J. Elisenda Grigsby

J. Elisenda Grigsby, Kathryn Lindsey, David Rolnick

The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? It is known that many different parameter settings can determine the same function. Moreover, the degree of this redundancy is inhomogeneous: for some networks, the only symmetries are permutation of neurons in a layer and positive scaling of parameters at a neuron, while other networks admit additional hidden symmetries. In this work, we prove that, for any network architecture where no layer is narrower than the input, there exist parameter settings with no hidden symmetries. We also describe a number of mechanisms through which hidden symmetries can arise, and empirically approximate the functional dimension of different network architectures at initialization. These experiments indicate that the probability that a network has no hidden symmetries decreases towards 0 as depth increases, while increasing towards 1 as width and input dimension increase.

J. Elisenda Grigsby, Kathryn Lindsey, Robert Meyerhoff et al.

It is well-known that the parameterized family of functions representable by fully-connected feedforward neural networks with ReLU activation function is precisely the class of piecewise linear functions with finitely many pieces. It is less well-known that for every fixed architecture of ReLU neural network, the parameter space admits positive-dimensional spaces of symmetries, and hence the local functional dimension near any given parameter is lower than the parametric dimension. In this work we carefully define the notion of functional dimension, show that it is inhomogeneous across the parameter space of ReLU neural network functions, and continue an investigation - initiated in [14] and [5] - into when the functional dimension achieves its theoretical maximum. We also study the quotient space and fibers of the realization map from parameter space to function space, supplying examples of fibers that are disconnected, fibers upon which functional dimension is non-constant, and fibers upon which the symmetry group acts non-transitively.

J. Elisenda Grigsby, Kathryn Lindsey, Marissa Masden

We apply a generalized piecewise-linear (PL) version of Morse theory due to Grunert-Kuhnel-Rote to define and study new local and global notions of topological complexity for fully-connected feedforward ReLU neural network functions, F: R^n -> R. Along the way, we show how to construct, for each such F, a canonical polytopal complex K(F) and a deformation retract of the domain onto K(F), yielding a convenient compact model for performing calculations. We also give a construction showing that local complexity can be arbitrarily high.

Thai Hoang, Kung-Hsiang Huang, Shirley Kokane et al. · salesforce, stanford

Large Action Models (LAMs) for AI Agents offer incredible potential but face challenges due to the need for high-quality training data, especially for multi-steps tasks that involve planning, executing tool calls, and responding to feedback. To address these issues, we present LAM SIMULATOR, a comprehensive framework designed for online exploration of agentic tasks with high-quality feedback. Our framework features a dynamic task query generator, an extensive collection of tools, and an interactive environment where Large Language Model (LLM) Agents can call tools and receive real-time feedback. This setup enables LLM Agents to explore and solve tasks autonomously, facilitating the discovery of multiple approaches to tackle any given task. The resulting action trajectory data are then used to create high-quality training datasets for LAMs. Our experiments on popular agentic benchmarks, ToolBench and CRMArena, highlight the effectiveness of LAM SIMULATOR: models trained with self-generated datasets using our framework achieve significant performance gains, up to a 49.3\% improvement over their original baselines. LAM SIMULATOR requires minimal human input during dataset creation, highlighting LAM SIMULATOR's efficiency and effectiveness in speeding up development of AI agents.

Jake Grigsby, Yuke Zhu, Michael Ryoo et al. · salesforce, stanford

Recent research looks to harness the general knowledge and reasoning of large language models (LLMs) into agents that accomplish user-specified goals in interactive environments. Vision-language models (VLMs) extend LLMs to multi-modal data and provide agents with the visual reasoning necessary for new applications in areas such as computer automation. However, agent tasks emphasize skills where accessible open-weight VLMs lag behind their LLM equivalents. For example, VLMs are less capable of following an environment's strict output syntax requirements and are more focused on open-ended question answering. Overcoming these limitations requires supervised fine-tuning (SFT) on task-specific expert demonstrations. Our work approaches these challenges from an offline-to-online reinforcement learning (RL) perspective. RL lets us fine-tune VLMs to agent tasks while learning from the unsuccessful decisions of our own model or more capable (larger) models. We explore an off-policy RL solution that retains the stability and simplicity of the widely used SFT workflow while allowing our agent to self-improve and learn from low-quality datasets. We demonstrate this technique with two open-weight VLMs across three multi-modal agent domains.

J. Elisenda Grigsby, Kathryn Lindsey

For any fixed feedforward ReLU neural network architecture, it is well-known that many different parameter settings can determine the same function. It is less well-known that the degree of this redundancy is inhomogeneous across parameter space. In this work, we discuss two locally applicable complexity measures for ReLU network classes and what we know about the relationship between them: (1) the local functional dimension [14, 18], and (2) a local version of VC dimension that we call persistent pseudodimension. The former is easy to compute on finite batches of points; the latter should give local bounds on the generalization gap, which would inform an understanding of the mechanics of the double descent phenomenon [7].

J. Elisenda Grigsby, Kathryn Lindsey

Let F:R^n -> R be a feedforward ReLU neural network. It is well-known that for any choice of parameters, F is continuous and piecewise (affine) linear. We lay some foundations for a systematic investigation of how the architecture of F impacts the geometry and topology of its possible decision regions for binary classification tasks. Following the classical progression for smooth functions in differential topology, we first define the notion of a generic, transversal ReLU neural network and show that almost all ReLU networks are generic and transversal. We then define a partially-oriented linear 1-complex in the domain of F and identify properties of this complex that yield an obstruction to the existence of bounded connected components of a decision region. We use this obstruction to prove that a decision region of a generic, transversal ReLU network F: R^n -> R with a single hidden layer of dimension (n + 1) can have no more than one bounded connected component.