arXiv subjects

Su Hyeong Lee

Publications and source records attributed to Su Hyeong Lee.

7 recordsLinked to original sources

arXiv2026

Deep Minds and Shallow Probes

Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a representation should therefore be stable under the relevant representation symmetries rather than be tied to a particular basis. We prove that, under standard nondegeneracy assumptions, behaviorally equivalent LLMs have hidden representations related by an invertible affine transformation. The resulting symmetry principle singles out a unique hierarchy of shallow coordinate-stable probes, with linear probes as its degree-1 member. We also show that a natural object for cross-model probe transfer is a shared probe-visible quotient--the representation modulo directions invisible to the probe family--rather than the full hidden state. Experiments on synthetic and real-world tasks support both predictions, showing where degree-2 probes help beyond linear ones and how quotient-based transfer enables coverage-aware monitor portability across model families. These results point toward a broader geometric representation theory of neural probing, with coverage-aware monitor transfer as a concrete operational consequence.

cs.LG↗

arXiv2026

Probabilistic Modeling of Latent Agentic Substructures in Deep Neural Networks

We develop a theory of intelligent agency grounded in probabilistic modeling for neural models. Agents are represented as outcome distributions with epistemic utility given by log score, and compositions are defined through weighted logarithmic pooling that strictly improves every member's welfare. We prove that strict unanimity is impossible under linear pooling or in binary outcome spaces, but possible with three or more outcomes. Our framework admits recursive structure via cloning invariance, continuity, and openness, while tilt-based analysis rules out trivial duplication. Finally, we formalize an agentic alignment phenomenon in LLMs using our theory: eliciting a benevolent persona ("Luigi'") induces an antagonistic counterpart ("Waluigi"), while a manifest-then-suppress Waluigi strategy yields strictly larger first-order misalignment reduction than pure Luigi reinforcement alone. These results clarify how developing a principled mathematical framework for how subagents can coalesce into coherent higher-level entities provides novel implications for alignment in agentic AI systems.

cs.LG↗

arXiv2025

On Defining Neural Averaging

What does it even mean to average neural networks? We investigate the problem of synthesizing a single neural network from a collection of pretrained models, each trained on disjoint data shards, using only their final weights and no access to training data. In forming a definition of neural averaging, we take insight from model soup, which appears to aggregate multiple models into a singular model while enhancing generalization performance. In this work, we reinterpret model souping as a special case of a broader framework: Amortized Model Ensembling (AME) for neural averaging, a data-free meta-optimization approach that treats model differences as pseudogradients to guide neural weight updates. We show that this perspective not only recovers model soup but enables more expressive and adaptive ensembling strategies. Empirically, AME produces averaged neural solutions that outperform both individual experts and model soup baselines, especially in out-of-distribution settings. Our results suggest a principled and generalizable notion of data-free model weight aggregation and defines, in one sense, how to perform neural averaging.

cs.LG↗

arXiv2025

Efficient Adaptive Federated Optimization

Adaptive optimization is critical in federated learning, where enabling adaptivity on both the server and client sides has proven essential for achieving optimal performance. However, the scalability of such jointly adaptive systems is often hindered by resource limitations in communication and memory. In this paper, we introduce a class of efficient adaptive algorithms, named $FedAda^2$ and its enhanced version $FedAda^2$++, designed specifically for large-scale, cross-device federated environments. $FedAda^2$ optimizes communication efficiency by avoiding the transfer of preconditioners between the server and clients. Additionally, $FedAda^2$++ extends this approach by incorporating memory-efficient adaptive optimizers on the client side, further reducing on-device memory usage. Theoretically, we demonstrate that $FedAda^2$ and $FedAda^2$++ achieve the same convergence rates for general, non-convex objectives as its more resource-intensive counterparts that directly integrate joint adaptivity. Extensive empirical evaluations on image and text datasets demonstrate both the advantages of joint adaptivity and the effectiveness of $FedAda^2$/$FedAda^2$++.

cs.LG↗

arXiv2025

Efficient Distributed Optimization under Heavy-Tailed Noise

Distributed optimization has become the default training paradigm in modern machine learning due to the growing scale of models and datasets. To mitigate communication overhead, local updates are often applied before global aggregation, resulting in a nested optimization approach with inner and outer steps. However, heavy-tailed stochastic gradient noise remains a significant challenge, particularly in attention-based models, hindering effective training. In this work, we propose TailOPT, an efficient framework designed to address heavy-tailed noise by leveraging adaptive optimization or clipping techniques. We establish convergence guarantees for the TailOPT framework under heavy-tailed noise with potentially unbounded gradient variance and local updates. Among its variants, we highlight a memory and communication efficient instantiation which we call $Bi^2Clip$, which performs coordinate-wise clipping at both the inner and outer optimizers, achieving adaptive-like performance (e.g., Adam) without the cost of maintaining or transmitting additional gradient statistics. Empirically, TailOPT, including $Bi^2Clip$, demonstrates superior performance on several language tasks and models, outperforming state-of-the-art methods.

cs.LG↗

arXiv2024

Sign Rank Limitations for Inner Product Graph Decoders

Inner product-based decoders are among the most influential frameworks used to extract meaningful data from latent embeddings. However, such decoders have shown limitations in representation capacity in numerous works within the literature, which have been particularly notable in graph reconstruction problems. In this paper, we provide the first theoretical elucidation of this pervasive phenomenon in graph data, and suggest straightforward modifications to circumvent this issue without deviating from the inner product framework.

cs.LG↗

arXiv2023

Chemical Integration of ODEs using Idealized Abstract Solutions

In this work, we propose a general inversion framework to non-uniquely invert a very large class of ordinary differential equations (ODEs) into chemical reaction networks. A thorough treatment of the relevant chemical reaction network theory from the literature is given. Various simulation results are provided to augment the selection procedure for the inverse framework, where a previously known kineticization strategy is shown to be deterministically excellent but undesirable in chemical simulations. The utility of the framework is verified by simulating reaction network forms of meaningful ODE systems, and their time series are analyzed. In particular, we provide simulations of deterministic chaotic attractors whose newly discovered reaction networks are non-equivalent with any existing chemical interpretations within the literature, as well as presenting exemplary figures which may form a roadmap to the successful biochemical implementation of the integration of ODE systems.

q-bio.MN↗