This paper presents a simple, effective, and cost-efficient strategy, named ModelSwitch, to improve LLM performance by scaling test-time compute. ModelSwitch builds upon the repeated-sampling-then-voting framework, with a novel twist: incorporating multiple models, even weaker ones, to leverage their complementary strengths that potentially arise from diverse training data and paradigms. By using sample consistency as a signal, our strategy dynamically switches between models. Theoretical analysis highlights the efficiency and performance advantages of our strategy. Extensive experiments on seven datasets demonstrate that our strategy not only outperforms self-consistency and state-of-the-art multi-agent debate approaches, but also significantly reduces inference costs. Additionally, our strategy requires only a few comparable LLMs to achieve optimal performance and can be extended with verification methods, demonstrating the potential of leveraging multiple LLMs in the generation-verification paradigm.

Theory of Mind (ToM) refers to the ability to reason about others’ mental states, and higher-order ToM involves considering that others also possess their own ToM. Equipping large language model (LLM)-driven agents with ToM has long been considered to improve their coordination in multiagent collaborative tasks. However, we find that misaligned ToM orders—mismatches in the depth of ToM reasoning between agents—can lead to insufficient or excessive reasoning about others, thereby impairing their coordination. To address this issue, we design an adaptive ToM (A-ToM) agent, which can align in ToM orders with its partner. Based on prior interactions, the agent estimates the partner’s likely ToM order and leverages this estimation to predict the partner’s action, thereby facilitating behavioral coordination. We conduct empirical evaluations on four multi-agent coordination tasks: a repeated matrix game, two grid navigation tasks and an Overcooked task. The results validate our findings on ToM alignment and demonstrate the effectiveness of our AToM agent. Furthermore, we discuss the generalizability of our A-ToM to non-LLM-based agents, as well as what would diminish the importance of ToM alignment.

Large language models (LLMs) often exhibit complementary strengths. Model routing harnesses these strengths by dynamically directing each query to the most suitable model, given a candidate model pool. However, routing performance relies on accurate model representations, and adding new models typically requires retraining, limiting scalability. To address these challenges, we propose a novel routing method using in-context vectors to represent model capabilities. The method proceeds in two stages. First, queries are embedded and projected into vectors, with a projector and LLM-based router trained to reconstruct the original queries, aligning vector representations with the router’s semantic space. Second, each candidate model is profiled on a query set, and the router learns---based on in-context vectors of query and model performance---to predict whether each model can correctly answer new queries. Extensive experiments demonstrate that our method achieves state-of-the-art routing performance in both in-distribution and out-of-distribution tasks. Moreover, our method allows for seamless integration of new models without retraining the router.

Proprietary models are increasingly dominating the race for ever-larger language models. Can open-source, smaller models remain competitive across a broad range of tasks? In this paper, we present the Avengers---a lightweight framework that leverages the collective intelligence of these smaller models. The Avengers builds upon four lightweight operations: (i) embedding: encode queries using a text embedding model; (ii) clustering: group queries based on their semantic similarity; (iii) scoring: scores each model's performance within each cluster; and (iv) voting: improve outputs via repeated sampling and voting. At inference time, each query is embedded and assigned to its nearest cluster. The top-performing model(s) within that cluster are selected to generate the response with repeated sampling. Remarkably, with 10 open-source models (~7B parameters each), the Avengers surpasses GPT-4o, 4.1, and 4.5 in average performance across 15 diverse datasets spanning mathematics, coding, logical reasoning, general knowledge, and affective tasks. In particular, it surpasses GPT-4.1 on mathematics tasks by 18.21% and on code tasks by 7.46%. Furthermore, the Avengers delivers superior out-of-distribution generalization, and remains robust across various embedding models, clustering algorithms, ensemble strategies, data efficiency, and values of its sole parameter---the number of clusters.

Unsupervised reinforcement learning (RL) aims to discover diverse behaviors that can accelerate the learning of downstream tasks. Previous methods typically focus on entropy-based exploration or empowerment-driven skill learning. However, entropy-based exploration struggles in large-scale state spaces (e.g., images), and empowerment-based methods with mutual information (MI) estimations have limitations in state exploration. To address these challenges, we propose a novel skill discovery objective that maximizes the deviation of the state density of one skill from the explored regions of other skills, encouraging inter-skill state diversity similar to the initial MI objective. For state-density estimation, we construct a novel conditional autoencoder with soft modularization for different skill policies in high-dimensional space. Meanwhile, to incentivize intra-skill exploration, we formulate an intrinsic reward based on the learned autoencoder that resembles count-based exploration in a compact latent space. Through extensive experiments in challenging state and image-based tasks, we find our method learns meaningful skills and achieves superior performance in various downstream tasks.

Reinforcement Learning from Human Feedback (RLHF) has shown great potential in fine-tuning Large Language Models (LLMs) to align with human preferences. Existing methods perform preference alignment from a fixed dataset, which can be limited in data coverage and the resulting reward model is hard to generalize in out-of-distribution responses. Thus, online RLHF is more desirable to empower the LLM to explore outside the support of the initial dataset by iteratively collecting the prompt-response pairs. In this paper, we study the fundamental problem in online RLHF, i.e., how to explore for LLM. We give a theoretical motivation in linear reward assumption to show that an optimistic reward with an upper confidence bound (UCB) term leads to a provably efficient RLHF policy. Then, we reformulate our objective to direct preference optimization with an exploration term, where the UCB-term can be converted to a count-based exploration bonus. We further propose a practical algorithm, named Count-based Online Preference Optimization (COPO), which leverages a simple coin-flip counting module to estimate the pseudo-count of a prompt-response pair in previously collected data. COPO encourages LLMs to balance exploration and preference optimization in an iterative manner, which enlarges the exploration space and the entire data coverage of iterative LLM policies. We conduct online RLHF experiments on Zephyr and Llama-3 models. The results on instruction-following and standard academic benchmarks show that COPO significantly increases performance.

Despite the growing popularity of graph attention mechanisms, their theoretical understanding remains limited. This paper aims to explore the conditions under which these mechanisms are effective in node classification tasks through the lens of Contextual Stochastic Block Models (CSBMs). Our theoretical analysis reveals that incorporating graph attention mechanisms is *not universally beneficial*. Specifically, by appropriately defining *structure noise* and *feature noise* in graphs, we show that graph attention mechanisms can enhance classification performance when structure noise exceeds feature noise. Conversely, when feature noise predominates, simpler graph convolution operations are more effective. Furthermore, we examine the over-smoothing phenomenon and show that, in the high signal-to-noise ratio (SNR) regime, graph convolutional networks suffer from over-smoothing, whereas graph attention mechanisms can effectively resolve this issue. Building on these insights, we propose a novel multi-layer Graph Attention Network (GAT) architecture that significantly outperforms single-layer GATs in achieving *perfect node classification* in CSBMs, relaxing the SNR requirement from $\omega(\sqrt{\log n})$ to $\omega(\sqrt{\log n} / \sqrt[3]{n})$. To our knowledge, this is the first study to delineate the conditions for perfect node classification using multi-layer GATs. Our theoretical contributions are corroborated by extensive experiments on both synthetic and real-world datasets, highlighting the practical implications of our findings.

The Singleton bound provides a fundamental limit on the maximum possible size of an error-correcting code of a given length and distance. However, recent work by Zhang et. al. [IEEE Trans. Comm., Dec. 2023] showed that in the context of the wiretap multipath network when the adversary has limited knowledge about the codewords and a vanishing probability of decoding error is permitted, a rate higher than the Singleton bound is achievable. Their results, however, are confined to an ideal setting where the adversary is allowed to behave non-causally. Motivated by real-world scenarios, this work considers communication over a wiretap multipath network in the presence of a causal adversary (i.e., the adversary which is only allowed to use the observations up to the current time slot to decide the current jamming strategy) and in the presence of passive feedback from the receiver to the transmitter. We characterize both the capacity and secrecy capacity of the wiretap multipath network, either with or without passive feedback. We observe that in comparison to the non-causal and non-feedback setting, the capacity and secrecy capacity can be strictly higher for a wide variety of parameters, demonstrating the benefits of causality and feedback.

We study the problem of reinforcement learning from human feedback (RLHF), a critical problem in training large language models, from a theoretical perspective. Our main contribution is the design of novel sample-efficient RLHF algorithms based on information-directed sampling (IDS), an online decision-making principle inspired by information theory. Our algorithms maximize the sum of the value function and a mutual information term that encourages exploration of the unknown environment (which quantifies the information gained about the environment through observed human feedback data). To tackle the challenge of large state spaces and improve sample efficiency, we construct a simplifiedsurrogate environmentand introduce a novel distance measure (named the$\ell _{g}$-distance), enabling our IDS-based algorithm to achieve a Bayesian regret upper bound of order$O(H^{3/2}\sqrt {\log (K(\epsilon)) T})$, whereHis the episode length,Tis the number of episode and$K(\epsilon)$is related to the covering number of the environment. Specializing to the tabular settings, this regret bound is of order$\tilde {O}(H^{2}\sqrt {SAT})$, whereSandAare the numbers of states and actions. Finally, we propose an Approximate-IDS algorithm that is computationally more efficient while maintaining nearly the same sample efficiency. The design principle of this approximate algorithm is not only effective in RLHF settings but also applicable to the standard RL framework. Moreover, our work showcases the value of information theory in reinforcement learning and in the training of large language models.

We study offline reinforcement learning (RL) with general function approximation. General function approximation is a powerful tool for algorithm design and analysis, but its adaptation to offline RL encounters several challenges due to varying approximation targets and assumptions that blur the real meanings of function assumptions. In this paper, we try to formulate and clarify the treatment of general function approximation in offline RL in two aspects: (1) analyzing different types of assumptions and their practical usage, and (2) understanding its role as a restriction on underlying MDPs from information-theoretic perspectives. Additionally, we introduce a new insight for lower bound establishing: one can exploit model-realizability to establish general-purpose lower bounds that can be generalized into other functions. Building upon this insight, we propose two generic lower bounds that contribute to a better understanding of offline RL with general function approximation.

Unsupervised Reinforcement Learning (RL) provides a promising paradigm for learning useful behaviors via reward-free per-training. Existing methods for unsupervised RL mainly conduct empowerment-driven skill discovery or entropy-based exploration. However, empowerment often leads to static skills, and pure exploration only maximizes the state coverage rather than learning useful behaviors. In this paper, we propose a novel unsupervised RL framework via an ensemble of skills, where each skill performs partition exploration based on the state prototypes. Thus, each skill can explore the clustered area locally, and the ensemble skills maximize the overall state coverage. We adopt state-distribution constraints for the skill occupancy and the desired cluster for learning distinguishable skills. Theoretical analysis is provided for the state entropy and the resulting skill distributions. Based on extensive experiments on several challenging tasks, we find our method learns well-explored ensemble skills and achieves superior performance in various downstream tasks compared to previous methods.

This work proposes an On-Off Keying (OOK) coding scheme for covert communication over complex Gaussian channels. In particular, a transmitter Alice employs phase deflection to covertly transmit information to a receiver Bob, simultaneously ensuring that the communication intent is concealed from a warden Willie. The utilization of phase deflection allows Alice to improve the transmission rate by leveraging Willie’s uncertainty about the received phase, without changing the codebook construction. Considering the asymmetry of the OOK codebook’s input distribution and shape constellation, we first analyze the relationship between the input distribution and the signal amplitude, and then propose a scheme that can achieve covert transmission with the input distribution of the “on” symbol$a_{n}=\mathcal {O}\left ({{\frac {1}{\sqrt {n}}}}\right)$and an average transmission power$\beta ^{2}=\mathcal {O}({1})$. We quantify the improvement brought from the phase resource as phase deflection gain and derive its closed-form expression by approximating the Kullback-Leibler (KL) divergence and mutual information through Taylor expansion. Numerical results show that our scheme achieves significant phase deflection gain, and the maximum gain can be achieved by fully utilizing the phase resources through three stages.

Maximum distance separable (MDS) codes are often considered to have the optimal error correction capability against malicious adversaries because they achieve the Singleton bound in terms of the rate-distance tradeoff. However, by allowing a vanishing probability of decoding error and considering an adversary with limited knowledge, it is interesting to understand whether a rate higher than the Singleton bound is achievable, and if so, what the optimal rate is. To answer these questions, we instantiate the aforementioned problem as a communication problem where the transmission medium is a wiretap multipath network that consists of multiple parallel links. A malicious adversary is able to eavesdrop on a subset of links, and also jam on a potentially overlapping subset of links. The primary objective is to ensure the communication is robust to adversarial jamming; additionally, another goal is to guarantee that the communication is information-theoretically secure with respect to the adversary. We present a complete characterization of both capacity and secrecy capacity as functions of the number of links that can be eavesdropped and/or jammed. Our achievability schemes are computationally efficient, and rely on a non-trivial combination of MDS codes and a pairwise hashing scheme.

This work investigates the phase gain of intelligent reflecting surface (IRS) covert communication over complex-valued additive white Gaussian noise (AWGN) channels. The transmitter Alice intends to transmit covert messages to the legitimate receiver Bob via reflecting the broadcast signals from a radio frequency (RF) source, while rendering the adversary Willie’s detector arbitrarily close to ineffective. Our analyses show that, compared to the covert capacity for classical AWGN channels, we can achieve a covertness gain of value 2 by leveraging Willie’s uncertainty of phase angles. This covertness gain is achieved when the number of possible phase angle pairsN= 2. More interestingly, our results show that the covertness gain will not further increase withNas long asN≥ 2, even if it approaches infinity.

This paper investigates fundamental limits of exact recovery in the general$d$-uniform hypergraph stochastic block model ($d$-HSBM), wherein$n$nodes are partitioned into$k$disjoint communities with relative sizes$(p_{1},\ldots , p_{k})$. Each subset of nodes with cardinality$d$is generated independently as an order-$d$hyperedge with a certain probability that depends on the ground-truth communities that the$d$nodes belong to. The goal is to exactly recover the$k$hidden communities based on the observed hypergraph. We show that there exists a sharp threshold such that exact recovery is achievable above the threshold and impossible below the threshold (apart from a small regime of parameters that will be specified precisely). This threshold is represented in terms of a quantity which we term as the generalized Chernoff-Hellinger divergence between communities. Our result for this general model recovers prior results for the standard SBM and$d$-HSBM with two symmetric communities as special cases. En route to proving our achievability results, we develop a polynomial-time two-stage algorithm that meets the threshold. The first stage adopts a certain hypergraph spectral clustering method to obtain a coarse estimate of communities, and the second stage refines each node individually via local refinement steps to ensure exact recovery.

This paper considers the problem of covert communication over binary-input discrete memoryless channels with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the communication is covert with respect to a warden. We present a single-letter lower bound and two single-letter upper bounds on the information-theoretically optimal throughput as a function of the given decoding metric, channel laws, and the desired level of covertness. These bounds match for a variety of scenarios of interest, such as (i) when the channel between the sender and receiver is a binary-input binary-output channel, and (ii) when the decoding metric is particularized to the so-called erasures-only metric. The lower bound is obtained based on a modified random coding union bound with pulse position modulation (PPM) codebooks, coupled with a non-standard expurgation argument. The upper bounds are based on the idea of translating the mismatched-decoding error of the original channel to the decoding error of an auxiliary channel.

This paper considers the problem of covert communication over binary-input discrete memoryless channels with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly suboptimal, and simultaneously to ensure that the communication is covert with respect to a warden. We present single-letter lower and upper bounds on the information-theoretically optimal throughput as a function of the given decoding metric, channel laws, and the desired level of covertness. These bounds match when the decoding metric is particularized to the erasures-only metric, yielding an exact single-letter expression for the so-called covert erasures-only capacity. The lower bound is obtained based on a modified random coding union bound with pulse position modulation (PPM) codebooks, coupled with a nonstandard expurgation argument. The proof of the upper bound relies on a non-trivial combination of analytical techniques for the problems of covert communication and mismatched decoding.

This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not known and can only be learned from the training sequences which are available. We further require the probability of the estimation error to decay either exponentially or sub-exponentially fast (corresponding respectively to the large and moderate deviations regimes in information theory parlance). Based on the training sequences as well as the test sequence consisting of a single change-point, we design a change-point estimator and further show that this estimator is optimal by establishing matching (strong) converses. This leads to a full characterization of the optimal confidence width (i.e., half the width of the confidence interval within which the true change-point is located at with high probability) as a function of the undetected error, under both the large and moderate deviations regimes.

Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC( q)), and may maliciously flip (up to) a certain fraction p of their transmitted bits based on his observations. We consider a setting where the communication must be simultaneously covert as well as reliable, i.e., James should be unable to accurately distinguish whether or not Alice is communicating, while Bob should be able to correctly recover Alice's message with high probability regardless of the adversarial jamming strategy. We show that, unlike the setting with passive adversaries, covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Ω(logn)) even when Bob has a better channel than James. We present lower and upper bounds on the information-theoretically optimal throughput as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. These bounds match for a wide range of parameters of interest. We also develop a computationally efficient coding scheme (based on concatenated codes) when the amount of shared key available is Ω(√n logn), and further show that this scheme can be implemented with much less amount of shared key when the adversary is assumed to be computationally bounded.

This paper considers the covert identification problem in which a sender aims to reliably convey an identification (ID) message to a set of receivers via a binary-input discrete memoryless channel (BDMC), and simultaneously to guarantee that the communication is covert with respect to a warden who monitors the communication via another independent BDMC. We prove a square-root law for the covert identification problem. This states that an ID message of size exp(exp(Θ(√{ n})) can be transmitted over n channel uses. We then characterize the exact pre-constant in the Θ(·) notation. This constant is referred to as the covert identification capacity. We show that it equals the recently developed covert capacity in the standard covert communication problem, and somewhat surprisingly, the covert identification capacity can be achieved without any shared key between the sender and receivers. The achievability proof relies on a random coding argument with pulse-position modulation (PPM), coupled with a second stage which performs code refinements. The converse proof relies on an expurgation argument as well as results for channel resolvability with stringent input constraints.

We consider the problem of recovering communities of users and communities of items (such as movies) based on a partially observed rating matrix as well as side-information in the form of similarity graphs of the users and items. The user-to-user and item-to-item similarity graphs are generated according to the celebrated stochastic block model (SBM). We develop a lower bound on the minimum expected number of observed ratings (also known as the sample complexity) needed for this recovery task, which is a function of various parameters including the quality of the graph side-information manifested in the intra-and inter-cluster probabilities of the SBMs. Our information-theoretic results quantify the benefits of the two-sided graph side-information for recovery, and further analysis reveals that the two pieces of graph side-information produce an interesting synergistic effect under certain scenarios. This means that if one observes only one of the two graphs, then the required sample complexity worsens to the case in which none of the graphs is observed. Thus both graphs are strictly needed to reduce the sample complexity.

We consider the problem of stealthy communication over a multipath network in the presence of an active adversary. The multipath network consists of multiple parallel noiseless links, and the adversary is able to eavesdrop and jam a subset of links. We consider two types of jamming- erasure jamming and overwrite jamming. We require the communication to be both stealthy and reliable, i.e., the adversary should be unable to detect whether or not meaningful communication is taking place, while the legitimate receiver should reconstruct any potential messages from the transmitter with high probability simultaneously. We provide inner and outer bounds on the stealthy capacities under both adversarial erasure and adversarial overwrite jamming.

This paper develops a concatenated coding scheme with polynomial computational complexity for covert communication over Binary Symmetric Channels (BSCs) and binary-input Discrete Memoryless Channels (DMCs). Our setting is as follows - a transmitter Alice wishes to potentially reliably transmit a message to a receiver Bob, while ensuring that the transmission taking place is covert with respect to a warden Willie (who hears Alice's transmission over another independent channel). Prior works showed that Alice can reliably and covertly transmit O(√n) message bits over n channel uses, but one drawback is that the computational complexity of the codes designed scales as 2Θ(√n). In this work we provide a capacity-achiveing coding scheme with provable guarantees on both reliability and covertness, and its computational complexity grows polynomially in the blocklength n.

We consider the problem of covert communication over continuous-time additive white Gaussian noise (AWGN) channels under spectral mask constraints. In addition to requiring the legitimate receiver to reliably decode, covert communication also requires that the warden is unable to estimate whether or not communication is taking place. The spectral mask at the transmitter restricts excessive radiation beyond the bandwidth of interest. We develop a communication scheme with theoretical guarantees for both covertness and reliability, based on pulse amplitude modulation (PAM) with Binary Phase Shift Keying (BPSK) and root raised cosine (RRC) carrier pulses. Given a fixed time T and a spectral mask with bandwidth parameter W, √ we show that one can transmit O( W T ) bits of information covertly and reliably, and our proposed scheme provides a lower bound on the covert capacity.

We consider the problem of stealth communication over a multipath network in the presence of an active adversary. The multipath network consists of multiple parallel noiseless links, and the adversary is able to eavesdrop and jam a subset of links. We consider two types of jamming - erasure jamming and overwrite jamming. We require the communication to be both stealthy and reliable, i.e., the adversary should be unable to detect whether or not meaningful communication is taking place, while the legitimate receiver should reconstruct any potential messages from the transmitter with high probability simultaneously. We provide inner bounds on the robust stealth capacities under both adversarial erasure and adversarial overwrite jamming.

Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and may maliciously flip (up to) a certain fraction p of their transmitted bits based on his observation. We consider a setting where the communication must be simultaneously covert as well as reliable, i.e., James should be unable to accurately distinguish whether or not Alice is communicating, while Bob should be able to correctly recover Alice's message with high probability regardless of the adversarial jamming strategy. We show that, unlike the setting with passive adversaries, reliable covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Ω(log n)) even when Bob has a better channel than James. We present inner and outer bounds on the information-theoretically optimal throughputs as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. Further, these bounds match for a wide range of parameters of interest.

In this paper, we design the first computationally efficient codes for simultaneously reliable and deniable communication over a Binary Symmetric Channel (BSC). Our setting is as follows. A transmitter Alice wishes to potentially reliably transmit a message to a receiver Bob, while ensuring that the transmission taking place is deniable from an eavesdropper Willie (who hears Alice's transmission over a noisier BSC). Prior works show that Alice can reliably and deniably transmit O(√n) bits over n channel uses without any shared secrets between Alice and Bob. One drawback of prior works is that the computational complexity of the codes designed scales as 2Θ(√n). In this work we provide the first computationally tractable codes with provable guarantees on both reliability and deniability, while simultaneously achieving the best known throughput for the problem.

We consider the problem of communication over a multi-path network in the presence of a causal adversary. The limited-view causal adversary is able to, based on the current and past observations, eavesdrop on a subset of links and also jam on a potentially overlapping subset of links. The goal is to ensure that the communication takes place reliably and secretly. We study two adversarial models - additive and overwrite jamming. For both adversarial models, we consider communication models both without and with passive feedback from decoder to encoder, i.e., the encoder sees everything that the decoder sees. The problem assumes transmissions are in the large alphabet regime. For both types of jamming models, we find the capacity under three scenarios - reliability without feedback, reliability and secrecy without feedback, and reliability with feedback. We observe that in comparison to the non-causal setting the capacity with a causal adversary is strictly increased for a wide variety of parameter settings, and present our intuition through several examples.

We consider reliable and secure communication of information over a multipath network. A transmitter Alice sends messages to the receiver Bob in the presence of a hidden adversary Calvin. The adversary Calvin can both eavesdrop and jam on (possibly non-identical) subsets of transmission links. The goal is to communicate reliably (intended receiver can understand the messages) and secretly (adversary cannot understand the messages). Two kinds of jamming, additive and overwrite, are considered. Additive jamming corresponds to wireless network model while overwrite jamming corresponds to wired network model and storage systems. The multipath network consists of C parallel links. Calvin can both jam and eavesdrop any zionumber of links, can eavesdrop (but not jam) any zi/onumber of links, and can jam (but not eavesdrop) any zo/inumber of links. We present the first “complete” information-theoretic characterization of maximum achievable rate as a function of the number of links that can be jammed and/or eavesdropped for equal and unequal link capacity multipath networks under additive and overwrite jamming in the large alphabet regime. Our achievability and converse proofs require non-trivial combination of information theoretic and coding theoretic ideas and our achievability schemes are computationally efficient. The PHaSE-Saving techniques1are used for achievability while a “stochastic” singleton bound is obtained for converse.