Traversing the solution space of neural networks with Hessian Null Space Continuation
20d
- Published
- Collected
Authors
Ann Huang, Mitchell Ostrow, Zhouyang Lu, William T. Redman, Leo Kozachkov, Kanaka Rajan
Categories
On a single task, deep networks can learn many solutions, depending on their optimizer, training data, architecture, and hyperparameters. Many of these solutions are mode-connected: rather than isolated points in weight space, they are connected by low-loss regions. Yet how their internal computation varies within these regions is unknown. A parallel line of work has identified the degeneracy of neural representations: many networks reach similar training loss with distinct internal structures. However, it is unclear how these solutions are related in weight space. We unify these subfields and show for the first time that many different internal mechanisms exist within a local mode-connected region in weight space. To do so, we introduce Hessian Null Space Continuation (HNC), a scalable method that uses local curvature to traverse regions of weight space that preserve network function, and can be steered toward solutions with specified properties. In RNNs trained on a memory task, HNC reaches drastically different representations and dynamics with maintained behavior. In ImageNet-trained Vision Transformers, HNC finds representations that differ more from the original network than any independently trained model with a different architecture or objective. In reinforcement-learning agents, HNC uncovers a distinct navigation strategy at comparable return and exposes reward hacking in an AI Safety Gridworld. Finally, HNC measures the local geometry of the solution set, showing how model size and task complexity shape its dimension and functional sensitivity. Our results show that a surprisingly large amount of representational diversity exists near a single trained solution, unseen by standard gradient-based optimization. HNC identifies and quantifies this diversity, opening new possibilities for mechanistic understanding of solution spaces and for model merging, editing, and fine-tuning.
overfeed.news indexes and links. We publish a short excerpt — the full article stays at arXiv AI Papers.
More from arXiv AI Papers
Log in to follow this source
Text-to-Image Generative Modeling Without Language Pretraining
Modern text-to-image (T2I) systems use internet-scale language pretraining for text-conditioned image generation. We ask whether language pretraining is necessary for strong T2I generation. We introduce Halcyon, a family of early-fusion multimodal autoregressive models pretrained entirely from scratch on GPIC, a dataset of 100M image-text pairs. Halcyon-0.52B outperforms LlamaGen-XL/8 (48.0 vs. 63.3 gFD) with 18.2less pretraining compute. Further, Halcyon-1.6B outperforms JiT-T2I-XXL/8++ (35.3 vs. 41.0 gFD) with 275less pretraining compute. Controlled experiments show that text-only pretraining does not improve T2I generation. Halcyon also learns image captioning by replacing caption dropout with I2T supervision, maintaining competitive T2I generation quality under the same pretraining budget. We show that strong T2I systems can be trained from scratch without internet-scale language pretraining. Code and models are available at https://cs.stanford.edu/~keshik/halcyon
Can It Actually Work? Synthesizing Functional CAD Mechanisms
While LLM agents can generate visually plausible CAD assemblies, these designs often fail to fulfill their intended physical functions. We study functional CAD design, a setting where agents interpret underspecified requests to construct and iteratively revise mechanisms that satisfy functional requirements in physical simulation. Verifying these requirements is nontrivial: different candidate mechanisms may realize the same function through entirely different components, controls, and operating sequences. To bridge this gap, we propose FunCAD-Harness, a framework that translates abstract requirements into candidate-specific physical tests and uses simulation feedback to guide design revisions. To systematically evaluate this capability, we introduce FunCADBench, a benchmark spanning 46 mechanism families with interdependent and multi-step operations. Experiments across frontier LLM agents show that FunCAD-Harness exposes subtle mechanical failures invisible to visual inspection, substantially improving functional success rates over standard simulation-augmented baselines. Ultimately, our work marks a step toward CAD agents capable of translating human intent into working mechanisms.
OpenVLHarness: Real World Visual Agentic Tool-Use with Multimodal Memory
Multimodal large language models (MLLMs) have made rapid progress on visual reasoning, yet many tasks require evidence that is difficult to obtain through internal reasoning alone: our controlled study on 22 benchmarks shows that simply increasing the inference budget of the base model yields only modest gains. Such tasks demand grounded perception, external knowledge, and numerical measurements obtained through heterogeneous tools, whose outputs must be made interpretable to the model and retained across reasoning steps. We introduce OpenVLHarness, a multimodal reasoning harness organized around a capability layer and persistent multimodal memory. The capability layer combines task-level tool interfaces with evidence rendering, providing consistent access to heterogeneous backends and converting their outputs into model-readable observations. Persistent multimodal memory retains the corresponding images, structured data, and web references as addressable artifacts throughout each query. A coding interface executes generated programs over stored data, enabling computations that combine results from multiple tools. Together, these mechanisms support an iterative process of acquiring, inspecting, and composing multimodal evidence. Evaluated on 22 benchmarks with eight open and proprietary backbones, OpenVLHarness improves average scores by 9.7-12.6 points over matched no-tool baselines, including +11.2 with Qwen3-VL-8B, +9.7 with Kimi K3, and +9.9 with GPT-6 Astra. With GPT-6 Luna at medium reasoning effort, OpenVLHarness outperforms the base model, Codex, and Visual Sketchpad at maximum effort by 7.7-8.5 points while incurring at most 37% of their model-token cost.
Reinforcement Learning with Visually Attributable On-Policy Self-Distillation
Multimodal reinforcement learning with verifiable rewards (RLVR) provides reliable task-level supervision, yet offers limited guidance for localizing errors in visual reasoning. On-policy self-distillation (OPSD) complements this supervision with dense token-level corrections from a privileged teacher equipped with an evidence-centered visual view. However, the resulting corrections may conflate visual evidence with non-visual shifts induced by linguistic priors, response style, or the privileged view itself. We formalize this phenomenon as privileged-correction contamination: a token-level correction is contaminated when its update direction cannot be consistently attributed to the privileged visual evidence. Directly distilling contaminated corrections may therefore reinforce erroneous token-level updates. To address this issue, we propose reinforcement learning with visually attributable on-policy self-distillation, an evidence-consistent paradigm that augments task-level RLVR supervision with privileged token-level corrections grounded in visual evidence. We instantiate this paradigm with Visual-Attribution Gating (VAG), which uses the verifier-derived advantage as the optimization anchor and validates each privileged correction against the contrast between evidence-present and evidence-degraded teacher views. By admitting only corrections directionally supported by this visual contrast, VAG preserves visually grounded guidance while suppressing inconsistent residuals. Experiments across six visual reasoning benchmarks show that VAG consistently outperforms GRPO and OPSD methods, establishing new state-of-the-art average performance.