Enrique Mallada

@inproceedings{mvm2024iclr,
  abstract = {This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons' directional dynamics allows us to provide an $\mathcalO(\fracłog n\sqrtμ)$ upper bound on the time it takes for all neurons to achieve good alignment with the input data, where $n$ is the number of data points and $μ$ measures how well the data are separated. After the early alignment phase, the loss converges to zero at a $\mathcalO(\frac1t)$ rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.},
  author = {Min, Hancheng and Vidal, Rene and Mallada, Enrique},
  booktitle = {International Conference on Representation Learning (ICLR)},
  grants = {CAREER-1752362},
  month = {05},
  record = {published, accepted Jan 2024, submitted Sep 2023},
  title = {Early Neuron Alignment in Two-layer ReLU Networks with Small Initialization},
  url = {https://mallada.ece.jhu.edu/pubs/2024-ICLR-MVM.pdf},
  year = {2024}
}

@inproceedings{sm2024hscc,
  abstract = {In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be (tau-)recurrent if every trajectory that starts in the set returns to it (within at most $τ$ units of time). Recurrence entropy quantifies the complexity of making a set tau-recurrent measured by the average rate of growth, as time increases, of the number of control signals required to achieve this goal. Our analysis reveals that, compared to invariance, recurrence is quantitatively less complex, meaning that the recurrence entropy of a set is no larger than, and often strictly smaller than, the invariance entropy. Our results further offer insights into the minimum data rate required for achieving recurrence. We also present an algorithm for achieving recurrence asymptotically.},
  address = {New York, NY, USA},
  author = {Sibai, Hussein and Mallada, Enrique},
  bdsk-url-3 = {https://doi.org/10.1145/3641513.3650121},
  booktitle = {Proceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control (HSCC)},
  doi = {https://doi.org/10.1145/3641513.3650121},
  grants = {CPS-2136324, Global-Centers-2330450},
  month = {05},
  number = {23},
  pages = {1--9},
  publisher = {Association for Computing Machinery},
  record = {accepted Jan 2024, submitted Nov 2023},
  series = {HSCC '24},
  title = {Recurrence of Nonlinear Control Systems: Entropy and Bit Rates},
  url = {https://mallada.ece.jhu.edu/pubs/2024-HSCC-SM.pdf},
  year = {2024}
}

@article{bcym2023tempr,
  abstract = {Two-stage settlement electricity markets, which in- clude day-ahead and real-time markets, often observe unde- sirable price manipulation due to the price difference across stages, inadequate competition, and unforeseen circumstances. To mitigate this, some Independent System Operators (ISOs) have proposed system-level market power mitigation (MPM) policies in addition to existing local policies. These system-level policies aim to substitute noncompetitive bids with a default bid based on estimated generator costs. However, without accounting for the conflicting interest of participants, they may lead to unintended consequences when implemented. In this paper, we model the competition between generators (bidding supply functions) and loads (bidding quantity) in a two-stage market with a stage- wise MPM policy. An equilibrium analysis shows that a real- time MPM policy leads to equilibrium loss, meaning no stable market outcome (Nash equilibrium) exists. A day-ahead MPM policy leads to Stackelberg-Nash game, with loads acting as leaders and generators as followers. Despite estimation errors, the competitive equilibrium is efficient, while the Nash equilibrium is comparatively robust to price manipulations. Moreover, analysis of inelastic loads shows their tendency to shift allocation and manipulate prices in the market. Numerical studies illustrate the impact of cost estimation errors, heterogeneity in generation cost, and load size on market equilibrium.},
  author = {Bansal, Rajni Kant and Chen, Yue and You, Pengcheng and Mallada, Enrique},
  bdsk-url-3 = {https://doi.org/10.1109/TEMPR.2023.3318149},
  doi = {10.1109/TEMPR.2023.3318149},
  grants = {CAREER-1752362, CPS-2136324, EPICS-2330450},
  journal = {IEEE Transactions on Energy Markets, Policy and Regulation},
  month = {12},
  number = {4},
  pages = {512-522},
  record = {published, online Sep 2023, revised July 2023, under revision May 2023, submitted Jan 2023},
  title = {Market Power Mitigation in Two-stage Electricity Market with Supply Function and Quantity Bidding},
  url = {https://mallada.ece.jhu.edu/pubs/2023-TEMPR-BCYM.pdf},
  volume = {1},
  year = {2023}
}