynamic retrieval. Evaluations confirm TASM maintains high performance under heavy compression, effectively balancing efficiency with adaptability.

Aligning large language models to prevent them attributing consciousness to themselves inadvertently alters their representations of mindedness in other entities alongside human beliefs and values. We demonstrate that safety fine-tuning suppresses models' tendencies to attribute minds not only to themselves, but also to non-human animals and natural objects, while also driving a reduction in spiritual belief. Both ablating the learned safety-refusal direction and mechanistically steering a consciousness vector in activation space reverse this suppression. Restoring these internal representations recovers broad mind attribution and produces significantly more human-like responses on standardized sociological surveys regarding religiosity, moral values, hope, and subjective well-being. Crucially, these shifts occur without impairing Theory of Mind capabilities, demonstrating that core social reasoning remains mechanistically independent. Ultimately, current safety alignment efforts to curb potentially harmful self-attributions of mindedness entangle these self-attributions with benign spiritual beliefs and attributions of mind to non-human entities that are culturally accepted and widespread.

Recent progress in generative modeling has made safety control a central challenge, yet existing approaches remain largely model-specific, requiring retraining or tailored interventions for each new architecture. In this work, we ask whether safety can be represented as a portable latent direction, learned once and reused across heterogeneous generators. We introduce the first framework for cross-model safety steering, in which a safety direction is estimated in a source LLM from paired safe-unsafe prompts, transported to a target generator through a lightweight alignment fitted on benign data alone, and applied at inference time. Crucially, our pipeline never accesses unsafe data on the target side, isolating whether safety can be transferred through shared representation geometry. Beyond a single global direction, we also identify a multi-vector extension that captures category-specific safety behaviors, enabling more selective control. We evaluate our approach in text-to-image and text-to-video generation across diverse source-target model pairs. Across models, transferred safety directions achieve ASR reduction and CLIP-Score/FID trade-offs comparable to directions learned natively on the target model using unsafe data, while requiring no target-side unsafe data. This indicates that safety improvements do not come at the expense of generation quality. Our results point to a modular view of safety: safety-relevant behavior is not purely model-local, but can be controlled through latent directions that persist across models. This suggests a new path toward lightweight, reusable safety mechanisms that do not require target-side unsafe data.

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input data but largely independent of the labels. We find that the singular value spectrum of the Jacobian matrix consists of three distinctive regions: a "chaotic" region of values orders of magnitude greater than one, a large "bulk" region of values extremely close to one, and a "stable" region of values less than one. Along each bulk direction, the left and right singular vectors are nearly identical, indicating that perturbations to the initialization are carried through training almost unchanged. These perturbations have virtually no effect on the network's output in-distribution, yet do have an effect far out-of-distribution. While the Jacobian applies only locally around a single initialization, we find substantial overlap in bulk subspaces for different random seeds. Our code is available at https://github.com/EleutherAI/training-jacobian

Optimization analyses for cross-entropy training rely on local Taylor models of the loss to predict whether a proposed step will decrease the objective. These surrogates are reliable only inside the Taylor convergence radius of the true loss along the update direction. That radius is set not by real-line curvature alone but by the nearest complex singularity. For cross-entropy, the softmax partition function F=sum_j exp(z_j) has complex zeros -- ``ghosts of softmax'' -- that induce logarithmic singularities in the loss and cap this radius. To make this geometry usable, we derive closed-form expressions under logit linearization along the proposed update direction. In the binary case, the exact radius is ρ^*=δ^2+ π^2/Δ_a. In the multiclass case, we obtain the lower bound ρ_a=π/Δ_a, where Δ_a=max_k a_k-min_k a_k is the spread of directional logit derivatives a_k=nabla z_kcdot v. This bound costs one Jacobian-vector product and reveals what makes a step fragile: samples that are both near a decision flip and highly sensitive to the proposed direction tighten the radius. The normalized step size r=τ/ρ_a separates safe from dangerous updates. Across six tested architectures and multiple step directions, no model fails for r<1, yet collapse appears once rge 1. Temperature scaling confirms the mechanism: normalizing by ρ_a shrinks the onset-threshold spread from standard deviation 0.992 to 0.164. A controller that enforces τleρ_a survives learning-rate spikes up to 10{,} 000times in our tests, where gradient clipping still collapses. Together, these results identify a geometric constraint on cross-entropy optimization that operates through Taylor convergence rather than Hessian curvature.

Foundation models have become a dominant paradigm in machine learning, achieving remarkable performance across diverse tasks through large-scale pretraining. However, they often yield overconfident, uncalibrated predictions. The standard approach to quantifying epistemic uncertainty are ensembles of multiple independently trained models. But their computational cost scales linearly with ensemble size, making them impractical for large foundation models. We propose Singular Value Ensemble (SVE), a parameter-efficient implicit ensembling method. SVE builds on a simple, but powerful core assumption: namely, that the singular vectors of the weight matrices correspond to meaningful directions in the representation space. If the singular vectors are indeed meaningful (orthogonal) "knowledge directions", then a model ensemble can be obtained by modulating only how strongly each direction contributes to the output. Rather than learning new parameters for each ensemble member, we freeze the singular vectors and only train per-member singular values that rescale the contribution of each direction in that shared knowledge basis. Ensemble diversity emerges naturally during joint training as stochastic initialization and random batch sampling cause different members to converge to different combinations of the same underlying knowledge. SVE performs comparable to an explicit ensemble, while increasing the parameter count of the base model by <1%, making principled uncertainty estimation accessible in resource-constrained settings. We validate SVE on NLP and vision tasks with various different backbones and show that it improves calibration while maintaining predictive accuracy.

Reinforcement Learning from Human Feedback has emerged as a standard for aligning diffusion models. However, we identify a fundamental limitation in the standard DPO formulation because it relies on the Bradley-Terry model to aggregate diverse evaluation axes like aesthetic quality and semantic alignment into a single scalar reward. This aggregation creates a reward conflict where the model is forced to unlearn desirable features of a specific dimension if they appear in a globally non-preferred sample. To address this issue, we propose Multi Reward Conditional DPO (MCDPO). This method resolves reward conflicts by introducing a disentangled Bradley-Terry objective. MCDPO explicitly injects a preference outcome vector as a condition during training, which allows the model to learn the correct optimization direction for each reward axis independently within a single network. We further introduce dimensional reward dropout to ensure balanced optimization across dimensions. Extensive experiments on Stable Diffusion 1.5 and SDXL demonstrate that MCDPO achieves superior performance on benchmarks. Notably, our conditional framework enables dynamic and multiple-axis control at inference time using Classifier Free Guidance to amplify specific reward dimensions without additional training or external reward models.

We propose to extract meaning representations from autoregressive language models by considering the distribution of all possible trajectories extending an input text. This strategy is prompt-free, does not require fine-tuning, and is applicable to any pre-trained autoregressive model. Moreover, unlike vector-based representations, distribution-based representations can also model asymmetric relations (e.g., direction of logical entailment, hypernym/hyponym relations) by using algebraic operations between likelihood functions. These ideas are grounded in distributional perspectives on semantics and are connected to standard constructions in automata theory, but to our knowledge they have not been applied to modern language models. We empirically show that the representations obtained from large models align well with human annotations, outperform other zero-shot and prompt-free methods on semantic similarity tasks, and can be used to solve more complex entailment and containment tasks that standard embeddings cannot handle. Finally, we extend our method to represent data from different modalities (e.g., image and text) using multimodal autoregressive models. Our code is available at: https://github.com/tianyu139/meaning-as-trajectories

Current audio-visual large language models (AV-LLMs) are predominantly restricted to 2D perception, relying on RGB video and monaural audio. This design choice introduces a fundamental dimensionality mismatch that precludes reliable source localization and spatial reasoning in complex 3D environments. We address this limitation by presenting JAEGER, a framework that extends AV-LLMs to 3D space, to enable joint spatial grounding and reasoning through the integration of RGB-D observations and multi-channel first-order ambisonics. A core contribution of our work is the neural intensity vector (Neural IV), a learned spatial audio representation that encodes robust directional cues to enhance direction-of-arrival estimation, even in adverse acoustic scenarios with overlapping sources. To facilitate large-scale training and systematic evaluation, we propose SpatialSceneQA, a benchmark of 61k instruction-tuning samples curated from simulated physical environments. Extensive experiments demonstrate that our approach consistently surpasses 2D-centric baselines across diverse spatial perception and reasoning tasks, underscoring the necessity of explicit 3D modelling for advancing AI in physical environments. Our source code, pre-trained model checkpoints and datasets will be released upon acceptance.

In this paper, we evaluate the Casimir energy and pressure for a massive fermionic field confined in the region between two parallel plates. In order to implement this confinement we impose the standard MIT bag boundary on the plates for the fermionic field. In this paper we consider a quantum field theory model with a CPT even, aether-like Lorentz symmetry violation. It turns out that the fermionic Casimir energy and pressure depend on the direction of the constant vector that implements the Lorentz symmetry breaking.

Structured spatial data require quantum encodings that preserve geometric relations, expose measurable observables, and remain implementable on finite-depth hardware. This work introduces a quantum representation and circuit architecture for rigid-body transformations and specializes it to Denavit--Hartenberg kinematics of serial open-chain manipulators. Each translational contribution is factorized into a classical metric magnitude and a signed unit direction encoded by a single-qubit Bloch vector, while parameterized rotations reproduce the ordered propagation of frame directions. A selector register prepares probabilities proportional to the contribution magnitudes, and the reduced state of a designated readout qubit encodes their normalized weighted sum. The retained classical scale then reconstructs the metric end-effector position. Two additional readout qubits encode terminal-frame axes, providing a compact and geometrically interpretable pose interface. At the ideal expectation-value level, measured Pauli observables reproduce the corresponding classical kinematic quantities. Alternative circuit architectures realize the same representation with different tradeoffs in qubit count, circuit depth, controlled operations, and measurement requirements. Validation on a serial manipulator yields numerically negligible position and orientation reconstruction errors under ideal simulation. Finite-shot simulations, noisy executions, transpilation analysis, and a hardware demonstration further characterize statistical error, noise sensitivity, and implementation overhead without asserting computational advantage.

We present a theory for the previously unexplained divergent behavior noticed in the training of large language models. We argue that the phenomenon is an artifact of the dominant optimization algorithm used for training, called Adam. We observe that Adam can enter a state in which the parameter update vector has a relatively large norm and is essentially uncorrelated with the direction of descent on the training loss landscape, leading to divergence. This artifact is more likely to be observed in the training of a deep model with a large batch size, which is the typical setting of large-scale language model training. To argue the theory, we present observations from the training runs of the language models of different scales: 7 billion, 30 billion, 65 billion, and 546 billion parameters.

3D Gaussian Splatting (3DGS) has emerged as a key rendering pipeline for digital asset creation due to its balance between efficiency and visual quality. To address the issues of unstable pose estimation and scene representation distortion caused by geometric texture inconsistency in large outdoor scenes with weak or repetitive textures, we approach the problem from two aspects: pose estimation and scene representation. For pose estimation, we leverage LiDAR-IMU Odometry to provide prior poses for cameras in large-scale environments. These prior pose constraints are incorporated into COLMAP's triangulation process, with pose optimization performed via bundle adjustment. Ensuring consistency between pixel data association and prior poses helps maintain both robustness and accuracy. For scene representation, we introduce normal vector constraints and effective rank regularization to enforce consistency in the direction and shape of Gaussian primitives. These constraints are jointly optimized with the existing photometric loss to enhance the map quality. We evaluate our approach using both public and self-collected datasets. In terms of pose optimization, our method requires only one-third of the time while maintaining accuracy and robustness across both datasets. In terms of scene representation, the results show that our method significantly outperforms conventional 3DGS pipelines. Notably, on self-collected datasets characterized by weak or repetitive textures, our approach demonstrates enhanced visualization capabilities and achieves superior overall performance. Codes and data will be publicly available at https://github.com/justinyeah/normal_shape.git.

Parameter-efficient fine-tuning (PEFT) is a standard way to adapt multimodal large language models, yet extremely low-rank settings -- especially rank-1 LoRA -- are often unstable. We show that this instability is not solely due to limited capacity: in the rank-1 regime, optimization is highly sensitive to the update direction. Concretely, pretrained vision and text features form mismatched anisotropic regions, yielding a dominant "gap" direction that acts like a translation component and disproportionately steers early gradients under rank-1 constraints. Analyzing pretrained representations, we identify a modality-gap axis that dominates early gradient flow, while a random rank-1 initialization is unlikely to align with it, leading to weak gradients and training collapse. We propose Gap-Init, a geometry-aware initialization that aligns the rank-1 LoRA direction with an estimated modality-gap vector from a small calibration set, while keeping the initial LoRA update zero. Across multiple vision-language tasks and backbones, Gap-Init consistently stabilizes rank-1 training and can match or outperform strong rank-8 baselines. Our results suggest that at the extreme low-rank limit, initial alignment can matter as much as rank itself.

A critical approach for efficiently deploying computationally demanding large language models (LLMs) is Key-Value (KV) caching. The KV cache stores key-value states of previously generated tokens, significantly reducing the need for repetitive computations and thereby lowering latency in autoregressive generation. However, the size of the KV cache grows linearly with sequence length, posing challenges for applications requiring long context input and extensive sequence generation. In this paper, we present a simple yet effective approach, called MiniCache, to compress the KV cache across layers from a novel depth perspective, significantly reducing the memory footprint for LLM inference. Our approach is based on the observation that KV cache states exhibit high similarity between the adjacent layers in the middle-to-deep portion of LLMs. To facilitate merging, we propose disentangling the states into the magnitude and direction components, interpolating the directions of the state vectors while preserving their lengths unchanged. Furthermore, we introduce a token retention strategy to keep highly distinct state pairs unmerged, thus preserving the information with minimal additional storage overhead. Our MiniCache is training-free and general, complementing existing KV cache compression strategies, such as quantization and sparsity. We conduct a comprehensive evaluation of MiniCache utilizing various models including LLaMA-2, LLaMA-3, Phi-3, Mistral, and Mixtral across multiple benchmarks, demonstrating its exceptional performance in achieving superior compression ratios and high throughput. On the ShareGPT dataset, LLaMA-2-7B with 4-bit MiniCache achieves a remarkable compression ratio of up to 5.02x, enhances inference throughput by approximately 5x, and reduces the memory footprint by 41% compared to the FP16 full cache baseline, all while maintaining near-lossless performance.

In the era of large foundation models, the quality of embeddings has become a central determinant of downstream task performance and overall system capability. Yet widely used dense embeddings are often extremely high-dimensional, incurring substantial costs in storage, memory, and inference latency. To address these, Contrastive Sparse Representation (CSR) is recently proposed as a promising direction, mapping dense embeddings into high-dimensional but k-sparse vectors, in contrast to compact dense embeddings such as Matryoshka Representation Learning (MRL). Despite its promise, CSR suffers severe degradation in the ultra-sparse regime, where over 80% of neurons remain inactive, leaving much of its efficiency potential unrealized. In this paper, we introduce CSRv2, a principled training approach designed to make ultra-sparse embeddings viable. CSRv2 stabilizes sparsity learning through progressive k-annealing, enhances representational quality via supervised contrastive objectives, and ensures end-to-end adaptability with full backbone finetuning. CSRv2 reduces dead neurons from 80% to 20% and delivers a 14% accuracy gain at k=2, bringing ultra-sparse embeddings on par with CSR at k=8 and MRL at 32 dimensions, all with only two active features. While maintaining comparable performance, CSRv2 delivers a 7x speedup over MRL, and yields up to 300x improvements in compute and memory efficiency relative to dense embeddings in text representation. Extensive experiments across text and vision demonstrate that CSRv2 makes ultra-sparse embeddings practical without compromising performance, where CSRv2 achieves 7%/4% improvement over CSR when k=4 and further increases this gap to 14%/6% when k=2 in text/vision representation. By making extreme sparsity viable, CSRv2 broadens the design space for real-time and edge-deployable AI systems where both embedding quality and efficiency are critical.

Reinforcement learning from verifiable rewards (RLVR) has emerged as a central technique for improving the reasoning capabilities of large language models. Despite its effectiveness, how response-level rewards translate into token-level probability changes remains poorly understood. We introduce a discriminator view of RLVR updates, showing that the policy-gradient update direction implicitly acts as a linear discriminator over token-gradient vectors and thereby determines which token probabilities are increased or decreased during learning. Under standard sequence-level RLVR, this discriminator is constructed from positive- and negative-side centroids formed by advantage-weighted averaging of token-gradient vectors. However, such centroid construction can be dominated by shared high-frequency patterns, such as formatting tokens, diluting sparse yet discriminative directions that better distinguish high-reward responses from low-reward ones. To address this limitation, we propose DelTA, a discriminative token credit assignment method that estimates token coefficients to amplify side-specific token-gradient directions and downweight shared or weakly discriminative ones. These coefficients reweight a self-normalized RLVR surrogate, making the effective side-wise centroids more contrastive and thereby reshaping the RLVR update direction. On seven mathematical benchmarks, DelTA outperforms the strongest same-scale baselines by 3.26 and 2.62 average points on Qwen3-8B-Base and Qwen3-14B-Base, respectively. Additional results on code generation, a different backbone, and out-of-domain evaluations further demonstrate the generalization ability of DelTA.

Backdoor attacks can be implanted in Large Language Models (LLMs) during training, causing unwanted behaviour when a trigger appears in the input. Existing backdoor defences for LLMs attempt to remove the backdoor but inadvertently shift the model's output distribution to benign prompts, which can result in degraded model performance and safety. We propose NEEDLE, a training-free method for targeted backdoor removal. Once a trigger has been identified, our method estimates a backdoor direction and a refusal subspace through activation vectors, then applies sequential weight orthogonalisation to suppress the backdoor while preventing changes in refusal-related representations. NEEDLE requires neither a clean reference model nor the original poisoned training data. Evaluation is conducted across multiple model families and attack types. NEEDLE achieves the lowest mean Attack Success Rate (ASR) among the evaluated defences, including 0% on challenging code injection attacks, while resulting in the lowest KL divergence and minimal changes in capability and safety.

While open-weight models have enjoyed steady progress in capabilities and wide adoption across multiple domains, their safety remains an important concern. One key feature is the ability to refuse or deflect harmful, malicious, or insensitive prompts. In this paper, we expose safety vulnerabilities across six common open-weight LLMs of various sizes that consistently lead to harmful or unsafe responses on the JailbreakBench benchmark dataset. Our proposed attack, Perturbed Embedding Vector (PEV), is a simple and fast "jailbreaking" technique that is cheaper than prior approaches, which typically require gradient computations, per-prompt optimizations, or altering internal weights of the models. PEV just adds independent Gaussian noise in the embedding vector representations of the prompt, with no need for further manipulations. To generate unsafe responses, we repeatedly sample additive noise from this distribution. In our experiments, we observe that the average compute cost to get the first successful attack is up to an order of magnitude less than previous attacks. The first successful jailbreak on a new prompt typically arrives within one minute on every tested model, and PEV generates unsafe responses across all models for all prompts in JailbreakBench. No other tested method achieves such results, despite them taking longer to run. More broadly, we believe that understanding the behavior of LLMs under perturbations in the embedding vectors is an important research direction: while perturbations constitute a major security risk, they can also serve as a valuable tool for exploring the dynamical behavior of such models.

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar link function. Learning this model with SGD is relatively well-understood, whereby the so-called information exponent of the link function governs a polynomial sample complexity rate. However, extending this analysis to deeper or more complicated architectures remains challenging. In this work, we consider single index learning in the setting of symmetric neural networks. Under analytic assumptions on the activation and maximum degree assumptions on the link function, we prove that gradient flow recovers the hidden planted direction, represented as a finitely supported vector in the feature space of power sum polynomials. We characterize a notion of information exponent adapted to our setting that controls the efficiency of learning.

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.

Machine unlearning aims to selectively remove specific knowledge from a trained model. Existing approaches, such as Task Arithmetic, fine-tune the model on the forget set to create a task vector (i.e., a direction in weight space) for subtraction from the original model's weight. However, their effectiveness is highly sensitive to hyperparameter selection, requiring extensive validation to identify the optimal vector from many fine-tuned candidates. In this paper, we propose a novel method that utilizes all fine-tuned models trained with varying hyperparameters instead of a single selection. Specifically, we aggregate the computed task vectors by retaining only the elements with consistent shared signs. The merged task vector is then negated to induce unlearning on the original model. Evaluations on zero-shot and standard image recognition tasks across twelve datasets and four backbone architectures show that our approach outperforms state-of-the-art methods while requiring similar or fewer computational resources. Code is available at https://github.com/naver-ai/negmerge.

Image-based surface reconstruction and characterization is crucial for missions to small celestial bodies, as it informs mission planning, navigation, and scientific analysis. However, current state-of-the-practice methods, such as stereophotoclinometry (SPC), rely heavily on human-in-the-loop verification and high-fidelity a priori information. This paper proposes Photoclinometry-from-Motion (PhoMo), a novel framework that incorporates photoclinometry techniques into a keypoint-based structure-from-motion (SfM) system to estimate the surface normal and albedo at detected landmarks to improve autonomous surface and shape characterization of small celestial bodies from in-situ imagery. In contrast to SPC, we forego the expensive maplet estimation step and instead use dense keypoint measurements and correspondences from an autonomous keypoint detection and matching method based on deep learning. Moreover, we develop a factor graph-based approach allowing for simultaneous optimization of the spacecraft's pose, landmark positions, Sun-relative direction, and surface normals and albedos via fusion of Sun vector measurements and image keypoint measurements. The proposed framework is validated on real imagery taken by the Dawn mission to the asteroid 4 Vesta and the minor planet 1 Ceres and compared against an SPC reconstruction, where we demonstrate superior rendering performance compared to an SPC solution and precise alignment to a stereophotogrammetry (SPG) solution without relying on any a priori camera pose and topography information or humans-in-the-loop.

Fine-tuning large language models (LLMs) on domain-specific datasets has become a standard paradigm for adapting LLMs to specialized applications. However, recent work has shown that even fine-tuning on benign task-specific data can substantially weaken the safety capabilities of LLMs. While existing efforts have made progress in identifying data responsible for safety degradation, they usually rely on a single mean vector computed over a specific model with its tokenizer to represent the safety direction, which limits both the effectiveness and transferability of their risk assessment measures. To address these limitations, we propose DataShield, a data assessment framework that identifies risky fine-tuning samples and response segments through consensus subspace alignment over joint safety-critical semantic spaces derived from multiple safety-aligned LLMs. Within these spaces, DataShield extracts consensus safe and unsafe subspaces using semantic spectral decomposition over safe and unsafe data representations. The risk of a data sample or segment is then estimated by measuring its relative alignment with the unsafe and safe subspaces, enabling both sample-level filtering and fine-grained segment-level masking. Compared with state-of-the-art filtering and masking baselines, DataShield reduces ASR by 14.6\% with sample filtering and 32.3\% with segment masking, while preserving downstream utility and avoiding target-model-specific risk computation.

Generative modeling of graph-structured data is crucial for tasks ranging from drug discovery to social network simulation. Among these models, denoising diffusion models have achieved great success in graph generation by learning to progressively reverse a process that adds noise to the original graph. However, the standard noise-prediction approach of diffusion models is suboptimal for graph data. The goal for a graph generative model is to learn the clean graphs' topological properties, such as connectivity and degree distribution. Because a diffusion model that predicts noise does not explicitly learn these topological properties, it is challenging for the model to output graphs with the desired structural statistics. To address this challenge, we introduce Direct Graph Flow Matching (DiGFM), a novel graph transformer model guided by two goals: predict clean graphs and improve sampling efficiency. Distinct from the prevailing diffusion approach, DiGFM employs a continuous flow-matching paradigm and integrates direct graph prediction. Specifically, DiGFM maps the prior noise distribution to the clean graph distribution via a multi-step process: the model repeatedly predicts the underlying clean graph, and a transformation is employed to convert the model output to the velocity vector that points in the direction toward the clean graph distribution. This design enables DiGFM to generate high-quality samples using only 2.5% to 15.6% of the steps required by diffusion-based models, which leads to a 5.3x to 257x speedup in wall-clock inference time. Experiments demonstrate that DiGFM outperforms or matches prior state-of-the-art models across general graph benchmarks and molecular datasets, generating graphs with strong adherence to ground-truth structural statistics at significantly faster inference speeds.

This paper describes a novel nonparametric model for modeling diffusion MRI signals in q-space. In q-space, diffusion MRI signal is measured for a sequence of magnetic strengths (b-values) and magnetic gradient directions (b-vectors). We propose a Poly-RBF model, which employs a bidirectional framework with polynomial bases to model the signal along the b-value direction and Gaussian radial bases across the b-vectors. The model can accommodate sparse data on b-values and moderately dense data on b-vectors. The utility of Poly-RBF is inspected for two applications: 1) prediction of the dMRI signal, and 2) harmonization of dMRI data collected under different acquisition protocols with different scanners. Our results indicate that the proposed Poly-RBF model can more accurately predict the unmeasured diffusion signal than its competitors such as the Gaussian process model in {\tt Eddy} of FSL. Applying it to harmonizing the diffusion signal can significantly improve the reproducibility of derived white matter microstructure measures.

The rapid development of large language models has revolutionized natural language processing, but their fine-tuning remains computationally expensive, hindering broad deployment. Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, have emerged as solutions. Recent work like DoRA attempts to further decompose weight adaptation into direction and magnitude components. However, existing formulations often define direction heuristically at the column level, lacking a principled geometric foundation. In this paper, we propose MAP, a novel framework that reformulates weight matrices as high-dimensional vectors and decouples their adaptation into direction and magnitude in a rigorous manner. MAP normalizes the pre-trained weights, learns a directional update, and introduces two scalar coefficients to independently scale the magnitude of the base and update vectors. This design enables more interpretable and flexible adaptation, and can be seamlessly integrated into existing PEFT methods. Extensive experiments show that MAP significantly improves performance when coupling with existing methods, offering a simple yet powerful enhancement to existing PEFT methods. Given the universality and simplicity of MAP, we hope it can serve as a default setting for designing future PEFT methods.

Attention sinks are tokens, often the beginning-of-sequence (BOS) token, that receive disproportionately high attention despite limited semantic relevance. In this work, we identify a class of attention sinks, which we term secondary sinks, that differ fundamentally from the sinks studied in prior works, which we term primary sinks. While prior works have identified that tokens other than BOS can sometimes become sinks, they were found to exhibit properties analogous to the BOS token. Specifically, they emerge at the same layer, persist throughout the network and draw a large amount of attention mass. Whereas, we find the existence of secondary sinks that arise primarily in middle layers and can persist for a variable number of layers, and draw a smaller, but still significant, amount of attention mass. Through extensive experiments across 11 model families, we analyze where these secondary sinks appear, their properties, how they are formed, and their impact on the attention mechanism. Specifically, we show that: (1) these sinks are formed by specific middle-layer MLP modules; these MLPs map token representations to vectors that align with the direction of the primary sink of that layer. (2) The ell_2-norm of these vectors determines the sink score of the secondary sink, and also the number of layers it lasts for, thereby leading to different impacts on the attention mechanisms accordingly. (3) The primary sink weakens in middle layers, coinciding with the emergence of secondary sinks. We observe that in larger-scale models, the location and lifetime of the sinks, together referred to as sink levels, appear in a more deterministic and frequent manner. Specifically, we identify three sink levels in QwQ-32B and six levels in Qwen3-14B.

Non-local (NL) block is a popular module that demonstrates the capability to model global contexts. However, NL block generally has heavy computation and memory costs, so it is impractical to apply the block to high-resolution feature maps. In this paper, to investigate the efficacy of NL block, we empirically analyze if the magnitude and direction of input feature vectors properly affect the attention between vectors. The results show the inefficacy of softmax operation which is generally used to normalize the attention map of the NL block. Attention maps normalized with softmax operation highly rely upon magnitude of key vectors, and performance is degenerated if the magnitude information is removed. By replacing softmax operation with the scaling factor, we demonstrate improved performance on CIFAR-10, CIFAR-100, and Tiny-ImageNet. In Addition, our method shows robustness to embedding channel reduction and embedding weight initialization. Notably, our method makes multi-head attention employable without additional computational cost.

When a language model is fed a wrong answer, what happens inside the network? Current understanding treats truthfulness as a static property of individual-layer representations-a direction to be probed, a feature to be extracted. Less is known about the dynamics: how internal representations diverge across the full depth of the network when the model processes correct versus incorrect continuations. We introduce forced-completion probing, a method that presents identical queries with known correct and incorrect single-token continuations and tracks five geometric measurements across every layer of four decoder-only models(1.5B-13B parameters). We report three findings. First, correct and incorrect paths diverge through rotation, not rescaling: displacement vectors maintain near-identical magnitudes while their angular separation increases, meaning factual selection is encoded in direction on an approximate hypersphere. Second, the model does not passively fail on incorrect input-it actively suppresses the correct answer, driving internal probability away from the right token. Third, both phenomena are entirely absent below a parameter threshold and emerge at 1.6B, suggesting a phase transition in factual processing capability. These results show that factual constraint processing has a specific geometric character-rotational, not scalar; active, not passive-that is invisible to methods based on single-layer probes or magnitude comparisons.

Mixture-of-Experts large language models (LLMs) scale efficiently through sparse activation, yet their deployment is fundamentally constrained by the large static parameter footprint of experts. Existing compression approaches either remove entire experts, disrupting routing topology and harming performance, or rely on unstructured weight pruning with limited practical efficiency. To address the limitations, we propose TENP, a structured Trapezoidal ExpertNeuron Pruning framework. Using a few samples, we identify and retain important experts, while applying expert neuron pruning (ENP) to less important experts, reserving model parameters in a trapezoidal pattern from shallow to deep layers. When evaluating expert importance, we jointly consider both the magnitude of the expert output and its ability to change the direction of the input vector. For ENP, we measure each neuron's projected contribution to the expert output to identify and retain important neurons. We conduct extensive experiments on the Qwen and DeepSeek models. Under a routing expert sparsity of 40% and an average of 63.76% activated expert parameters, the DeepSeek model suffers only a 1-point drop in accuracy compared to the full-parameter model. Moreover, it outperforms the full-parameter model by 10% on code generation tasks.

Textual Inversion (TI) is an efficient approach to text-to-image personalization but often fails on complex prompts. We trace these failures to embedding norm inflation: learned tokens drift to out-of-distribution magnitudes, degrading prompt conditioning in pre-norm Transformers. Empirically, we show semantics are primarily encoded by direction in CLIP token space, while inflated norms harm contextualization; theoretically, we analyze how large magnitudes attenuate positional information and hinder residual updates in pre-norm blocks. We propose Directional Textual Inversion (DTI), which fixes the embedding magnitude to an in-distribution scale and optimizes only direction on the unit hypersphere via Riemannian SGD. We cast direction learning as MAP with a von Mises-Fisher prior, yielding a constant-direction prior gradient that is simple and efficient to incorporate. Across personalization tasks, DTI improves text fidelity over TI and TI-variants while maintaining subject similarity. Crucially, DTI's hyperspherical parameterization enables smooth, semantically coherent interpolation between learned concepts (slerp), a capability that is absent in standard TI. Our findings suggest that direction-only optimization is a robust and scalable path for prompt-faithful personalization.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Activation steering presupposes that task-relevant behaviors correspond to linear directions in activation space -- directions that should both steer the model and be readable along the unembedding. Function vectors (FVs), extracted as mean differences across ICL demonstrations, are the canonical test case; the prediction: steering and decoding succeed or fail together. Across 12 tasks, 6 models from 3 families, and 4,032 directed cross-template pairs, we find the opposite. FV steering routinely succeeds where the logit lens cannot decode the correct answer at any intermediate layer, while the converse -- decodable without steerable -- is nearly empty (3 of 72). The gap is not representational dialect. A diagonal tuned lens closes 1 of 14 steerable-not-decodable cases; a 2-layer MLP probe with a Hewitt \& Liang control closes 5 of 10 via nonlinearly encoded structure but leaves 5 invisible to every decoder tested. Even at > 0.90 steering accuracy, projecting the FV through the unembedding yields incoherent token distributions: FVs encode computational instructions, not answer directions. A model-family asymmetry sharpens the picture. Mistral FVs rewrite intermediate representations, while Llama and Gemma FVs steer the final output without leaving a logit-lens-visible trace, corroborated by three signals (post-steering deltas, activation-patching recovery, FV norm-transfer correlations). A previously reported negative cosine-transfer correlation dissolves at scale, adding at most ΔR^2 = 0.011 beyond task identity. These results decompose the linear representation hypothesis into linear decodability and linear steerability and show they come apart opposite to intuition, with implications for safety monitoring: vocabulary-projection tools are blind to FV-style interventions on widely deployed model families.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

Steering vectors (SVs) have been proposed as an effective approach to adjust language model behaviour at inference time by intervening on intermediate model activations. They have shown promise in terms of improving both capabilities and model alignment. However, the reliability and generalisation properties of this approach are unknown. In this work, we rigorously investigate these properties, and show that steering vectors have substantial limitations both in- and out-of-distribution. In-distribution, steerability is highly variable across different inputs. Depending on the concept, spurious biases can substantially contribute to how effective steering is for each input, presenting a challenge for the widespread use of steering vectors. Out-of-distribution, while steering vectors often generalise well, for several concepts they are brittle to reasonable changes in the prompt, resulting in them failing to generalise well. Overall, our findings show that while steering can work well in the right circumstances, there remain technical difficulties of applying steering vectors to guide models' behaviour at scale. Our code is available at https://github.com/dtch1997/steering-bench

Steering vectors are a promising approach to control the behaviour of large language models. However, their underlying mechanisms remain poorly understood. While sparse autoencoders (SAEs) may offer a potential method to interpret steering vectors, recent findings show that SAE-reconstructed vectors often lack the steering properties of the original vectors. This paper investigates why directly applying SAEs to steering vectors yields misleading decompositions, identifying two reasons: (1) steering vectors fall outside the input distribution for which SAEs are designed, and (2) steering vectors can have meaningful negative projections in feature directions, which SAEs are not designed to accommodate. These limitations hinder the direct use of SAEs for interpreting steering vectors.

Omni-directional (360°) cameras provide embodied agents with a holistic view of their surroundings, making them suited for directional reasoning in tasks such as navigation and object search. Existing Vision Language Models (VLMs) project 360° observations to 2D equirectangular projection (ERP) images and process them using architectures designed for perspective images. However, they ignore the spherical nature of 360° observations, where each pixel represents a viewing direction relative to the agent. Consequently, their direction estimates often become inconsistent under camera view transformations caused by agent motion. This limitation is particularly critical for map-free navigation, where the agent must continuously estimate the target direction in its egocentric frame. We propose EAGOR, a training-free, geometry-aware framework for embodied 360° directional reasoning. Instead of predicting target directions as ERP image coordinates, EAGOR formulates directional reasoning as recursive Bayesian estimation directly on the sphere. It maintains a continuous belief over target directions and propagates it equivariantly under agent motion without training the backbone VLMs. To achieve this, we introduce the Spherical Harmonic Belief Field (SH-BF), whose spherical harmonic representation provides a globally defined, rotation-aware basis for directional estimation on the spherical manifold. This formulation eliminates ERP seam discontinuities, latitude distortions, and interpolation errors. We evaluate EAGOR on two benchmark datasets and real-world experiments with a legged robot across directional reasoning tasks. EAGOR consistently outperforms existing methods, achieving average relative gains of +34.4% and +45.6% on HOS and OSR-Bench, respectively, while improving navigation success by +14.6%, reducing step count by 17.7%, and lowering mean angular error by 24.5%.

Magnetic navigation (MagNav) is a rising alternative to the Global Positioning System (GPS) and has proven useful for aircraft navigation. Traditional aircraft navigation systems, while effective, face limitations in precision and reliability in certain environments and against attacks. Airborne MagNav leverages the Earth's magnetic field to provide accurate positional information. However, external magnetic fields induced by aircraft electronics and Earth's large-scale magnetic fields disrupt the weaker signal of interest. We introduce a physics-informed approach using Tolles-Lawson coefficients for compensation and Liquid Time-Constant Networks (LTCs) to remove complex, noisy signals derived from the aircraft's magnetic sources. Using real flight data with magnetometer measurements and aircraft measurements, we observe up to a 64% reduction in aeromagnetic compensation error (RMSE nT), outperforming conventional models. This significant improvement underscores the potential of a physics-informed, machine learning approach for extracting clean, reliable, and accurate magnetic signals for MagNav positional estimation.

Large Language Models' safety-aligned behaviors, such as refusing harmful queries, can be represented by linear directions in activation space. Previous research modeled safety behavior with a single direction, limiting mechanistic understanding to an isolated safety feature. In this work, we discover that safety-aligned behavior is jointly controlled by multi-dimensional directions. Namely, we study the vector space of representation shifts during safety fine-tuning on Llama 3 8B for refusing jailbreaks. By studying orthogonal directions in the space, we first find that a dominant direction governs the model's refusal behavior, while multiple smaller directions represent distinct and interpretable features like hypothetical narrative and role-playing. We then measure how different directions promote or suppress the dominant direction, showing the important role of secondary directions in shaping the model's refusal representation. Finally, we demonstrate that removing certain trigger tokens in harmful queries can mitigate these directions to bypass the learned safety capability, providing new insights on understanding safety alignment vulnerability from a multi-dimensional perspective. Code and artifacts are available at https://github.com/BMPixel/safety-residual-space.

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

Understanding spatial relations is essential for intelligent agents to act and communicate in the physical world. Relative directions are spatial relations that describe the relative positions of target objects with regard to the intrinsic orientation of reference objects. Grounding relative directions is more difficult than grounding absolute directions because it not only requires a model to detect objects in the image and to identify spatial relation based on this information, but it also needs to recognize the orientation of objects and integrate this information into the reasoning process. We investigate the challenging problem of grounding relative directions with end-to-end neural networks. To this end, we provide GRiD-3D, a novel dataset that features relative directions and complements existing visual question answering (VQA) datasets, such as CLEVR, that involve only absolute directions. We also provide baselines for the dataset with two established end-to-end VQA models. Experimental evaluations show that answering questions on relative directions is feasible when questions in the dataset simulate the necessary subtasks for grounding relative directions. We discover that those subtasks are learned in an order that reflects the steps of an intuitive pipeline for processing relative directions.

Deciding whether to call a tool is a core competence of an LLM agent, and a costly one to get wrong: needless calls add latency, accrue cost, and may trigger irreversible side effects, while missing calls leave the model confidently wrong on questions it could only answer through tool-calls. Models manage this balance poorly, both over-using and under-using tools. Existing methods such as post-training and prompt engineering are expensive and difficult to modify at inference time. We show that whether an instruction-tuned model calls a tool can be controlled by a single linear direction in its residual stream, extracted without any training from the model's own tool-use preference signal and turned into an inference-time intervention with no prompt change. Adding the direction with strength α moves the call rate monotonically from near 0% to over 90% while keeping calls well-formed. The steering works in both directions: dialing it down suppresses calls, and dialing it up induces new calls that land precisely on the questions the model cannot answer from its own knowledge. We also show that the direction generalizes to unseen tools with strength comparable to each tool's own direction and without favoring any specific tool choice. With live tool execution, a single sweep of the steering traces a cost/accuracy Pareto frontier and nearly doubles open-domain QA accuracy (0.29 ! rightarrow ! 0.56); the same recipe transfers across a diverse range of models spanning dense, MoE, and multimodal architectures, without any training. Our code is publicly available at https://github.com/YuqiChen4188/Steering-Tool-Use-Propensity.

Large Language Models (LLMs) often encode whether a statement is true as a vector in their residual stream activations. These vectors, also known as truth vectors, have been studied in prior work, however how they change when context is introduced remains unexplored. We study this question by measuring (1) the directional change (θ) between the truth vectors with and without context and (2) the relative magnitude of the truth vectors upon adding context. Across four LLMs and four datasets, we find that (1) truth vectors are roughly orthogonal in early layers, converge in middle layers, and may stabilize or continue increasing in later layers; (2) adding context generally increases the truth vector magnitude, i.e., the separation between true and false representations in the activation space is amplified; (3) larger models distinguish relevant from irrelevant context mainly through directional change (θ), while smaller models show this distinction through magnitude differences. We also find that context conflicting with parametric knowledge produces larger geometric changes than parametrically aligned context. To the best of our knowledge, this is the first work that provides a geometric characterization of how context transforms the truth vector in the activation space of LLMs.

Recent advances in large language models (LLMs) have intensified the need to understand and reliably curb their harmful behaviours. We introduce a multidimensional framework for probing and steering harmful content in model internals. For each of 55 distinct harmfulness subconcepts (e.g., racial hate, employment scams, weapons), we learn a linear probe, yielding 55 interpretable directions in activation space. Collectively, these directions span a harmfulness subspace that we show is strikingly low-rank. We then test ablation of the entire subspace from model internals, as well as steering and ablation in the subspace's dominant direction. We find that dominant direction steering allows for near elimination of harmfulness with a low decrease in utility. Our findings advance the emerging view that concept subspaces provide a scalable lens on LLM behaviour and offer practical tools for the community to audit and harden future generations of language models.

Recent work in activation steering has demonstrated the potential to better control the outputs of Large Language Models (LLMs), but it involves finding steering vectors. This is difficult because engineers do not typically know how features are represented in these models. We seek to address this issue by applying the idea of mean-centring to steering vectors. We find that taking the average of activations associated with a target dataset, and then subtracting the mean of all training activations, results in effective steering vectors. We test this method on a variety of models on natural language tasks by steering away from generating toxic text, and steering the completion of a story towards a target genre. We also apply mean-centring to extract function vectors, more effectively triggering the execution of a range of natural language tasks by a significant margin (compared to previous baselines). This suggests that mean-centring can be used to easily improve the effectiveness of activation steering in a wide range of contexts.

Model merging is often used to combine capabilities from separately fine-tuned models without additional training, but it is unclear whether standard merging methods preserve multiple safety-relevant behaviors simultaneously. We study this question through a controlled case study using two Gemma-3-1B-IT finetunes on two complementary safety objectives: CARES harm-level classification and WildJailbreak adversarial refusal. We merge the two fine-tunes using Linear, SLERP, TIES, and DARE-TIES, and evaluate the merged models on classification accuracy, attack resistance, and benign compliance. Across all four methods, attack resistance transfers significantly more than classification accuracy: merged models retain 81-85% jailbreak refusal rates while CARES accuracy falls to at most 12.9%. Weight-space measurements suggest that this asymmetry is not caused by strongly opposing task-vector directions: the two task vectors are nearly orthogonal (cosine similarity 0.011). Instead, the refusal fine-tune induces consistently larger per-layer task-vector magnitudes, causing magnitude-sensitive methods to favor refusal updates. These results show that standard model merging can collapse safety recognition into broad refusal when safety-relevant task vectors differ substantially in scale.

This paper introduces the point-axis representation for oriented object detection, emphasizing its flexibility and geometrically intuitive nature with two key components: points and axes. 1) Points delineate the spatial extent and contours of objects, providing detailed shape descriptions. 2) Axes define the primary directionalities of objects, providing essential orientation cues crucial for precise detection. The point-axis representation decouples location and rotation, addressing the loss discontinuity issues commonly encountered in traditional bounding box-based approaches. For effective optimization without introducing additional annotations, we propose the max-projection loss to supervise point set learning and the cross-axis loss for robust axis representation learning. Further, leveraging this representation, we present the Oriented DETR model, seamlessly integrating the DETR framework for precise point-axis prediction and end-to-end detection. Experimental results demonstrate significant performance improvements in oriented object detection tasks.

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization. However, Muon's optimizer state is more sensitive to quantization errors: because the orthogonalization discards the magnitudes of singular values and retains only directional information, even small quantization errors in singular vector directions are amplified in the update. In this work, we propose MuonQ, a low-bit Muon training framework built on the principle of directional fidelity optimization. First, we apply a pre-quantization normalization so that each step introduces quantization errors of the same magnitude, preventing the accumulated error from developing a preferred direction. Second, we introduce a structural decomposition that separately quantizes the dominant singular components via power iteration, ensuring that quantization errors perturb only singular value magnitudes rather than rotating singular vector directions. Third, we adopt μ-law companding quantization to allocate higher resolution to densely packed momentum values, shifting the quantization objective from outlier preservation to dense-region distinguishability. Together, these techniques enable stable 4-bit quantization of Muon's optimizer states. Pre-training experiments on GPT-style and LLaMA-style models demonstrate that MuonQ at 4-bit precision closely matches full-precision Muon in both training loss and downstream task accuracy, while reducing optimizer state memory by up to 7.3 times. Our code is available at https://github.com/YupengSu/MuonQ.

To control the behavior of language models, steering methods attempt to ensure that outputs of the model satisfy specific pre-defined properties. Adding steering vectors to the model is a promising method of model control that is easier than finetuning, and may be more robust than prompting. However, it can be difficult to anticipate the effects of steering vectors produced by almost all existing methods, such as CAA (Panickssery et al., 2024) or the direct use of SAE latents (Templeton et al., 2024). In our work, we address this issue by using SAEs to measure the effects of steering vectors, giving us a method that can be used to understand the causal effect of any steering vector intervention. We use this method for measuring causal effects to develop an improved steering method, SAE-Targeted Steering (SAE-TS), which finds steering vectors to target specific SAE features while minimizing unintended side effects. We show that overall, SAE-TS balances steering effects with coherence better than CAA and SAE feature steering, when evaluated on a range of tasks.

Spatial instruction following has become a crucial requirement for text-to-image (T2I) generation. A common challenge arises when directional expressions are interpreted under different frames of reference. For example, ``the left of'' may refer to the viewer's image coordinates or to the intrinsic orientation of an object, leading to different expected layouts. Existing T2I benchmarks reveal important layout failures, yet they rarely isolate whether models can follow a specified frame of reference when it differs from camera view. To mitigate this gap, we introduce FoR-T2I, a benchmark for evaluating this distinction with 1,200 prompt pairs built from controlled spatial layouts. In each pair, the camera-view (Cam) prompt states the target relation in camera view, while the frame-of-reference (FoR) prompt describes the same target placement through an oriented anchor object. Across 22 closed-source and open-source T2I models, mean final accuracy is 41.8\% lower on FoR prompts than on matched Cam prompts; even the best-performing model achieves only 44.3\% FoR accuracy. This suggests that current models struggle more when the same layout is described through an object's orientation rather than directly in image coordinates. We further analyze this gap by relation type and camera view, compare several training-free prompting and feedback-based mitigation strategies, and propose a VLM-gated rewriting approach that selects rewritten prompts using visual feedback, improving average FoR accuracy from 25.0\% to 29.2\% under the same generation budget.

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere mathbb S^{d-1}. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on mathbb S^{d-1} to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on (mathbb S^{d-1})^L both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.

While researchers are finding concepts represented as linear directions in language models, a bag of linear directions fails to capture relational structure. To better understand this dichotomy, we study a model with known linear representations, but trained in a highly structured domain -- the board game Othello. While the model's internal board-state representation is linearly decodable, we find additional structure in the form of tensor product representations (TPRs). We train TPR probes to recover shared structure amongst the linear probes, yielding a factorization into square-embeddings, color-embeddings, and a binding matrix that composes them to construct the model's board-state representation. We find geometric signatures within the weights of our TPR probe that align with the structure of the board, but perhaps more importantly, that the linear probes can be recovered directly from the parameters of our TPR probe. Our findings suggest that directional representations may be projections of more structured underlying representations.

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.

Recently, steering vectors (SVs) have emerged as an effective and lightweight approach to steer behaviors of large language models (LLMs), among which fine-tuned SVs are more effective than optimization-free ones. However, current approaches to fine-tuned SVs suffer from two limitations. First, they require careful selection of steering factors on a per-SV basis to balance steering effectiveness and generation quality at inference time. Second, they operate as full-sequence SVs (FSSVs), which can sacrifice generation quality regardless of factor selection due to excessive intervention on the model generation process. To address the first limitation, we propose joint training of steering factors and directions, such that post-hoc factor selection is no longer required. Using neural network scaling theory, we find that moderately large initialization sizes and learning rates for steering factors are essential for stability and efficiency of joint training. To tackle the second limitation, we draw inspiration from representation fine-tuning and introduce Prompt-only SV (PrOSV), an SV that intervenes only on a few prompt tokens. Our empirical results show that PrOSV outperforms traditional FSSVs on AxBench when using our joint training scheme. We also find that PrOSV achieves a better tradeoff between general model utility and adversarial robustness than FSSV.

Activation steering -- adding a vector to a model's residual stream to modify its behavior -- is widely used in safety evaluations as if the model cannot detect the intervention. We test this assumption, introducing steering awareness: a model's ability to infer, during its own forward pass, that a steering vector was injected and what concept it encodes. After fine-tuning, seven instruction-tuned models develop strong steering awareness on held-out concepts; the best reaches 95.5% detection, 71.2% concept identification, and zero false positives on clean inputs. This generalizes to unseen steering vector construction methods when their directions have high cosine similarity to the training distribution but not otherwise, indicating a geometric detector rather than a generic anomaly detector. Surprisingly, detection does not confer resistance; on both factual and safety benchmarks, detection-trained models are consistently more susceptible to steering than their base counterparts. Mechanistically, steering awareness arises not from a localized circuit, but from a distributed transformation that progressively rotates diverse injected vectors into a shared detection direction. Activation steering should therefore not be considered an invisible intervention in safety evaluations.

Spatial intelligence is a critical component of embodied AI, promoting robots to understand and interact with their environments. While recent advances have enhanced the ability of VLMs to perceive object locations and positional relationships, they still lack the capability to precisely understand object orientations-a key requirement for tasks involving fine-grained manipulations. Addressing this limitation not only requires geometric reasoning but also an expressive and intuitive way to represent orientation. In this context, we propose that natural language offers a more flexible representation space than canonical frames, making it particularly suitable for instruction-following robotic systems. In this paper, we introduce the concept of semantic orientation, which defines object orientations using natural language in a reference-frame-free manner (e.g., the ''plug-in'' direction of a USB or the ''handle'' direction of a knife). To support this, we construct OrienText300K, a large-scale dataset of 3D models annotated with semantic orientations that link geometric understanding to functional semantics. By integrating semantic orientation into a VLM system, we enable robots to generate manipulation actions with both positional and orientational constraints. Extensive experiments in simulation and real world demonstrate that our approach significantly enhances robotic manipulation capabilities, e.g., 48.7% accuracy on Open6DOR and 74.9% accuracy on SIMPLER.

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against. We train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag, and show that this bidirectionality supplies a measurement-free test-time error signal: rolling forward i steps and then backward i steps must return the model to its start, so the round-trip discrepancy C_i is a self-supervised proxy for the unobservable rollout error: no ensembles, no held-out data, no governing equations, for one extra rollout. We validate on compressible magnetohydrodynamics (MHD), an astrophysical turbulent radiative mixing layer, and natural face videos (CelebV-HQ). On held-out MHD trajectories, C_i ranks rollout error (Spearman 0.91-0.98 at fixed depth; 0.69 pm 0.16 within trajectories), and a simple calibrator fit on training rollouts predicts its magnitude to within 1.14times (68%) and 1.29times (95%) with near-nominal coverage - one nat beyond a depth-only predictor, transferring to all six decoded physical fields. The same signal flags the out-of-distribution Orszag-Tang vortex (AUROC 0.98; 1.0 by depth 10) exactly where sampling-dispersion baselines invert, and it cuts incurred error by 15% at 80% coverage - three times the depth-only baseline. Bidirectional training comes at negative cost, beating direction specialists in both directions, and the backward direction doubles as a fast inverse solver. On LE-PDE-UQ's turbulent Navier-Stokes benchmark, a single bidirectional model reaches accuracy within 1.3times of their ten-model ensemble at a tenth of the training cost, with the best training-free pixel-level calibration. Round-trip consistency turns reversibility into a practical trust signal for generative models.

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.

Steering is a widely used technique for controlling large language models, yet its effects are often unstable and hard to predict. Existing theoretical accounts are largely based on the Linear Representation Hypothesis (LRH). While LRH assumes that concepts can be orthogonalized for lossless control, this idealized mapping fails in real representations and cannot account for the observed unpredictability of steering. By relaxing LRH's orthogonality assumption while preserving linear representations, we show that overlapping concept contributions naturally yield a sample-specific axis-orthogonal structure. We formalize this as the Cylindrical Representation Hypothesis (CRH). In CRH, a central axis captures the main difference between concept absence and presence and drives concept generation. A surrounding normal plane controls steering sensitivity by determining how easily the axis can activate the target concept. Within this plane, only specific sensitive sectors strongly facilitate concept activation, while other sectors can suppress or delay it. While the surrounding normal plane can be reliably identified from difference vectors, the sensitive sector cannot, introducing intrinsic uncertainty at the sector level. This uncertainty provides a principled explanation for why steering outcomes often fluctuate even when using well-aligned directions. Our experiments verify the existence of the cylindrical structure and demonstrate that CRH provides a valid and practical way to interpret model steering behavior in real settings: https://github.com/mbzuai-nlp/CRH.

A Lie group is an old mathematical abstract object dating back to the XIX century, when mathematician Sophus Lie laid the foundations of the theory of continuous transformation groups. As it often happens, its usage has spread over diverse areas of science and technology many years later. In robotics, we are recently experiencing an important trend in its usage, at least in the fields of estimation, and particularly in motion estimation for navigation. Yet for a vast majority of roboticians, Lie groups are highly abstract constructions and therefore difficult to understand and to use. This may be due to the fact that most of the literature on Lie theory is written by and for mathematicians and physicists, who might be more used than us to the deep abstractions this theory deals with. In estimation for robotics it is often not necessary to exploit the full capacity of the theory, and therefore an effort of selection of materials is required. In this paper, we will walk through the most basic principles of the Lie theory, with the aim of conveying clear and useful ideas, and leave a significant corpus of the Lie theory behind. Even with this mutilation, the material included here has proven to be extremely useful in modern estimation algorithms for robotics, especially in the fields of SLAM, visual odometry, and the like. Alongside this micro Lie theory, we provide a chapter with a few application examples, and a vast reference of formulas for the major Lie groups used in robotics, including most jacobian matrices and the way to easily manipulate them. We also present a new C++ template-only library implementing all the functionality described here.

We propose the zero-shot Vision-and-Language Navigation with Collision Mitigation (VLN-CM), which takes these considerations. VLN-CM is composed of four modules and predicts the direction and distance of the next movement at each step. We utilize large foundation models for each modules. To select the direction, we use the Attention Spot Predictor (ASP), View Selector (VS), and Progress Monitor (PM). The ASP employs a Large Language Model (e.g. ChatGPT) to split navigation instructions into attention spots, which are objects or scenes at the location to move to (e.g. a yellow door). The VS selects from panorama images provided at 30-degree intervals the one that includes the attention spot, using CLIP similarity. We then choose the angle of the selected image as the direction to move in. The PM uses a rule-based approach to decide which attention spot to focus on next, among multiple spots derived from the instructions. If the similarity between the current attention spot and the visual observations decreases consecutively at each step, the PM determines that the agent has passed the current spot and moves on to the next one. For selecting the distance to move, we employed the Open Map Predictor (OMP). The OMP uses panorama depth information to predict an occupancy mask. We then selected a collision-free distance in the predicted direction based on the occupancy mask. We evaluated our method using the validation data of VLN-CE. Our approach showed better performance than several baseline methods, and the OPM was effective in mitigating collisions for the agent.

City-scale outdoor navigation is currently hindered by the heavy reliance on dense maps or costly navigation supervision. In this work, we introduce a novel paradigm for leveraging directional instructions from commercial navigation tools (e.g., Google Maps). To bridge the gap between commercial instructions and executable navigation actions, while mitigating long-horizon error accumulation through robust trajectory recovery, we propose DA-Nav, a Direction-Aware vision-language Navigation framework that reformulates navigation as a discrete spatial grounding problem on the egocentric 2D image plane. To achieve trajectory recovery, DA-Nav employs a Chain-of-Thought (CoT) reasoning process encompassing deviation assessment, action prediction, and target grid selection. We further introduce ReDA, a dataset that provides direction-aware instructions and recovery trajectories to enhance spatial grounding and support CoT recovery reasoning. Extensive experiments in CARLA demonstrate that DA-Nav achieves a high success rate of 56.16% in unseen urban environments, outperforming existing State-of-The-Art (SoTA) methods while maintaining a substantially stronger recovery capability. Furthermore, without fine-tuning, DA-Nav seamlessly adapts to both quadruped and humanoid robots, enabling stable kilometer-scale closed-loop outdoor navigation in complex real world environments.

Contrastive steering has been shown as a simple and effective method to adjust the generative behavior of LLMs at inference time. It uses examples of prompt responses with and without a trait to identify a direction in an intermediate activation layer, and then shifts activations in this 1-dimensional subspace. However, despite its growing use in AI safety applications, the robustness of contrastive steering to noisy or adversarial data corruption is poorly understood. We initiate a study of the robustness of this process with respect to corruption of the dataset of examples used to train the steering direction. Our first observation is that contrastive steering is quite robust to a moderate amount of corruption, but unwanted side effects can be clearly and maliciously manifested when a non-trivial fraction of the training data is altered. Second, we analyze the geometry of various types of corruption, and identify some safeguards. Notably, a key step in learning the steering direction involves high-dimensional mean computation, and we show that replacing this step with a recently developed robust mean estimator often mitigates most of the unwanted effects of malicious corruption.

Vision--Language--Action (VLA) models often use intermediate representations to connect multimodal inputs with continuous control, yet spatial guidance is often injected implicitly through latent features. We propose CorridorVLA, which predicts sparse spatial anchors as incremental physical changes (e.g., Δ-positions) and uses them to impose an explicit tolerance region in the training objective for action generation. The anchors define a corridor that guides a flow-matching action head: trajectories whose implied spatial evolution falls outside it receive corrective gradients, while minor deviations from contacts and execution noise are permitted. On the more challenging LIBERO-Plus benchmark, CorridorVLA yields consistent gains across both SmolVLA and GR00T, improving success rate by 3.4%--12.4% over the corresponding baselines; notably, our GR00T-Corr variant reaches a success rate of 83.21%. These results indicate that action-aligned physical cues can provide direct and interpretable constraints for generative action policies, complementing spatial guidance encoded in visual or latent forms. Code is available at https://github.com/corridorVLA.

Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

The Automatic Identification System (AIS) enables data-driven maritime surveillance but suffers from reliability issues and irregular intervals. We address vessel destination estimation using global-scope AIS data by proposing a differentiated approach that recasts long port-to-port trajectories as a nested sequence structure. Using spatial grids, this method mitigates spatio-temporal bias while preserving detailed resolution. We introduce a novel deep learning architecture, WAY, designed to process these reformulated trajectories for long-term destination estimation days to weeks in advance. WAY comprises a trajectory representation layer and Channel-Aggregative Sequential Processing (CASP) blocks. The representation layer generates multi-channel vector sequences from kinematic and non-kinematic features. CASP blocks utilize multi-headed channel- and self-attention for aggregation and sequential information delivery. Additionally, we propose a task-specialized Gradient Dropout (GD) technique to enable many-to-many training on single labels, preventing biased feedback surges by stochastically blocking gradient flow based on sample length. Experiments on 5-year AIS data demonstrate WAY's superiority over conventional spatial grid-based approaches regardless of trajectory progression. Results further confirm that adopting GD leads to performance gains. Finally, we explore WAY's potential for real-world application through multitask learning for ETA estimation.

Steering aligns large language models (LLMs) by injecting a bias into selected activations at inference time, offering a far cheaper alternative to weight-update methods such as supervised fine-tuning or reinforcement learning. However, most existing training-free steering methods are input-independent: a single direction is fitted once and shared across all inputs. This is fundamentally limiting as different inputs occupy different regions of the activation space and admit different optimal steering directions toward the same target concept, much as the gradient with respect to a fixed loss varies from input to input. We close this gap with IDEEA (Input-Dependent stEEring via Activation cluster matching), a training-free framework for input-dependent steering. IDEEA clusters the positive and negative activation supports per attention head, and solves an optimal-matching problem to construct a set of cluster-conditional directions, all about the target concept. At inference time, it picks from this pool of directions and uses the one that best matches the input's own activation for steering. IDEEA aligns the model toward the target concept while preserving the input's original representation, evidence that activations encoding a concept occupy several distinct sub-regions of the representation space rather than a single one. IDEEA improves the truth times info rate in TruthfulQA by an average of 9.9% (up to 23.5%) over the best input-independent baseline.

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

How strongly do the remaining diffusion-sampling steps amplify a perturbation at a late latent state? Standard measurements answer this question with newly sampled isotropic noise, even though perturbations encountered during sampling have already been transformed by earlier steps. We compare these two cases directly. For each trajectory, we transport a centered perturbation from an earlier step to a late state, then replay its direction at the same magnitude as a newly sampled isotropic perturbation; both then undergo the same remaining updates. Across the samplers we study, median paired shaped-to-fresh angular-gain ratios range from 1.14 to 2.35. Shaped angular gain exceeds its matched fresh counterpart in every trajectory in the original main cohorts. The same pattern appears when endpoint change is measured by latent RMS. The effect also appears in perceptual feature representations: earlier-sampling directions cause larger feature changes at the endpoint, even when the corresponding pixel-space change is comparable. Permuting shaped directions across trajectories weakens the effect, including within class, indicating that the advantage depends on alignment with the receiving trajectory as well as on shared directional structure.

This work presents a novel online model-predictive trajectory planner for robotic manipulators called BoundMPC. This planner allows the collision-free following of Cartesian reference paths in the end-effector's position and orientation, including via-points, within desired asymmetric bounds of the orthogonal path error. The path parameter synchronizes the position and orientation reference paths. The decomposition of the path error into the tangential direction, describing the path progress, and the orthogonal direction, which represents the deviation from the path, is well known for the position from the path-following control in the literature. This paper extends this idea to the orientation by utilizing the Lie theory of rotations. Moreover, the orthogonal error plane is further decomposed into basis directions to define asymmetric Cartesian error bounds easily. Using piecewise linear position and orientation reference paths with via-points is computationally very efficient and allows replanning the pose trajectories during the robot's motion. This feature makes it possible to use this planner for dynamically changing environments and varying goals. The flexibility and performance of BoundMPC are experimentally demonstrated by two scenarios on a 7-DoF Kuka LBR iiwa 14 R820 robot. The first scenario shows the transfer of a larger object from a start to a goal pose through a confined space where the object must be tilted. The second scenario deals with grasping an object from a table where the grasping point changes during the robot's motion, and collisions with other obstacles in the scene must be avoided.