Session 4: \u3cem\u3eAn Overview of Deep Learning and Universality\u3c/em\u3e

In recent years machine learning, and in particular deep learning has emerged as a powerful and robust tool for solving problems in fields ranging from robotics, to medicine, materials science, cosmology and beyond. As work on applications has advanced, so too has theory advanced to guide, explain, interpret deep learning. In this talk I will provide an overview on universality of neural networks. I will explain what it means for a neural network to be a universal approximator, qualitatively and quantitatively, and give examples of these results applied to existing networks. Finally, I will conclude by discussing some recent work on manifold universality in the nascent field of geometric machine learning

Globally Injective ReLU Networks

Publisher Copyright: © 2022 Michael Puthawala, Konik Kothari, Matti Lassas, Ivan Dokmanic, Maarten de Hoop.Injectivity plays an important role in generative models where it enables inference; in inverse problems and compressed sensing with generative priors it is a precursor to well posedness. We establish sharp characterizations of injectivity of fully-connected and convolutional ReLU layers and networks. First, through a layerwise analysis, we show that an expansivity factor of two is necessary and sufficient for injectivity by constructing appropriate weight matrices. We show that global injectivity with iid Gaussian matrices, a commonly used tractable model, requires larger expansivity between 3.4 and 10.5. We also characterize the stability of inverting an injective network via worst-case Lipschitz constants of the inverse. We then use arguments from differential topology to study injectivity of deep networks and prove that any Lipschitz map can be approximated by an injective ReLU network. Finally, using an argument based on random projections, we show that an end-to-end-rather than layerwise-doubling of the dimension suffices for injectivity. Our results establish a theoretical basis for the study of nonlinear inverse and inference problems using neural networks.Peer reviewe

Predictors for long-term survival free from whole brain radiation therapy in patients treated with radiosurgery for limited brain metastases

PURPOSE: To identify predictors for prolonged survival free from salvage whole brain radiation therapy (WBRT) in patients with brain metastases treated with stereotactic radiosurgery (SRS) as their initial radiotherapy approach. MATERIALS AND METHODS: Patients with brain metastases treated with SRS from 2001 to 2013 at our institution were identified. SRS without WBRT was typically offered to patients with 1-4 brain metastases, Karnofsky performance status \u3e /=70, and life expectancy \u3e /=3 months. Three hundred and eight patients met inclusion criteria for analysis. Medical records were reviewed for patient, disease, and treatment information. Two comparison groups were identified: those with \u3e /=1-year WBRT-free survival (N = 104), and those who died or required salvage WBRT within 3 months of SRS (N = 56). Differences between these groups were assessed by univariate and multivariate analyses. RESULTS: Median survival for all patients was 11 months. Among patients with \u3e /=1-year WBRT-free survival, median survival was 33 months (12-107 months) with only 21% requiring salvage WBRT. Factors significantly associated with prolonged WBRT-free survival on univariate analysis (p \u3c 0.05) included younger age, asymptomatic presentation, RTOG RPA class I, fewer brain metastases, surgical resection, breast primary, new or controlled primary, absence of extracranial metastatic disease, and oligometastatic disease burden ( \u3c /=5 metastatic lesions). After controlling for covariates, asymptomatic presentation, breast primary, single brain metastasis, absence of extracranial metastases, and oligometastatic disease burden remained independent predictors for favorable WBRT-free survival. CONCLUSION: A subset of patients with brain metastases can achieve long-term survival after upfront SRS without the need for salvage WBRT. Predictors identified in this study can help select patients that might benefit most from a treatment strategy of SRS alone

Prospective multi-center trial utilizing electronic brachytherapy for the treatment of endometrial cancer

<p>Abstract</p> <p>Background</p> <p>A modified form of high dose rate (HDR) brachytherapy has been developed called Axxent Electronic Brachytherapy (EBT). EBT uses a kilovolt X-ray source and does not require treatment in a shielded vault or a HDR afterloader unit. A multi-center clinical study was carried out to evaluate the success of treatment delivery, safety and toxicity of EBT in patients with endometrial cancer.</p> <p>Methods</p> <p>A total of 15 patients with stage I or II endometrial cancer were enrolled at 5 sites. Patients were treated with vaginal EBT alone or in combination with external beam radiation.</p> <p>Results</p> <p>The prescribed doses of EBT were successfully delivered in all 15 patients. From the first fraction through 3 months follow-up, there were 4 CTC Grade 1 adverse events and 2 CTC Grade II adverse events reported that were EBT related. The mild events reported were dysuria, vaginal dryness, mucosal atrophy, and rectal bleeding. The moderate treatment related adverse events included dysuria, and vaginal pain. No Grade III or IV adverse events were reported. The EBT system performed well and was associated with limited acute toxicities.</p> <p>Conclusions</p> <p>EBT shows acute results similar to HDR brachytherapy. Additional research is needed to further assess the clinical efficacy and safety of EBT in the treatment of endometrial cancer.</p

Structure activity relationships of αv integrin antagonists for pulmonary fibrosis by variation in aryl substituents

Antagonism of alphav beta6 is emerging as a potential treatment of idiopathic pulmonary fibrosis based on strong target validation. Starting from an alphav beta3 antagonist lead and through simple variation in the nature and position of aryl substituent, the discovery of compounds with improved alphav beta6 activity is described. The compounds also have physicochemical properties commensurate with oral bioavailability and are high quality starting points for a drug discovery programme. Compounds 33S and 43E1 are pan alphav antagonists having ca 100 nM potency against alphav beta3, alphav beta5, alphav beta6 and alphav beta8 in cell adhesion assays. Detailed structure activity relationships with these integrins are described which also reveal substituents providing partial selectivity (defined as at least a 0.7 log difference in pIC50 values between the integrins in question) for alphav beta3 and alphav beta5

Cell autonomous expression of inflammatory genes in biologically aged fibroblasts associated with elevated NF-kappaB activity

<p>Abstract</p> <p>Background</p> <p>Chronic inflammation is a well-known corollary of the aging process and is believed to significantly contribute to morbidity and mortality of many age-associated chronic diseases. However, the mechanisms that cause age-associated inflammatory changes are not well understood. Particularly, the contribution of cell stress responses to age-associated inflammation in 'non-inflammatory' cells remains poorly defined. The present cross-sectional study focused on differences in molecular signatures indicative of inflammatory states associated with biological aging of human fibroblasts from donors aged 22 to 92 years.</p> <p>Results</p> <p>Gene expression profiling revealed elevated steady-state transcript levels consistent with a chronic inflammatory state in fibroblast cell-strains obtained from older donors. We also observed enhanced NF-κB DNA binding activity in a subset of strains, and the NF-κB profile correlated with mRNA expression levels characteristic of inflammatory processes, which include transcripts coding for cytokines, chemokines, components of the complement cascade and MHC molecules. This intrinsic low-grade inflammatory state, as it relates to aging, occurs in cultured cells irrespective of the presence of other cell types or the <it>in vivo </it>context.</p> <p>Conclusion</p> <p>Our results are consistent with the view that constitutive activation of inflammatory pathways is a phenomenon prevalent in aged fibroblasts. It is possibly part of a cellular survival process in response to compromised mitochondrial function. Importantly, the inflammatory gene expression signature described here is cell autonomous, i.e. occurs in the absence of prototypical immune or pro-inflammatory cells, growth factors, or other inflammatory mediators.</p