Unlike distance metric learning where the subsequent tasks utilizing the estimated distance metric is the usual focus, the proposal focuses on the estimated metric characterizing the geometry structure. Despite the illustrated taxi and MNIST examples, it is still open to finding more compelling applications that target the data space geometry. Interpreting mathematical concepts such as Riemannian metric and geodesic in the context of potential application (e.g., cognition and perception research where similarity measures are common) could be inspiring. Our proposal requires sufficiently dense data, which could be demanding, especially for high-dimensional data due to the curse of dimensionality. Dimensional reduction (e.g., manifold embedding as in the MNIST example) can substantially alleviate the curse of dimensionality, and the dense data requirement will more likely hold true.

In each communication round, each client uniformly samples points in the neighborhood of their projected point (top-right plot), and jointly train the solution simplex.

Liu et al. [2018] first showed that stationary importance sampling methods can be viewed as Rao-Blackwellization of IS estimator, and claimed that the expectation of the likelihood-ratios conditioned on state and action is equal to the distribution ratio, as stated in Property 1. For completeness, we present a proof of Property 1. Recall that d This gives us the expression " This additional marginalization step over time allows us to consider time-independent distribution ratios. Then, using the law of total expectation, we can write the expectation of the second sum in (4) as: " Assumption 1. Plugging in the final expression from (5) back into (4) gives us " Note that in the infinite horizon setting where L!1and for finite n, (6) becomes " Similarly, by generalizing this pattern it can be observed that on unrolling n times, we will get, 1 " 0 X For all experiments, we utilize the domains and algorithm implementations from Caltech OPE Benchmarking Suite (COBS) library by Voloshin et al. [2019]. We include a brief description of each of these domains below, and a full description of each can be found in the work by Voloshin et al. [2019]. Graph Environment The Graph environment is a two-chain environment with 2L states and 2 actions.

The advancement of large language models (LLMs) is critically dependent on the availability of high-quality datasets for Supervised Fine-Tuning (SFT), alignment tasks like Direct Preference Optimization (DPO), etc. In this work, we present a comprehensive synthetic data generation framework that facilitates scalable, configurable, and high-fidelity generation of synthetic data tailored for these training paradigms. Our approach employs a modular and configuration-based pipeline capable of modeling complex dialogue flows with minimal manual intervention. This framework uses a dual-stage quality tagging mechanism, combining heuristic rules and LLM-based evaluations, to automatically filter and score data extracted from OASST-formatted conversations, ensuring the curation of high-quality dialogue samples. The resulting datasets are structured under a flexible schema supporting both SFT and DPO use cases, enabling seamless integration into diverse training workflows. Together, these innovations offer a robust solution for generating and managing synthetic conversational data at scale, significantly reducing the overhead of data preparation in LLM training pipelines.

Virtual representations of physical critical infrastructures, such as water or energy plants, are used for simulations and digital twins to ensure resilience and continuity of their services. These models usually require 3D point clouds from laser scanners that are expensive to acquire and require specialist knowledge to use. In this article, we present a graph generation pipeline based on photogrammetry. The pipeline detects relevant objects and predicts their relation using RGB images and depth data generated by a stereo camera. This more cost-effective approach uses deep learning for object detection and instance segmentation of the objects, and employs user-defined heuristics or rules to infer their relations. Results of two hydraulic systems show that this strategy can produce graphs close to the ground truth while its flexibility allows the method to be tailored to specific applications and its transparency qualifies it to be used in the high stakes decision-making that is required for critical infrastructures.

We lay the theoretical foundation for automating optimizer design in gradient-based learning. Based on the greedy principle, we formulate the problem of designing optimizers as maximizing the instantaneous decrease in loss. By treating an optimizer as a function that translates loss gradient signals into parameter motions, the problem reduces to a family of convex optimization problems over the space of optimizers. Solving these problems under various constraints not only recovers a wide range of popular optimizers as closed-form solutions, but also produces the optimal hyperparameters of these optimizers with respect to the problems at hand. This enables a systematic approach to design optimizers and tune their hyperparameters according to the gradient statistics that are collected during the training process. Furthermore, this optimization of optimization can be performed dynamically during training. Just as optimizers train their models by feeding them parameter velocities θ, models can also fit the optimizers to the underlying tasks by feeding gradients g. We are interested in the problem of designing optimiz-ers that maximize the utility of gradient-based learning for a given task. The process of learning manifests as the parameter motion θ driven by the gradient force g applied at each step t. Physics requires a constitutive law that relates kinematic motion to its motive force. In gradient-based learning, optimizers take that role. We can represent an optimizer as a positive semidefinite operator Q 0 that linearly translates the gradients into the parameter updates, θ = Q g. (1) Later sections will reveal that many existing optimizers fall into this category. Q g. (2) Adhering to the greedy paradigm, we turn our original problem of maximizing the utility of learning into a different optimization problem that maximizes this loss drop with respect to the optimizer Q: maximize Problem P1 reveals two design options that bound this maximum: (1) the trust region implied by the feasible set Q Q, and (2) the gradient distribution under the expectation E. Our main focus is on how these two factors determine the optimal optimizer Q Optimizers and their hyperparameters can be dynamically tuned or even be replaced by better ones according to the intermediate probes from the gradients in the middle of training. By reverse engineering commonly used optimizers, we draw the landscape of optimizers that have driven the success of machine learning (Robbins & Monro, 1951; Kingma & Ba, 2015; Loshchilov & Hutter, 2019; Gupta et al., 2018; Martens & Grosse, 2015) into a single picture. This lets us better use the well-studied optimizers in practice and also suggest extensions to them. Note that Σ is a symmetric and positive semidefinite (PSD) matrix of shape d d.

Modern neural networks exhibit a striking property: basins of attraction in the loss landscape are often connected by low-loss paths, yet optimization dynamics generally remain confined to a single convex basin (Baity-Jesi et al., 2019; Juneja et al., 2023) and rarely explore intermediate points. We resolve this paradox by identifying entropic barriers arising from the interplay between curvature variations along these paths and noise in optimization dynamics. Empirically, we find that curvature systematically rises away from minima, producing effective forces that bias noisy dynamics back toward the endpoints -- even when the loss remains nearly flat. These barriers persist longer than energetic barriers, shaping the late-time localization of solutions in parameter space. Our results highlight the role of curvature-induced entropic forces in governing both connectivity and confinement in deep learning landscapes. Deep neural networks trained, in the overparametrized regime, exhibit a number of surprising and counterintuitive properties. One of the most striking is the observation that distinct solutions, found with standard optimization algorithms, are often connected by low-loss paths in parameter space (Garipov et al., 2018; Draxler et al., 2018; Frankle et al., 2020). Such mode connectivity results imply that the landscape is far less rugged than once assumed: minima that appear isolated are, in fact, linked by paths of low, nearly constant loss. At the same time, however, optimization dynamics display a seemingly contradictory behavior.

When using an LLM through an API provider, users expect the served model to remain consistent over time, a property crucial for the reliability of downstream applications and the reproducibility of research. Existing audit methods are too costly to apply at regular time intervals to the wide range of available LLM APIs. This means that model updates are left largely unmonitored in practice. In this work, we show that while LLM log probabilities (logprobs) are usually non-deterministic, they can still be used as the basis for cost-effective continuous monitoring of LLM APIs. We apply a simple statistical test based on the average value of each token logprob, requesting only a single token of output. This is enough to detect changes as small as one step of fine-tuning, making this approach more sensitive than existing methods while being 1,000x cheaper. We introduce the TinyChange benchmark as a way to measure the sensitivity of audit methods in the context of small, realistic model changes. LLM API providers typically offer version-pinned endpoints, signaling to users that a given endpoint will serve a consistent model. Users of APIs tend to rely on this consistency: developers want to avoid unexpected regressions in their applications; researchers seek reproducibility in their experiments; regulators perform initial compliance assessments, and assume that the API will keep serving the same model afterward (Y an & Zhang, 2022).