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Invited Session

Invited Session

Invited Session

Invited Session

Invited Session

Invited Session

10:30 | Self-Play Preference Optimization for Language Model Alignment ABSTRACT. Traditional reinforcement learning from human feedback (RLHF) approaches relying on parametric models like the Bradley-Terry model fall short in capturing the intransitivity and irrationality in human preferences. Recent advancements suggest that directly working with preference probabilities can yield a more accurate reflection of human preferences, enabling more flexible and accurate language model alignment. In this paper, we propose a self-play- based method for language model alignment, which treats the problem as a constant-sum two-player game aimed at identifying the Nash equilibrium policy. Our approach, dubbed Self-Play Preference Optimization (SPPO), approximates the Nash equilibrium through iterative policy updates and enjoys a theoretical convergence guarantee. Our method can effectively increase the log-likelihood of the chosen response and decrease that of the rejected response, which cannot be trivially achieved by symmetric pairwise loss such as Direct Preference Optimization (DPO) and Identity Preference Optimization (IPO). In our experiments, using only 60k prompts (without responses) from the UltraFeedback dataset and without any prompt augmentation, by leveraging a pre-trained preference model PairRM with only 0.4B parameters, SPPO can obtain a model from fine-tuning Mistral-7B-Instruct-v0.2 that achieves the state-of-the-art length- controlled win-rate of 28.53% against GPT-4-Turbo on AlpacaEval 2.0. It also outperforms the (iterative) DPO and IPO on MT-Bench and the Open LLM Leaderboard. Starting from a stronger base model Llama-3-8B-Instruct, we are able to achieve a length-controlled win rate of 38.77%. Notably, the strong performance of SPPO is achieved without additional external supervision (e.g., responses, preferences, etc.) from GPT-4 or other stronger language models. |

10:50 | Pluralistic Alignment Framework for Learning from Heterogeneous Preferences ABSTRACT. Large foundation models pretrained on raw web-scale data are not readily deployable without additional step of extensive alignment to human preferences. Such alignment is typically done by collecting large amounts of pairwise comparisons from humans ("Do you prefer output A or B?") and learning a reward model or a policy with the Bradley-Terry-Luce (BTL) model as a proxy for a human's underlying implicit preferences. These methods generally suffer from assuming a universal preference shared by all humans, which lacks the flexibility of adapting to plurality of opinions and preferences. In this work, we propose PAL, a framework to model human preference complementary to existing pretraining strategies, which incorporates plurality from the ground up. We propose using the ideal point model as a lens to view alignment using preference comparisons. Together with our novel reformulation and using mixture modeling, our framework captures the plurality of population preferences while simultaneously learning a common preference latent space across different preferences, which can few-shot generalize to new, unseen users. Our approach enables us to use the penultimate-layer representation of large foundation models and simple MLP layers to learn reward functions that are on-par with the existing large state-of-the-art reward models, thereby enhancing efficiency of reward modeling significantly. We show that PAL achieves competitive reward model accuracy compared to strong baselines on 1) Language models with Summary dataset ; 2) Image Generative models with Pick-a-Pic dataset ; 3) A new semisynthetic heterogeneous dataset generated using Anthropic Personas. Finally, our experiments also highlight the shortcoming of current preference datasets that are created using rigid rubrics which wash away heterogeneity, and call for more nuanced data collection approaches. |

11:10 | Shaping opinions in social networks with shadow banning ABSTRACT. The proliferation of harmful content and misinformation on social networks necessitates content moderation policies to maintain platform health. One such policy is shadow banning, which limits content visibility. The danger of shadow banning is that it can be misused by social media platforms to manipulate opinions. Here we present an optimization based approach to shadow banning that can shape opinions into a desired distribution and scale to large networks. Simulations on real network topologies show that our shadow banning policies can shift opinions and increase or decrease opinion polarization. We find that if one shadow bans with the aim of shifting opinions in a certain direction, the resulting shadow banning policy can appear neutral. This shows the potential for social media platforms to misuse shadow banning without being detected. Our results demonstrate the power and danger of shadow banning for opinion manipulation in social networks. |

11:30 | Prelimit Coupling and Steady-State Convergence of Constant-stepsize Nonsmooth Contractive Stochastic Approximation ABSTRACT. Motivated by Q-learning, we study nonsmooth contractive stochastic approximation (SA) with constant stepsize. We establish the weak convergence of the iterates to a stationary limit distribution in Wasserstein distance. Furthermore, we propose a prelimit coupling technique for establishing steady-state convergence and characterize the limit of the stationary distribution as the stepsize goes to zero. As an intermediate step, we show that the general nonsmooth contractive SA is asymptotically equivalent to the contractive SA with only additive Gaussian noise. This universal result is of independent interest and can be a powerful tool for analyzing SA. By steady-state convergence result, we derive that the asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize, which stands in sharp contrast to smooth SA. This bias characterization allows for the use of Richardson-Romberg extrapolation for bias reduction in nonsmooth SA. |

11:50 | Beyond PCA: A Gram-Schmidt Approach to Feature Extraction PRESENTER: Bahram Yaghooti ABSTRACT. Linear feature extraction at the presence of nonlinear dependencies among the data is a fundamental challenge in unsupervised learning. We propose using a Gram-Schmidt (GS) type orthogonalization process over function spaces in order to detect and remove redundant dimensions. Specifically, by applying the GS process over a family of functions which presumably captures the nonlinear dependencies in the data, we construct a series of covariance matrices that can either be used to identify new large-variance directions, or to remove those dependencies from the principal components. In the former case, we provide information-theoretic guarantees in terms of entropy reduction. In the latter, we prove that under certain assumptions the resulting algorithms detect and remove nonlinear dependencies whenever those dependencies lie in the linear span of the chosen function family. Both proposed methods extract linear features from the data while removing nonlinear redundancies. We provide simulation results on synthetic and real-world datasets which show improved performance over state-of-the-art feature extraction algorithms. |

10:30 | Acceptance in Postselected Asymptotic Quantum State Discrimination ABSTRACT. In postselected discrimination of a quantum state when n copies of the states are available, the error can be made arbitrary small by designing appropriate measurements. In this paper, we investigate usability of such error-minimizing measurements. We first characterize such error-minimizing joint measurements on n-copies of the state. We show that as far as error is concerned, minimum error can be obtained by performing a set of separate measurements on individual copies, thus removing the need to perform a joint measurement. We then characterize the acceptance of these measurements that represent the probability that the decision is not rejected. We derive an upper bound on the acceptance and show that it decreases exponentially with n. This indicates that acceptance in such error minimizing measurements vanishes with n. We conclude that although such a measurement achieves vanishing error as n tends to infinity, the probability that it makes a decision also vanishes, which limits the utility of these measurements for postselected state discrimination. In the end, we have derived error exponents for finite acceptance and shown that the benefit of postselection vanishes in asymmetric case and reduces in symmetric case. |

10:50 | PRESENTER: Ahmad Bennakhi ABSTRACT. This paper aims to outline the effectiveness of modern universal gate quantum computers when utilizing dif- ferent configurations to solve the B-SAT(Boolean Satisfiability) problem. The quantum computing experiments are performed using Grover’s Search algorithm to find a valid solution. The experiments are performed under different variations to demon- strate their effects on the results. Changing the number of shots, qubit mapping, and using a different quantum processor are all among the experimental variables. The study also branches into a dedicated experiment highlighting a peculiar behavior that IBM quantum processors exhibit when running circuits with a certain number of shots. |

11:10 | Authenticated partial correction over AV-MACs: toward characterization and coding ABSTRACT. In this paper we study $\gamma$ partial correction over a $t$-user arbitrarily varying multiple-access channel (AV-MAC). We first present necessary channel conditions for the $\gamma$ partially correcting authentication capacity region to have nonempty interior. We then give a block length extension scheme which preserves positive rate tuples from a short code with zero probability of $\gamma$ partial correction error, noting that the flexibility of $\gamma$ partial correction prevents pure codeword concatenation from being successful. Finally, we offer a case study of a particular AV-MAC satisfying the necessary conditions for partial correction. |

11:30 | Graph Codes for Dual-Parameter Barrier Channels PRESENTER: Saar Stern ABSTRACT. A ternary barrier channel is a non-symmetric error model defined previously to address emerging applications. Conveniently, it admits a code-construction method comprising two binary constituent codes. In this paper we propose a decoding algorithm that decodes the two constituent codes jointly by message passing on a graph representing the two codes' parity-check constraints. The messages exchanged by the algorithm are likelihoods calculated from incoming messages, and they are derived in the paper based on the exact dependence between the binary values of the two codewords. Simulation results demonstrate that the proposed decoder has superior error-rate performance compared to prior decoding approaches. |

11:50 | PRESENTER: Michele Pacenti ABSTRACT. Recently, Lin and Pryadko presented the quantum two-block group algebra codes, a generalization of bicycle codes obtained from Cayley graphs of non-Abelian groups. We notice that their construction is naturally suitable to obtain a quantum equivalent of the well-known classical Margulis code. In this paper, we first present an alternative description of the two-block group algebra codes using the left-right Cayley complex; then, we show how to modify the construction of Margulis to get a two-block algebra code. Finally, we construct several quantum Margulis codes and evaluate their performance with numerical simulations. |

Invited Session

Invited Session

10:30 | SPIR with Colluding and Non-Replicated Servers from a Noisy Channel PRESENTER: Amirhossein Shekofteh ABSTRACT. We study the problem of Symmetric Private Information Retrieval (SPIR) in a scenario involving $L$ non-replicated and colluding servers, and $M$ independent files. In this setting, communication takes place through a noisy multiple-access channel and a noiseless public channel. %, each split into $L$ segments, are stored across different servers. The client must retrieve one of the $M$ files such that $(i)$ the client's choice must not be revealed to any server; $(ii)$ the client must not learn any information about non-selected files. Our primary contribution is showing an achievable rate for this SPIR problem, and showing that positive rates can still be achieved even when all servers collude, without requiring common randomness shared among servers. The key idea involves first proving an achievable rate for the special case with $M=2$ files. Then, we iteratively apply our coding scheme $M-1$ times to generalize our achievable rate to $M>2$ files. Furthermore, by distributing files across multiple servers, we demonstrate on an example that our derived achievable rate can outperform single-server settings. |

10:50 | Strategies for Rate Optimization in Joint Sensing and Communication over Channels with Memory ABSTRACT. Joint communication and sensing (JCAS) is one of the promising technologies envisioned for future generations of wireless systems. Several attempts have been made to formulate the problem from an information-theoretic perspective, assuming underlying discrete memoryless channels and leveraging classical rate-distortion trade-offs. However, communication channels often have memory and strategies to improve data rates with the help of sensing in such scenarios is not yet well understood. In this paper, we consider a generic system model for joint communication and sensing, and present a novel and greedy-type strategy to achieve optimal average rate, assuming a channel model with memory. In particular, in the considered channel model, the channel state follows a finite state Markov chain. We also characterize how the solutions to communication and sensing problems complement each other in such scenarios. To the best of authors' knowledge, this is the first attempt towards understanding rate-optimized strategies in JCAS systems involving channels with memory from a communication-theoretic perspective. |

11:10 | Contraction Coefficients of Product Symmetric Channels PRESENTER: Dongmin Lee ABSTRACT. Contraction coefficients for Kullback-Leibler (KL) divergence are channel-dependent constants that are used to sharpen data processing inequalities for KL divergence into strong data processing inequalities. In this work, we present a method to analytically compute the KL contraction coefficients of product $q$-ary symmetric channels. Although such contraction coefficients have many applications in information theory as well as probability and statistics more broadly, deriving exact values is considered to be challenging for complex channels such as product channels. While recent discoveries have reduced the search space of the optimization problems defining contraction coefficients significantly, the problem is still far from trivial. We find that the symmetry inherent in channels such as the $q$-ary symmetric channel allows for further simplification, making an exact closed-form expression for contraction coefficients for KL divergence possible to derive. We begin by obtaining the KL contraction coefficients of product binary symmetric channels, and then generalize our results to larger alphabets. Our methods are not specific to product $q$-ary symmetric channels and can be used for wider classes of channels that satisfy certain symmetry properties. |

11:30 | Finite-Length Coding Bounds via Guesswork PRESENTER: Alexander Mariona ABSTRACT. Existing bounds on the maximum channel coding rate achievable at finite block lengths are not always meaningful at moderate lengths and for low-noise channels, even when the channel model is simple. We offer a new framework for deriving achievability and converse bounds, along with a simple and accurate approximation, based on guesswork and the GRAND family of decoding algorithms. This approach is theoretically applicable to any channel model; we use it to produce implicit but computable bounds for the binary symmetric channel and the binary additive white Gaussian noise channel. Our approach for the latter is based on a 1-bit quantization of the soft information and offers quantitative insight into the marginal value of this amount of information compared to hard decision and full soft information decoding. For moderate lengths and low-noise settings, our results for both channel models improve on the state-of-the-art. |

11:50 | Higher-order Interpretations of Deepcode, a Learned Feedback Code ABSTRACT. We present an interpretation of Deepcode, a learned feedback code that showcases higher-order error correction relative to an earlier interpretable model. By interpretation, we mean succinct analytical encoder and decoder expressions (albeit with learned parameters) in which the role of feedback in achieving error correction is easy to understand. By higher-order, we mean that longer sequences of large noise values are acted upon by the encoder (which has access to these through the feedback) and used in error correction at the decoder in a two-stage decoding process. |

Invited Session

Invited Session

14:30 | Weyl Calculus and Exactly Solvable Schrödinger Bridges with Quadratic State Cost PRESENTER: Abhishek Halder ABSTRACT. Schrödinger bridge--a stochastic dynamical generalization of optimal mass transport--exhibits a learning-control duality. Viewed as a stochastic control problem, the Schrödinger bridge finds an optimal control policy that steers a given joint state statistics to another while minimizing the total control effort subject to controlled diffusion and deadline constraints. Viewed as a stochastic learning problem, the Schrödinger bridge finds the most-likely distribution-valued trajectory connecting endpoint distributional observations, i.e., solves the two point boundary-constrained maximum likelihood problem over the manifold of probability distributions. Recent works have shown that solving the Schrödinger bridge problem with state cost requires finding the Markov kernel associated with a reaction-diffusion PDE where the state cost appears as a state-dependent reaction rate. We explain how ideas from Weyl calculus in quantum mechanics, specifically the Weyl operator and the Weyl symbol, can help determine such Markov kernels. We illustrate these ideas by explicitly finding the Markov kernel for the case of quadratic state cost via Weyl calculus, recovering our earlier results but avoiding tedious computation with Hermite polynomials. |

14:50 | Stochastic interpolants: A unifying framework for flows and diffusions ABSTRACT. We introduce a class of generative models that unifies flows and diffusions. These models are constructed through the use of a continuous-time stochastic process known as a stochastic interpolant, which bridges two arbitrary probability densities exactly in finite time. We show that the time-dependent density of the stochastic interpolant satisfies a first-order transport equation, as well as an infinite family of forward and backward Fokker-Planck equations with tunable diffusion coefficients. This viewpoint leads to both deterministic and stochastic generative models based on ordinary or stochastic differential equations with an adjustable level of noise that can be optimized to maximize performance. We discuss how the resulting drift functions can be characterized variationally and learned efficiently over flexible parametric classes such as neural networks. We highlight the advantages of our formalism and the tradeoffs between deterministic and stochastic sampling with numerical examples in image generation, image inpainting, probabilistic forecasting of dynamical systems, and few-step sampling. |

15:10 | A Fisher-Rao gradient flow for entropy-regularised Markov decision processes in Polish spaces ABSTRACT. We study the global convergence of a Fisher-Rao policy gradient flow for infinite-horizon entropy-regularised Markov decision processes with Polish state and action space. The flow is a continuous-time analogue of a policy mirror descent method. We establish the global well-posedness of the gradient flow and demonstrate its exponential convergence to the optimal policy. Moreover, we prove the flow is stable with respect to gradient evaluation, offering insights into the performance of a natural policy gradient flow with log-linear policy parameterisation. To overcome challenges stemming from the lack of the convexity of the objective function and the discontinuity arising from the entropy regulariser, we leverage the performance difference lemma and the duality relationship between the gradient and mirror descent flows. |

15:30 | Nonlinear Filtering with Brenier Optimal Transport Maps ABSTRACT. This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states, due to the weight degeneracy issue. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step. Unlike SIR particle filters, the OT formulation does not require the analytical form of the likelihood. Moreover, it allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare the OT method to the SIR particle filter and the ensemble Kalman filter, evaluating the performance in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions. |

15:50 | Scalable computations for nonlinear balanced truncation model reduction ABSTRACT. Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems on nonlinear manifolds and preserves either open- or closed-loop observability and controllability aspects of the nonlinear system. Three computational challenges have so far prevented its deployment on large-scale systems: (a) the computation of Hamilton-Jacobi-(Bellman) equations that are needed for characterization of controllability and observability aspects, (b) a scalable strategy to compute the nonlinear coordinate transformation to balance the system, and (c) efficient model reduction and reduced-order model (ROM) simulation on the resulting nonlinear balanced manifolds. We present a novel unifying and scalable approach to balanced truncation for large-scale control-affine nonlinear systems that consider a Taylor-series based approach to solve both a class of parametrized Hamilton-Jacobi-Bellman equations as well as the balancing transforms. This specific tensor structure for the coefficients of the Taylor series (tensors themselves) allows for scalability up to thousands of states. The talk will illustrate the strength and scalability of the algorithm on several semi-discretized nonlinear partial differential equations, including a nonlinear heat equation, vibrating beams, Burgers' equation and the Kuramoto-Sivashinsky equation. |

16:10 | Harmonic Path Integral Diffusion ABSTRACT. In this paper, we propose a novel solution for sampling from a continuously valued multi-variate probability distribution, either explicitly known (up to a normalization factor) or represented via ground truth samples. Our method initiates the target distribution from a delta function positioned at the origin of the state space and optimally grows it. We frame the problem as a stochastic optimal control challenge of the path-integral type, where the cost-to-go function includes a quadratic term in the control, a quadratic term in the state vector, and a terminal term. This formulation allows for an analytical solution and leads to the development of several sampling algorithms, both with and without the use of neural networks. We compare these algorithms to existing state-of-the-art methods in terms of accuracy and complexity, demonstrating their performance on benchmark examples of varying sizes. |

Invited Session

14:30 | Generalized Barrier Functions: Integral Conditions & Recurrent Relaxations ABSTRACT. Barrier functions constitute an effective tool for assessing and enforcing safety-critical constraints on dynamical systems. To this end, one is required to find a function $h$ that satisfies a Lyapunov-like differential condition, thereby ensuring the invariance of its zero super-level set $h_{\ge 0}$. This methodology, however, does not prescribe a general method for finding the function $h$ that satisfies such differential conditions, which, in general, can be a daunting task. In this paper, we seek to overcome this limitation by developing a generalized barrier condition that makes the search for $h$ easier. We do this in two steps. First, we develop integral barrier conditions that reveal equivalent asymptotic behavior to the differential ones, but without requiring differentiability of $h$. Subsequently, we further replace the stringent invariance requirement on $h\geq0$ with a more flexible concept known as recurrence. A set is ($\tau$-)recurrent if every trajectory that starts in the set returns to it (within $\tau$ seconds) infinitely often. We show that, under mild conditions, a simple sign distance function can satisfy our relaxed condition and that the ($\tau$-)recurrence of the super-level set $h_{\geq 0}$ is sufficient to guarantee the system's safety. |

14:50 | Adaptive Online Model Update Algorithm for Predictive Control in Networked Systems ABSTRACT. In this article, we introduce an adaptive online model update algorithm designed for predictive control applications in networked systems, particularly focusing on power distribution systems. Unlike traditional methods that depend on historical data for offline model identification, our approach utilizes real-time data for continuous model updates. This method integrates seamlessly with existing online control and optimization algorithms and provides timely updates in response to real-time changes. This methodology offers significant advantages, including a reduction in the communication network bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt after disturbances. Furthermore, our algorithm is tailored for non-linear convex models, enhancing its applicability to practical scenarios. The efficacy of the proposed method is validated through a numerical study, demonstrating improved control performance using a synthetic IEEE test case. |

15:10 | Optimal Infinite-Horizon Mixed $H_2 / H_\infty$ Control PRESENTER: Taylan Kargin ABSTRACT. We study the problem of mixed $H_2 / H_\infty$ control in the infinite-horizon setting. We identify the optimal causal controller that minimizes the $\Htwo$-cost of the closed-loop system subject to an $H_\infty$ constraint. Megretski proved that the optimal mixed $H_2 / H_\infty$ controller is non-rational whenever the constraint is active, without giving an explicit construction of the controller. In this work, we provide the first exact closed-form solution to the infinite-horizon mixed $H_2 / H_\infty$ control in the frequency domain. While the optimal controller is non-rational, our formulation provides a finite-dimensional parameterization of the optimal controller. Leveraging this fact, we introduce an efficient iterative algorithm that finds the optimal causal controller in the frequency domain. We show that this algorithm is convergent when the system is scalar and present numerical evidence for exponential convergence of the proposed algorithm. Finally, we show how to find the best (in $H_\infty$ norm) fixed-order rational approximations of the optimal mixed $H_2 / H_\infty$ controller, and study its performance. |

15:30 | A synthesis approach for distributed H2 control problems with communication delays PRESENTER: Yuanji Zou ABSTRACT. In this work, we present an explicit solution to the distributed H2 optimal control problem. It's assumed that the plant and the controller are interconnected dynamic systems, interacting over the same directed network with reliable links, which satisfies the quadratic invariance condition. The resulting control structure involves both sparsity and delays. We provide an algorithm that uses the solution of the discrete-time algebraic Riccati Equations (DARE) for standard H2 optimal controller to initiate the Youla Paramterization and cast the distributed H2 problem into a convex model matching problem. We find the optimal Youla parameter that parameterized the optimal distributed \H2 controller in finite computations by solving an extra discrete-time algebraic Riccati Equations (DARE) associated with the vectorized closed loop maps compared to standard centralized \(\mathcal{H}_2\) problems. Employing the backward recursion of Riccati equations, we can find the optimal solution explicitly. Besides the algorithm, we also provide a novel theorem that enables us to check the existence of stabilizing controllers in the wanted structure. This theorem can be useful for generic network distributed control problems other than \(\mathcal{H}_2\). Finally, we validate this methodology on a 4-car platoon system and compare it to the optimal centralized controller, the optimal delay-free structured controller, and a decentralized PID controller. |

14:30 | A Hypothesis Testing-based Framework for Cyber Deception with Sludging PRESENTER: Pramod K. Varshney ABSTRACT. In this paper, we present a novel hypothesis testing framework to model an attacker’s decision-making during the reconnaissance phase and employ the framework to design strategic deception strategies that can provide the attacker with optimally falsified information structures. We characterize the criterion for such structures to “blind” the attacker, i.e., to completely confuse it, as well as the optimal falsification strategy when the attacker cannot be blinded. We also characterize optimal information acquisition costs that can be imposed on the attacker to maximally “sludge” its decision-making process during the reconnaissance phase. Numerical results have been presented to gain important insights into the developed strategies. |

14:50 | Privacy-Utility Tradeoff Based on $\alpha$-lift ABSTRACT. Information density and its exponential form, known as lift, play a central role in information privacy leakage measures. $\alpha$-lift is the power-mean of lift, which is tunable between the worst-case measure max-lift ($\alpha=\infty$) and more relaxed versions ($\alpha<\infty$). This paper investigates the optimization problem of the privacy-utility tradeoff (PUT) where $\alpha$-lift and mutual information are privacy and utility measures, respectively. Due to the nonlinear nature of $\alpha$-lift for $\alpha<\infty$, finding the optimal solution is challenging. Therefore, we propose a heuristic algorithm to estimate the optimal utility for each value of $\alpha$, inspired by the optimal solution for $\alpha=\infty$ and the convexity of $\alpha$-lift with respect to the lift, which we prove. The numerical results show the superiority of the algorithm compared to a previous algorithm in the literature and indicate the effective range of $\alpha$ and privacy budget $\eps$ with good PUT performance. |

15:10 | A New Framework for Designing Polynomial Codes for Private Information Retrieval ABSTRACT. This paper presents a framework for designing Private Information Retrieval (PIR) schemes in settings where the data is stored in a coded form (using MDS codes) and in the presence of collusion between servers. The framework is based on polynomial codes and provides a simple and efficient way to construct PIR schemes for several PIR problems and a broad range of system parameters. We prove that our framework has the best-known download rate and achieves asymptotic capability for strictly linear PIR schemes. One of the distinguishing features of this framework is its simplicity and ease of implementation, making it an attractive choice for practical retrieval schemes. We demonstrate the flexibility of our framework by demonstrating its use in solving private linear computation problems. |

15:30 | Distributed Matrix Multiplication: Download Rate, Randomness and Privacy Trade-Offs PRESENTER: Amirhosein Morteza ABSTRACT. We study the trade-off between communication rate and privacy for distributed batch matrix multiplication of two independent sequences of matrices A and B with uniformly distributed entries. In our setting, B is publicly accessible by all the servers while A must remain private. The user is interested in finding the product AB with the responses from the k fastest servers. For a given parameter α ∈ [0, 1], our privacy constraint must ensure that any set of ℓ colluding servers cannot learn more than a fraction α of A. Additionally, we study the trade-off between the amount of local randomness needed at the encoder and privacy, which to the best of our knowledge no previous work has characterized. Finally, we establish the optimal trade-offs when the matrices are square and identify a linear relationship between information leakage and communication rate. |

15:50 | Influence Chain Recovery and Application in Distributed Fact-Checking ABSTRACT. This study investigates the distributed fact-checking problem, where a series of fact-checkers (agents) with interconnected influence evaluate a sequence of statements from a source. Each statement has a hidden binary label (true or false), and each agent assigns their own true or false label to the statement. The agents' opinions follow a hidden directed chain, with a leader followed by ordered followers. Our goals are to: (i) recover the directed chain (the relative order of agents), and (ii) decode the true label of each statement. We demonstrate that if the source is biased, the directed chain can be recovered through the observation of agents' labels. However, an unbiased source allows recovery of only the undirected influence chain. For the latter, we propose two low-complexity algorithms to recover the undirected chain, along with a decoder to estimate the true statement label based on observed agent opinions. |